Spacecraft localization by indirect linear measurements from a single antenna

Purpose: The purpose of this paper is to present a two-stage approach for estimation of spacecraft’s position and velocity by indirect linear measurements from a single antenna. Design/methodology/approach: In the first stage, direct nonlinear antenna measurements are transformed to linear x-y-z coordinate measurements of spacecraft’s position, and statistical characteristics of orbit determination errors are analyzed. Variances of orbit parameters’ errors are chosen as the accuracy criteria. In the second stage, the outputs of the first stage are improved by the designed Extended Kalman Filter for estimation of the spacecraft’s position and velocity on indirect linear x-y-z measurements. Findings: The complex content of the measurement matrix in the conventional method causes periodic singularities in simulation results. In addition, the convergence of the filter using direct measurements is highly dependent on the initialization parameters’ values due to the nonlinear partial derivatives in the Jacobian measurement matrix. The comparison of the accuracy of both methods shows that the estimation by using indirect measurements reduces the absolute estimation errors. The simulation results show that the proposed two-stage procedure performs both with better estimation accuracy and better convergence characteristics. The method based on indirect measurements provides an unnoticeably short transient duration. Practical implications: The proposed method can be recommended for satellite orbit estimation regarding its presented superiorities. Originality/value: Inputting the single antenna measurements to the filter indirectly results in a quite simpler measurement matrix. As a result, the convergence of the filter is faster and estimation errors are lower.