Cramer-Rao bounds of angle-of-arrival and polarisation estimation for various triads

This work derives the closed-form CraméŕRao bounds (CRBs) for the estimation of an incident far-field point-sourcés azimuth-elevation arriving angles and polarisation parameters. The receiving antennas are a triad of spatially collocated but orthogonally oriented dipole(s) and/or loop(s). The CRBs for all 20 possible compositions of such a triad are derived. The derived CRBs are verified by Monte Carlo simulations of maximum-likelihood estimation. Furthermore, the CRBs of triads with two antennas (one dipole and one loop) oriented along the z-axis plus another dipole/loop oriented along the x/y-axis have been simplified in the following three commonly encountered polarisation states: (i) horizontally linear polarisation, (ii) vertically linear polarisation and (iii) right-circular polarisation. Observations are obtained from the derived CRBs to help engineers select antennas among the 20 different triad-compositions for direction finding and polarisation estimation.