Sequential Mixed Cost-Based Multi-Sensor and Relative Dynamics Robust Fusion for Spacecraft Relative Navigation

Abstract

The non-redescending convex functions degrade the filtering robustness, whereas the redescending non-convex functions improve filtering robustness, but they tend to converge towards local minima. This work investigates the properties of convex and non-convex cost functions from robustness and stability perspectives, respectively. To improve filtering robustness and stability to the high level of non-Gaussian noise, a sequential mixed convex and non-convex cost strategy is presented. To avoid the matrix singularity induced by applying the non-convex function, the M-estimation type Kalman filter is transformed into its information filtering form. Further, to address the problem of the estimation consistency in the iterated unscented Kalman filter, the iterated sigma point filtering framework is adopted using the statistical linear regression method. The simulation results show that, under different levels of heavy-tailed non-Gaussian noise, the mixed cost strategy can avoid the non-convex function-based filters falling into the local minimum, and further can improve the robustness of the convex function-based filter. Therefore, the mixed cost strategy provides a comprehensive improvement in the efficiency of the robust iterated filter.

Keywords

• cost function
• local minimum
• non-Gaussian noise
• M-estimation
• Kalman filter
• iterative methods