Maximum Correntropy Square Root Gauss-Hermite Quadrature Information Filter for Multiple Sensor Estimation

For multiple sensor estimation in nonlinear Gaussian environment, the traditional Gauss-Hermite quadrature information filter (GHQIF) has great performance. However, due to the precision loss caused by rounding errors, GHQIF may cause a series of problems such as system divergence. Therefore, the square root GHQIF (SRGHQIF) is first proposed in this paper; it ensures the symmetry and semipositive quality of covariance matrices, also improves the numerical stability and estimation accuracy. Furthermore, practical systems are usually non-Gaussian, and the GHQIF and SRGHQIF under the minimum mean square error (MMSE) rule both deteriorate seriously in this situation. Therefore, replacing MMSE rule with robust maximum correntropy criterion (MCC) as the optimal criterion, a new information filter called the maximum correntropy SRGHQIF (MCSRGHQIF) is proposed, which can improve the robustness of the SRGHQIF against impulsive noise. The predicted information matrix and vector of the SRGHQIF are calculated and then corrected and reconstructed with the MCC. In addition, fixed-point theory is used to iteratively update the estimation information vector, which can obtain better estimation results. Finally, the target tracking simulation results verify that the MCSRGHQIF is a very effective algorithm for multiple sensor estimation in nonlinear non-Gaussian environment, and the newly proposed MCSRGHQIF retains the frameworks and advantages of the SRGHQIF and MCC.