A New Efficient Filtering Model for GPS/SINS Ultratight Integration System

Wang, Chaochen; Bo, Yuming; Jiang, Changhui

doi:https://doi.org/10.1155/2020/9158185

Mathematical Problems in Engineering

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Abstract Introduction Model Results Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2020 | Article ID 9158185 | https://doi.org/10.1155/2020/9158185

A New Efficient Filtering Model for GPS/SINS Ultratight Integration System

Chaochen Wang,¹Yuming Bo,¹and Changhui Jiang¹

Academic Editor: Saeed Eftekhar Azam

Received06 Dec 2019

Revised11 Jan 2020

Accepted14 Feb 2020

Published19 Mar 2020

Abstract

Global Positioning System (GPS) and strap-down inertial navigation system (SINS) are recognized as highly complementary and widely employed in the community. The GPS has the advantage of providing precise navigation solutions without divergence, but the GPS signals might be blocked and attenuated. The SINS is a totally self-contained navigation system which is hardly disturbed. The GPS/SINS integration system could utilize the advantages of both the GPS and SINS and provide more reliable navigation solutions. According to the data fusion strategies, the GPS/SINS integrated system could be divided into three different modes: loose, tight, and ultratight integration (LI, TI, and UTC). In the loose integration mode, position and velocity difference from the GPS and SINS are employed to compose measurement vector, in which the vector dimension has nothing to do with the amount of the available satellites. However, in the tight and ultratight modes, difference of pseudoranges and pseudorange rates from the GPS and SINS are employed to compose the measurement vector, in which the measurement vector dimension increases with the amount of available satellites. In addition, compared with the loose integration mode, clock bias and drift are included in the integration state model. The two characteristics magnify the computation load of the tight and ultratight modes. In this paper, a new efficient filter model was proposed and evaluated. Two schemes were included in this design for reducing the computation load. Firstly, a difference between pseudorange measurements was determined, by which clock bias and drift were excluded from the integration state model. This step reduced the dimension of the state vector. Secondly, the integration filter was divided into two subfilters: pseudorange subfilter and pseudorange rate subfilter. A federated filter was utilized to estimate the state errors optimally. In the second step, the two subfilters could run in parallel and the measurement vector was divided into two subvectors with lower dimension. A simulation implemented in MATLAB software was conducted to evaluate the performance of the new efficient integration method in UTC. The simulation results showed that the method could reduce the computation load with the navigation solutions almost unchanged.

1. Introduction

Recently, Global Positioning System (GPS) triggers a revolution in position, navigation, and timing (PNT). Smartphones, vehicles, pedestrians, and ships all employ GPS to provide continuous and precise positioning, navigation, and timing (PNT) information [1–5]. With the satellites in space covering the earth, the GPS receiver around the world can receive the broadcast satellite signals and output PNT information [1–5]. With the fast development of GPS receiver design and manufacturing technology, currently, a low-cost handheld receiver is capable of positioning accurately in open sky. A GPS chip receiver has been embedded in mobile devices for Location-Based Service (LBS), which makes great influence on people’s daily life. However, for a standalone GPS receiver, signal challenging environment might hinder its extensive applications, for instance, NLOS (none-of-sight) and multipath (MP) signal in urban canyons and dynamic stress under high dynamic; these negative factors may affect the signal availability or navigation solution accuracy and integrity. Without enough satellites with “clean” signals available, the receiver will fail to output correct PNT information [2–8]. For instance, the NLOS signals will cause the pseudorange bias, signal blockage will influence the satellite geometry distribution, and the MP will also influence the errors in pseudorange measurements [2–14].

Researchers have been working on improving the receivers’ ability and performance of positioning under signal-challenging environments [9–14]. Hsu proposed the multipath mitigation and NLOS detection method using vector tracking with machine learning method [9, 10]. In addition, the dual-polarization antenna and 3D city model were employed for NLOS detection, correction, and exclusion [11, 12]. Petovello investigated extending the integration time for enhancing the weak signal tracking [13, 14]. Apart from enhancing the standalone receiver’s performance, integrating the GPS with other sensors has been one of the most promising and effective methods, especially the GPS/SINS integration [15–27].

The SINS is a sort of self-contained navigation system, which is hardly disturbed. The SINS processes the angular and acceleration measurements from the inertial measurement unit (IMU), and then 3D georeference information is generated without transmitting or receiving any outside signals [6–8]. However, the random noises contained in the angular and acceleration measurements will lead to the navigation solution errors accumulating dramatically over time [6–8]. Therefore, the SINS is usually integrated with the GPS for providing more stable and reliable navigation solutions. When the GPS works well, it can calibrate the SINS and compensate the errors through the integration. When the GPS is unavailable attenuated, the SINS can provide short-term accurate navigation solutions instead of the GPS. Moreover, for dynamic applications, the SINS can provide navigation solutions at higher rate, which can fill the gap between GPS information and smooth the navigation solutions [15–17].

In recent years, researchers are attracted to improve and enhance GPS/SINS integration system performance. Generally, there are two extensive approaches: modifying the integration model or modifying the integration filter [17–22]. As aforementioned, GPS/SINS integration can be divided into three modes: loose, tight, and ultratight integration (LI, TI, and UTC). The integration architecture is classified according to the levels of the measurements included in the GPS/SINS data fusion and whether SINS information is employed to aid GPS signal tracking [21, 22]. The most widely used mode is the loose integration method, in which navigation solutions from the GPS and SINS are directly employed to compose measurement vector and estimate SINS state errors. For the TI or UTC, pseudorange and pseudorange rate measurements from the GPS and SINS are employed as the integration filter measurements. Compared with LI, clock bias and drift are included in the TI or UTC state model, the dimension of TI or UTC measurement vector increases over the amount of available satellites. Various UTC implementations were published [22–26]. For instance, vector tracking was employed in UTC substituting scalar tracking [27–30]. In the aspects of the integration filter modification, nonlinear Kalman filter (cubature Kalman Filter, CKF; unscented Kalman filter, UKF) and some advanced Kalman filter variants were investigated in the GPS/SINS integration system for enhancing the GPS/SINS integration performance [23–31]. However, limited research had been conducted on how to reduce the computation load of the UTC integration filter.

In this paper, a new efficient UTC integration filter was proposed, investigated, and assessed. In the proposed method, a pseudorange/pseudorange rate measurement difference scheme was employed to exclude clock bias and drift error from the UTC integration filtering model, which reduces the dimension of the state vector. Based on this, the measurement vector was divided into two subvectors with much lower dimension: pseudorange and pseudorange rates subvector. With the above operation, the integration filter was divided into two individual subfilters and a federated Kalman filter was employed to fuse them and obtain optimal estimation of state errors. In this architecture, the dimension reduction of the state and measurement vector could enhance the real-time performance of the UTC integration.

The remainder of this paper is organized as follows: Section 2 gives the integration model in detail including the difference scheme and integration filter model. Section 3 presents the simulation and the result analysis; then, the paper is concluded.

2. Model and Method

This section explains the integration model in detail. In the GPS/SINS UTC model, SINS device errors and clock bias/drift are employed as state variable. The measurement model is constructed based on the pseudorange and pseudorange rate errors between GPS and SINS considering clock bias and drift. Section 2.1 shows the conventional ultratight integration filtering model, and section 2.2 illustrates the measurement difference scheme and the new integration filtering model. Section 2.3 shows the architecture of the federated Kalman filter (FKF), which is employed in the state errors estimation.

2.1. The Integration Model

2.1.1. The Integration Filter State Model

The integration scheme includes 17 states, and the state vector is defined aswhere the vector is the error of pitch, roll, and yaw angles, the vector is the error of east, north, and up velocity in E-N-U navigation frames, the vector is the latitude, longitude and height (LLH) errors, the vector is the gyroscope bias in the body frame, the vector is the accelerometer bias, and the variables and are the clock bias and the clock drift expressed in meters and drift meters/second.

The integration filter is commonly a Kalman filter; thus, the state equations can be written aswhere is the state transfer matrix and is the system error matrix.where is the system dynamic matrix of the SINS and is the system dynamic matrix of GPS clock error [18–21].

2.1.2. The Integration Filter Observation Model

The measurement vector of the integration model is composed of pseudorange error and the pseudorange rate difference between the GPS and SINS. Supposing the user’s real position is , the calculated position from the INS is and the position vector of the satellite is . Thus, the pseudorange between the satellite and the receiver can be written as

The real range is

After the first-order linearization, equation (4) can be written as the following equation:where

In the GPS receiver, the GPS pseudorange error model usually includes the satellite clock error, atmospheric error, receiver clock error, and other factors. After correcting ionospheric error and tropospheric error, the pseudorange error model can be written as

Thus, the difference between the GPS and SINS pseudorange can be written as

The pseudorange rate measurement vector can be written aswherewhere is the position transformation matrix from E-N-U coordinates to ECEF coordinates, respectively. Similarly, the pseudorange rate measurement can be written aswhere is the SINS velocity error vector in ECEF coordinates. The equations are detailed in [11, 12]. The pseudorange rate measurement vector can be written aswherewhere is the velocity transformation matrix from E-N-U coordinates to ECEF coordinates, respectively. Thus, the measurement equation can be written as

2.2. The Differential Scheme

As aforementioned, channels from the same receiver share a common clock bias and drift. Difference between channels can definitely exclude clock bias and clock drift from the UTC model. Pseudorange error differential equations can be written as follows:

Similarly, the pseudorange rate error differential equations are as follows:

The new model of the integration filter is as follows:

The new state vector is

The measurement vector is

2.3. The Federated Filter Scheme

For reducing the dimension of the measurement vector, a simple federated filter (FEF) with two subfilters are designed and employed to optimally fuse the measurements; the FEF architecture is shown in Figure 1. The state vector is identical to equation (19), and the detailed description of the subfilters is given in equations (21)–(24). Equations (21) and (22) are the pseudorange subfilter state vector and measurement vector:

The state vector and measurement vector of the pseudorange rate differential subfilter are as follows:

3. Experiment and Results

A simulation was implemented and conducted in MATLAB software. Dynamic trajectory was generated to assess the new UTC filtering method. Navigation solutions including position, velocity, and altitude were compared between UTC with difference and the UTC without difference, which aimed to explore whether excluding clock bias and drift makes a negative impact on navigation solution accuracy. Table 1 shows the parameter setting of the SINS parameters included in the simulation. A constant value and white Gaussian noise (WGN) were added to the gyroscope and accelerometer ideal measurements.

3.1. Navigation Solution Comparison

Figure 2 shows the position errors between C-UTC and D-UTC. C-UTC refers to conventional ultratight integration, and D-UTC refers to ultratight integration with measurements difference. The red line represents the results of C-UTC, and cyan lines represent the results of D-UTC. Firstly, Table 2 lists the mean values and root mean square errors (RMSE) of the position. The mean and RMSE values of latitude errors has a significant difference because of a sharp fluctuation at the beginning. Specially, longitude and altitude errors perform similar mean values and RMSE values. Secondly, Figure 3 presents the velocity errors between C-UTC and D-UTC. The red line represents the results of C-UTC, and the cyan lines represent the results of D-UTC. Table 3 lists the mean values and root mean square errors (RMSE) of the velocity. Table 3 also lists the error comparison, and it can be seen that the two methods have similar results. Thirdly, Figure 4 plots the errors of altitude errors including pitch errors, roll angle errors, and yaw angle errors. Table 4 lists the mean values and RMSE values of the three-axis angle errors. Similarly, Table 3 shows the altitude error analysis, and the two methods obtain almost identical mean values and RMSE values.

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3.2. Computation Load Comparison

Table 5 gives the state and measurement vector comparison, (N) refers to the number of the available satellites. Obviously, the D-UTC has lower state and measurement vector dimension than that of C-UTC. Table 6 presents the computation load comparison of the two methods, with the computer settings (Intel Core I7 Processor, 16GB RAM), C-UTC accomplishes the integration filter within 8.56 ms (average of 100 times), and the D-UTC spends shorter time which is 5.98 ms. The efficiency obtains 30.14% improvement with the new integration filter.

4. Conclusions

This paper investigated an efficient integration method of the GPS/SINS UTC system. The method composed of two steps. The first step was the pseudorange and pseudorange rate differential method which could remove the clock bias and clock drift from the state equation, which helped to reduce the dimension of the state equation. In the second step, a federated filtering method was employed to substitute the traditional centralized Kalman filtering. The subfilters were pseudorange subfilter and pseudorange rate subfilter. The subfilters and the main filter were all Kalman filters, which aimed to reduce the dimension of the measurement matrix and improved the robustness of the system. At last, the results presented by the comparison of the position, velocity, altitude errors, and computation load. The proposed method could reduce the computation load without heavily changing the navigation solution accuracy.

Data Availability

The source code used to support the findings of this study is available from the corresponding author upon request.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

Acknowledgments

This work was supported by the Fundamental Research Funds for the Central Universities (no.30916011336) and the China Postdoctoral Science Foundation (no.2016T90461).

References

Y. Chen, J. Tang, C. Jiang et al., “The accuracy comparison of three simultaneous localization and mapping (SLAM)-based indoor mapping technologies,” Sensors, vol. 18, no. 10, p. 3228, 2018.
View at: Publisher Site | Google Scholar
C. Jiang, S. Chen, Y. Chen et al., “Performance analysis of a deep simple recurrent unit recurrent neural network (SRU-RNN) in MEMS gyroscope de-noising,” Sensors, vol. 18, no. 12, p. 4471, 2018.
View at: Publisher Site | Google Scholar
X.-L. Wang and Y.-F. Li, “An innovative scheme for SINS/GPS ultra-tight integration system with low-grade IMU,” Aerospace Science and Technology, vol. 23, no. 1, pp. 452–460, 2012.
View at: Publisher Site | Google Scholar
C. Jiang, Y. Chen, S. Chen et al., “A mixed deep recurrent neural network for MEMS gyroscope noise suppressing,” Electronics, vol. 8, no. 2, p. 181, 2019.
View at: Publisher Site | Google Scholar
X. Chen, J. Yu, and M. Gu, “Study on tightly-coupled GPS/SINS integrated navigation system by using software GPS receiver,” in Proceedings of the 2011 IEEE International Instrumentation and Measurement Technology Conference, pp. 1–4, IEEE, Binjiang, China, May 2011.
View at: Publisher Site | Google Scholar
W. D. Zhou, X. W. Qiao, Y. R. Ji et al., “SINS/GPS tightly integrated navigation system based on quaternion square root unscented Kalman filter,” Systems Engineering & Electronics, vol. 32, no. 12, pp. 2643–2647, 2010.
View at: Google Scholar
C. Jiang, S. Chen, Y. Chen et al., “A MEMS IMU de-noising method using long short term memory recurrent neural networks (LSTM-RNN),” Sensors, vol. 18, no. 10, p. 3470, 2018.
View at: Publisher Site | Google Scholar
C. Jiang, S. Chen, Y. Chen, Y. Bo, and C. Wang, “Performance analysis of GNSS vector tracking loop based GNSS/CSAC integrated navigation system,” Journal of Aeronautics, Astronautics and Aviation, vol. 49, no. 4, pp. 289–297, 2017.
View at: Google Scholar
N. Wang and L. Wang, “Research of GPS/sins tightly integrated navigation algorithm in inertial coordinate,” Modern Electronics Technique, vol. 20, 2011.
View at: Google Scholar
C. Jiang, S. Chen, Y. Chen, and Y. Bo, “Research on chip scale atomic clock driven GNSS/SINS deeply integrated navigation system for augmented performance,” IET Sonar Radar and Navigation, vol. 13, no. 2, pp. 326–331, 2018.
View at: Google Scholar
L.-T. Hsu, S.-S. Jan, P. D. Groves, and N. Kubo, “Multipath mitigation and NLOS detection using vector tracking in urban environments,” GPS Solutions, vol. 19, no. 2, pp. 249–262, 2015.
View at: Publisher Site | Google Scholar
L.-T Hsu, “GNSS multipath detection using a machine learning approach,” in Proceedings of the 2017 IEEE 20th International Conference on Intelligent Transportation Systems (ITSC), IEEE, Yokohama, Japan, October 2017.
View at: Publisher Site | Google Scholar
L.-T. Hsu, Y. Gu, and S. Kamijo, “NLOS correction/exclusion for GNSS measurement using RAIM and city building models,” Sensors, vol. 15, no. 7, pp. 17329–17349, 2015.
View at: Publisher Site | Google Scholar
C. Jiang, S. Chen, Y. Chen, and Y. Bo, “Research on a chip scale atomic clock aided vector tracking loop,” IET Radar, Sonar & Navigation, vol. 13, no. 7, pp. 1101–1106, 2019.
View at: Publisher Site | Google Scholar
C. O’Driscoll, M. G. Petovello, and G. Lachapelle, “Choosing the coherent integration time for Kalman filter-based carrier-phase tracking of GNSS signals,” GPS Solutions, vol. 15, no. 4, pp. 345–356, 2011.
View at: Publisher Site | Google Scholar
Z. He and M. Petovello, “Performance comparison of Kalman filter and maximum likelihood carrier phase tracking for weak GNSS signals,” in Proceedings of the 2015 International Conference on Indoor Positioning and Indoor Navigation (IPIN), pp. 1–8, IEEE, Banff, AB, Canada, October 2015.
View at: Publisher Site | Google Scholar
J. J. Guo, X. F. Cai, and C. He, “Design and implementation of the tightly-coupled SINS/GPS integrated navigation system based on FPGA for target missile,” Applied Mechanics and Materials, vol. 313-314, pp. 287–290, 2013.
View at: Publisher Site | Google Scholar
H. Qi and J. B. Moore, “Direct Kalman filtering approach for GPS/INS integration,” IEEE Transactions on Aerospace and Electronic Systems, vol. 38, no. 2, pp. 687–693, 2002.
View at: Publisher Site | Google Scholar
M. G. Petovello and G. Lachapelle, “Comparison of vector-based software receiver implementations with application to ultra-tight GPS/INS integration,” in Proceedings of the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2006), vol. 6, Fort Worth, TX, USA, September 2006.
View at: Google Scholar
S. Alban, D. M. Akos, S. M. Rock, and D. Gebre-Egziabher, “Performance analysis and architectures for INS-aided GPS tracking loops,” in Proceedings of the Institute of Navigation National Technical Meeting, pp. 611–622, Institute of Navigation, Anaheim, CA, USA, January 2003.
View at: Google Scholar
B. Vik and T. I. Fossen, “A nonlinear observer for GPS and INS integration,” in Proceedings of the 40th IEEE Conference on Decision and Control, vol. 3, pp. 2956–2961, IEEE, Orlando, FL, USA, December 2001.
View at: Publisher Site | Google Scholar
A. Almagbile, J. Wang, and W. Ding, “Evaluating the performances of adaptive Kalman filter methods in GPS/INS integration,” Journal of Global Positioning Systems, vol. 9, no. 1, pp. 33–40, 2010.
View at: Publisher Site | Google Scholar
E. J. Ohlmeyer, “Analysis of an ultra-tightly coupled GPS/INS system in jamming,” in Proceedings of the 2006 IEEE/ION Position, Location, and Navigation Symposium, pp. 44–53, IEEE, Coronado, CA, USA, April 2006.
View at: Publisher Site | Google Scholar
Y. Geng and J. Wang, “Adaptive estimation of multiple fading factors in Kalman filter for navigation applications,” GPS Solutions, vol. 12, no. 4, pp. 273–279, 2008.
View at: Publisher Site | Google Scholar
M. Rhudy, Y. Gu, J. Gross, and M. R. Napolitano, “Evaluation of matrix square root operations for UKF within a UAV GPS/INS sensor fusion application,” International Journal of Navigation and Observation, vol. 2011, Article ID 416828, 11 pages, 2011.
View at: Publisher Site | Google Scholar
D. J. Jwo, C. F. Yang, C. H. Chuang, and T. Y. Lee, “Performance enhancement for ultra-tight GPS/INS integration using a fuzzy adaptive strong tracking unscented Kalman filter,” Nonlinear Dynamics, vol. 73, no. 1-2, pp. 377–395, 2013.
View at: Publisher Site | Google Scholar
G. Hu, S. Gao, and Y. Zhong, “A derivative UKF for tightly coupled INS/GPS integrated navigation,” ISA Transactions, vol. 56, pp. 135–144, 2015.
View at: Publisher Site | Google Scholar
Y. Zhao, “Performance evaluation of cubature Kalman filter in a GPS/IMU tightly-coupled navigation system,” Signal Processing, vol. 119, pp. 67–79, 2016.
View at: Publisher Site | Google Scholar
Z. Zhou, Y. Li, C. Rizos, and Y. Shen, “A robust integration of GPS and MEMS-INS through trajectory-constrained adaptive Kalman filtering,” in Proceedings of the ION GNSS, pp. 22–25, Savannah, Georgia, September 2009.
View at: Google Scholar
C. Jiang, S. Chen, Y. Bo, Y. Wang, and Z. Sun, “Performance improvement of GPS/SINS ultra-tightly integrated navigation system utilizing a robust cubature kalman filter,” Journal of Aeronautics, Astronautics and Aviation, vol. 49, no. 1, pp. 49–55, 2017.
View at: Google Scholar
C. Jiang, S. Chen, Y. Bo, Y. Chen, T. Wei, and C. Wang, “Research of a fault tolerant vector tracking based GNSS/SINS deep integration navigation system,” Journal of Aeronautics, Astronautics and Aviation, vol. 49, no. 3, pp. 185–194, 2017.
View at: Google Scholar

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Copyright © 2020 Chaochen Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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