Crame acute accent r-rao lower bound for pulsar rotation parameters estimation with X-ray pulsar observation data

In this paper, the Crame acute accent r-Rao Lower Bound (CRLB) for estimating the rotation parameters of pulsars using X-ray pulsar observa-tion 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 x 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 com-parison between the minimum variance estimator and other estimators.(c) 2022 COSPAR. Published by Elsevier B.V. All rights reserved.

Automated summary

The paper deduces the Crame r-Rao Lower Bound (CRLB) for estimating pulsar rotation parameters using X-ray pulsar observation data and presents the calculation equation. To verify the correctness of the deduced equation, X-ray pulsar observation data is used to estimate pulsar rotation parameters, and the root mean square error (RMSE) of the estimated parameters is obtained through repeated experiments. The experimental results show that the RMSE approaches the estimated CRLB as the observation time increases, with the error between the RMSE and the CRLB staying at 10-11 order of magnitude when the observation time is 2.4 x 106 s. This confirms that the deduced CRLB 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, providing a benchmark for comparisons with other estimators.