Performance-Specified Moving-Horizon State Estimation With Minimum Risk

This paper is concerned with the estimation of the state of a linear dynamic system when the measurements may contain outliers. The most common method for outlier detection utilizes the traditional Neyman-Pearson (NP) Kalman filter approach which ignores all residuals greater than a designer specified threshold. When measurements with outliers are used (i.e., missed detections), the estimated state becomes incorrect and the computed state error covariance is too small, yielding an over confidence in the estimator in the incorrect state estimate. When valid measurements are ignored, information is lost, but this is only critical if it causes the performance specification to be violated. In signal rich applications, with a large number of sensor measurements, a smaller subset of measurements than is accepted by the NP approach, could be able to achieve the specified level of performance with lower risk of including an outlier in the set of utilized measurements. In the moving-horizon approach used herein, the number of measurements available for state estimation is affected by both the number of measurements per time step and the number of time steps over which measurements are retained. This moving horizon, performance-specified, risk-averse state estimation approach will be formulated in an optimization setting that selects measurements from within the window, to achieve a specified level of performance while minimizing the incurred risk. Simulation results are included, which demonstrate the application of the technique and its enhanced performance and robustness to outliers relative to traditional methods.