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Integrating the precise GPS carrier phases and INS sensor technologies is a methodology that has been applied indispensably in those application fields requiring accurate and reliable position, velocity, and attitude information. However, conventional integration approaches with a single GPS reference station may not fulfil the demanding performance requirements, especially in the position component, when the baseline length between the reference station and mobile user’s GPS receiver is greater than a few tens of kilometres. This is because their positioning performance is primarily dependent on the common mode of errors of GPS measurements. To address this constraint, a novel GPS/INS integration scheme using multiple GPS reference stations is proposed here that can improve its positioning accuracy by modelling the baseline-dependent errors. In this paper, the technical issues concerned with implementing the proposed scheme are described, including the GPS network correction modelling and integrated GPS/INS filtering. In addition, the results from the processing of the simulated measurements are presented to characterise the system performance. As a result, it has been established that the integration of GPS/INS with multiple reference stations would make it possible to ensure centimetre-level positioning accuracy, even if the baseline length reaches about 100 km.

The carrier phase-based Global Positioning System (GPS) has become an essential technique for a wide range of precise positioning applications, such as kinematic positioning and vehicle navigation and guidance. However, there are several constraints on the use of this technique. Firstly, an assurance of satellite signal line-of-sight is a critical requirement, yet GPS signals can be obstructed by buildings, bridges, and even tree foliage. Under these circumstances, the GPS system is unable to continuously carry out its positioning task because of the insufficient number of tracked satellites. Furthermore, the impact of baseline-dependent GPS errors, such as orbit uncertainties, and atmospheric effects, further constrains the applicable baseline length between reference and mobile user receiver to perhaps 10–15 km. These constraints have led to the development of several network-based GPS kinematic positioning techniques, including the virtual reference station approach [

Some of the restrictions of carrier phase-based GPS technology can be addressed by its integration with an inertial navigation system (INS). The INS is a self-contained navigation unit providing position, velocity and attitude information based on measurements by its ensemble of sensors (typically a set of accelerometers and gyroscopes). Its disadvantage is that INS navigation accuracy deteriorates rapidly with time due to the presence of sensor biases and a double-integration mechanisation algorithm. However, an appropriate integration of INS with GPS can take advantage of each technology’s strengths, delivering a high data-rate complete navigation solution with both superior short-term and long-term accuracies [

This paper proposes a GPS/INS integration scheme with multiple GPS references for use in highly precise long-baseline kinematic positioning. This approach utilises measurements from multiple reference stations to model the GPS baseline-dependent errors and to apply them to mobile receiver observations before updating the integration filter. Hence, the applicable baseline length is extended with centimetre-level positioning accuracy. After discussing the concept of the employment of multiple reference stations with the integrated GPS/INS, some technical issues required for the implementation of the algorithm are described. This is followed by the description of measurement simulations and test results with an emphasis on the effects of employing multiple reference stations in the integrated GPS/INS data processing.

The proposed integration approach is comprised of two components, namely the stationary reference measurement processing and the mobile positioning instrumentation. The role of the multiple GPS reference stations is to generate the so-called network corrections that model the baseline-dependent errors at a mobile station, whereas the mobile platform component is an integrated GPS/INS device. As illustrated in

The GPS baseline-dependent errors are estimated based on the pre-determined coordinates of the reference stations. It is prerequisite to correctly resolve the double differenced (DD) carrier phase ambiguities between the reference stations to generate the accurate corrections. For real-time measurements with baselines over a few tens of kilometres, several integer ambiguity resolution algorithms have been proposed [

The performance of positioning and navigation with the multiple GPS reference stations is largely dependent on the ability of an algorithm to separate the site-dependent errors from the DD residuals computed by subtracting the ambiguities and geometric distances from the DD measurements.

A detailed expression of the dynamic matrix can be given by:

The error states in _{P}_{V}_{A}_{M}

The so-called corrections, modelled by interpolating the baseline-dependent errors at the reference stations with respect to the position of a mobile station, should be applied for mobile GPS receiver measurements to reduce these errors. Over the past decades, a number of interpolation methods have been proposed, including the linear combination model, distance-based linear interpolation method, and linear interpolation method [_{i}_{i}

The mobile platform within the coverage of the reference network can apply the following 2-D linear model to interpolate the baseline-dependent errors:

The integration of GPS with INS has been implemented using a tightly-coupled Kalman filtering technique, which utilises a single filter to process all the data in the DD measurements domain. The integrated processing procedure employed in this study is presented in

In this GPS/INS integration, the DD GPS carrier phases are used to update the Kalman filter to estimate the navigation and INS sensor errors. The DD measurements are formed by differencing between two single differences (SD) across two different satellites at each epoch. In the case of a medium baseline up to 100 km, the measurements can be mathematically represented as:

By applying the network correction,

However,

Three sets of simulated GPS and INS measurements have been processed in this section to test the performance of the algorithms implemented and to evaluate the achievable accuracy of the position and attitude parameter estimation.

All the test measurements were generated using a GNSS/INS simulator consisting of trajectory profile generation, GPS satellite, and INS measurements simulation modules [

The measurement simulation begins with defining a reference trajectory (the time, coordinate, velocity, and attitude) for a moving vehicle. In the INS data generation, specific force (acceleration) and angular velocity is firstly computed, based on the given trajectory profile. Then, the related sensor errors, accelerometer/gyro bias, scale factor and noise, as well as the effects associated with the Earth’s rotation and gravity, are computed and added to the generated true measurements. All the data generated are stored in a binary format at a rate of 64 Hz. On the other hand, the geometric distances between the receiver and the satellite are initially computed to simulate the GPS observations. The biases, errors and measurement noise are then added to the geometric distance. These simulations were performed with respect to a tactical-grade INS (e.g., gyro drift 5 deg/h and accelerometer bias 500 μg) and dual-frequency geodetic GPS receivers.

Three different scenarios, denoted as CASE1, CASE2, and CASE3, were considered in the GPS/INS simulation, depending on baseline length between the master reference and the mobile station. Because MREF is selected as the master reference station, the baseline lengths range from 57 km to 101 km in these scenarios.

All the simulated measurements were processed in post-mission mode using self-programmed software to estimate the navigation parameters. However, it is important to note that all the algorithms are applicable for the real-time implementation. Although the main goal of this study was to investigate the impact of including the multiple reference stations in the GPS/INS integration in terms of the accuracy of the position and attitude estimation, the performance of the implemented algorithms at each step of data processing was tested, which includes the baseline-dependent errors estimation, the network correction modelling, and the ambiguity resolution

The data processing of the integrated GPS/INS with multiple reference stations begins with the carrier phase ambiguity resolution between the stations. By applying the procedure described in Section 3, it was possible to fix the ambiguities to their correct values within a few seconds. Because MREF was selected as a master reference station, three baselines, denoted as MREF-REF1, MREF-REF2, and MREF-REF3, were composed in the data processing.

The Kalman filters processed the DD residuals computed at the reference stations in parallel to estimate the baseline-dependent errors with the minimising impact of the site-dependent errors. For example, the results from the filtering for the L1 and L2 of space vehicle (SV) 8 in CASE I are shown in

Ambiguity resolution (AR) is one of the most crucial procedures for achieving the goal of high accuracy carrier phases-based GPS positioning and navigation applications. Due to the existence of the baseline-dependent errors, the ability to correctly resolve the integer ambiguities is restricted to relatively short distances between the reference station and the mobile receiver. To correctly resolve the ambiguities, the residual errors of the DD carrier phases should be theoretically smaller than a half-wavelength, corresponding to about 10 cm and 12 cm for the L1 and L2 phase observations, respectively. It is almost impossible to resolve the correct ambiguities using the single reference AR technique in the case of the medium baseline. However, the proposed integration technique is expected to correctly fix the ambiguities by modelling the baseline-dependent errors based on the multiple reference stations and using the INS-predicted position obtained from its mechanisation. An instantaneous AR procedure with single-epoch observations was carried out to demonstrate its performance. The results are summarised in

An integration of GPS/INS with multiple-reference stations for long-baseline kinematic positioning has been proposed in this paper, with the objective of improving the accuracy of the position estimation in the case of baseline lengths up to about 100 km. The algorithms concerned with implementing the proposed scheme are addressed, which include the AR between reference stations, the estimation of the baseline-dependent errors, the network correction modelling, and the integrated GPS/INS processing with an emphasis on the Kalman filter design. Three GPS and INS simulated measurement sets on mobile platforms were processed to characterise not only the performance of the algorithms implemented, but also the achievable accuracy of the position and attitude estimation. The results show that the accuracy of the position component was significantly improved to be a few centimetres through modelling the baseline-dependent errors based on the multiple reference stations. Because the accuracy of the attitude estimation based on INS depends primarily on the quality of the gyro sensors, marginal improvement was observed in the component. In conclusion, more research on quality control algorithms for the integration and further tests with real data sets will be carried out in the near future.

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (KRF-2007-331-D00481).

Configuration of the tightly-coupled GPS/INS integration using GPS multiple reference stations.

An estimation procedure for GPS baseline-dependent error utilising the Kalman Filter.

Layout of the GPS multiple reference station and testing areas.

Generated reference trajectory.

Filtering results to generate the GPS baseline-dependent errors of SV8 (CASE I).

Impact of Kalman filtering in the estimation of the GPS baseline-dependent errors of SV8(CASE I).

Interpolated GPS baseline-dependent errors (network corrections).

DD residuals of mobile receivers.

Example of the estimated navigation parameters (CASE I).

Coordinate differences between the references and estimates.

Success rate of the ambiguity resolutions (epoch-by-epoch).

| |||
---|---|---|---|

99.7% | 100.0% | 99.0% |

Statistical summary of the coordinate differences between the references and estimates (unit: centimetres).

I | 3.8 | ±.16.5 | 41.5 | ±.17.1 | 41.7 | ±23.8 | 0.3 | ±0.7 | 0.1 | ±1.1 | 1.1 | ±1.3 |

II | 5.1 | ±11.4 | 10.5 | ±32.8 | 11.7 | ±34.7 | 0.0 | ±0.7 | 0.5 | ±1.0 | 0.6 | ±1.3 |

III | 13.4 | ±17.5 | 29.8 | ±26.3 | 32.7 | ±31.6 | 0.1 | ±0.7 | 0.1 | ±1.0 | 0.1 | ±1.3 |

Statistical summary of the attitude parameter differences between the references and estimates (unit: arc-minutes).

I | 2.50 | ±2.50 | 0.69 | ±0.72 | 2.69 | ±1.32 | 1.92 | ±2.26 | 0.53 | ±0.64 | 2.67 | ±1.27 |

II | 2.11 | ±2.61 | 0.72 | ±0.77 | 2.56 | ±1.33 | 1.88 | ±2.28 | 0.53 | ±0.64 | 2.66 | ±1.27 |

III | 2.62 | ±2.71 | 0.74 | ±0.77 | 2.69 | ±1.32 | 1.93 | ±2.28 | 0.53 | ±0.64 | 2.68 | ±1.27 |