Instrumental-Variable Methods and Sensor Trajectory Optimization for State Uncertainty Regions in Target Motion Analysis With Finite Bearing Measurements

Abstract

This article focuses on state uncertainty region quantification and construction in target motion analysis (TMA) with finite bearing measurements. The traditional tool for the region either only works under ideal experimental assumptions, consumes much computation time, or behaves poorly when the target observability is limited. By incorporating an instrumental-variable (IV) matrix, we develop the IV Bayesian frequentist bounds (IVBFBs) method under a Gaussian prior and measurement noise. The method quantifies the uncertainty region with guaranteed coverage probability (CP) and constructs a closed-form hyperellipsoid bound for the candidate states. In this method, each uncertainty region candidate is taken as a reference function based on the model prediction error and compared with several benchmark values from the error resamples. If the function value does not rank the highest, this candidate is covered in the region with guaranteed probability. To enable real-time application of the IVBFB, the recursive IVBFB (RIVBFB) method is further proposed to contain target locations in an elliptical region sequentially. Moreover, we prove that sensor trajectory optimization can shrink the upper bound of region size. Then, an analytical next-waypoint optimization approach under physical constraints is integrated with the RIVBFB to reduce the uncertainty region area. Finally, extensive simulations verify the effectiveness of our proposed methods.