Optimization-Based Outlier Accommodation Using Information Constraints for CAV State Estimation in Urban Environments

Accurate vehicle localization relies on sensor measurements that may be prone to outliers. This results in an inherent trade-off between incorporating additional measurements to potentially achieve higher estimation accuracy at the risk of including outlier measurements. The Risk-Averse Performance Specified (RAPS) state estimation approach addresses this trade-off by optimally selecting a subset of measurements to minimize a cost related to outlier risk while achieving a target performance quantified as an information constraint. The existing literature lacks a computationally efficient method suitable for implementation in real-time applications such as transportation and does not address situations where the performance specification is infeasible. This article focuses on the Diagonal RAPS (DiagRAPS) formulation makes contributions in several directions. First, it develops DiagRAPS for both binary and non-binary measurement selection variables. Algorithms suitable for real-time applications are proposed within Linear Programming and Mixed-Integer Linear Programming optimization frameworks, achieving polynomial time-complexity. The convergence and computation costs of these algorithms are discussed. Second, a convex programming problem is derived for the binary DiagRAPS, enabling a globally optimal solution. Third, a soft constraint relaxation approach is introduced for situations where the specified performance is unfeasible. Experimental evaluations using real-world Gloabal Navigation Satellite Systems data from challenging urban environments demonstrate the efficacy of these approaches. The results reveal that the locally optimal approach achieves state estimation performance comparable to the global solution. Both binary and non-binary DiagRAPS outperform traditional methods, showing improvements in Society of Automotive Engineers requirements of at least 14% for horizontal and 22% for vertical. Notably, the non-binary approach yields the lowest computation cost and the best overall performance.