Research On Generalized-Maximum-Likelihood-Based Nonlinear Robust State Estimation Method

Spacecraft relative navigation techniques serve extensive applications in spacecraft rendezvous and docking,spacecraft formation flight and active space debris removal.Considering autonomy,complexity and high reliability requirements of space missions,the navigation system needs to be capable of providing high navigation accuracy and coping with complex noise environment.This work is conducted for the relative navigation of spacecrafts in elliptical orbits.Considering estimator’s large initial errors,high level of non-Gaussian observation noise,and unknown or time-varying statistical characteristics of observation noise,we investigate the iterative update strategy,recursive update strategy,characteristics of robust kernel functions,and robust adaptive update strategy of nonlinear robust filter.The research contents are specified as follows:To avoid degradation in approximating nonlinear model induced by the fixed-point iterative strategy,from the perspective of nonlinear optimization,two Gauss-Newton(GN)-based robust and iterative strategies are rigorously derived and proposed;to further improve the robustness of proposed strategies,the modified covariances from the previous iteration are introduced to the current loop,then a novel robust cost function is built for the improved iterative strategy.The simulation results show that the GN-based robust iterative strategies outperform the fixed-point iterative strategy without inducing a heavy computational burden,and the improved iterative strategy further improves the robust filtering efficiency.To reduce the impact of large initial errors on robust filtering efficiency,a nonlinear robust recursive update strategy is proposed.By using the statistical linear regression method,the recursive update strategy is introduced into the nonlinear filtering framework;a nonlinear regression model considering the correlation between the state and observation noise is developed,and then a novel robust strategy is designed to reweight the state covariance,the observation noise covariance,and the cross-covariance between them,respectively,to obtain the desired robust nonlinear system;analogous to the nonlinear recursive update strategy,a robust recursive update strategy is derived,and the update strategy of observation noise covariance is given to ensure the consistency of observation information.The simulation results show that,during the update phase with large initial errors,the estimation accuracy and consistency of the recursive update strategy outperform those of the iterative update strategy without inducing a heavy computational burden.To improve the ability of robust filters in coping with high level of non-Gaussian observation noise,a mixed convex and non-convex robust function strategy and a nonlinear information filtering framework based on the improved robust iterative strategy are proposed,respectively.To avoid the non-convex function from falling into local optimum,a mixed strategy of convex and non-convex robust functions is proposed;to avoid the matrix singularity problem by applying this mixed strategy,by using statistical linear regression methods,two Gauss-Newton-based robust information filtering methods are proposed,and they are analyzed from the perspective of filtering stability and robustness,respectively;on this basis,an improved robust sigma-point information filter is further proposed;considering the special structure of information filter,the mixed robust function strategy is extended to multi-sensor information fusion,and a distributed robust iterated sigmapoint information filter is proposed.The simulation results show that,under general level of heavy-tailed non-Gaussian noise,the mixed convex and non-convex function strategy can avoid the problems of applying a single robust function;under high level of heavytailed non-Gaussian noise,the two robust information filters have their own advantages and disadvantages in filtering stability and robustness,while the improved filter provides both advantages.The mixed robust function strategy is also applicable to distributed systems and facilitates the distributed information filter to achieve better performance under heavy-tailed non-Gaussian noise.To reduce the impact of observation noise with unknown or time-varying statistical properties on robust filtering efficiency,the Sage-Husa adaptive strategy is introduced into the robust filter,and then a robust adaptive update strategy is proposed.The Sage-Husa adaptive strategy is extended to nonlinear systems by using the statistical linear regression,and an exponential fading factor is introduced to improve the adaptive capability of the estimator;the presented Gauss-Newton-based robust iterative strategy and its improved strategy are combined with the Sage-Husa adaptive strategy,respectively,then robust adaptive sigma-point Kalman filtering and improved robust adaptive sigma-point information filtering methods are presented;to balance filter’s estimation accuracy and consistency,two methods of modifying innovation suitable to the two robust adaptive filtering frameworks are given,respectively.The simulation results show that the proposed robust adaptive filter can better adapt to the corresponding complex noise environment than the single adaptive or robust filter,furthermore the improved filtering algorithm obtains better estimation accuracy and stronger tracking ability of time-varying noise characteristics.