Approximate Analytic Quadratic-Optimization Solution for TDOA-Based Passive Multi-Satellite Localization with Earth Constraint

Abstract

In this paper, we make an investigation of the problem of passive multi-satellite localization based on time differences of arrival (TDOA) with Earth constraint (EC). By utilizing TDOA measurements and EC, the problem of estimating target position is formulated as a quadratically constrained quadratic optimization. Following this, the approximate analytic solution of target position is obtained by using the method of Lagrange multipliers and deleting the infeasible roots of polynomial in the Lagrange multiplier. Simulation results show that the proposed method can achieve the Cramer-Rao lower bound (CRLB) with EC for three typical scenarios, even in the worst case, e.g., in the presence of large TDOA measurement errors with even target being far from the subastral point. However, the existing TDOA localization methods will deviate from the CRLB with EC as the measurement error of TDOA increases. Thus, the proposed method is more robust compared with the existing methods. In addition, the EC has a significant impact on the TDOA localization performance. Compared with the case of no EC, the EC can make a one-order-magnitude improvement in localization precision.