Asymptotic Performance of TDOA Estimation using Satellites

TL;DR

This paper derives asymptotic lower bounds on satellite-based localization error, showing that TDOA estimators perform nearly as well as ideal estimators in dense satellite networks, with accuracy improving as satellites approach Earth.

Contribution

It introduces a novel asymptotic analysis of localization bounds using satellite networks, providing closed-form expressions that depend only on network statistics.

Findings

TDOA estimators approach ideal performance in dense networks.

Localization accuracy improves as satellites get closer to Earth.

Vertical localization is less accurate and more sensitive to receiver field-of-view.

Abstract

We present novel lower bounds on the localization error using a network of satellites randomly deployed on a sphere around Earth. Our new analysis approach characterizes the localization performance by its asymptotic behavior as the number of satellites gets large while assuming a dense network. Using the law of large numbers, we derive closed-form expressions for the asymptotic Cramer Rao bound (CRB) from which we draw valuable insights. The resulting expressions depend solely on the network statistics and are not a function of a particular network configuration. We consider two types of estimators. The first uses the exact statistical model, and hence employs both timing and amplitude information. The second estimator ignores the amplitudes and hence uses only time difference of arrival (TDOA) information. The asymptotic CRB indicates that for practical system setup, a TDOA estimator approaches the performance of the ideal estimator. For both estimators, the localization accuracy improves as satellites get closer to Earth. The latter finding is essential in light of the proliferation of low-Earth-orbit (LEO) satellites and motivates a further study of localization-performance in such networks. Besides, we show that the vertical localization accuracy is lower than the horizontal accuracy and is also more sensitive to the receiver field-of-view.