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Special Issue "Inertial Sensors and Systems"

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

Deadline for manuscript submissions: closed (31 May 2015).

Special Issue Editor

Prof. Dr. Gert F. Trommer
E-Mail Website
Guest Editor
Institute of Systems Optimization (ITE), Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 1, 76131 Karlsruhe, Germany
Tel. +49-721-608-42620; Fax: +49-721-608-42623
Interests: inertial sensors and systems; unmanned aerial systems (UAS); indoor navigation; guidance, navigation and control of mobile platforms
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

The key elements in all systems for navigation, localization, and stabilization are inertial sensors. This includes high precision systems for aerospace or maritime applications, medium performance systems for land vehicles and indoor navigation, as well as the low performance consumer market for smart phones and games.

There is a growing progress in the performance of both high end inertial sensors as well as low cost sensors, which are steadily approaching the tactical grade performance region.

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

Accelerometers
MEMS Gyroscopes
Vibrating Gyroscopes
Nuclear Magnetic Resonance Gyroscope
High Performance Fiber Optic Gyroscopes
Advanced Sensor Characterization Techniques
Sensor Error Modeling and Online Calibration

Prof. Dr. Gert F. Trommer
Guest Editor

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • inertial sensors
  • navigation
  • gyroscopes
  • accelerometers
  • mems sensors
  • fiber optic gyroscopes
  • calibration
  • error modeling

Published Papers (36 papers)

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Research

Open AccessArticle
A Dual-Linear Kalman Filter for Real-Time Orientation Determination System Using Low-Cost MEMS Sensors
Sensors 2016, 16(2), 264; https://doi.org/10.3390/s16020264 - 20 Feb 2016
Cited by 23
Abstract
To provide a long-time reliable orientation, sensor fusion technologies are widely used to integrate available inertial sensors for the low-cost orientation estimation. In this paper, a novel dual-linear Kalman filter was designed for a multi-sensor system integrating MEMS gyros, an accelerometer, and a [...] Read more.
To provide a long-time reliable orientation, sensor fusion technologies are widely used to integrate available inertial sensors for the low-cost orientation estimation. In this paper, a novel dual-linear Kalman filter was designed for a multi-sensor system integrating MEMS gyros, an accelerometer, and a magnetometer. The proposed filter precludes the impacts of magnetic disturbances on the pitch and roll which the heading is subjected to. The filter can achieve robust orientation estimation for different statistical models of the sensors. The root mean square errors (RMSE) of the estimated attitude angles are reduced by 30.6% under magnetic disturbances. Owing to the reduction of system complexity achieved by smaller matrix operations, the mean total time consumption is reduced by 23.8%. Meanwhile, the separated filter offers greater flexibility for the system configuration, as it is possible to switch on or off the second stage filter to include or exclude the magnetometer compensation for the heading. Online experiments were performed on the homemade miniature orientation determination system (MODS) with the turntable. The average RMSE of estimated orientation are less than 0.4° and 1° during the static and low-dynamic tests, respectively. More realistic tests on two-wheel self-balancing vehicle driving and indoor pedestrian walking were carried out to evaluate the performance of the designed MODS when high accelerations and angular rates were introduced. Test results demonstrate that the MODS is applicable for the orientation estimation under various dynamic conditions. This paper provides a feasible alternative for low-cost orientation determination. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Inertial Sensor Error Reduction through Calibration and Sensor Fusion
Sensors 2016, 16(2), 235; https://doi.org/10.3390/s16020235 - 17 Feb 2016
Cited by 10
Abstract
This paper presents the comparison between cooperative and local Kalman Filters (KF) for estimating the absolute segment angle, under two calibration conditions. A simplified calibration, that can be replicated in most laboratories; and a complex calibration, similar to that applied by commercial vendors. [...] Read more.
This paper presents the comparison between cooperative and local Kalman Filters (KF) for estimating the absolute segment angle, under two calibration conditions. A simplified calibration, that can be replicated in most laboratories; and a complex calibration, similar to that applied by commercial vendors. The cooperative filters use information from either all inertial sensors attached to the body, Matricial KF; or use information from the inertial sensors and the potentiometers of an exoskeleton, Markovian KF. A one minute walking trial of a subject walking with a 6-DoF exoskeleton was used to assess the absolute segment angle of the trunk, thigh, shank, and foot. The results indicate that regardless of the segment and filter applied, the more complex calibration always results in a significantly better performance compared to the simplified calibration. The interaction between filter and calibration suggests that when the quality of the calibration is unknown the Markovian KF is recommended. Applying the complex calibration, the Matricial and Markovian KF perform similarly, with average RMSE below 1.22 degrees. Cooperative KFs perform better or at least equally good as Local KF, we therefore recommend to use cooperative KFs instead of local KFs for control or analysis of walking. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
A New Analytic Alignment Method for a SINS
Sensors 2015, 15(11), 27930-27953; https://doi.org/10.3390/s151127930 - 04 Nov 2015
Cited by 6
Abstract
Analytic alignment is a type of self-alignment for a Strapdown inertial navigation system (SINS) that is based solely on two non-collinear vectors, which are the gravity and rotational velocity vectors of the Earth at a stationary base on the ground. The attitude of [...] Read more.
Analytic alignment is a type of self-alignment for a Strapdown inertial navigation system (SINS) that is based solely on two non-collinear vectors, which are the gravity and rotational velocity vectors of the Earth at a stationary base on the ground. The attitude of the SINS with respect to the Earth can be obtained directly using the TRIAD algorithm given two vector measurements. For a traditional analytic coarse alignment, all six outputs from the inertial measurement unit (IMU) are used to compute the attitude. In this study, a novel analytic alignment method called selective alignment is presented. This method uses only three outputs of the IMU and a few properties from the remaining outputs such as the sign and the approximate value to calculate the attitude. Simulations and experimental results demonstrate the validity of this method, and the precision of yaw is improved using the selective alignment method compared to the traditional analytic coarse alignment method in the vehicle experiment. The selective alignment principle provides an accurate relationship between the outputs and the attitude of the SINS relative to the Earth for a stationary base, and it is an extension of the TRIAD algorithm. The selective alignment approach has potential uses in applications such as self-alignment, fault detection, and self-calibration. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Research on the Rapid and Accurate Positioning and Orientation Approach for Land Missile-Launching Vehicle
Sensors 2015, 15(10), 26606-26620; https://doi.org/10.3390/s151026606 - 20 Oct 2015
Cited by 6
Abstract
Getting a land vehicle’s accurate position, azimuth and attitude rapidly is significant for vehicle based weapons’ combat effectiveness. In this paper, a new approach to acquire vehicle’s accurate position and orientation is proposed. It uses biaxial optical detection platform (BODP) to aim at [...] Read more.
Getting a land vehicle’s accurate position, azimuth and attitude rapidly is significant for vehicle based weapons’ combat effectiveness. In this paper, a new approach to acquire vehicle’s accurate position and orientation is proposed. It uses biaxial optical detection platform (BODP) to aim at and lock in no less than three pre-set cooperative targets, whose accurate positions are measured beforehand. Then, it calculates the vehicle’s accurate position, azimuth and attitudes by the rough position and orientation provided by vehicle based navigation systems and no less than three couples of azimuth and pitch angles measured by BODP. The proposed approach does not depend on Global Navigation Satellite System (GNSS), thus it is autonomous and difficult to interfere. Meanwhile, it only needs a rough position and orientation as algorithm’s iterative initial value, consequently, it does not have high performance requirement for Inertial Navigation System (INS), odometer and other vehicle based navigation systems, even in high precise applications. This paper described the system’s working procedure, presented theoretical deviation of the algorithm, and then verified its effectiveness through simulation and vehicle experiments. The simulation and experimental results indicate that the proposed approach can achieve positioning and orientation accuracy of 0.2 m and 20″ respectively in less than 3 min. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
GPS Cycle Slip Detection Considering Satellite Geometry Based on TDCP/INS Integrated Navigation
Sensors 2015, 15(10), 25336-25365; https://doi.org/10.3390/s151025336 - 30 Sep 2015
Cited by 10
Abstract
This paper presents a means of carrier phase cycle slip detection for an inertial-aided global positioning system (GPS), which is based on consideration of the satellite geometry. An integrated navigation solution incorporating a tightly coupled time differenced carrier phase (TDCP) and inertial navigation [...] Read more.
This paper presents a means of carrier phase cycle slip detection for an inertial-aided global positioning system (GPS), which is based on consideration of the satellite geometry. An integrated navigation solution incorporating a tightly coupled time differenced carrier phase (TDCP) and inertial navigation system (INS) is used to detect cycle slips. Cycle-slips are detected by comparing the satellite-difference (SD) and time-difference (TD) carrier phase measurements obtained from the GPS satellites with the range estimated by the integrated navigation solution. Additionally the satellite geometry information effectively improves the range estimation performance without a hardware upgrade. And the covariance obtained from the TDCP/INS filter is used to compute the threshold for determining cycle slip occurrence. A simulation and the results of a vehicle-based experiment verify the cycle slip detection performance of the proposed algorithm. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Error Model and Compensation of Bell-Shaped Vibratory Gyro
Sensors 2015, 15(9), 23684-23705; https://doi.org/10.3390/s150923684 - 17 Sep 2015
Cited by 2
Abstract
A bell-shaped vibratory angular velocity gyro (BVG), inspired by the Chinese traditional bell, is a type of axisymmetric shell resonator gyroscope. This paper focuses on development of an error model and compensation of the BVG. A dynamic equation is firstly established, based on [...] Read more.
A bell-shaped vibratory angular velocity gyro (BVG), inspired by the Chinese traditional bell, is a type of axisymmetric shell resonator gyroscope. This paper focuses on development of an error model and compensation of the BVG. A dynamic equation is firstly established, based on a study of the BVG working mechanism. This equation is then used to evaluate the relationship between the angular rate output signal and bell-shaped resonator character, analyze the influence of the main error sources and set up an error model for the BVG. The error sources are classified from the error propagation characteristics, and the compensation method is presented based on the error model. Finally, using the error model and compensation method, the BVG is calibrated experimentally including rough compensation, temperature and bias compensation, scale factor compensation and noise filter. The experimentally obtained bias instability is from 20.5°/h to 4.7°/h, the random walk is from 2.8°/h1/2 to 0.7°/h1/2 and the nonlinearity is from 0.2% to 0.03%. Based on the error compensation, it is shown that there is a good linear relationship between the sensing signal and the angular velocity, suggesting that the BVG is a good candidate for the field of low and medium rotational speed measurement. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
An SINS/GNSS Ground Vehicle Gravimetry Test Based on SGA-WZ02
Sensors 2015, 15(9), 23477-23495; https://doi.org/10.3390/s150923477 - 16 Sep 2015
Cited by 2
Abstract
In March 2015, a ground vehicle gravimetry test was implemented in eastern Changsha to assess the repeatability and accuracy of ground vehicle SINS/GNSS gravimeter—SGA-WZ02. The gravity system developed by NUDT consisted of a Strapdown Inertial Navigation System (SINS), a Global Navigation Satellite System [...] Read more.
In March 2015, a ground vehicle gravimetry test was implemented in eastern Changsha to assess the repeatability and accuracy of ground vehicle SINS/GNSS gravimeter—SGA-WZ02. The gravity system developed by NUDT consisted of a Strapdown Inertial Navigation System (SINS), a Global Navigation Satellite System (GNSS) remote station on test vehicle, a GNSS static master station on the ground, and a data logging subsystem. A south-north profile of 35 km along the highway in eastern Changsha was chosen and four repeated available measure lines were obtained. The average speed of a vehicle is 40 km/h. To assess the external ground gravity disturbances, precise ground gravity data was built by CG-5 precise gravimeter as the reference. Under relative smooth conditions, internal accuracy among repeated lines shows an average agreement at the level of 1.86 mGal for half wavelengths about 1.1 km, and 1.22 mGal for 1.7 km. The root-mean-square (RMS) of difference between calculated gravity data and reference data is about 2.27 mGal/1.1 km, and 1.74 mGal/1.7 km. Not all of the noises caused by vehicle itself and experiments environments were eliminated in the primary results. By means of selecting reasonable filters and improving the GNSS observation conditions, further developments in ground vehicle gravimetry are promising. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Field Balancing and Harmonic Vibration Suppression in Rigid AMB-Rotor Systems with Rotor Imbalances and Sensor Runout
Sensors 2015, 15(9), 21876-21897; https://doi.org/10.3390/s150921876 - 31 Aug 2015
Cited by 13
Abstract
Harmonic vibrations of high-speed rotors in momentum exchange devices are primary disturbances for attitude control of spacecraft. Active magnetic bearings (AMBs), offering the ability to control the AMB-rotor dynamic behaviors, are preferred in high-precision and micro-vibration applications, such as high-solution Earth observation satellites. [...] Read more.
Harmonic vibrations of high-speed rotors in momentum exchange devices are primary disturbances for attitude control of spacecraft. Active magnetic bearings (AMBs), offering the ability to control the AMB-rotor dynamic behaviors, are preferred in high-precision and micro-vibration applications, such as high-solution Earth observation satellites. However, undesirable harmonic displacements, currents, and vibrations also occur in the AMB-rotor system owing to the mixed rotor imbalances and sensor runout. To compensate the rotor imbalances and to suppress the harmonic vibrations, two control methods are presented. Firstly, a four degrees-of-freedom AMB-rotor model with the static imbalance, dynamic imbalance, and the sensor runout are described. Next, a synchronous current reduction approach with a variable-phase notch feedback is proposed, so that the rotor imbalances can be identified on-line through the analysis of the synchronous displacement relationships of the geometric, inertial, and rotational axes of the rotor. Then, the identified rotor imbalances, which can be represented at two prescribed balancing planes of the rotor, are compensated by discrete add-on weights whose masses are calculated in the vector form. Finally, a repetitive control algorithm is utilized to suppress the residual harmonic vibrations. The proposed field balancing and harmonic vibration suppression strategies are verified by simulations and experiments performed on a control moment gyro test rig with a rigid AMB-rotor system. Compared with existing methods, the proposed strategies do not require trial weights or an accurate model of the AMB-rotor system. Moreover, the harmonic displacements, currents, and vibrations can be well-attenuated simultaneously. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Initial Alignment of Large Azimuth Misalignment Angles in SINS Based on Adaptive UPF
Sensors 2015, 15(9), 21807-21823; https://doi.org/10.3390/s150921807 - 31 Aug 2015
Cited by 25
Abstract
The case of large azimuth misalignment angles in a strapdown inertial navigation system (SINS) is analyzed, and a method of using the adaptive UPF for the initial alignment is proposed. The filter is based on the idea of a strong tracking filter; through [...] Read more.
The case of large azimuth misalignment angles in a strapdown inertial navigation system (SINS) is analyzed, and a method of using the adaptive UPF for the initial alignment is proposed. The filter is based on the idea of a strong tracking filter; through the introduction of the attenuation memory factor to effectively enhance the corrections of the current information residual error on the system, it reduces the influence on the system due to the system simplification, and the uncertainty of noise statistical properties to a certain extent; meanwhile, the UPF particle degradation phenomenon is better overcome. Finally, two kinds of non-linear filters, UPF and adaptive UPF, are adopted in the initial alignment of large azimuth misalignment angles in SINS, and the filtering effects of the two kinds of nonlinear filter on the initial alignment were compared by simulation and turntable experiments. The simulation and turntable experiment results show that the speed and precision of the initial alignment using adaptive UPF for a large azimuth misalignment angle in SINS under the circumstance that the statistical properties of the system noise are certain or not have been improved to some extent. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Measurement Model and Precision Analysis of Accelerometers for Maglev Vibration Isolation Platforms
Sensors 2015, 15(8), 20053-20068; https://doi.org/10.3390/s150820053 - 14 Aug 2015
Cited by 6
Abstract
High precision measurement of acceleration levels is required to allow active control for vibration isolation platforms. It is necessary to propose an accelerometer configuration measurement model that yields such a high measuring precision. In this paper, an accelerometer configuration to improve measurement accuracy [...] Read more.
High precision measurement of acceleration levels is required to allow active control for vibration isolation platforms. It is necessary to propose an accelerometer configuration measurement model that yields such a high measuring precision. In this paper, an accelerometer configuration to improve measurement accuracy is proposed. The corresponding calculation formulas of the angular acceleration were derived through theoretical analysis. A method is presented to minimize angular acceleration noise based on analysis of the root mean square noise of the angular acceleration. Moreover, the influence of installation position errors and accelerometer orientation errors on the calculation precision of the angular acceleration is studied. Comparisons of the output differences between the proposed configuration and the previous planar triangle configuration under the same installation errors are conducted by simulation. The simulation results show that installation errors have a relatively small impact on the calculation accuracy of the proposed configuration. To further verify the high calculation precision of the proposed configuration, experiments are carried out for both the proposed configuration and the planar triangle configuration. On the basis of the results of simulations and experiments, it can be concluded that the proposed configuration has higher angular acceleration calculation precision and can be applied to different platforms. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Keeping a Good Attitude: A Quaternion-Based Orientation Filter for IMUs and MARGs
Sensors 2015, 15(8), 19302-19330; https://doi.org/10.3390/s150819302 - 06 Aug 2015
Cited by 83
Abstract
Orientation estimation using low cost sensors is an important task for Micro Aerial Vehicles (MAVs) in order to obtain a good feedback for the attitude controller. The challenges come from the low accuracy and noisy data of the MicroElectroMechanical System (MEMS) technology, which [...] Read more.
Orientation estimation using low cost sensors is an important task for Micro Aerial Vehicles (MAVs) in order to obtain a good feedback for the attitude controller. The challenges come from the low accuracy and noisy data of the MicroElectroMechanical System (MEMS) technology, which is the basis of modern, miniaturized inertial sensors. In this article, we describe a novel approach to obtain an estimation of the orientation in quaternion form from the observations of gravity and magnetic field. Our approach provides a quaternion estimation as the algebraic solution of a system from inertial/magnetic observations. We separate the problems of finding the “tilt” quaternion and the heading quaternion in two sub-parts of our system. This procedure is the key for avoiding the impact of the magnetic disturbances on the roll and pitch components of the orientation when the sensor is surrounded by unwanted magnetic flux. We demonstrate the validity of our method first analytically and then empirically using simulated data. We propose a novel complementary filter for MAVs that fuses together gyroscope data with accelerometer and magnetic field readings. The correction part of the filter is based on the method described above and works for both IMU (Inertial Measurement Unit) and MARG (Magnetic, Angular Rate, and Gravity) sensors. We evaluate the effectiveness of the filter and show that it significantly outperforms other common methods, using publicly available datasets with ground-truth data recorded during a real flight experiment of a micro quadrotor helicopter. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Three Three-Axis IEPE Accelerometers on the Inner Liner of a Tire for Finding the Tire-Road Friction Potential Indicators
Sensors 2015, 15(8), 19251-19263; https://doi.org/10.3390/s150819251 - 05 Aug 2015
Cited by 8
Abstract
Direct tire-road contact friction estimation is essential for future autonomous cars and active safety systems. Friction estimation methods have been proposed earlier for driving conditions in the presence of a slip angle or slip ratio. However, the estimation of the friction from a [...] Read more.
Direct tire-road contact friction estimation is essential for future autonomous cars and active safety systems. Friction estimation methods have been proposed earlier for driving conditions in the presence of a slip angle or slip ratio. However, the estimation of the friction from a freely-rolling tire is still an unsolved topic. Knowing the existing friction potential would be beneficial since vehicle control systems could be adjusted before any remarkable tire force has been produced. Since accelerometers are well-known and robust, and thus a promising sensor type for intelligent tires, this study uses three three-axis IEPE accelerometers on the inner liner of a tire to detect friction potential indicators on two equally smooth surfaces with different friction levels. The equal roughness was chosen for both surfaces in order to study the friction phenomena by neglecting the effect of surface texture on vibrations. The acceleration data before the contact is used to differentiate the two friction levels between the tire and the road. In addition, the contact lengths from the three accelerometers are used to validate the acceleration data. A method to differentiate the friction levels on the basis of the acceleration signal is also introduced. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
A Method for Oscillation Errors Restriction of SINS Based on Forecasted Time Series
Sensors 2015, 15(7), 17433-17452; https://doi.org/10.3390/s150717433 - 17 Jul 2015
Cited by 4
Abstract
Continuity, real-time, and accuracy are the key technical indexes of evaluating comprehensive performance of a strapdown inertial navigation system (SINS). However, Schuler, Foucault, and Earth periodic oscillation errors significantly cut down the real-time accuracy of SINS. A method for oscillation error restriction of [...] Read more.
Continuity, real-time, and accuracy are the key technical indexes of evaluating comprehensive performance of a strapdown inertial navigation system (SINS). However, Schuler, Foucault, and Earth periodic oscillation errors significantly cut down the real-time accuracy of SINS. A method for oscillation error restriction of SINS based on forecasted time series is proposed by analyzing the characteristics of periodic oscillation errors. The innovative method gains multiple sets of navigation solutions with different phase delays in virtue of the forecasted time series acquired through the measurement data of the inertial measurement unit (IMU). With the help of curve-fitting based on least square method, the forecasted time series is obtained while distinguishing and removing small angular motion interference in the process of initial alignment. Finally, the periodic oscillation errors are restricted on account of the principle of eliminating the periodic oscillation signal with a half-wave delay by mean value. Simulation and test results show that the method has good performance in restricting the Schuler, Foucault, and Earth oscillation errors of SINS. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
LiDAR Scan Matching Aided Inertial Navigation System in GNSS-Denied Environments
Sensors 2015, 15(7), 16710-16728; https://doi.org/10.3390/s150716710 - 10 Jul 2015
Cited by 35
Abstract
A new scan that matches an aided Inertial Navigation System (INS) with a low-cost LiDAR is proposed as an alternative to GNSS-based navigation systems in GNSS-degraded or -denied environments such as indoor areas, dense forests, or urban canyons. In these areas, INS-based Dead [...] Read more.
A new scan that matches an aided Inertial Navigation System (INS) with a low-cost LiDAR is proposed as an alternative to GNSS-based navigation systems in GNSS-degraded or -denied environments such as indoor areas, dense forests, or urban canyons. In these areas, INS-based Dead Reckoning (DR) and Simultaneous Localization and Mapping (SLAM) technologies are normally used to estimate positions as separate tools. However, there are critical implementation problems with each standalone system. The drift errors of velocity, position, and heading angles in an INS will accumulate over time, and on-line calibration is a must for sustaining positioning accuracy. SLAM performance is poor in featureless environments where the matching errors can significantly increase. Each standalone positioning method cannot offer a sustainable navigation solution with acceptable accuracy. This paper integrates two complementary technologies—INS and LiDAR SLAM—into one navigation frame with a loosely coupled Extended Kalman Filter (EKF) to use the advantages and overcome the drawbacks of each system to establish a stable long-term navigation process. Static and dynamic field tests were carried out with a self-developed Unmanned Ground Vehicle (UGV) platform—NAVIS. The results prove that the proposed approach can provide positioning accuracy at the centimetre level for long-term operations, even in a featureless indoor environment. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
An Inertial and Optical Sensor Fusion Approach for Six Degree-of-Freedom Pose Estimation
Sensors 2015, 15(7), 16448-16465; https://doi.org/10.3390/s150716448 - 08 Jul 2015
Cited by 14
Abstract
Optical tracking provides relatively high accuracy over a large workspace but requires line-of-sight between the camera and the markers, which may be difficult to maintain in actual applications. In contrast, inertial sensing does not require line-of-sight but is subject to drift, which may [...] Read more.
Optical tracking provides relatively high accuracy over a large workspace but requires line-of-sight between the camera and the markers, which may be difficult to maintain in actual applications. In contrast, inertial sensing does not require line-of-sight but is subject to drift, which may cause large cumulative errors, especially during the measurement of position. To handle cases where some or all of the markers are occluded, this paper proposes an inertial and optical sensor fusion approach in which the bias of the inertial sensors is estimated when the optical tracker provides full six degree-of-freedom (6-DOF) pose information. As long as the position of at least one marker can be tracked by the optical system, the 3-DOF position can be combined with the orientation estimated from the inertial measurements to recover the full 6-DOF pose information. When all the markers are occluded, the position tracking relies on the inertial sensors that are bias-corrected by the optical tracking system. Experiments are performed with an augmented reality head-mounted display (ARHMD) that integrates an optical tracking system (OTS) and inertial measurement unit (IMU). Experimental results show that under partial occlusion conditions, the root mean square errors (RMSE) of orientation and position are 0.04° and 0.134 mm, and under total occlusion conditions for 1 s, the orientation and position RMSE are 0.022° and 0.22 mm, respectively. Thus, the proposed sensor fusion approach can provide reliable 6-DOF pose under long-term partial occlusion and short-term total occlusion conditions. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Inertial Sensing Based Assessment Methods to Quantify the Effectiveness of Post-Stroke Rehabilitation
Sensors 2015, 15(7), 16196-16209; https://doi.org/10.3390/s150716196 - 06 Jul 2015
Cited by 6
Abstract
In clinical settings, traditional stroke rehabilitation evaluation methods are subjectively scored by occupational therapists, and the assessment results vary individually. To address this issue, this study aims to develop a stroke rehabilitation assessment system by using inertial measurement units. The inertial signals from [...] Read more.
In clinical settings, traditional stroke rehabilitation evaluation methods are subjectively scored by occupational therapists, and the assessment results vary individually. To address this issue, this study aims to develop a stroke rehabilitation assessment system by using inertial measurement units. The inertial signals from the upper extremities were acquired, from which three quantitative indicators were extracted to reflect rehabilitation performance during stroke patients’ movement examination, i.e., shoulder flexion. Both healthy adults and stroke patients were recruited to correlate the proposed quantitative evaluation indices and traditional rehab assessment scales. Especially, as a unique feature of the study the weight for each of three evaluation indicators was estimated by the least squares method. The quantitative results demonstrate the proposed method accurately reflects patients’ recovery from pre-rehabilitation, and confirm the feasibility of applying inertial signals to evaluate rehab performance through feature extraction. The implemented assessment scheme appears to have the potential to overcome some shortcomings of traditional assessment methods and indicates rehab performance correctly. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Foot Pose Estimation Using an Inertial Sensor Unit and Two Distance Sensors
Sensors 2015, 15(7), 15888-15902; https://doi.org/10.3390/s150715888 - 03 Jul 2015
Cited by 11
Abstract
There are many inertial sensor-based foot pose estimation algorithms. In this paper, we present a methodology to improve the accuracy of foot pose estimation using two low-cost distance sensors (VL6180) in addition to an inertial sensor unit. The distance sensor is a time-of-flight [...] Read more.
There are many inertial sensor-based foot pose estimation algorithms. In this paper, we present a methodology to improve the accuracy of foot pose estimation using two low-cost distance sensors (VL6180) in addition to an inertial sensor unit. The distance sensor is a time-of-flight range finder and can measure distance up to 20 cm. A Kalman filter with 21 states is proposed to estimate both the calibration parameter (relative pose of distance sensors with respect to the inertial sensor unit) and foot pose. Once the calibration parameter is obtained, a Kalman filter with nine states can be used to estimate foot pose. Through four activities (walking, dancing step, ball kicking, jumping), it is shown that the proposed algorithm significantly improves the vertical position estimation. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
Open AccessArticle
Mass and Force Sensing of an Adsorbate on a Beam Resonator Sensor
Sensors 2015, 15(7), 14871-14886; https://doi.org/10.3390/s150714871 - 24 Jun 2015
Cited by 7
Abstract
The mass sensing superiority of a micro-/nano-mechanical resonator sensor over conventional mass spectrometry has been, or at least is being firmly established. Because the sensing mechanism of a mechanical resonator sensor is the shifts of resonant frequencies, how to link the shifts of [...] Read more.
The mass sensing superiority of a micro-/nano-mechanical resonator sensor over conventional mass spectrometry has been, or at least is being firmly established. Because the sensing mechanism of a mechanical resonator sensor is the shifts of resonant frequencies, how to link the shifts of resonant frequencies with the material properties of an analyte formulates an inverse problem. Besides the analyte/adsorbate mass, many other factors, such as position and axial force, can also cause the shifts of resonant frequencies. The in situ measurement of the adsorbate position and axial force is extremely difficult if not impossible, especially when an adsorbate is as small as a molecule or an atom. Extra instruments are also required. In this study, an inverse problem of using three resonant frequencies to determine the mass, position and axial force is formulated and solved. The accuracy of the inverse problem solving method is demonstrated, and how the method can be used in the real application of a nanomechanical resonator is also discussed. Solving the inverse problem is helpful to the development and application of a mechanical resonator sensor for two reasons: reducing extra experimental equipment and achieving better mass sensing by considering more factors. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Performance Analysis of Several GPS/Galileo Precise Point Positioning Models
Sensors 2015, 15(6), 14701-14726; https://doi.org/10.3390/s150614701 - 19 Jun 2015
Cited by 10
Abstract
This paper examines the performance of several precise point positioning (PPP) models, which combine dual-frequency GPS/Galileo observations in the un-differenced and between-satellite single-difference (BSSD) modes. These include the traditional un-differenced model, the decoupled clock model, the semi-decoupled clock model, and the between-satellite single-difference [...] Read more.
This paper examines the performance of several precise point positioning (PPP) models, which combine dual-frequency GPS/Galileo observations in the un-differenced and between-satellite single-difference (BSSD) modes. These include the traditional un-differenced model, the decoupled clock model, the semi-decoupled clock model, and the between-satellite single-difference model. We take advantage of the IGS-MGEX network products to correct for the satellite differential code biases and the orbital and satellite clock errors. Natural Resources Canada’s GPSPace PPP software is modified to handle the various GPS/Galileo PPP models. A total of six data sets of GPS and Galileo observations at six IGS stations are processed to examine the performance of the various PPP models. It is shown that the traditional un-differenced GPS/Galileo PPP model, the GPS decoupled clock model, and the semi-decoupled clock GPS/Galileo PPP model improve the convergence time by about 25% in comparison with the un-differenced GPS-only model. In addition, the semi-decoupled GPS/Galileo PPP model improves the solution precision by about 25% compared to the traditional un-differenced GPS/Galileo PPP model. Moreover, the BSSD GPS/Galileo PPP model improves the solution convergence time by about 50%, in comparison with the un-differenced GPS PPP model, regardless of the type of BSSD combination used. As well, the BSSD model improves the precision of the estimated parameters by about 50% and 25% when the loose and the tight combinations are used, respectively, in comparison with the un-differenced GPS-only model. Comparable results are obtained through the tight combination when either a GPS or a Galileo satellite is selected as a reference. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Inertial Sensor-Based Touch and Shake Metaphor for Expressive Control of 3D Virtual Avatars
Sensors 2015, 15(6), 14435-14457; https://doi.org/10.3390/s150614435 - 18 Jun 2015
Cited by 4
Abstract
In this paper, we present an inertial sensor-based touch and shake metaphor for expressive control of a 3D virtual avatar in a virtual environment. An intuitive six degrees-of-freedom wireless inertial motion sensor is used as a gesture and motion control input device with [...] Read more.
In this paper, we present an inertial sensor-based touch and shake metaphor for expressive control of a 3D virtual avatar in a virtual environment. An intuitive six degrees-of-freedom wireless inertial motion sensor is used as a gesture and motion control input device with a sensor fusion algorithm. The algorithm enables user hand motions to be tracked in 3D space via magnetic, angular rate, and gravity sensors. A quaternion-based complementary filter is implemented to reduce noise and drift. An algorithm based on dynamic time-warping is developed for efficient recognition of dynamic hand gestures with real-time automatic hand gesture segmentation. Our approach enables the recognition of gestures and estimates gesture variations for continuous interaction. We demonstrate the gesture expressivity using an interactive flexible gesture mapping interface for authoring and controlling a 3D virtual avatar and its motion by tracking user dynamic hand gestures. This synthesizes stylistic variations in a 3D virtual avatar, producing motions that are not present in the motion database using hand gesture sequences from a single inertial motion sensor. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
A Flight Test of the Strapdown Airborne Gravimeter SGA-WZ in Greenland
Sensors 2015, 15(6), 13258-13269; https://doi.org/10.3390/s150613258 - 05 Jun 2015
Cited by 4
Abstract
An airborne gravimeter is one of the most important tools for gravity data collection over large areas with mGal accuracy and a spatial resolution of several kilometers. In August 2012, a flight test was carried out to determine the feasibility and to assess [...] Read more.
An airborne gravimeter is one of the most important tools for gravity data collection over large areas with mGal accuracy and a spatial resolution of several kilometers. In August 2012, a flight test was carried out to determine the feasibility and to assess the accuracy of the new Chinese SGA-WZ strapdown airborne gravimeter in Greenland, in an area with good gravity coverage from earlier marine and airborne surveys. An overview of this new system SGA-WZ is given, including system design, sensor performance and data processing. The processing of the SGA-WZ includes a 160 s length finite impulse response filter, corresponding to a spatial resolution of 6 km. For the primary repeated line, a mean r.m.s. deviation of the differences was less than 1.5 mGal, with the error estimate confirmed from ground truth data. This implies that the SGA-WZ could meet standard geophysical survey requirements at the 1 mGal level. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Classifying Step and Spin Turns Using Wireless Gyroscopes and Implications for Fall Risk Assessments
Sensors 2015, 15(5), 10676-10685; https://doi.org/10.3390/s150510676 - 06 May 2015
Cited by 10
Abstract
Recent studies have reported a greater prevalence of spin turns, which are more unstable than step turns, in older adults compared to young adults in laboratory settings. Currently, turning strategies can only be identified through visual observation, either in-person or through video. This [...] Read more.
Recent studies have reported a greater prevalence of spin turns, which are more unstable than step turns, in older adults compared to young adults in laboratory settings. Currently, turning strategies can only be identified through visual observation, either in-person or through video. This paper presents two unique methods and their combination to remotely monitor turning behavior using three uniaxial gyroscopes. Five young adults performed 90° turns at slow, normal, and fast walking speeds around a variety of obstacles while instrumented with three IMUs (attached on the trunk, left and right shank). Raw data from 360 trials were analyzed. Compared to visual classification, the two IMU methods’ sensitivity/specificity to detecting spin turns were 76.1%/76.7% and 76.1%/84.4%, respectively. When the two methods were combined, the IMU had an overall 86.8% sensitivity and 92.2% specificity, with 89.4%/100% sensitivity/specificity at slow speeds. This combined method can be implemented into wireless fall prevention systems and used to identify increased use of spin turns. This method allows for longitudinal monitoring of turning strategies and allows researchers to test for potential associations between the frequency of spin turns and clinically relevant outcomes (e.g., falls) in non-laboratory settings. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
A Novel Artificial Fish Swarm Algorithm for Recalibration of Fiber Optic Gyroscope Error Parameters
Sensors 2015, 15(5), 10547-10568; https://doi.org/10.3390/s150510547 - 05 May 2015
Cited by 9
Abstract
The artificial fish swarm algorithm (AFSA) is one of the state-of-the-art swarm intelligent techniques, which is widely utilized for optimization purposes. Fiber optic gyroscope (FOG) error parameters such as scale factors, biases and misalignment errors are relatively unstable, especially with the environmental disturbances [...] Read more.
The artificial fish swarm algorithm (AFSA) is one of the state-of-the-art swarm intelligent techniques, which is widely utilized for optimization purposes. Fiber optic gyroscope (FOG) error parameters such as scale factors, biases and misalignment errors are relatively unstable, especially with the environmental disturbances and the aging of fiber coils. These uncalibrated error parameters are the main reasons that the precision of FOG-based strapdown inertial navigation system (SINS) degraded. This research is mainly on the application of a novel artificial fish swarm algorithm (NAFSA) on FOG error coefficients recalibration/identification. First, the NAFSA avoided the demerits (e.g., lack of using artificial fishes’ pervious experiences, lack of existing balance between exploration and exploitation, and high computational cost) of the standard AFSA during the optimization process. To solve these weak points, functional behaviors and the overall procedures of AFSA have been improved with some parameters eliminated and several supplementary parameters added. Second, a hybrid FOG error coefficients recalibration algorithm has been proposed based on NAFSA and Monte Carlo simulation (MCS) approaches. This combination leads to maximum utilization of the involved approaches for FOG error coefficients recalibration. After that, the NAFSA is verified with simulation and experiments and its priorities are compared with that of the conventional calibration method and optimal AFSA. Results demonstrate high efficiency of the NAFSA on FOG error coefficients recalibration. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
A Self-Alignment Algorithm for SINS Based on Gravitational Apparent Motion and Sensor Data Denoising
Sensors 2015, 15(5), 9827-9853; https://doi.org/10.3390/s150509827 - 27 Apr 2015
Cited by 8
Abstract
Initial alignment is always a key topic and difficult to achieve in an inertial navigation system (INS). In this paper a novel self-initial alignment algorithm is proposed using gravitational apparent motion vectors at three different moments and vector-operation. Simulation and analysis showed that [...] Read more.
Initial alignment is always a key topic and difficult to achieve in an inertial navigation system (INS). In this paper a novel self-initial alignment algorithm is proposed using gravitational apparent motion vectors at three different moments and vector-operation. Simulation and analysis showed that this method easily suffers from the random noise contained in accelerometer measurements which are used to construct apparent motion directly. Aiming to resolve this problem, an online sensor data denoising method based on a Kalman filter is proposed and a novel reconstruction method for apparent motion is designed to avoid the collinearity among vectors participating in the alignment solution. Simulation, turntable tests and vehicle tests indicate that the proposed alignment algorithm can fulfill initial alignment of strapdown INS (SINS) under both static and swinging conditions. The accuracy can either reach or approach the theoretical values determined by sensor precision under static or swinging conditions. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Integration of GPS Precise Point Positioning and MEMS-Based INS Using Unscented Particle Filter
Sensors 2015, 15(4), 7228-7245; https://doi.org/10.3390/s150407228 - 25 Mar 2015
Cited by 21
Abstract
Integration of Global Positioning System (GPS) and Inertial Navigation System (INS) integrated system involves nonlinear motion state and measurement models. However, the extended Kalman filter (EKF) is commonly used as the estimation filter, which might lead to solution divergence. This is usually encountered [...] Read more.
Integration of Global Positioning System (GPS) and Inertial Navigation System (INS) integrated system involves nonlinear motion state and measurement models. However, the extended Kalman filter (EKF) is commonly used as the estimation filter, which might lead to solution divergence. This is usually encountered during GPS outages, when low-cost micro-electro-mechanical sensors (MEMS) inertial sensors are used. To enhance the navigation system performance, alternatives to the standard EKF should be considered. Particle filtering (PF) is commonly considered as a nonlinear estimation technique to accommodate severe MEMS inertial sensor biases and noise behavior. However, the computation burden of PF limits its use. In this study, an improved version of PF, the unscented particle filter (UPF), is utilized, which combines the unscented Kalman filter (UKF) and PF for the integration of GPS precise point positioning and MEMS-based inertial systems. The proposed filter is examined and compared with traditional estimation filters, namely EKF, UKF and PF. Tightly coupled mechanization is adopted, which is developed in the raw GPS and INS measurement domain. Un-differenced ionosphere-free linear combinations of pseudorange and carrier-phase measurements are used for PPP. The performance of the UPF is analyzed using a real test scenario in downtown Kingston, Ontario. It is shown that the use of UPF reduces the number of samples needed to produce an accurate solution, in comparison with the traditional PF, which in turn reduces the processing time. In addition, UPF enhances the positioning accuracy by up to 15% during GPS outages, in comparison with EKF. However, all filters produce comparable results when the GPS measurement updates are available. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
An Evaluation of Skylight Polarization Patterns for Navigation
Sensors 2015, 15(3), 5895-5913; https://doi.org/10.3390/s150305895 - 10 Mar 2015
Cited by 14
Abstract
Skylight polarization provides a significant navigation cue for certain polarization-sensitive animals. However, the precision of the angle of polarization (AOP) of skylight for vehicle orientation is not clear. An evaluation of AOP must be performed before it is utilized. This paper reports an [...] Read more.
Skylight polarization provides a significant navigation cue for certain polarization-sensitive animals. However, the precision of the angle of polarization (AOP) of skylight for vehicle orientation is not clear. An evaluation of AOP must be performed before it is utilized. This paper reports an evaluation of AOP of skylight by measuring the skylight polarization patterns of clear and cloudy skies using a full-sky imaging polarimetry system. AOP measurements of skylight are compared with the pattern calculated by the single-scattering Rayleigh model and these differences are quantified. The relationship between the degree of polarization (DOP) and the deviation of AOP of skylight is thoroughly studied. Based on these, a solar meridian extracted method is presented. The results of experiments reveal that the DOP is a key parameter to indicate the accuracy of AOP measurements, and all the output solar meridian orientations extracted by our method in both clear and cloudy skies can achieve a high accuracy for vehicle orientation. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Tightly Coupled Integration of Ionosphere-Constrained Precise Point Positioning and Inertial Navigation Systems
Sensors 2015, 15(3), 5783-5802; https://doi.org/10.3390/s150305783 - 10 Mar 2015
Cited by 15
Abstract
The continuity and reliability of precise GNSS positioning can be seriously limited by severe user observation environments. The Inertial Navigation System (INS) can overcome such drawbacks, but its performance is clearly restricted by INS sensor errors over time. Accordingly, the tightly coupled integration [...] Read more.
The continuity and reliability of precise GNSS positioning can be seriously limited by severe user observation environments. The Inertial Navigation System (INS) can overcome such drawbacks, but its performance is clearly restricted by INS sensor errors over time. Accordingly, the tightly coupled integration of GPS and INS can overcome the disadvantages of each individual system and together form a new navigation system with a higher accuracy, reliability and availability. Recently, ionosphere-constrained (IC) precise point positioning (PPP) utilizing raw GPS observations was proven able to improve both the convergence and positioning accuracy of the conventional PPP using ionosphere-free combined observations (LC-PPP). In this paper, a new mode of tightly coupled integration, in which the IC-PPP instead of LC-PPP is employed, is implemented to further improve the performance of the coupled system. We present the detailed mathematical model and the related algorithm of the new integration of IC-PPP and INS. To evaluate the performance of the new tightly coupled integration, data of both airborne and vehicle experiments with a geodetic GPS receiver and tactical grade inertial measurement unit are processed and the results are analyzed. The statistics show that the new approach can further improve the positioning accuracy compared with both IC-PPP and the tightly coupled integration of the conventional PPP and INS. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
A Performance Improvement Method for Low-Cost Land Vehicle GPS/MEMS-INS Attitude Determination
Sensors 2015, 15(3), 5722-5746; https://doi.org/10.3390/s150305722 - 09 Mar 2015
Cited by 21
Abstract
Global positioning system (GPS) technology is well suited for attitude determination. However, in land vehicle application, low-cost single frequency GPS receivers which have low measurement quality are often used, and external factors such as multipath and low satellite visibility in the densely built-up [...] Read more.
Global positioning system (GPS) technology is well suited for attitude determination. However, in land vehicle application, low-cost single frequency GPS receivers which have low measurement quality are often used, and external factors such as multipath and low satellite visibility in the densely built-up urban environment further degrade the quality of the GPS measurements. Due to the low-quality receivers used and the challenging urban environment, the success rate of the single epoch ambiguity resolution for dynamic attitude determination is usually quite low. In this paper, a micro-electro-mechanical system (MEMS)—inertial navigation system (INS)-aided ambiguity resolution method is proposed to improve the GPS attitude determination performance, which is particularly suitable for land vehicle attitude determination. First, the INS calculated baseline vector is augmented with the GPS carrier phase and code measurements. This improves the ambiguity dilution of precision (ADOP), resulting in better quality of the unconstrained float solution. Second, the undesirable float solutions caused by large measurement errors are further filtered and replaced using the INS-aided ambiguity function method (AFM). The fixed solutions are then obtained by the constrained least squares ambiguity decorrelation (CLAMBDA) algorithm. Finally, the GPS/MEMS-INS integration is realized by the use of a Kalman filter. Theoretical analysis of the ADOP is given and experimental results demonstrate that our proposed method can significantly improve the quality of the float ambiguity solution, leading to high success rate and better accuracy of attitude determination. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Magnetometer-Augmented IMU Simulator: In-Depth Elaboration
Sensors 2015, 15(3), 5293-5310; https://doi.org/10.3390/s150305293 - 04 Mar 2015
Cited by 11
Abstract
The location of objects is a growing research topic due, for instance, to the expansion of civil drones or intelligent vehicles. This expansion was made possible through the development of microelectromechanical systems (MEMS), inexpensive and miniaturized inertial sensors. In this context, this article [...] Read more.
The location of objects is a growing research topic due, for instance, to the expansion of civil drones or intelligent vehicles. This expansion was made possible through the development of microelectromechanical systems (MEMS), inexpensive and miniaturized inertial sensors. In this context, this article describes the development of a new simulator which generates sensor measurements, giving a specific input trajectory. This will allow the comparison of pose estimation algorithms. To develop this simulator, the measurement equations of every type of sensor have to be analytically determined. To achieve this objective, classical kinematic equations are used for the more common sensors, i.e., accelerometers and rate gyroscopes. As nowadays, the MEMS inertial measurement units (IMUs) are generally magnetometer-augmented, an absolute world magnetic model is implemented. After the determination of the perfect measurement (through the error-free sensor models), realistic error models are developed to simulate real IMU behavior. Finally, the developed simulator is subjected to different validation tests. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
Open AccessArticle
A Stationary North-Finding Scheme for an Azimuth Rotational IMU Utilizing a Linear State Equality Constraint
Sensors 2015, 15(2), 4368-4387; https://doi.org/10.3390/s150204368 - 13 Feb 2015
Cited by 5
Abstract
The Kalman filter (KF) has always been used to improve north-finding performance under practical conditions. By analyzing the characteristics of the azimuth rotational inertial measurement unit (ARIMU) on a stationary base, a linear state equality constraint for the conventional KF used in the [...] Read more.
The Kalman filter (KF) has always been used to improve north-finding performance under practical conditions. By analyzing the characteristics of the azimuth rotational inertial measurement unit (ARIMU) on a stationary base, a linear state equality constraint for the conventional KF used in the fine north-finding filtering phase is derived. Then, a constrained KF using the state equality constraint is proposed and studied in depth. Estimation behaviors of the concerned navigation errors when implementing the conventional KF scheme and the constrained KF scheme during stationary north-finding are investigated analytically by the stochastic observability approach, which can provide explicit formulations of the navigation errors with influencing variables. Finally, multiple practical experimental tests at a fixed position are done on a postulate system to compare the stationary north-finding performance of the two filtering schemes. In conclusion, this study has successfully extended the utilization of the stochastic observability approach for analytic descriptions of estimation behaviors of the concerned navigation errors, and the constrained KF scheme has demonstrated its superiority over the conventional KF scheme for ARIMU stationary north-finding both theoretically and practically. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
Open AccessArticle
A Simultaneously Calibration Approach for Installation and Attitude Errors of an INS/GPS/LDS Target Tracker
Sensors 2015, 15(2), 3575-3592; https://doi.org/10.3390/s150203575 - 04 Feb 2015
Cited by 2
Abstract
To obtain the absolute position of a target is one of the basic topics for non-cooperated target tracking problems. In this paper, we present a simultaneously calibration method for an Inertial navigation system (INS)/Global position system (GPS)/Laser distance scanner (LDS) integrated system based [...] Read more.
To obtain the absolute position of a target is one of the basic topics for non-cooperated target tracking problems. In this paper, we present a simultaneously calibration method for an Inertial navigation system (INS)/Global position system (GPS)/Laser distance scanner (LDS) integrated system based target positioning approach. The INS/GPS integrated system provides the attitude and position of observer, and LDS offers the distance between the observer and the target. The two most significant errors are taken into jointly consideration and analyzed: (1) the attitude measure error of INS/GPS; (2) the installation error between INS/GPS and LDS subsystems. Consequently, a INS/GPS/LDS based target positioning approach considering these two errors is proposed. In order to improve the performance of this approach, a novel calibration method is designed to simultaneously estimate and compensate these two main errors. Finally, simulations are conducted to access the performance of the proposed target positioning approach and the designed simultaneously calibration method. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
Open AccessArticle
Adaptive Data Filtering of Inertial Sensors with Variable Bandwidth
Sensors 2015, 15(2), 3282-3298; https://doi.org/10.3390/s150203282 - 02 Feb 2015
Cited by 8
Abstract
MEMS (micro-electro-mechanical system)-based inertial sensors, i.e., accelerometers and angular rate sensors, are commonly used as a cost-effective solution for the purposes of navigation in a broad spectrum of terrestrial and aerospace applications. These tri-axial inertial sensors form an inertial measurement unit (IMU), [...] Read more.
MEMS (micro-electro-mechanical system)-based inertial sensors, i.e., accelerometers and angular rate sensors, are commonly used as a cost-effective solution for the purposes of navigation in a broad spectrum of terrestrial and aerospace applications. These tri-axial inertial sensors form an inertial measurement unit (IMU), which is a core unit of navigation systems. Even if MEMS sensors have an advantage in their size, cost, weight and power consumption, they suffer from bias instability, noisy output and insufficient resolution. Furthermore, the sensor’s behavior can be significantly affected by strong vibration when it operates in harsh environments. All of these constitute conditions require treatment through data processing. As long as the navigation solution is primarily based on using only inertial data, this paper proposes a novel concept in adaptive data pre-processing by using a variable bandwidth filtering. This approach utilizes sinusoidal estimation to continuously adapt the filtering bandwidth of the accelerometer’s data in order to reduce the effects of vibration and sensor noise before attitude estimation is processed. Low frequency vibration generally limits the conditions under which the accelerometers can be used to aid the attitude estimation process, which is primarily based on angular rate data and, thus, decreases its accuracy. In contrast, the proposed pre-processing technique enables using accelerometers as an aiding source by effective data smoothing, even when they are affected by low frequency vibration. Verification of the proposed concept is performed on simulation and real-flight data obtained on an ultra-light aircraft. The results of both types of experiments confirm the suitability of the concept for inertial data pre-processing. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Research on Initial Alignment and Self-Calibration of Rotary Strapdown Inertial Navigation Systems
Sensors 2015, 15(2), 3154-3171; https://doi.org/10.3390/s150203154 - 30 Jan 2015
Cited by 43
Abstract
The errors of inertial sensors affect the navigation accuracy of the strapdown inertial navigation system (SINS) and are accumulated over time in nature. In order to continuously maintain the high navigation accuracy of vehicles for a long time period, an initial alignment and [...] Read more.
The errors of inertial sensors affect the navigation accuracy of the strapdown inertial navigation system (SINS) and are accumulated over time in nature. In order to continuously maintain the high navigation accuracy of vehicles for a long time period, an initial alignment and self-calibration is necessary after the SINS starts. Additionally, the observability analysis is one of the key techniques during the initial alignment and self-calibration process. For marine systems, the observability of inertial sensor errors is extremely low, as their motion states are always slow. Therefore, studying the rotating SINS is urgent. Since traditional analysis methods have their limitations, the global observation analysis method was used in this paper. On the basis of this method, the relationship between the observability and the kinestate of the rotating SINS has been established. After the discussion about the factors that affect the observability in detail, the design principle of the initial alignment and self-calibration rotating scheme, which is appropriate for marine systems, id proposed. With the proposed principle, a novel initial alignment and self-calibration method, named the eight-position rotating scheme, is designed. Simulations and experiments are carried out to verify its performance. The results have shown that compared with other rotating schemes and the static state, the estimated accuracy of the eight-position scheme rotating about axes x and y was the best, and the position error was significantly reduced with this new rotating scheme. The feasibility and effectiveness of the proposed design principle and the rotating scheme were verified. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
Open AccessArticle
Analysis of Frequency Response and Scale-Factor of Tuning Fork Micro-Gyroscope Operating at Atmospheric Pressure
Sensors 2015, 15(2), 2453-2472; https://doi.org/10.3390/s150202453 - 22 Jan 2015
Cited by 5
Abstract
This paper presents a study of the frequency response and the scale-factor of a tuning fork micro-gyroscope operating at atmospheric pressure in the presence of an interference sense mode by utilizing the approximate transfer function. The optimal demodulation phase (ODP), which is always [...] Read more.
This paper presents a study of the frequency response and the scale-factor of a tuning fork micro-gyroscope operating at atmospheric pressure in the presence of an interference sense mode by utilizing the approximate transfer function. The optimal demodulation phase (ODP), which is always ignored in vacuum packaged micro-gyroscopes but quite important in gyroscopes operating at atmospheric pressure, is obtained through the transfer function of the sense mode, including the primary mode and the interference mode. The approximate transfer function of the micro-gyroscope is deduced in consideration of the interference mode and the ODP. Then, the equation describing the scale-factor of the gyroscope is also obtained. The impacts of the interference mode and Q-factor on the frequency response and the scale-factor of the gyroscope are analyzed through numerical simulations. The relationship between the scale-factor and the demodulation phase is also illustrated and gives an effective way to find out the ODP in practice. The simulation results predicted by the transfer functions are in close agreement with the results of the experiments. The analyses and simulations can provide constructive guidance on bandwidth and sensitivity designs of the micro-gyroscopes operating at atmospheric pressure. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
Open AccessArticle
Inertial Sensor Self-Calibration in a Visually-Aided Navigation Approach for a Micro-AUV
Sensors 2015, 15(1), 1825-1860; https://doi.org/10.3390/s150101825 - 16 Jan 2015
Cited by 18
Abstract
This paper presents a new solution for underwater observation, image recording, mapping and 3D reconstruction in shallow waters. The platform, designed as a research and testing tool, is based on a small underwater robot equipped with a MEMS-based IMU, two stereo cameras and [...] Read more.
This paper presents a new solution for underwater observation, image recording, mapping and 3D reconstruction in shallow waters. The platform, designed as a research and testing tool, is based on a small underwater robot equipped with a MEMS-based IMU, two stereo cameras and a pressure sensor. The data given by the sensors are fused, adjusted and corrected in a multiplicative error state Kalman filter (MESKF), which returns a single vector with the pose and twist of the vehicle and the biases of the inertial sensors (the accelerometer and the gyroscope). The inclusion of these biases in the state vector permits their self-calibration and stabilization, improving the estimates of the robot orientation. Experiments in controlled underwater scenarios and in the sea have demonstrated a satisfactory performance and the capacity of the vehicle to operate in real environments and in real time. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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Open AccessArticle
Inertial Sensor-Based Smoother for Gait Analysis
Sensors 2014, 14(12), 24338-24357; https://doi.org/10.3390/s141224338 - 17 Dec 2014
Cited by 12
Abstract
An off-line smoother algorithm is proposed to estimate foot motion using an inertial sensor unit (three-axis gyroscopes and accelerometers) attached to a shoe. The smoother gives more accurate foot motion estimation than filter-based algorithms by using all of the sensor data instead of [...] Read more.
An off-line smoother algorithm is proposed to estimate foot motion using an inertial sensor unit (three-axis gyroscopes and accelerometers) attached to a shoe. The smoother gives more accurate foot motion estimation than filter-based algorithms by using all of the sensor data instead of using the current sensor data. The algorithm consists of two parts. In the first part, a Kalman filter is used to obtain initial foot motion estimation. In the second part, the error in the initial estimation is compensated using a smoother, where the problem is formulated in the quadratic optimization problem. An efficient solution of the quadratic optimization problem is given using the sparse structure. Through experiments, it is shown that the proposed algorithm can estimate foot motion more accurately than a filter-based algorithm with reasonable computation time. In particular, there is significant improvement in the foot motion estimation when the foot is moving off the floor: the z-axis position error squared sum (total time: 3.47 s) when the foot is in the air is 0.0807 m2 (Kalman filter) and 0.0020 m2 (the proposed smoother). Full article
(This article belongs to the Special Issue Inertial Sensors and Systems)
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