Cramér-rao lower bound for pulsar rotation parameters estimation with X-ray pulsar observation data

In this paper, the Cramér-Rao Lower Bound (CRLB) for estimating the rotation parameters of pulsars using X-ray pulsar observation data is deduced, and the calculation equation is presented. In order to verify the correctness of the deduced equation, we use the X-ray pulsar observation data to estimate pulsar rotation parameters, and obtain the root mean square error (RMSE) of the estimated pulsar rotation parameters through conducting repeated experiments. The experimental results suggest that when the observation time increases, the RMSE gradually approaches the estimated CRLB, and that when the observation time is 2.4 × 10⁶ s, the error between the RMSE of pulsar frequency estimation and the CRLB stays at 10^?11 order of magnitude. This verifies that the CRLB expression deduced in this paper is the theoretical lower bound for estimating pulsar rotation parameters. The deduced CRLB in this paper helps determine the minimum variance estimator for pulsar rotation parameter estimation using X-ray pulsar data, providing a benchmark for the comparison between the minimum variance estimator and other estimators.