Modified CRB for Location and Velocity Estimation using Signals of Opportunity

TL;DR

This paper develops a modified Bayesian CRLB to analyze how asynchronous clocks affect the accuracy of localizing sensors using signals of opportunity from known-position beacons.

Contribution

It introduces a new CRLB formulation that accounts for clock asynchronism, providing a more accurate bound on localization errors in such scenarios.

Findings

Quantifies the impact of clock skew and offset on localization accuracy.

Derives the Fisher information matrix for the modified CRLB.

Provides insights into the error bounds due to asynchronous clocks.

Abstract

We consider the problem of localizing two sensors using signals of opportunity from beacons with known positions. Beacons and sensors have asynchronous local clocks or oscillators with unknown clock skews and offsets. We model clock skews as random, and analyze the biases introduced by clock asynchronism in the received signals. By deriving the equivalent Fisher information matrix for the modified Bayesian Cram\'er-Rao lower bound (CRLB) of sensor position and velocity estimation, we quantify the errors caused by clock asynchronism.