B-spline based arm length estimation algorithm for space-borne gravitational wave detection

Data preprocessing is an essential step in space-borne gravitational wave detection, aimed at calibrating the data while suppressing noise. Time delay interferometry represents the primary technique for eliminating laser frequency noise, relying on precise arm length information. In this study, we combined pseudo-random noise ranging and Doppler measurements from TianQin’s data to create an observation equation and established an arm length model using a cubic B-spline function. To ensure accurate representation of the arm length and relative velocity, we employed quadruple-precision orbit information to simulate the observation data and determine reasonable spline node distances through fitting analysis. By utilizing the weighted least squares algorithm, we could estimate arm length information with millimeter-level accuracy. We investigated the contributions of the spline model’s smoothing function and additional Doppler measurement information to arm length estimation accuracy while analyzing the impact of weighting coefficients on the estimation results. Finally, we compared the accuracy of our proposed algorithm with that of the existing Kalman filter algorithm.