Optimal Sensor Placement for Dilution of Precision Minimization Via Quadratically Constrained Fractional Programming

Abstract

An approach to find the global optimal solution of the dilution of precision (DOP) problem is presented. The DOP optimization problem considered assumes an environment comprising multiple randomly predeployed sensors (or navigation sources) and an additional sensor is to be introduced at the location that minimizes variations of the DOP problem (e.g., weighted geometric DOP, horizontal DOP, vertical DOP, etc.). It is shown that the DOP problem can be formulated as a quadratically constrained fractional quadratic program. An algorithm for solving this program is presented and Monte Carlo simulation results are given demonstrating convergence of the proposed approach to the global optimal solution. Additionally, Monte Carlo simulation results are presented, demonstrating the efficacy of the proposed algorithm to solving the DOP minimization problem versus using nonlinear numerical optimization solvers, which often converge to local optima. Also, the superiority of the proposed approach is demonstrated against other approaches that approximate the DOP minimization problem.