A Revisit to D-Criterion-Based Sensor Trajectory Planning in Bearing-Only Target Motion Analysis

In this article, a revisit is paid on the D-criterionbased sensor path optimization in bearing-only target motion analysis (TMA). For a nearly constant velocity (CV) target motion model, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4 \times 4$ </tex-math></inline-formula> Fisher information matrix (FIM) of the target starting location and velocity estimate vector in the D-criterion is brought under investigation. First, we analyze the structure of the FIM determinant increment regarding to the nextway point and develop its expression. Next, the relation between maximizing the FIM determinant increment with respect to the nextway point and other criteria in references is studied. It is revealed that the FIM determinant increment is equal to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \times 2$ </tex-math></inline-formula> Bayesian FIM determinant increment regarding to next target location estimate and serves as an upper bound of the majority of other criteria. Traditional numerical optimization of the increment cost function with respect to the nextway point is very time-consuming. In this article, the increment cost function is relaxed by eigenvalue decomposition into its lower bound. The candidate optimizers of the relaxed cost are analytically solved on different constraint boundaries and compared for a quick suboptimal solution. Finally, simulation results on target tracking cases verify the theoretical findings mentioned above, and more importantly, the advantages of the proposed method over other planning strategies.