Moving-horizon estimation for discrete-time linear systems with measurements subject to outliers

Abstract

Moving-horizon state estimation is addressed for discrete-time linear systems with disturbances acting on the dynamic and measurement equations. In particular, the measurement noises can take abnormal values, usually called outliers. For such systems, one can adopt a Kalman filter with estimate update that depends on the result of a statistical test on the residuals. As an alternative to such a method, we propose a robust moving-horizon estimator. Such a method provides estimates of the state variables obtained by minimizing a set of least-squares cost functions by leaving out in turn all the measurements that can be affected by outliers. At each time instant, the estimate that corresponds to the lowest cost is retained and propagated ahead at the next step, where the procedure is repeated with the new batch of measures. The stability of the estimation error for the proposed moving-horizon estimator is proved under mild conditions concerning the observability of the free-noise dynamic equations and the selection of a tuning parameter in the cost function. The effectiveness the proposed method as compared with the Kalman filter is shown by means of simulations on a simple example. 53rd IEEE Conference on Decision and Control

Moving-horizon estimation with guaranteed robustness for discrete-time linear systems and measurements subject to outliers

“…with ξ = 0.2, ω = 0.5 rad/s, and sampling period T = 0.5 s. The initial states were generated as white Gaussian noises with mean [1 1] and covariance P 0 = diag (2,2). White Gaussian processes with means equal to zero and covariances Q = diag(1, 1), and r = 0.01, 0.1, 1.0 (except in case of outlier) were chosen as system and measurement disturbances, respectively.…”

“…Thus, one may check abnormal residuals via a threshold test to skip the Kalman estimate update with such residuals. This procedure can be motivated from a theoretical point of view by using the maximum likelihood criterion [2].…”

“…Based on the preliminary results of [2], here we focus on MHE for linear discrete-time systems with measurements contaminated by outliers. Toward this end, first we will prove the stability of the estimation error and, second, the robustness to outliers.…”

Study of positioning estimation with user position affected by outlier: a case study of moving-horizon estimation filter

“…The results of the comparison are added to a single value of a synthetic outlier, then the position estimation is performed, and the measurements of pseudo range are obtained. Using the same concept, the outlier identification algorithm and the MHE are used in parallel as in [23], [24], and some other additional measures can be clubbed with the same. The output results obtained from the simulation are exclusively designed for the positioning estimation of the measurements subjected to outliers and free noise of GPS positioning having the original code [21].…”

Data-Based Moving Horizon Estimation for Linear Discrete-Time Systems

“…Earlier model-based MHE proofs that were specifically developed for linear systems have mostly been done under the assumption that no disturbances are present[17] or result in similar estimation error bounds that get worse with increasing horizon L[18], similar to[15],[16] 3. With slight abuse of notation, we denote by x(x, u) and h(x) the state and corresponding output sequence starting at initial condition x and generated by the input sequence u.…”