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

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.