Cramer-Rao Bounds for FOA and TOA Estimation from Galileo Search and Rescue Signal

Considering the uncertainty of message bit width, the Cramer-Rao Bounds (CRBs) for Frequency Of Arrival (FOA) and Time Of Arrival (TOA) estimation from single Galileo Search And Rescue (SAR) signal are researched. Calculation expressions for the elements of Fisher information matrix of Galileo SAR signal are acquired. When calculating the sum of the square of dirac delta function, the properties of dirac delta function and Parsevals theorem are used to transform the computation from time-domain to frequency-domain, and the closed-form analytical solution of CRBs for FOA and TOA estimation are derived. Numerical calculation, Monte Carlo simulation and measurement results validate the effectiveness of the CRBs above which can be used to evaluate the performance of estimation algorithm for the parameters above.