A Novel Robust Kalman Filter Algorithm With Unknown Noise Statistics for SINS/GPS Integrated Navigation

基於未知雜訊的SINS/GPS組合導航新穎魯棒卡爾曼濾波演算法

Xin Lai(賴欣) ； Fu-Xin Yang(楊福鑫)

《中國機械工程學刊》 44卷1期 (2023/02) Pp. 49-58

摘要

The estimation of process noise is often inaccurate due to factors such as ambient noise and maneuvering during carrier motion in practical applications. The higher precision and stability of integrated navigation system are pivotal for systems such as vehicles and aircraft. To solve the problem of uncertainty of unknown parameter estimation in the integrated navigation system, a novel robust expectation-maximization based Kalman filter (EMKF) algorithm is proposed in the paper. The prediction error covariance matrix and measurement noise covariance matrix are estimated adaptively using the online expectation-maximization (EM) method. The remarkable advantages of the EM-KF algorithm in this paper include the following. The online EM is employed to calculate maximum likelihood (ML) estimation of parameters, which converges in each iteration with successive likelihood increments, ensuring local convergence of the iterations; Adaptive estimation of the prediction error covariance matrix and measurement noise covariance matrix can reduce the reliance on prior information and the influence of noise on measurement estimates; The proposed EMKF has remarkable navigation and robustness in complex environment. Simulations and the field test results illustrate that the proposed EM-KF algorithm has strong robustness and accuracy, and enables high accuracy navigation of moving vehicles for a long time.

關鍵字

Expectation-maximization method ； Kalman filter ； Uncertain noise ； Strapdown inertial navigation system ； Global positioning system ； Integrated navigation

並列摘要

在實際應用中，由於環境雜訊和載體運動時的機動等因素的影響，過程雜訊的估計往往不準確。因此提高組合導航系統的精度和穩定性對車輛和飛機等系統至關重要。針對組合導航系統中未知參數估計的不確定性問題，提出了一種魯棒的基於期望最大化的卡爾曼濾波（EM-KF）演算法。採用線上期望最大化（EM）方法自我調整估計預測誤差協方差矩陣和測量雜訊協方差矩陣。本文提出的EM-KF演算法的顯著優點包括：該演算法利用線上EM演算法對參數進行最大似然估計，每次反覆運算的最大似然估計隨著似然增量的增加而收斂，保證了反覆運算的局部收斂性；自我調整估計預測誤差協方差矩陣和測量雜訊協方差矩陣可以減少對先驗資訊的依賴並減少雜訊對測量估計的影響；本文所提出的EM-KF在複雜環境下具有良好的導航精度和魯棒性。模擬和現場測試結果表明，該演算法具有較強的魯棒性和精度，能夠實現長時間的高精度移動車輛導航。