Parameterized TDOA: TDOA estimation for mobile target localization in a time-division broadcast positioning system

TL;DR

This paper introduces a novel P-TDOA method for mobile target localization in TDBPS, enabling concurrent TDOA estimation from sequential measurements, thus allowing classical TDOA techniques to be applied effectively.

Contribution

The paper proposes a new polynomial-based P-TDOA estimation method that approximates time-varying TDOA, bridging the gap between sequential measurements and the need for concurrent TDOA estimates.

Findings

P-TDOA closely approaches the CRLB under certain conditions.

Numerical simulations show substantial improvements over existing methods.

The method enables classical TDOA techniques to be used for mobile targets.

Abstract

In a time-division broadcast positioning system (TDBPS), localizing mobile targets using classical time difference of arrival (TDOA) methods poses significant challenges. Concurrent TDOA measurements are infeasible because targets receive signals from different anchors and extract their transmission times at different reception times, as well as at varying positions. Traditional TDOA estimation schemes implicitly assume that the target remains stationary during the measurement period, which is impractical for mobile targets exhibiting high dynamics. Existing methods for mobile target localization are mostly specialized and rely on motion modeling and do not rely on the concurrent TDOA measurements. This issue limits their direct use of the well-established classical TDOA-based localization methods and complicating the entire localization process. In this paper, to obtain concurrent TDOA estimates at any instant out of the sequential measurements for direct use of existing TDOA-based localization methods, we propose a novel TDOA estimation method, termed parameterized TDOA (P-TDOA). By approximating the time-varying TDOA as a polynomial function over a short period, we transform the TDOA estimation problem into a model parameter estimation problem and derive the desired TDOA estimates thereafter. Theoretical analysis shows that, under certain conditions, the proposed P-TDOA method closely approaches the Cramer-Rao Lower Bound (CRLB) for TDOA estimation in concurrent measurement scenarios, despite measurements being obtained sequentially. Extensive numerical simulations validate our theoretical analysis and demonstrate the effectiveness of the proposed method, highlighting substantial improvements over existing approaches across various scenarios.