A MIT-Based Nonlinear Adaptive Set-Membership Filter for the Ellipsoidal Estimation of Mobile Robots' States

Abstract

The adaptive extended set-membership filter (AESMF) for nonlinear ellipsoidal estimation suffers a mismatch between real process noise and its set boundaries, which may result in unstable estimation. In this paper, a MIT method-based adaptive set-membership filter, for the optimization of the set boundaries of process noise, is developed and applied to the nonlinear joint estimation of both time-varying states and parameters. As a result of using the proposed MIT-AESMF, the estimation effectiveness and boundary accuracy of traditional AESMF are substantially improved. Simulation results have shown the efficiency and robustness of the proposed method.

Experimental Investigation for RUAV's Actuator Fault Detections with AESMF

“…Set qki∈R as the i -th diagonal element in Q k at time k , trueq^ki∈R as the i -th diagonal element in trueQ^k at time k , trueQ^k as the estimation of Q k at time k ; then, at time k +1, k =0, 1, 2,…, the AESMF algorithm [29] can be summarized as follows:…”

“…as the i-th diagonal element in Q k at time k, Q k as the estimation of Q k at time k; then, at time k+1, k=0, 1, 2,..., the AESMF algorithm [29] can be summarized as follows:…”

“…This will lead to the ESMF's estimated uncertain boundary being too large to deviate and will cause the filter to diverge during estimation of robots' UBB process noise, such as in the case of an RUAV's actuator fault. To solve this problem, the authors have proposed an AESMF [29] to address the process noise uncertain boundary issue for online robots' dynamics estimation. This method applies gradient descent optimization rules and conducts online calculation to obtain the minimal ellipsoid boundaries of the prediction error, which also ensures that the filter's health-index satisfies the working conditions for uncertainty dynamics.…”

“…Since this adaptive strategy for process noise boundary is based on gradient descent (GD), according to step 5), this type of AESMF is referred to as GD-ESMF in following experiments. For the details about the GD-ESMF algorithm, please refer to [29].…”