This paper deals with the estimation of the noise covariance matrices of systems described by state-space models. Stress is laid on the systematic survey and classification of both the recursive an...

Noise covariance matrices in state-space models: A survey and comparison of estimation methods—Part I

Tightly coupled GNSS/INS has been widely approved as a promising substitute for standalone GNSS in urban areas navigation. However, due to the frequent GNSS signal outages, the filter used in GNSS/INS should be insensitive to the less informative observations. In this paper, a novel sigma-points update method is proposed to enhance the robustness of cubature Kalman filter (CKF) under the circumstance of unavailable observations. First, the problems of existing sampling-based filters are analyzed. Then, by transforming the posterior sigma-points error matrix from prediction phase of filtering to the posterior domain of update, the updated sigma-points are expected to capture the covariance more precisely than traditional sigma-points. Finally, an improved CKF (ICKF) is developed by embedding these points into the Bayesian estimation framework, and the upper bounds of error covariance matrices are analyzed theoretically. Signal outages with different durations are simulated and results demonstrate that ICKF outperforms state-of-the-art methods.

Improved Cubature Kalman Filter for GNSS/INS Based on Transformation of Posterior Sigma-Points Error

In-flight initial alignment for small UAV MEMS-based navigation via adaptive unscented Kalman filtering approach

Robust weighted fusion Kalman predictors with uncertain noise variances

X-ray pulsar-based navigation using time-differenced measurement

Robust Kalman filtering for discrete-time nonlinear systems with parameter uncertainties

Robust multiple model adaptive estimation for spacecraft autonomous navigation

Summary

An efficient multiple-model adaptive estimation (MMAE) algorithm is presented for time-variant system with both system and measurement uncertainties, whose statistics are supposed to be unknown. The model uncertainties are described by a set of noise covariance matrices, such that a small model set is sufficient to achieve good estimation performance. To demonstrate the feasibility of the presented MMAE for the considered time-variant uncertain system, a proof is provided that shows the filtering convergence. The performance of the algorithm is evaluated via different operating scenarios of double line-of-sight measuring space surveillance. Simulation results demonstrate that the MMAE algorithm outperforms the robust filtering algorithms in the presence of the uncertainty and yields positioning accuracy similar to the extended Kalman filter in the absence of the uncertainty. Copyright © 2015 John Wiley & Sons, Ltd.

Multiple-model adaptive estimation for space surveillance with measurement uncertainty

An augmented multiple-model adaptive estimation (MMAE) algorithm is presented for a time-varying system, where the model uncertainty may occur occasionally. Generally, it is difficult for a single filter to achieve superior performance for both the certain system and the uncertain system. An algorithm that is designed for an uncertain system may yield suboptimal performance in the situation, where the model uncertainty does not occur. To cope with this problem, we propose to use two filters in parallel in a multiple-model framework. One of the filters, an augmented Kalman filter (AKF), provides estimates of uncertain parameters when the model uncertainties occur, whereas the second filter, a Kalman filter (KF), yields high precision in the absence of the uncertainties. A practical example is given in simulation to show the potential application of the presented algorithm. It indicates that the augmented MMAE is efficient to deal with the occasional model uncertainty.

An Augmented Multiple-Model Adaptive Estimation for Time-Varying Uncertain Systems

Purpose – The purpose of this paper is to present a variable structure multiple model adaptive estimator (VSMMAE) for liaison navigation system. Liaison navigation is an autonomous navigation method where inter-satellite range measurements are used to estimate the orbits of all participating spacecrafts simultaneously. Design/methodology/approach – To overcome the problem caused by an inaccurate initial state, a navigation algorithm is designed based on the multiple model adaptive estimation technique. The multiple models are constructed by different initial error covariance matrices. To reduce the computational cost, the likely-model set (LMS) algorithm is adopted to eliminate the unlikely models. Findings – It is specified that the performance of the liaison navigation based on the extended Kalman filter (EKF) is sensitive to the initial error. Simulation results show that the VSMMAE outperforms the EKF in the presence of a large initial error. Practical implications – The presented algorithm is applica...

Kai Xiong

Papers

Robust Kalman filtering for discrete-time nonlinear systems with parameter uncertainties

Robust multiple model adaptive estimation for spacecraft autonomous navigation

Multiple-model adaptive estimation for space surveillance with measurement uncertainty

An Augmented Multiple-Model Adaptive Estimation for Time-Varying Uncertain Systems

Spacecraft autonomous navigation using multiple model adaptive estimator