Output outlier robust state estimation

Abstract

This work addresses state estimation in presence of outliers in observed data. Outlying data and measurements have a most relevant impact in many control and signal processing applications including marine systems related ones: underwater navigation systems exploiting acoustic data, for example, are frequently affected by outlying measurements. Other on-board sensors and devices are likely to produce measurements contaminated by outlier because of the harsh operating conditions of marine systems. Given the general interest for dealing with measurement outliers in a number of applications, this paper describes a state estimation solution exhibiting robustness to output outliers. The system model is assumed to be linear (either time varying or time invariant) discrete time. The proposed observer is designed by extending an outlier robust static parameter identification algorithm to the case of a linear dynamic plant. The designed estimator has a predictor/corrector structure like the Kalman filter and the Luenberger observer. Simulation and experimental results are provided illustrating the robustness of the derived solution to measurement outliers as compared with the Kalman filter. The proposed solution is also compared with alternative outlier robust state estimation filters showing its effectiveness, in particular, in the presence of measurements outliers occurring in a consecutive sequence. Because of its deterministic execution time and limited numerical complexity, the proposed state estimator can be readily applied in real-time applications. Figure 4. Noisy output with outliers (depicted as blue stars, D 0:2) and non-outliers in grey generated through the model in (41). [Colour figure can be viewed at wileyonlinelibrary.com] The LEL Filter column refers to the interval of singular values over 3000 Monte Carlo runs assuming outliers generated through the model in (41). LEL, least entropy like.with synthetic and real data have been discussed showing the potentiality of the proposed filter as compared with the standard KF. Comparison with alternative robust filtering approaches have shown its robustness to sequences of successive measurement outliers as well. The proposed robust LEL filter may be exploited in real-time applications because of its limited and predictable (i.e. deterministic) computational effort.

Stubborn and Dead-Zone Redesign for Nonlinear Observers and Filters

“…, m} \ I the set of indexes j for which σ j < |γ j |. The derivative of Ve, computed from (8) and (13), and the first inequality in (25), satisfies…”

“…Depending on the characteristics of the measurement noise, different approaches may be pursued to improve the observer performances. For instance, in the case of output measurements affected by outliers, that is, perturbations of impulsive nature affecting the measurement for a very short time, the majority of the existing methods focus on a discrete-time representation and mainly deal with identification problems, see, e.g., [2], [25], [44] and the references therein. When considering high-frequency measurement noise, a number of high-gain approaches have been developed, see, e.g., [1], [10], [11], [13], [18], [20], [42], [43].…”

LQG Online Learning

“…Finally, we mention that various different approaches to deal with learning time-varying parameters online were presented, e.g., also in [13,33,35], in some cases in the context of state estimation of dynamical systems in the presence of outliers [1,18]. As a possible extension, one could combine those approaches with the regularization of the updates included in our model, whose beneficial effects have been just demonstrated also in this time-varying case.…”

Outlier accommodation in moving‐horizon state estimation: A risk‐averse performance‐specified approach

“…There is a vast amount of literature aimed at improving the robustness of the Kalman filter (KF) in presence of outliers. Most of the results rely on the idea of setting the KF to make it robust to outliers . Many alternative noise models have been proposed, usually in the form of heavy‐tailed non‐Gaussian distributions, t‐distributed noise models or ad hoc cost functions for the update step.…”

“…In the work of Alessandri and Zaccarian, an observer is proposed with a saturated output injection in such a way to mitigate the effect of outliers on the error dynamic. An observer is designed by De Palma and Indiveri by extending an outlier robust static parameter identification algorithm to the case of a linear dynamic plant. The designed estimator has a predictor/corrector structure like the KF and the Luenberger observer.…”