An improved Kalman filter algorithm for tightly GNSS/INS integrated navigation system

Yuelin Yuan; Fei Li; Jialiang Chen; Yu Wang; Kai Liu; Yuelin Yuan; Fei Li; Jialiang Chen; Yu Wang; Kai Liu

doi:10.3934/mbe.2024040

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 1: 963-983. doi: 10.3934/mbe.2024040

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An improved Kalman filter algorithm for tightly GNSS/INS integrated navigation system

Yuelin Yuan ¹,
Fei Li ²,
Jialiang Chen ²,
Yu Wang ^{3
,
,},
Kai Liu ^{2
,
,}

1.
School of Electronic Science, National University of Defense Technology, Changsha 410005, China
2.
School of Transportation and Logistics, Dalian University of Technology, Dalian 116024, China
3.
School of Traffic and Transportation Engineering, Dalian Jiaotong University, Dalian 116028, China

Received: 22 September 2023 Revised: 19 November 2023 Accepted: 06 December 2023 Published: 22 December 2023

The Kalman filter based on singular value decomposition (SVD) can sufficiently reduce the accumulation of rounding errors and is widely used in various applications with numerical calculations. However, in order to improve the filtering performance and adaptability in a tightly GNSS/INS (Global Navigation Satellite System and Inertial Navigation System) integrated navigation system, we propose an improved robust method to satisfy the requirements. To solve the issue of large fluctuations in GNSS signals faced by the conventional method that uses a fixed noise covariance, the proposed method constructs a correction variable through the innovation and the new matrix which is obtained by performing SVD on the original matrix, dynamically correcting the noise covariance and has better robustness. In addition, the derived SVD form of the information filter (IF) extends its application. The proposed method has higher positioning accuracy and can be better applied to tightly coupled GNSS/INS navigation simulations and physical experiments. The experimental results show that, compared with the traditional Kalman algorithm based on SVD, the proposed algorithm*s maximum error is reduced by 45.77%. Compared with the traditional IF algorithm, the root mean squared error of the proposed IF algorithm in the form of SVD is also reduced by 4.7%.
- Kalman filter,
- SVD,
- tightly coupled GNSS/INS navigation,
- covariance matching,
- information filter
Citation: Yuelin Yuan, Fei Li, Jialiang Chen, Yu Wang, Kai Liu. An improved Kalman filter algorithm for tightly GNSS/INS integrated navigation system[J]. Mathematical Biosciences and Engineering, 2024, 21(1): 963-983. doi: 10.3934/mbe.2024040

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Abstract

The Kalman filter based on singular value decomposition (SVD) can sufficiently reduce the accumulation of rounding errors and is widely used in various applications with numerical calculations. However, in order to improve the filtering performance and adaptability in a tightly GNSS/INS (Global Navigation Satellite System and Inertial Navigation System) integrated navigation system, we propose an improved robust method to satisfy the requirements. To solve the issue of large fluctuations in GNSS signals faced by the conventional method that uses a fixed noise covariance, the proposed method constructs a correction variable through the innovation and the new matrix which is obtained by performing SVD on the original matrix, dynamically correcting the noise covariance and has better robustness. In addition, the derived SVD form of the information filter (IF) extends its application. The proposed method has higher positioning accuracy and can be better applied to tightly coupled GNSS/INS navigation simulations and physical experiments. The experimental results show that, compared with the traditional Kalman algorithm based on SVD, the proposed algorithm*s maximum error is reduced by 45.77%. Compared with the traditional IF algorithm, the root mean squared error of the proposed IF algorithm in the form of SVD is also reduced by 4.7%.

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