Optimal Sensor Placement for TDOA-Based Source Localization with Sensor Location Errors

TL;DR

This paper investigates optimal sensor placement for TDOA-based source localization considering sensor location errors, demonstrating that small errors have negligible impact and that optimized placement improves localization accuracy.

Contribution

It establishes that optimal sensor placement under location errors is equivalent to the error-free case and validates this through extensive simulations.

Findings

Sensor location errors have minimal impact on OSP performance when errors are small.

Optimized sensor placement outperforms random placement in localization accuracy.

The derived OSP-SLN strategy is validated through simulations and open-sourced.

Abstract

The accuracy of time difference of arrival (TDOA)-based source localization is influenced by sensor location deployment. Many studies focus on optimal sensor placement (OSP) for TDOA-based localization without sensor location noises (OSP-WSLN). In practice, there are sensor location errors due to installation deviations, etc, which implies the necessity of studying OSP under sensor location noises (OSP-SLN). There are two fundamental problems: What is the OSP-SLN strategy? To what extent do sensor location errors affect the performance of OSP-SLN? For the first one, under the assumption of the near-field and full set of TDOA, minimizing the trace of the Cramer-Rao bound is used as optimization criteria. Based on this, a concise equality, namely Eq. (18), is proven to show that OSP-SLN is equivalent to OSP-WSLN. Extensive simulations validate both equality and equivalence and respond to the second problem: not large sensor position errors give an ignorable negative impact on the performance of OSP-SLN quantified by the trace of CRB. Also, simulations show source localization accuracy with OSP-SLN outperforms that with random placement. These simulations validate our derived OSP-SLN and its effectiveness. We have open-sourced the code for community use.