Outlier Accommodation in Nonlinear State Estimation: A Risk-Averse Performance- Specified Approach

This article presents a novel state estimation approach to the challenge of preventing outlier measurements from affecting the accuracy and reliability of state estimation. Since outliers can degrade the performance of state estimation, outlier accommodation is critical. The most common method for outlier accommodation utilizes a Neyman–Pearson (NP)-type test in a (extended) Kalman filter (KF) to detect and remove residuals greater than a designer specified threshold. Such threshold-based methods may use residuals arbitrarily close to the threshold, even when they are not needed to achieve an application’s performance specification. Outlier measurements that pass the residual test (i.e., missed detections) result in incorrect information being incorporated into the state and error covariance estimates. Once the state and covariance are incorrect, subsequent outlier decisions may be incorrect, possibly causing divergence. Risk-averse performance-specified (RAPS) state estimation works within an optimization setting to choose a set of measurements that achieves a performance specification with (locally) minimum risk of outlier inclusion. This article derives and formulates the RAPS solution for outlier accommodation. The approach applies to both linear and nonlinear applications. The main focus of this article is nonlinear applications. Linear applications are a special case of the results herein. This article contains RAPS implementation results for the nonlinear application that uses global navigation satellite systems (GNSSs) and inertial measurements to estimate the state of a vehicle. The RAPS performance is compared with the traditional NP-EKF.