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Special Issue "Inertial Sensors and Systems 2016"

A special issue of Sensors (ISSN 1424-8220). This special issue belongs to the section "Physical Sensors".

Deadline for manuscript submissions: closed (30 November 2016).

Special Issue Editor

Prof. Dr. Jörg F. Wagner
E-Mail Website
Guest Editor
Professor for Adaptive Structures in Aerospace, University of Stuttgart, Pfaffenwaldring 31, 70569 Stuttgart, Germany
Tel. +49-711-685-67046; Fax: +49-711-685-51008
Interests: mechanics and mechatronics (structural dynamics, flight mechanics, gyro technology, testing technology, biomechanics); system theory (observers, optimization); navigation (inertial and integrated systems); history of science (gyro technology, aerospace); airborne and large telescopes
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Special Issue Information

Dear Colleagues,

The traditional key elements in inertial and integrated systems for navigation, positioning, and vehicle guidance and control are gyroscopes and accelerometers, i.e., inertial sensors. This includes high precision devices for aerospace and maritime applications, medium performance systems for land vehicles and indoor navigation, as well as the low performance consumer market for smart phones and games.

Due to many decades of research and development, there is remarkable progress in the performance and in the price—performance ratio of inertial sensors. Currently, this especially concerns fiber optical gyroscopes as well as MEMS gyroscopes and accelerometers. Future inertial systems may, therefore, also have more than only the minimal set of required inertial sensors. This concerns not only aspects of redundancy, but also the parallel motion measurement, at several points, of a moving vehicle.

This Special Issue aims to highlight advances in the development, testing, and modeling of inertial sensors, on the component level, as well as of Inertial Navigation Systems (INS) and integrated systems based on gyroscopes and accelerometers. Topics include, but are not limited to:

  • Accelerometers
  • Gyroscopes
  • Future technologies for inertial sensors
  • Advanced sensor characterization and error modeling techniques
  • Online and offline calibration
  • Inertial and integrated navigation systems
  • Sensors and technologies for aiding inertial systems
  • New and unconventional applications for inertial sensors

Prof. Dr. Joerg F. Wagner
Guest Editor

Manuscript Submission Information

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Keywords

  • inertial sensors and systems
  • navigation
  • gyroscopes
  • accelerometers
  • MEMS sensors
  • vehicle guidance and control
  • integrated systems
  • aiding technology for INS

Published Papers (41 papers)

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Open AccessArticle
INS/GNSS Integration for Aerobatic Flight Applications and Aircraft Motion Surveying
Sensors 2017, 17(5), 941; https://doi.org/10.3390/s17050941 - 26 Apr 2017
Cited by 17
Abstract
This paper presents field tests of challenging flight applications obtained with a new family of lightweight low-power INS/GNSS (inertial navigation system/global satellite navigation system) solutions based on MEMS (micro-electro-mechanical- sensor) machined sensors, being used for UAV (unmanned aerial [...] Read more.
This paper presents field tests of challenging flight applications obtained with a new family of lightweight low-power INS/GNSS (inertial navigation system/global satellite navigation system) solutions based on MEMS (micro-electro-mechanical- sensor) machined sensors, being used for UAV (unmanned aerial vehicle) navigation and control as well as for aircraft motion dynamics analysis and trajectory surveying. One key is a 42+ state extended Kalman-filter-based powerful data fusion, which also allows the estimation and correction of parameters that are typically affected by sensor aging, especially when applying MEMS-based inertial sensors, and which is not yet deeply considered in the literature. The paper presents the general system architecture, which allows iMAR Navigation the integration of all classes of inertial sensors and GNSS (global navigation satellite system) receivers from very-low-cost MEMS and high performance MEMS over FOG (fiber optical gyro) and RLG (ring laser gyro) up to HRG (hemispherical resonator gyro) technology, and presents detailed flight test results obtained under extreme flight conditions. As a real-world example, the aerobatic maneuvers of the World Champion 2016 (Red Bull Air Race) are presented. Short consideration is also given to surveying applications, where the ultimate performance of the same data fusion, but applied on gravimetric surveying, is discussed. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Use of the Magnetic Field for Improving Gyroscopes’ Biases Estimation
Sensors 2017, 17(4), 832; https://doi.org/10.3390/s17040832 - 11 Apr 2017
Cited by 6
Abstract
An accurate orientation is crucial to a satisfactory position in pedestrian navigation. The orientation estimation, however, is greatly affected by errors like the biases of gyroscopes. In order to minimize the error in the orientation, the biases of gyroscopes must be estimated and [...] Read more.
An accurate orientation is crucial to a satisfactory position in pedestrian navigation. The orientation estimation, however, is greatly affected by errors like the biases of gyroscopes. In order to minimize the error in the orientation, the biases of gyroscopes must be estimated and subtracted. In the state of the art it has been proposed, but not proved, that the estimation of the biases can be accomplished using magnetic field measurements. The objective of this work is to evaluate the effectiveness of using magnetic field measurements to estimate the biases of medium-cost micro-electromechanical sensors (MEMS) gyroscopes. We carry out the evaluation with experiments that cover both, quasi-error-free turn rate and magnetic measurements and medium-cost MEMS turn rate and magnetic measurements. The impact of different homogeneous magnetic field distributions and magnetically perturbed environments is analyzed. Additionally, the effect of the successful biases subtraction on the orientation and the estimated trajectory is detailed. Our results show that the use of magnetic field measurements is beneficial to the correct biases estimation. Further, we show that different magnetic field distributions affect differently the biases estimation process. Moreover, the biases are likewise correctly estimated under perturbed magnetic fields. However, for indoor and urban scenarios the biases estimation process is very slow. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
A Coarse Alignment Method Based on Digital Filters and Reconstructed Observation Vectors
Sensors 2017, 17(4), 709; https://doi.org/10.3390/s17040709 - 29 Mar 2017
Cited by 4
Abstract
In this paper, a coarse alignment method based on apparent gravitational motion is proposed. Due to the interference of the complex situations, the true observation vectors, which are calculated by the apparent gravity, are contaminated. The sources of the interference are analyzed in [...] Read more.
In this paper, a coarse alignment method based on apparent gravitational motion is proposed. Due to the interference of the complex situations, the true observation vectors, which are calculated by the apparent gravity, are contaminated. The sources of the interference are analyzed in detail, and then a low-pass digital filter is designed in this paper for eliminating the high-frequency noise of the measurement observation vectors. To extract the effective observation vectors from the inertial sensors’ outputs, a parameter recognition and vector reconstruction method are designed, where an adaptive Kalman filter is employed to estimate the unknown parameters. Furthermore, a robust filter, which is based on Huber’s M-estimation theory, is developed for addressing the outliers of the measurement observation vectors due to the maneuver of the vehicle. A comprehensive experiment, which contains a simulation test and physical test, is designed to verify the performance of the proposed method, and the results show that the proposed method is equivalent to the popular apparent velocity method in swaying mode, but it is superior to the current methods while in moving mode when the strapdown inertial navigation system (SINS) is under entirely self-contained conditions. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Improving Observability of an Inertial System by Rotary Motions of an IMU
Sensors 2017, 17(4), 698; https://doi.org/10.3390/s17040698 - 28 Mar 2017
Cited by 8
Abstract
It has been identified that the inertial system is not a completely observable system in the absence of maneuvers. Although the velocity errors and the accelerometer bias in the vertical direction can be solely observable, other error states, including the attitude errors, the [...] Read more.
It has been identified that the inertial system is not a completely observable system in the absence of maneuvers. Although the velocity errors and the accelerometer bias in the vertical direction can be solely observable, other error states, including the attitude errors, the accelerometer biases in the east and north directions, and the gyro biases, are just jointly observable states with velocity measurements, which degrades the estimation accuracy of these error states. This paper proposes an innovative method to improve the system observability for a Micro-Electro-Mechanical-System (MEMS)-based Inertial Navigation System (INS) in the absence of maneuvers by rotary motions of the Inertial Measurement Unit (IMU). Three IMU rotation schemes, namely IMU continuous rotation about the X, Y and Z axes are employed. The observability is analyzed for the rotating system with a control-theoretic approach, and tests are also conducted based on a turntable to verify the improvements on the system observability by IMU rotations. Both theoretical analysis and the results indicate that the system observability is improved by proposed IMU rotations, the roll and pitch errors, the accelerometer biases in the east and north directions, the gyro biases become observable states in the absence of vehicle maneuvers. Although the azimuth error is still unobservable, the enhanced estimability of the gyro bias in the vertical direction can effectively mitigate the azimuth error accumulation. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Accurate Compensation of Attitude Angle Error in a Dual-Axis Rotation Inertial Navigation System
Sensors 2017, 17(3), 615; https://doi.org/10.3390/s17030615 - 17 Mar 2017
Cited by 7
Abstract
In the dual-axis rotation inertial navigation system (INS), besides the gyro error, accelerometer error, rolling misalignment angle error, and the gimbal angle error, the shaft swing angle and the axis non-orthogonal angle also affect the attitude accuracy. Through the analysis of the structure, [...] Read more.
In the dual-axis rotation inertial navigation system (INS), besides the gyro error, accelerometer error, rolling misalignment angle error, and the gimbal angle error, the shaft swing angle and the axis non-orthogonal angle also affect the attitude accuracy. Through the analysis of the structure, we can see that the shaft swing angle and axis non-orthogonal angle will produce coning errors which cause the fluctuation of the attitude. According to the analysis of the rotation vector, it can be seen that the coning error will generate additional drift velocity along the rotating shaft, which can reduce the navigation precision of the system. In this paper, based on the establishment of the modulation average frame, the vector projection is carried out, and then the attitude conversion matrix and the attitude error matrix mainly including the shaft swing angle and axis non-orthogonal are obtained. Because the attitude angles are given under the static condition, the shaft swing angle and the axis non-orthogonal angle are estimated by the static Kalman filter (KF). This kind of KF method has been widely recognized as the standard optimal estimation tool for estimating the parameters such as coning angles (α1 , α2), initial phase angles (ϕ12), and the non-perpendicular angle (η). In order to carry out the system level verification, a dual axis rotation INS is designed. Through simulation and experiments, the results show that the amplitudes of the attitude angles’ variation are reduced by about 20%–30% when the shaft rotates. The attitude error equation is reasonably simplified and the calibration method is accurate enough. The attitude accuracy is further improved. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Inertial Motion Capture Costume Design Study
Sensors 2017, 17(3), 612; https://doi.org/10.3390/s17030612 - 17 Mar 2017
Cited by 8
Abstract
The paper describes a scalable, wearable multi-sensor system for motion capture based on inertial measurement units (IMUs). Such a unit is composed of accelerometer, gyroscope and magnetometer. The final quality of an obtained motion arises from all the individual parts of the described [...] Read more.
The paper describes a scalable, wearable multi-sensor system for motion capture based on inertial measurement units (IMUs). Such a unit is composed of accelerometer, gyroscope and magnetometer. The final quality of an obtained motion arises from all the individual parts of the described system. The proposed system is a sequence of the following stages: sensor data acquisition, sensor orientation estimation, system calibration, pose estimation and data visualisation. The construction of the system’s architecture with the dataflow programming paradigm makes it easy to add, remove and replace the data processing steps. The modular architecture of the system allows an effortless introduction of a new sensor orientation estimation algorithms. The original contribution of the paper is the design study of the individual components used in the motion capture system. The two key steps of the system design are explored in this paper: the evaluation of sensors and algorithms for the orientation estimation. The three chosen algorithms have been implemented and investigated as part of the experiment. Due to the fact that the selection of the sensor has a significant impact on the final result, the sensor evaluation process is also explained and tested. The experimental results confirmed that the choice of sensor and orientation estimation algorithm affect the quality of the final results. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
MEMS and FOG Technologies for Tactical and Navigation Grade Inertial Sensors—Recent Improvements and Comparison
Sensors 2017, 17(3), 567; https://doi.org/10.3390/s17030567 - 11 Mar 2017
Cited by 11
Abstract
In the following paper, we present an industry perspective of inertial sensors for navigation purposes driven by applications and customer needs. Microelectromechanical system (MEMS) inertial sensors have revolutionized consumer, automotive, and industrial applications and they have started to fulfill the high end tactical [...] Read more.
In the following paper, we present an industry perspective of inertial sensors for navigation purposes driven by applications and customer needs. Microelectromechanical system (MEMS) inertial sensors have revolutionized consumer, automotive, and industrial applications and they have started to fulfill the high end tactical grade performance requirements of hybrid navigation systems on a series production scale. The Fiber Optic Gyroscope (FOG) technology, on the other hand, is further pushed into the near navigation grade performance region and beyond. Each technology has its special pros and cons making it more or less suitable for specific applications. In our overview paper, we present latest improvements at NG LITEF in tactical and navigation grade MEMS accelerometers, MEMS gyroscopes, and Fiber Optic Gyroscopes, based on our long-term experience in the field. We demonstrate how accelerometer performance has improved by switching from wet etching to deep reactive ion etching (DRIE) technology. For MEMS gyroscopes, we show that better than 1°/h series production devices are within reach, and for FOGs we present how limitations in noise performance were overcome by signal processing. The paper also intends a comparison of the different technologies, emphasizing suitability for different navigation applications, thus providing guidance to system engineers. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters—Part II: Observability/Estimability Analysis
Sensors 2017, 17(3), 439; https://doi.org/10.3390/s17030439 - 23 Feb 2017
Cited by 9
Abstract
This paper presents the second part of a study aiming at the error state selection in Kalman filters applied to the stationary self-alignment and calibration (SSAC) problem of strapdown inertial navigation systems (SINS). The observability properties of the system are systematically investigated, and [...] Read more.
This paper presents the second part of a study aiming at the error state selection in Kalman filters applied to the stationary self-alignment and calibration (SSAC) problem of strapdown inertial navigation systems (SINS). The observability properties of the system are systematically investigated, and the number of unobservable modes is established. Through the analytical manipulation of the full SINS error model, the unobservable modes of the system are determined, and the SSAC error states (except the velocity errors) are proven to be individually unobservable. The estimability of the system is determined through the examination of the major diagonal terms of the covariance matrix and their eigenvalues/eigenvectors. Filter order reduction based on observability analysis is shown to be inadequate, and several misconceptions regarding SSAC observability and estimability deficiencies are removed. As the main contributions of this paper, we demonstrate that, except for the position errors, all error states can be minimally estimated in the SSAC problem and, hence, should not be removed from the filter. Corroborating the conclusions of the first part of this study, a 12-state Kalman filter is found to be the optimal error state selection for SSAC purposes. Results from simulated and experimental tests support the outlined conclusions. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Reduced-Drift Virtual Gyro from an Array of Low-Cost Gyros
Sensors 2017, 17(2), 352; https://doi.org/10.3390/s17020352 - 11 Feb 2017
Cited by 5
Abstract
A Kalman filter approach for combining the outputs of an array of high-drift gyros to obtain a virtual lower-drift gyro has been known in the literature for more than a decade. The success of this approach depends on the correlations of the random [...] Read more.
A Kalman filter approach for combining the outputs of an array of high-drift gyros to obtain a virtual lower-drift gyro has been known in the literature for more than a decade. The success of this approach depends on the correlations of the random drift components of the individual gyros. However, no method of estimating these correlations has appeared in the literature. This paper presents an algorithm for obtaining the statistical model for an array of gyros, including the cross-correlations of the individual random drift components. In order to obtain this model, a new statistic, called the “Allan covariance” between two gyros, is introduced. The gyro array model can be used to obtain the Kalman filter-based (KFB) virtual gyro. Instead, we consider a virtual gyro obtained by taking a linear combination of individual gyro outputs. The gyro array model is used to calculate the optimal coefficients, as well as to derive a formula for the drift of the resulting virtual gyro. The drift formula for the optimal linear combination (OLC) virtual gyro is identical to that previously derived for the KFB virtual gyro. Thus, a Kalman filter is not necessary to obtain a minimum drift virtual gyro. The theoretical results of this paper are demonstrated using simulated as well as experimental data. In experimental results with a 28-gyro array, the OLC virtual gyro has a drift spectral density 40 times smaller than that obtained by taking the average of the gyro signals. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Loose and Tight GNSS/INS Integrations: Comparison of Performance Assessed in Real Urban Scenarios
Sensors 2017, 17(2), 255; https://doi.org/10.3390/s17020255 - 29 Jan 2017
Cited by 27
Abstract
Global Navigation Satellite Systems (GNSSs) remain the principal mean of positioning in many applications and systems, but in several types of environment, the performance of standalone receivers is degraded. Although many works show the benefits of the integration between GNSS and Inertial Navigation [...] Read more.
Global Navigation Satellite Systems (GNSSs) remain the principal mean of positioning in many applications and systems, but in several types of environment, the performance of standalone receivers is degraded. Although many works show the benefits of the integration between GNSS and Inertial Navigation Systems (INSs), tightly-coupled architectures are mainly implemented in professional devices and are based on high-grade Inertial Measurement Units (IMUs). This paper investigates the performance improvements enabled by the tight integration, using low-cost sensors and a mass-market GNSS receiver. Performance is assessed through a series of tests carried out in real urban scenarios and is compared against commercial modules, operating in standalone mode or featuring loosely-coupled integrations. The paper describes the developed tight-integration algorithms with a terse mathematical model and assesses their efficacy from a practical perspective. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Gravity Compensation Using EGM2008 for High-Precision Long-Term Inertial Navigation Systems
Sensors 2016, 16(12), 2177; https://doi.org/10.3390/s16122177 - 18 Dec 2016
Cited by 9
Abstract
The gravity disturbance vector is one of the major error sources in high-precision and long-term inertial navigation applications. Specific to the inertial navigation systems (INSs) with high-order horizontal damping networks, analyses of the error propagation show that the gravity-induced errors exist almost exclusively [...] Read more.
The gravity disturbance vector is one of the major error sources in high-precision and long-term inertial navigation applications. Specific to the inertial navigation systems (INSs) with high-order horizontal damping networks, analyses of the error propagation show that the gravity-induced errors exist almost exclusively in the horizontal channels and are mostly caused by deflections of the vertical (DOV). Low-frequency components of the DOV propagate into the latitude and longitude errors at a ratio of 1:1 and time-varying fluctuations in the DOV excite Schuler oscillation. This paper presents two gravity compensation methods using the Earth Gravitational Model 2008 (EGM2008), namely, interpolation from the off-line database and computing gravity vectors directly using the spherical harmonic model. Particular attention is given to the error contribution of the gravity update interval and computing time delay. It is recommended for the marine navigation that a gravity vector should be calculated within 1 s and updated every 100 s at most. To meet this demand, the time duration of calculating the current gravity vector using EGM2008 has been reduced to less than 1 s by optimizing the calculation procedure. A few off-line experiments were conducted using the data of a shipborne INS collected during an actual sea test. With the aid of EGM2008, most of the low-frequency components of the position errors caused by the gravity disturbance vector have been removed and the Schuler oscillation has been attenuated effectively. In the rugged terrain, the horizontal position error could be reduced at best 48.85% of its regional maximum. The experimental results match with the theoretical analysis and indicate that EGM2008 is suitable for gravity compensation of the high-precision and long-term INSs. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
A New Continuous Rotation IMU Alignment Algorithm Based on Stochastic Modeling for Cost Effective North-Finding Applications
Sensors 2016, 16(12), 2113; https://doi.org/10.3390/s16122113 - 13 Dec 2016
Cited by 3
Abstract
Based on stochastic modeling of Coriolis vibration gyros by the Allan variance technique, this paper discusses Angle Random Walk (ARW), Rate Random Walk (RRW) and Markov process gyroscope noises which have significant impacts on the North-finding accuracy. A new continuous rotation alignment algorithm [...] Read more.
Based on stochastic modeling of Coriolis vibration gyros by the Allan variance technique, this paper discusses Angle Random Walk (ARW), Rate Random Walk (RRW) and Markov process gyroscope noises which have significant impacts on the North-finding accuracy. A new continuous rotation alignment algorithm for a Coriolis vibration gyroscope Inertial Measurement Unit (IMU) is proposed in this paper, in which the extended observation equations are used for the Kalman filter to enhance the estimation of gyro drift errors, thus improving the north-finding accuracy. Theoretical and numerical comparisons between the proposed algorithm and the traditional ones are presented. The experimental results show that the new continuous rotation alignment algorithm using the extended observation equations in the Kalman filter is more efficient than the traditional two-position alignment method. Using Coriolis vibration gyros with bias instability of 0.1°/h, a north-finding accuracy of 0.1° (1σ) is achieved by the new continuous rotation alignment algorithm, compared with 0.6° (1σ) north-finding accuracy for the two-position alignment and 1° (1σ) for the fixed-position alignment. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
A Novel Gravity Compensation Method for High Precision Free-INS Based on “Extreme Learning Machine”
Sensors 2016, 16(12), 2019; https://doi.org/10.3390/s16122019 - 29 Nov 2016
Cited by 4
Abstract
In recent years, with the emergency of high precision inertial sensors (accelerometers and gyros), gravity compensation has become a major source influencing the navigation accuracy in inertial navigation systems (INS), especially for high-precision INS. This paper presents preliminary results concerning the effect of [...] Read more.
In recent years, with the emergency of high precision inertial sensors (accelerometers and gyros), gravity compensation has become a major source influencing the navigation accuracy in inertial navigation systems (INS), especially for high-precision INS. This paper presents preliminary results concerning the effect of gravity disturbance on INS. Meanwhile, this paper proposes a novel gravity compensation method for high-precision INS, which estimates the gravity disturbance on the track using the extreme learning machine (ELM) method based on measured gravity data on the geoid and processes the gravity disturbance to the height where INS has an upward continuation, then compensates the obtained gravity disturbance into the error equations of INS to restrain the INS error propagation. The estimation accuracy of the gravity disturbance data is verified by numerical tests. The root mean square error (RMSE) of the ELM estimation method can be improved by 23% and 44% compared with the bilinear interpolation method in plain and mountain areas, respectively. To further validate the proposed gravity compensation method, field experiments with an experimental vehicle were carried out in two regions. Test 1 was carried out in a plain area and Test 2 in a mountain area. The field experiment results also prove that the proposed gravity compensation method can significantly improve the positioning accuracy. During the 2-h field experiments, the positioning accuracy can be improved by 13% and 29% respectively, in Tests 1 and 2, when the navigation scheme is compensated by the proposed gravity compensation method. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
MEMS IMU Error Mitigation Using Rotation Modulation Technique
Sensors 2016, 16(12), 2017; https://doi.org/10.3390/s16122017 - 29 Nov 2016
Cited by 12
Abstract
Micro-electro-mechanical-systems (MEMS) inertial measurement unit (IMU) outputs are corrupted by significant sensor errors. The navigation errors of a MEMS-based inertial navigation system will therefore accumulate very quickly over time. This requires aiding from other sensors such as Global Navigation Satellite Systems (GNSS). However, [...] Read more.
Micro-electro-mechanical-systems (MEMS) inertial measurement unit (IMU) outputs are corrupted by significant sensor errors. The navigation errors of a MEMS-based inertial navigation system will therefore accumulate very quickly over time. This requires aiding from other sensors such as Global Navigation Satellite Systems (GNSS). However, it will still remain a significant challenge in the presence of GNSS outages, which are typically in urban canopies. This paper proposed a rotary inertial navigation system (INS) to mitigate navigation errors caused by MEMS inertial sensor errors when external aiding information is not available. A rotary INS is an inertial navigator in which the IMU is installed on a rotation platform. Application of proper rotation schemes can effectively cancel and reduce sensor errors. A rotary INS has the potential to significantly increase the time period that INS can bridge GNSS outages and make MEMS IMU possible to maintain longer autonomous navigation performance when there is no external aiding. In this research, several IMU rotation schemes (rotation about X-, Y- and Z-axes) are analyzed to mitigate the navigation errors caused by MEMS IMU sensor errors. As the IMU rotation induces additional sensor errors, a calibration process is proposed to remove the induced errors. Tests are further conducted with two MEMS IMUs installed on a tri-axial rotation table to verify the error mitigation by IMU rotations. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Anatomical Calibration through Post-Processing of Standard Motion Tests Data
Sensors 2016, 16(12), 2011; https://doi.org/10.3390/s16122011 - 28 Nov 2016
Cited by 6
Abstract
The inertial measurement unit is popularly used as a wearable and flexible tool for human motion tracking. Sensor-to-body alignment, or anatomical calibration (AC), is fundamental to improve accuracy and reliability. Current AC methods either require extra movements or are limited to specific joints. [...] Read more.
The inertial measurement unit is popularly used as a wearable and flexible tool for human motion tracking. Sensor-to-body alignment, or anatomical calibration (AC), is fundamental to improve accuracy and reliability. Current AC methods either require extra movements or are limited to specific joints. In this research, the authors propose a novel method to achieve AC from standard motion tests (such as walking, or sit-to-stand), and compare the results with the AC obtained from specially designed movements. The proposed method uses the limited acceleration range on medial-lateral direction, and applies principal component analysis to estimate the sagittal plane, while the vertical direction is estimated from acceleration during quiet stance. The results show a good correlation between the two sets of IMUs placed on frontal/back and lateral sides of head, trunk and lower limbs. Moreover, repeatability and convergence were verified. The AC obtained from sit-to-stand and walking achieved similar results as the movements specifically designed for upper and lower body AC, respectively, except for the feet. Therefore, the experiments without AC performed can be recovered through post-processing on the walking and sit-to-stand data. Moreover, extra movements for AC can be avoided during the experiment and instead achieved through the proposed method. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Advanced Pedestrian Positioning System to Smartphones and Smartwatches
Sensors 2016, 16(11), 1903; https://doi.org/10.3390/s16111903 - 11 Nov 2016
Cited by 11
Abstract
In recent years, there has been an increasing interest in the development of pedestrian navigation systems for satellite-denied scenarios. The popularization of smartphones and smartwatches is an interesting opportunity for reducing the infrastructure cost of the positioning systems. Nowadays, smartphones include inertial sensors [...] Read more.
In recent years, there has been an increasing interest in the development of pedestrian navigation systems for satellite-denied scenarios. The popularization of smartphones and smartwatches is an interesting opportunity for reducing the infrastructure cost of the positioning systems. Nowadays, smartphones include inertial sensors that can be used in pedestrian dead-reckoning (PDR) algorithms for the estimation of the user’s position. Both smartphones and smartwatches include WiFi capabilities allowing the computation of the received signal strength (RSS). We develop a new method for the combination of RSS measurements from two different receivers using a Gaussian mixture model. We also analyze the implication of using a WiFi network designed for communication purposes in an indoor positioning system when the designer cannot control the network configuration. In this work, we design a hybrid positioning system that combines inertial measurements, from low-cost inertial sensors embedded in a smartphone, with RSS measurements through an extended Kalman filter. The system has been validated in a real scenario, and results show that our system improves the positioning accuracy of the PDR system thanks to the use of two WiFi receivers. The designed system obtains an accuracy up to 1.4 m in a scenario of 6000 m 2 . Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Coarse Alignment of Marine Strapdown INS Based on the Trajectory Fitting of Gravity Movement in the Inertial Space
Sensors 2016, 16(10), 1714; https://doi.org/10.3390/s16101714 - 15 Oct 2016
Cited by 3
Abstract
A ship experiences the random motion of sea waves during its travels. Hence, the coarse alignment of the marine strapdown Inertial Navigation System (INS) suffers from rocking disturbances such as pitch and roll. In this paper, a novel approach of marine coarse alignment [...] Read more.
A ship experiences the random motion of sea waves during its travels. Hence, the coarse alignment of the marine strapdown Inertial Navigation System (INS) suffers from rocking disturbances such as pitch and roll. In this paper, a novel approach of marine coarse alignment was proposed for avoiding the resulting loss of accuracy from rocking disturbances. Unlike several current techniques, our alignment scheme is intuitional and concise. Moreover, the coarse alignment can be implemented without any external information. The gravity vector and its derivative expressed within the inertial frame can describe the attitude matrix between an inertial frame and the local geographic frame. We address the challenge of calculating the gravity derivative by the least-squares fitting of the trajectory of the gravity movement in the inertial frame. Meanwhile, the integration of angular rates measured by gyroscopes allows one to compute the attitude matrix between the inertial frame and the body frame. The coarse alignment can be thus accomplished by the combination of the above two attitude matrices. The experimental results show that the coarse alignment is effective with high accuracy and stability for demanding marine applications. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Design of a Piezoelectric Accelerometer with High Sensitivity and Low Transverse Effect
Sensors 2016, 16(10), 1587; https://doi.org/10.3390/s16101587 - 26 Sep 2016
Cited by 7
Abstract
In order to meet the requirements of cable fault detection, a new structure of piezoelectric accelerometer was designed and analyzed in detail. The structure was composed of a seismic mass, two sensitive beams, and two added beams. Then, simulations including the maximum stress, [...] Read more.
In order to meet the requirements of cable fault detection, a new structure of piezoelectric accelerometer was designed and analyzed in detail. The structure was composed of a seismic mass, two sensitive beams, and two added beams. Then, simulations including the maximum stress, natural frequency, and output voltage were carried out. Moreover, comparisons with traditional structures of piezoelectric accelerometer were made. To verify which vibration mode is the dominant one on the acceleration and the space between the mass and glass, mode analysis and deflection analysis were carried out. Fabricated on an n-type single crystal silicon wafer, the sensor chips were wire-bonged to printed circuit boards (PCBs) and simply packaged for experiments. Finally, a vibration test was conducted. The results show that the proposed piezoelectric accelerometer has high sensitivity, low resonance frequency, and low transverse effect. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
A Novel Zero Velocity Interval Detection Algorithm for Self-Contained Pedestrian Navigation System with Inertial Sensors
Sensors 2016, 16(10), 1578; https://doi.org/10.3390/s16101578 - 24 Sep 2016
Cited by 9
Abstract
Zero velocity update (ZUPT) plays an important role in pedestrian navigation algorithms with the premise that the zero velocity interval (ZVI) should be detected accurately and effectively. A novel adaptive ZVI detection algorithm based on a smoothed pseudo Wigner–Ville distribution to remove multiple [...] Read more.
Zero velocity update (ZUPT) plays an important role in pedestrian navigation algorithms with the premise that the zero velocity interval (ZVI) should be detected accurately and effectively. A novel adaptive ZVI detection algorithm based on a smoothed pseudo Wigner–Ville distribution to remove multiple frequencies intelligently (SPWVD-RMFI) is proposed in this paper. The novel algorithm adopts the SPWVD-RMFI method to extract the pedestrian gait frequency and to calculate the optimal ZVI detection threshold in real time by establishing the function relationships between the thresholds and the gait frequency; then, the adaptive adjustment of thresholds with gait frequency is realized and improves the ZVI detection precision. To put it into practice, a ZVI detection experiment is carried out; the result shows that compared with the traditional fixed threshold ZVI detection method, the adaptive ZVI detection algorithm can effectively reduce the false and missed detection rate of ZVI; this indicates that the novel algorithm has high detection precision and good robustness. Furthermore, pedestrian trajectory positioning experiments at different walking speeds are carried out to evaluate the influence of the novel algorithm on positioning precision. The results show that the ZVI detected by the adaptive ZVI detection algorithm for pedestrian trajectory calculation can achieve better performance. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
An Online Gravity Modeling Method Applied for High Precision Free-INS
Sensors 2016, 16(10), 1541; https://doi.org/10.3390/s16101541 - 23 Sep 2016
Cited by 12
Abstract
For real-time solution of inertial navigation system (INS), the high-degree spherical harmonic gravity model (SHM) is not applicable because of its time and space complexity, in which traditional normal gravity model (NGM) has been the dominant technique for gravity compensation. In this paper, [...] Read more.
For real-time solution of inertial navigation system (INS), the high-degree spherical harmonic gravity model (SHM) is not applicable because of its time and space complexity, in which traditional normal gravity model (NGM) has been the dominant technique for gravity compensation. In this paper, a two-dimensional second-order polynomial model is derived from SHM according to the approximate linear characteristic of regional disturbing potential. Firstly, deflections of vertical (DOVs) on dense grids are calculated with SHM in an external computer. And then, the polynomial coefficients are obtained using these DOVs. To achieve global navigation, the coefficients and applicable region of polynomial model are both updated synchronously in above computer. Compared with high-degree SHM, the polynomial model takes less storage and computational time at the expense of minor precision. Meanwhile, the model is more accurate than NGM. Finally, numerical test and INS experiment show that the proposed method outperforms traditional gravity models applied for high precision free-INS. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Navigation Aiding by a Hybrid Laser-Camera Motion Estimator for Micro Aerial Vehicles
Sensors 2016, 16(9), 1516; https://doi.org/10.3390/s16091516 - 16 Sep 2016
Cited by 11
Abstract
Micro Air Vehicles (MAVs) equipped with various sensors are able to carry out autonomous flights. However, the self-localization of autonomous agents is mostly dependent on Global Navigation Satellite Systems (GNSS). In order to provide an accurate navigation solution in absence of GNSS signals, [...] Read more.
Micro Air Vehicles (MAVs) equipped with various sensors are able to carry out autonomous flights. However, the self-localization of autonomous agents is mostly dependent on Global Navigation Satellite Systems (GNSS). In order to provide an accurate navigation solution in absence of GNSS signals, this article presents a hybrid sensor. The hybrid sensor is a deep integration of a monocular camera and a 2D laser rangefinder so that the motion of the MAV is estimated. This realization is expected to be more flexible in terms of environments compared to laser-scan-matching approaches. The estimated ego-motion is then integrated in the MAV’s navigation system. However, first, the knowledge about the pose between both sensors is obtained by proposing an improved calibration method. For both calibration and ego-motion estimation, 3D-to-2D correspondences are used and the Perspective-3-Point (P3P) problem is solved. Moreover, the covariance estimation of the relative motion is presented. The experiments show very accurate calibration and navigation results. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Drift Reduction in Pedestrian Navigation System by Exploiting Motion Constraints and Magnetic Field
Sensors 2016, 16(9), 1455; https://doi.org/10.3390/s16091455 - 09 Sep 2016
Cited by 19
Abstract
Pedestrian navigation systems (PNS) using foot-mounted MEMS inertial sensors use zero-velocity updates (ZUPTs) to reduce drift in navigation solutions and estimate inertial sensor errors. However, it is well known that ZUPTs cannot reduce all errors, especially as heading error is not observable. Hence, [...] Read more.
Pedestrian navigation systems (PNS) using foot-mounted MEMS inertial sensors use zero-velocity updates (ZUPTs) to reduce drift in navigation solutions and estimate inertial sensor errors. However, it is well known that ZUPTs cannot reduce all errors, especially as heading error is not observable. Hence, the position estimates tend to drift and even cyclic ZUPTs are applied in updated steps of the Extended Kalman Filter (EKF). This urges the use of other motion constraints for pedestrian gait and any other valuable heading reduction information that is available. In this paper, we exploit two more motion constraints scenarios of pedestrian gait: (1) walking along straight paths; (2) standing still for a long time. It is observed that these motion constraints (called “virtual sensor”), though considerably reducing drift in PNS, still need an absolute heading reference. One common absolute heading estimation sensor is the magnetometer, which senses the Earth’s magnetic field and, hence, the true heading angle can be calculated. However, magnetometers are susceptible to magnetic distortions, especially in indoor environments. In this work, an algorithm, called magnetic anomaly detection (MAD) and compensation is designed by incorporating only healthy magnetometer data in the EKF updating step, to reduce drift in zero-velocity updated INS. Experiments are conducted in GPS-denied and magnetically distorted environments to validate the proposed algorithms. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Weak and Dynamic GNSS Signal Tracking Strategies for Flight Missions in the Space Service Volume
Sensors 2016, 16(9), 1412; https://doi.org/10.3390/s16091412 - 02 Sep 2016
Cited by 1
Abstract
Weak-signal and high-dynamics are of two primary concerns of space navigation using GNSS (Global Navigation Satellite System) in the space service volume (SSV). The paper firstly defines a reference assumption third-order phase-locked loop (PLL) as the baseline of an onboard GNSS receiver, and [...] Read more.
Weak-signal and high-dynamics are of two primary concerns of space navigation using GNSS (Global Navigation Satellite System) in the space service volume (SSV). The paper firstly defines a reference assumption third-order phase-locked loop (PLL) as the baseline of an onboard GNSS receiver, and proves the incompetence of this conventional architecture. Then an adaptive four-state Kalman filter (KF)-based algorithm is introduced to realize the optimization of loop noise bandwidth, which can adaptively regulate its filter gain according to the received signal power and line-of-sight (LOS) dynamics. To overcome the matter of losing lock in weak-signal and high-dynamic environments, an open loop tracking strategy aided by an inertial navigation system (INS) is recommended, and the traditional maximum likelihood estimation (MLE) method is modified in a non-coherent way by reconstructing the likelihood cost function. Furthermore, a typical mission with combined orbital maneuvering and non-maneuvering arcs is taken as a destination object to test the two proposed strategies. Finally, the experiment based on computer simulation identifies the effectiveness of an adaptive four-state KF-based strategy under non-maneuvering conditions and the virtue of INS-assisted methods under maneuvering conditions. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
A Long-Term Performance Enhancement Method for FOG-Based Measurement While Drilling
Sensors 2016, 16(8), 1186; https://doi.org/10.3390/s16081186 - 28 Jul 2016
Cited by 8
Abstract
In the oil industry, the measurement-while-drilling (MWD) systems are usually used to provide the real-time position and orientation of the bottom hole assembly (BHA) during drilling. However, the present MWD systems based on magnetic surveying technology can barely ensure good performance because of [...] Read more.
In the oil industry, the measurement-while-drilling (MWD) systems are usually used to provide the real-time position and orientation of the bottom hole assembly (BHA) during drilling. However, the present MWD systems based on magnetic surveying technology can barely ensure good performance because of magnetic interference phenomena. In this paper, a MWD surveying system based on a fiber optic gyroscope (FOG) was developed to replace the magnetic surveying system. To accommodate the size of the downhole drilling conditions, a new design method is adopted. In order to realize long-term and high position precision and orientation surveying, an integrated surveying algorithm is proposed based on inertial navigation system (INS) and drilling features. In addition, the FOG-based MWD error model is built and the drilling features are analyzed. The state-space system model and the observation updates model of the Kalman filter are built. To validate the availability and utility of the algorithm, the semi-physical simulation is conducted under laboratory conditions. The results comparison with the traditional algorithms show that the errors were suppressed and the measurement precision of the proposed algorithm is better than the traditional ones. In addition, the proposed method uses a lot less time than the zero velocity update (ZUPT) method. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
On Inertial Body Tracking in the Presence of Model Calibration Errors
Sensors 2016, 16(7), 1132; https://doi.org/10.3390/s16071132 - 22 Jul 2016
Cited by 23
Abstract
In inertial body tracking, the human body is commonly represented as a biomechanical model consisting of rigid segments with known lengths and connecting joints. The model state is then estimated via sensor fusion methods based on data from attached inertial measurement units (IMUs). [...] Read more.
In inertial body tracking, the human body is commonly represented as a biomechanical model consisting of rigid segments with known lengths and connecting joints. The model state is then estimated via sensor fusion methods based on data from attached inertial measurement units (IMUs). This requires the relative poses of the IMUs w.r.t. the segments—the IMU-to-segment calibrations, subsequently called I2S calibrations—to be known. Since calibration methods based on static poses, movements and manual measurements are still the most widely used, potentially large human-induced calibration errors have to be expected. This work compares three newly developed/adapted extended Kalman filter (EKF) and optimization-based sensor fusion methods with an existing EKF-based method w.r.t. their segment orientation estimation accuracy in the presence of model calibration errors with and without using magnetometer information. While the existing EKF-based method uses a segment-centered kinematic chain biomechanical model and a constant angular acceleration motion model, the newly developed/adapted methods are all based on a free segments model, where each segment is represented with six degrees of freedom in the global frame. Moreover, these methods differ in the assumed motion model (constant angular acceleration, constant angular velocity, inertial data as control input), the state representation (segment-centered, IMU-centered) and the estimation method (EKF, sliding window optimization). In addition to the free segments representation, the optimization-based method also represents each IMU with six degrees of freedom in the global frame. In the evaluation on simulated and real data from a three segment model (an arm), the optimization-based method showed the smallest mean errors, standard deviations and maximum errors throughout all tests. It also showed the lowest dependency on magnetometer information and motion agility. Moreover, it was insensitive w.r.t. I2S position and segment length errors in the tested ranges. Errors in the I2S orientations were, however, linearly propagated into the estimated segment orientations. In the absence of magnetic disturbances, severe model calibration errors and fast motion changes, the newly developed IMU centered EKF-based method yielded comparable results with lower computational complexity. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Systematic Calibration for Ultra-High Accuracy Inertial Measurement Units
Sensors 2016, 16(6), 940; https://doi.org/10.3390/s16060940 - 22 Jun 2016
Cited by 12
Abstract
An inertial navigation system (INS) has been widely used in challenging GPS environments. With the rapid development of modern physics, an atomic gyroscope will come into use in the near future with a predicted accuracy of 5 × 10−6°/h or better. [...] Read more.
An inertial navigation system (INS) has been widely used in challenging GPS environments. With the rapid development of modern physics, an atomic gyroscope will come into use in the near future with a predicted accuracy of 5 × 10−6°/h or better. However, existing calibration methods and devices can not satisfy the accuracy requirements of future ultra-high accuracy inertial sensors. In this paper, an improved calibration model is established by introducing gyro g-sensitivity errors, accelerometer cross-coupling errors and lever arm errors. A systematic calibration method is proposed based on a 51-state Kalman filter and smoother. Simulation results show that the proposed calibration method can realize the estimation of all the parameters using a common dual-axis turntable. Laboratory and sailing tests prove that the position accuracy in a five-day inertial navigation can be improved about 8% by the proposed calibration method. The accuracy can be improved at least 20% when the position accuracy of the atomic gyro INS can reach a level of 0.1 nautical miles/5 d. Compared with the existing calibration methods, the proposed method, with more error sources and high order small error parameters calibrated for ultra-high accuracy inertial measurement units (IMUs) using common turntables, has a great application potential in future atomic gyro INSs. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
An IMU Evaluation Method Using a Signal Grafting Scheme
Sensors 2016, 16(6), 854; https://doi.org/10.3390/s16060854 - 10 Jun 2016
Cited by 1
Abstract
As various inertial measurement units (IMUs) from different manufacturers appear every year, it is not affordable to evaluate every IMU through tests. Therefore, this paper presents an IMU evaluation method by grafting data from the tested IMU to the reference data from a [...] Read more.
As various inertial measurement units (IMUs) from different manufacturers appear every year, it is not affordable to evaluate every IMU through tests. Therefore, this paper presents an IMU evaluation method by grafting data from the tested IMU to the reference data from a higher-grade IMU. The signal grafting (SG) method has several benefits: (a) only one set of field tests with a higher-grade IMU is needed, and can be used to evaluate numerous IMUs. Thus, SG is effective and economic because all data from the tested IMU is collected in the lab; (b) it is a general approach to compare navigation performances of various IMUs by using the same reference data; and, finally, (c) through SG, one can first evaluate an IMU in the lab, and then decide whether to further test it. Moreover, this paper verified the validity of SG to both medium- and low-grade IMUs, and presents and compared two SG strategies, i.e., the basic-error strategy and the full-error strategy. SG provided results similar to field tests, with a difference of under 5% and 19.4%–26.7% for tested tactical-grade and MEMS IMUs. Meanwhile, it was found that dynamic IMU errors were essential to guarantee the effect of the SG method. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Backward Secondary-Wave Coherence Errors in Photonic Bandgap Fiber Optic Gyroscopes
Sensors 2016, 16(6), 851; https://doi.org/10.3390/s16060851 - 08 Jun 2016
Cited by 3
Abstract
Photonic bandgap fiber optic gyroscope (PBFOG) is a novel fiber optic gyroscope (FOG) with excellent environment adaptability performance compared to a conventional FOG. In this work we find and investigate the backward secondary-wave coherence (BSC) error, which is a bias error unique to [...] Read more.
Photonic bandgap fiber optic gyroscope (PBFOG) is a novel fiber optic gyroscope (FOG) with excellent environment adaptability performance compared to a conventional FOG. In this work we find and investigate the backward secondary-wave coherence (BSC) error, which is a bias error unique to the PBFOG and caused by the interference between back-reflection-induced and backscatter-induced secondary waves. Our theoretical and experimental results show a maximum BSC error of ~4.7°/h for a 300-m PBF coil with a diameter of 10 cm. The BSC error is an important error source contributing to bias instability in the PBFOG and has to be addressed before practical applications of the PBFOG can be implemented. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Stride Counting in Human Walking and Walking Distance Estimation Using Insole Sensors
Sensors 2016, 16(6), 823; https://doi.org/10.3390/s16060823 - 04 Jun 2016
Cited by 16
Abstract
This paper proposes a novel method of estimating walking distance based on a precise counting of walking strides using insole sensors. We use an inertial triaxial accelerometer and eight pressure sensors installed in the insole of a shoe to record walkers’ movement data. [...] Read more.
This paper proposes a novel method of estimating walking distance based on a precise counting of walking strides using insole sensors. We use an inertial triaxial accelerometer and eight pressure sensors installed in the insole of a shoe to record walkers’ movement data. The data is then transmitted to a smartphone to filter out noise and determine stance and swing phases. Based on phase information, we count the number of strides traveled and estimate the movement distance. To evaluate the accuracy of the proposed method, we created two walking databases on seven healthy participants and tested the proposed method. The first database, which is called the short distance database, consists of collected data from all seven healthy subjects walking on a 16 m distance. The second one, named the long distance database, is constructed from walking data of three healthy subjects who have participated in the short database for an 89 m distance. The experimental results show that the proposed method performs walking distance estimation accurately with the mean error rates of 4.8% and 3.1% for the short and long distance databases, respectively. Moreover, the maximum difference of the swing phase determination with respect to time is 0.08 s and 0.06 s for starting and stopping points of swing phases, respectively. Therefore, the stride counting method provides a highly precise result when subjects walk. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Instantaneous Observability of Tightly Coupled SINS/GPS during Maneuvers
Sensors 2016, 16(6), 765; https://doi.org/10.3390/s16060765 - 27 May 2016
Cited by 3
Abstract
The tightly coupled strapdown inertial navigation system (SINS)/global position system (GPS) has been widely used. The system observability determines whether the system state can be estimated by a filter efficiently or not. In this paper, the observability analysis of a two-channel and a [...] Read more.
The tightly coupled strapdown inertial navigation system (SINS)/global position system (GPS) has been widely used. The system observability determines whether the system state can be estimated by a filter efficiently or not. In this paper, the observability analysis of a two-channel and a three-channel tightly coupled SINS/GPS are performed, respectively, during arbitrary translational maneuvers and angle maneuvers, where the translational maneuver and angle maneuver are modeled. A novel instantaneous observability matrix (IOM) based on a reconstructed psi-angle model is proposed to make the theoretical analysis simpler, which starts from the observability definition directly. Based on the IOM, a series of theoretical analysis are performed. Analysis results show that almost all kinds of translational maneuver and angle maneuver can make a three-channel system instantaneously observable, but there is no one translational maneuver or angle maneuver can make a two-channel system instantaneously observable. The system’s performance is investigated when the system is not instantaneously observable. A series of simulation studies based on EKF are performed to confirm the analytic conclusions. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Self-Locking Avoidance and Stiffness Compensation of a Three-Axis Micromachined Electrostatically Suspended Accelerometer
Sensors 2016, 16(5), 711; https://doi.org/10.3390/s16050711 - 18 May 2016
Cited by 8
Abstract
A micromachined electrostatically-suspended accelerometer (MESA) is a kind of three-axis inertial sensor based on fully-contactless electrostatic suspension of the proof mass (PM). It has the potential to offer broad bandwidth, high sensitivity, wide dynamic range and, thus, would be perfectly suited for land [...] Read more.
A micromachined electrostatically-suspended accelerometer (MESA) is a kind of three-axis inertial sensor based on fully-contactless electrostatic suspension of the proof mass (PM). It has the potential to offer broad bandwidth, high sensitivity, wide dynamic range and, thus, would be perfectly suited for land seismic acquisition. Previous experiments showed that it is hard to lift up the PM successfully during initial levitation as the mass needs to be levitated simultaneously in all six degrees of freedom (DoFs). By analyzing the coupling electrostatic forces and torques between three lateral axes, it is found there exists a self-locking zone due to the cross-axis coupling effect. To minimize the cross-axis coupling and solve the initial levitation problem, this paper proposes an effective control scheme by delaying the operation of one lateral actuator. The experimental result demonstrates that the PM can be levitated up with six-DoF suspension operation at any initial position. We also propose a feed-forward compensation approach to minimize the negative stiffness effect inherent in electrostatic suspension. The experiment results demonstrate that a more broadband linear amplitude-frequency response and higher suspension stiffness can be achieved, which is crucial to maintain high vector fidelity for potential use as a three-component MEMS geophone. The preliminary performance tests of the three-axis linear accelerometer were conducted under normal atmospheric pressure and room temperature. The main results and noise analysis are presented. It is shown that vacuum packaging of the MEMS sensor is essential to extend the bandwidth and lower the noise floor, especially for low-noise seismic data acquisition. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Carrying Position Independent User Heading Estimation for Indoor Pedestrian Navigation with Smartphones
Sensors 2016, 16(5), 677; https://doi.org/10.3390/s16050677 - 11 May 2016
Cited by 7
Abstract
This paper proposes a novel heading estimation approach for indoor pedestrian navigation using the built-in inertial sensors on a smartphone. Unlike previous approaches constraining the carrying position of a smartphone on the user’s body, our approach gives the user a larger freedom by [...] Read more.
This paper proposes a novel heading estimation approach for indoor pedestrian navigation using the built-in inertial sensors on a smartphone. Unlike previous approaches constraining the carrying position of a smartphone on the user’s body, our approach gives the user a larger freedom by implementing automatic recognition of the device carrying position and subsequent selection of an optimal strategy for heading estimation. We firstly predetermine the motion state by a decision tree using an accelerometer and a barometer. Then, to enable accurate and computational lightweight carrying position recognition, we combine a position classifier with a novel position transition detection algorithm, which may also be used to avoid the confusion between position transition and user turn during pedestrian walking. For a device placed in the trouser pockets or held in a swinging hand, the heading estimation is achieved by deploying a principal component analysis (PCA)-based approach. For a device held in the hand or against the ear during a phone call, user heading is directly estimated by adding the yaw angle of the device to the related heading offset. Experimental results show that our approach can automatically detect carrying positions with high accuracy, and outperforms previous heading estimation approaches in terms of accuracy and applicability. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
An Improved Alignment Method for the Strapdown Inertial Navigation System (SINS)
Sensors 2016, 16(5), 621; https://doi.org/10.3390/s16050621 - 29 Apr 2016
Cited by 17
Abstract
In this paper, an innovative inertial navigation system (INS) mechanization and the associated Kalman filter (KF) are developed to implement a fine alignment for the strapdown INS (SINS) on stationary base. The improved mechanization is established in the pseudo-geographic frame, which is rebuilt [...] Read more.
In this paper, an innovative inertial navigation system (INS) mechanization and the associated Kalman filter (KF) are developed to implement a fine alignment for the strapdown INS (SINS) on stationary base. The improved mechanization is established in the pseudo-geographic frame, which is rebuilt based on the initial position. The new mechanization eliminates the effects of linear movement errors on the heading by decoupling. Compared with the traditional local-level mechanization, it has more advantages. The proposed algorithm requires lower coarse alignment accuracy in both the open-loop and closed-loop KFs and hence can improve the system reliability and decrease the total alignment time. Moreover, for the closed-loop KF, it can decrease oscillation caused by the system errors and improve the closed-loop system stability. In addition, the proposed algorithm can also be applied to polar alignment. The performance of the proposed algorithm is verified by both simulations and experiments and the results exhibit the superior performance of the proposed approach. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Optimal Design of a Center Support Quadruple Mass Gyroscope (CSQMG)
Sensors 2016, 16(5), 613; https://doi.org/10.3390/s16050613 - 28 Apr 2016
Cited by 14
Abstract
This paper reports a more complete description of the design process of the Center Support Quadruple Mass Gyroscope (CSQMG), a gyro expected to provide breakthrough performance for flat structures. The operation of the CSQMG is based on four lumped masses in a circumferential [...] Read more.
This paper reports a more complete description of the design process of the Center Support Quadruple Mass Gyroscope (CSQMG), a gyro expected to provide breakthrough performance for flat structures. The operation of the CSQMG is based on four lumped masses in a circumferential symmetric distribution, oscillating in anti-phase motion, and providing differential signal extraction. With its 4-fold symmetrical axes pattern, the CSQMG achieves a similar operation mode to Hemispherical Resonant Gyroscopes (HRGs). Compared to the conventional flat design, four Y-shaped coupling beams are used in this new pattern in order to adjust mode distribution and enhance the synchronization mechanism of operation modes. For the purpose of obtaining the optimal design of the CSQMG, a kind of applicative optimization flow is developed with a comprehensive derivation of the operation mode coordination, the pseudo mode inhibition, and the lumped mass twisting motion elimination. The experimental characterization of the CSQMG was performed at room temperature, and the center operation frequency is 6.8 kHz after tuning. Experiments show an Allan variance stability 0.12°/h (@100 s) and a white noise level about 0.72°/h/√Hz, which means that the CSQMG possesses great potential to achieve navigation grade performance. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Sample-Wise Aiding in GPS/INS Ultra-Tight Integration for High-Dynamic, High-Precision Tracking
Sensors 2016, 16(4), 519; https://doi.org/10.3390/s16040519 - 11 Apr 2016
Cited by 9
Abstract
By aiding GPS receiver tracking loops with INS estimates of signal dynamics, GPS/INS ultra-tight coupling can improve the navigation performance in challenging environments. Traditionally the INS data are injected into the loops once every loop update interval, which limits the levels of dynamics [...] Read more.
By aiding GPS receiver tracking loops with INS estimates of signal dynamics, GPS/INS ultra-tight coupling can improve the navigation performance in challenging environments. Traditionally the INS data are injected into the loops once every loop update interval, which limits the levels of dynamics accommodated. This paper presents a sample-wise aiding method, which interpolates the aiding Doppler into each digital sample of the local signal to further eliminate the dynamic errors. The relationship between the tracking error and the aiding rate is derived analytically. Moreover, the effects of sample-wise aiding using linear and spline interpolations are simulated and compared with traditional aiding under different INS data update rates. Finally, extensive tests based on a digital IF (intermediate frequency) signal simulator and a software receiver validate the theoretical equations and demonstrate that the dynamic stress error can be significantly reduced by sample-wise aiding. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Mechanical Coupling Error Suppression Technology for an Improved Decoupled Dual-Mass Micro-Gyroscope
Sensors 2016, 16(4), 503; https://doi.org/10.3390/s16040503 - 08 Apr 2016
Cited by 5
Abstract
This paper presents technology for the suppression of the mechanical coupling errors for an improved decoupled dual-mass micro-gyroscope (DDMG). The improved micro-gyroscope structure decreases the moment arm of the drive decoupled torque, which benefits the suppression of the non-ideal decoupled error. Quadrature correction [...] Read more.
This paper presents technology for the suppression of the mechanical coupling errors for an improved decoupled dual-mass micro-gyroscope (DDMG). The improved micro-gyroscope structure decreases the moment arm of the drive decoupled torque, which benefits the suppression of the non-ideal decoupled error. Quadrature correction electrodes are added to eliminate the residual quadrature error. The structure principle and the quadrature error suppression means of the DDMG are described in detail. ANSYS software is used to simulate the micro-gyroscope structure to verify the mechanical coupling error suppression effect. Compared with the former structure, simulation results demonstrate that the rotational displacements of the sense frame in the improved structure are substantially suppressed in the drive mode. The improved DDMG structure chip is fabricated by the deep dry silicon on glass (DDSOG) process. The feedback control circuits with quadrature control loops are designed to suppress the residual mechanical coupling error. Finally, the system performance of the DDMG prototype is tested. Compared with the former DDMG, the quadrature error in the improved dual-mass micro-gyroscope is decreased 9.66-fold, and the offset error is decreased 6.36-fold. Compared with the open loop sense, the feedback control circuits with quadrature control loop decrease the bias drift by 20.59-fold and the scale factor non-linearity by 2.81-fold in the ±400°/s range. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
A Novel Digital Closed Loop MEMS Accelerometer Utilizing a Charge Pump
Sensors 2016, 16(3), 389; https://doi.org/10.3390/s16030389 - 18 Mar 2016
Cited by 5
Abstract
This paper presents a novel digital closed loop microelectromechanical system (MEMS) accelerometer with the architecture and experimental evaluation. The complicated timing diagram or complex power supply in published articles are circumvented by using a charge pump system of adjustable output voltage fabricated in [...] Read more.
This paper presents a novel digital closed loop microelectromechanical system (MEMS) accelerometer with the architecture and experimental evaluation. The complicated timing diagram or complex power supply in published articles are circumvented by using a charge pump system of adjustable output voltage fabricated in a 2P4M 0.35 µm complementary metal-oxide semiconductor (CMOS) process, therefore making it possible for interface circuits of MEMS accelerometers to be integrated on a single die on a large scale. The output bitstream of the sigma delta modulator is boosted by the charge pump system and then applied on the feedback comb fingers to form electrostatic forces so that the MEMS accelerometer can operate in a closed loop state. Test results agree with the theoretical formula nicely. The nonlinearity of the accelerometer within ±1 g is 0.222% and the long-term stability is about 774 µg. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
Particle Filter with Novel Nonlinear Error Model for Miniature Gyroscope-Based Measurement While Drilling Navigation
Sensors 2016, 16(3), 371; https://doi.org/10.3390/s16030371 - 15 Mar 2016
Cited by 8
Abstract
The derivation of a conventional error model for the miniature gyroscope-based measurement while drilling (MGWD) system is based on the assumption that the errors of attitude are small enough so that the direction cosine matrix (DCM) can be approximated or simplified by the [...] Read more.
The derivation of a conventional error model for the miniature gyroscope-based measurement while drilling (MGWD) system is based on the assumption that the errors of attitude are small enough so that the direction cosine matrix (DCM) can be approximated or simplified by the errors of small-angle attitude. However, the simplification of the DCM would introduce errors to the navigation solutions of the MGWD system if the initial alignment cannot provide precise attitude, especially for the low-cost microelectromechanical system (MEMS) sensors operated in harsh multilateral horizontal downhole drilling environments. This paper proposes a novel nonlinear error model (NNEM) by the introduction of the error of DCM, and the NNEM can reduce the propagated errors under large-angle attitude error conditions. The zero velocity and zero position are the reference points and the innovations in the states estimation of particle filter (PF) and Kalman filter (KF). The experimental results illustrate that the performance of PF is better than KF and the PF with NNEM can effectively restrain the errors of system states, especially for the azimuth, velocity, and height in the quasi-stationary condition. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Open AccessArticle
An Anchor-Based Pedestrian Navigation Approach Using Only Inertial Sensors
Sensors 2016, 16(3), 334; https://doi.org/10.3390/s16030334 - 07 Mar 2016
Cited by 11
Abstract
In inertial-based pedestrian navigation, anchors can effectively compensate the positioning errors originating from deviations of Inertial Measurement Units (IMUs), by putting constraints on pedestrians’ motions. However, these anchors often need to be deployed beforehand, which can greatly increase system complexity, rendering it unsuitable [...] Read more.
In inertial-based pedestrian navigation, anchors can effectively compensate the positioning errors originating from deviations of Inertial Measurement Units (IMUs), by putting constraints on pedestrians’ motions. However, these anchors often need to be deployed beforehand, which can greatly increase system complexity, rendering it unsuitable for emergency response missions. In this paper, we propose an anchor-based pedestrian navigation approach without any additional sensors. The anchors are defined as the intersection points of perpendicular corridors and are considered characteristics of building structures. In contrast to these real anchors, virtual anchors are extracted from the pedestrian’s trajectory and are considered as observations of real anchors, which can accordingly be regarded as inferred building structure characteristics. Then a Rao-Blackwellized particle filter (RBPF) is used to solve the joint estimation of positions (trajectory) and maps (anchors) problem. Compared with other building structure-based methods, our method has two advantages. The assumption on building structure is minimum and valid in most cases. Even if the assumption does not stand, the method will not lead to positioning failure. Several real-scenario experiments are conducted to validate the effectiveness and robustness of the proposed method. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Review

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Open AccessReview
Micromachined Fluid Inertial Sensors
Sensors 2017, 17(2), 367; https://doi.org/10.3390/s17020367 - 14 Feb 2017
Cited by 16
Abstract
Micromachined fluid inertial sensors are an important class of inertial sensors, which mainly includes thermal accelerometers and fluid gyroscopes, which have now been developed since the end of the last century for about 20 years. Compared with conventional silicon or quartz inertial sensors, [...] Read more.
Micromachined fluid inertial sensors are an important class of inertial sensors, which mainly includes thermal accelerometers and fluid gyroscopes, which have now been developed since the end of the last century for about 20 years. Compared with conventional silicon or quartz inertial sensors, the fluid inertial sensors use a fluid instead of a solid proof mass as the moving and sensitive element, and thus offer advantages of simple structures, low cost, high shock resistance, and large measurement ranges while the sensitivity and bandwidth are not competitive. Many studies and various designs have been reported in the past two decades. This review firstly introduces the working principles of fluid inertial sensors, followed by the relevant research developments. The micromachined thermal accelerometers based on thermal convection have developed maturely and become commercialized. However, the micromachined fluid gyroscopes, which are based on jet flow or thermal flow, are less mature. The key issues and technologies of the thermal accelerometers, mainly including bandwidth, temperature compensation, monolithic integration of tri-axis accelerometers and strategies for high production yields are also summarized and discussed. For the micromachined fluid gyroscopes, improving integration and sensitivity, reducing thermal errors and cross coupling errors are the issues of most concern. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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Other

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Open AccessTechnical Note
Inertial Navigation System/Doppler Velocity Log (INS/DVL) Fusion with Partial DVL Measurements
Sensors 2017, 17(2), 415; https://doi.org/10.3390/s17020415 - 22 Feb 2017
Cited by 25
Abstract
The Technion autonomous underwater vehicle (TAUV) is an ongoing project aiming to develop and produce a small AUV to carry on research missions, including payload dropping, and to demonstrate acoustic communication. Its navigation system is based on an inertial navigation system (INS) aided [...] Read more.
The Technion autonomous underwater vehicle (TAUV) is an ongoing project aiming to develop and produce a small AUV to carry on research missions, including payload dropping, and to demonstrate acoustic communication. Its navigation system is based on an inertial navigation system (INS) aided by a Doppler velocity log (DVL), magnetometer, and pressure sensor (PS). In many INSs, such as the one used in TAUV, only the velocity vector (provided by the DVL) can be used for aiding the INS, i.e., enabling only a loosely coupled integration approach. In cases of partial DVL measurements, such as failure to maintain bottom lock, the DVL cannot estimate the vehicle velocity. Thus, in partial DVL situations no velocity data can be integrated into the TAUV INS, and as a result its navigation solution will drift in time. To circumvent that problem, we propose a DVL-based vehicle velocity solution using the measured partial raw data of the DVL and additional information, thereby deriving an extended loosely coupled (ELC) approach. The implementation of the ELC approach requires only software modification. In addition, we present the TAUV six degrees of freedom (6DOF) simulation that includes all functional subsystems. Using this simulation, the proposed approach is evaluated and the benefit of using it is shown. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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