Distance-Azimuth Joint Cramér-Rao Lower Bound for Spherical-wavefront-based Scatterer Localization

Abstract

In our previous work a scatterer-localization algorithm based on maximum-likelihood estimation was derived using spherical wavefront assumption. Individual Cramér-Rao Lower Bounds (CRLBs) for distance and azimuth estimation were presented. As a continuation, we now derive a joint CRLB for both distance and azimuth. The novelty lying in the joint CRLB is that the underlying Fisher Information Matrix (FIM) is a non-diagonal partition matrix, yielding the fact that the CRLB obtained is tighter than the CRLBs derived individually. A closed-form representation of the approximate of the joint CRLB is presented which is expressed as a function of the FIM elements. Monte-Carlo simulations are performed to assess the validity and the accuracy of the derived bounds. Finally, the applicability of the derived CRLB is illustrated for vehicle or obstacle localization when a vehicle-mounted millimeter-wave environment-sensing system is considered.