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

This paper presents a novel state estimation approach for linear dynamic systems when measurements are corrupted by outliers. Since outliers can degrade the performance of state estimation, outlier accommodation is critical. The standard approach combines outlier detection utilizing Neyman-Pearson (NP) type tests with a Kalman filter (KF). This approach ignores all residuals greater than a designer-specified threshold. When measurements with outliers are used (ie, missed detections), both the state estimate and the error covariance matrix become corrupted. This corrupted state and covariance estimate are then the basis for all subsequent outlier decisions. When valid measurements are rejected (ie, false alarms), potentially using the corrupted state estimate and error covariance, measurement information is lost. Either using invalid information or discarding too much valid information can result in divergence of the KF. An alternative approach is moving-horizon (MH) state estimation, which maintains all recent measurement data within a moving window with a time horizon of length L. In MH approaches, 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 L over which measurements are retained. Risk-averse performance-specified (RAPS) state estimation works within an optimization setting to choose a set of measurements that achieves a performance specification with minimum risk of outlier inclusion. This paper derives and formulates the MH-RAPS solution for outlier accommodation. The paper also presents implementation results. The MH-RAPS application uses Global Navigation Satellite Systems measurements to estimate the state of a moving platform using a position, velocity, and acceleration model. In this application, MH-RAPS performance is compared with MH-NP state estimation.