Design and stability of moving horizon estimator for discrete-time linear systems subject to multiple measurement outliers

Abstract

This paper considers the state estimation problem for discrete-time linear systems suffering from dense measurement anomalies. Conventional moving horizon estimation algorithms can be used to solve the case containing sparse measurement anomalies, but their performance degrades dramatically as the number of outliers increases. To address this problem, we propose two outliers exclusion-moving horizon estimation strategies. That is, at each sampling instant, solving a set of least-squares cost functions aims to exclude all possible outliers. The state estimates corresponding to the optimal cost are retained and propagated to the next instant, and the procedure is repeated when new information arrives. The stability of the estimation error of the estimators is proved under moderate conditions, namely the observability of the noise-free state equation and the choice of the tuning parameters in the cost function. The simulation results demonstrate the robustness of the proposed approaches in the presence of dense outliers.

A novel robust moving horizon estimator for discrete-time linear systems subject to measurement outliers

“…Unlike the studies in [6,7], this paper is concerned with the problem of measurements being corrupted by outliers. To ensure the stability of the moving horizon estimator, it is necessary to impose a limit on the number of outliers in a batch of measurements [30,31]. The work in [30] investigated the MHE problem in the presence of a single outlier in the sliding window and was later extended to scenarios involving multiple outliers in [31].…”

“…To ensure the stability of the moving horizon estimator, it is necessary to impose a limit on the number of outliers in a batch of measurements [30,31]. The work in [30] investigated the MHE problem in the presence of a single outlier in the sliding window and was later extended to scenarios involving multiple outliers in [31]. This paper considers the general case of multiple outliers in the sliding window, which can occur at any instant, yet there is an upper bound on their number.…”

“…This method can only address the case with a single outlier in the sliding window, and its estimation performance degrades significantly when multiple outliers are present. Later, Liu et al [31] extended this method to scenarios where multiple outliers occur within the sliding window, improving the estimation accuracy with the sacrifice of computational efficiency. In [32], a riskaverse performance-specified MHE strategy was proposed.…”

“…These methods also fail to consider the presence of state or disturbance constraints. Although MHE-based robust estimators [19,[30][31][32] can address the shortcomings of the aforementioned methods, they face the challenge of poor real-time performance. Consider that the MHE method has the advantages of explicit handling constraints and intrinsic robustness, making it an excellent design choice for estimators.…”

“…Based on previous results in [31], we first present a set of least-squares cost functions to attempt to eliminate potential measurement outliers and provide state estimates. To address the high computational burden caused by mixedinteger optimization, we introduce an outlier detection mechanism.…”