A Novel Progressive Gaussian Approximate Filter with Variable Step Size Based on a Variational Bayesian Approach

The selection of step sizes in the progressive Gaussian approximate filter (PGAF) is important, and it is difficult to select optimal values in practical applications. Furthermore, in the PGAF, significant integral approximation errors are generated by the repeated approximate calculations of the Gaussian weighted integrals, which results in an inaccurate measurement noise covariance matrix (MNCM). To solve these problems, in this paper, the step sizes and the MNCM are jointly estimated based on the variational Bayesian (VB) approach. By incorporating the adaptive estimates of step sizes and the MNCM into the PGAF framework, a novel PGAF with variable step size is proposed. Simulation results illustrate that the proposed filter has higher estimation accuracy than existing state-of-the-art nonlinear Gaussian approximate filters.

[1]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[2]  Ondrej Straka,et al.  Stochastic Integration Filter , 2013, IEEE Transactions on Automatic Control.

[3]  Uwe D. Hanebeck,et al.  PGF 42: Progressive Gaussian filtering with a twist , 2013, Proceedings of the 16th International Conference on Information Fusion.

[4]  Yonggang Zhang,et al.  Embedded cubature Kalman filter with adaptive setting of free parameter , 2015, Signal Process..

[5]  D.G. Tzikas,et al.  The variational approximation for Bayesian inference , 2008, IEEE Signal Processing Magazine.

[6]  Ming Xin,et al.  High-degree cubature Kalman filter , 2013, Autom..

[7]  Yonggang Zhang,et al.  Interpolatory cubature Kalman filters , 2015 .

[8]  Ángel F. García-Fernández,et al.  Analysis of Kalman Filter Approximations for Nonlinear Measurements , 2013, IEEE Transactions on Signal Processing.

[9]  Renato Zanetti,et al.  Recursive Update Filtering for Nonlinear Estimation , 2012, IEEE Transactions on Automatic Control.

[10]  Yonggang Zhang,et al.  A Novel Adaptive Kalman Filter With Inaccurate Process and Measurement Noise Covariance Matrices , 2018, IEEE Transactions on Automatic Control.

[11]  Uwe D. Hanebeck,et al.  Progressive Gaussian filtering using explicit likelihoods , 2014, 17th International Conference on Information Fusion (FUSION).

[12]  Ming Xin,et al.  Sparse-grid quadrature nonlinear filtering , 2012, Autom..

[13]  S. Haykin,et al.  Cubature Kalman Filters , 2009, IEEE Transactions on Automatic Control.

[14]  Yonggang Zhang,et al.  Design of Sigma-Point Kalman Filter with Recursive Updated Measurement , 2016, Circuits Syst. Signal Process..

[15]  Yonggang Zhang,et al.  Gaussian approximate filter with progressive measurement update , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[16]  Xiaoxu Wang,et al.  Gaussian filter for nonlinear systems with correlated noises at the same epoch , 2015, Autom..

[17]  Kazufumi Ito,et al.  Gaussian filters for nonlinear filtering problems , 2000, IEEE Trans. Autom. Control..