Single‐step geolocation for a non‐circular source in the presence of satellite orbit perturbations

Abstract

Abstract This study addresses the problem of geolocating a strictly non‐circular source on the surface of Earth by a cluster of passive satellites. The known satellite positions and velocities are subject to random errors. The authors propose a single‐step satellite geolocation algorithm that directly localises the transmitter from sensor outputs using the information of time delays and Doppler shifts but without explicitly estimating them. It exploits the non‐circular property of signals and a priori information of satellite orbit error distribution to jointly calibrate orbit errors and determine the longitude and latitude of the transmitter based on the ellipsoidal Earth model, which integrates an alternating iteration scheme for the estimation of various unknowns instead of the exhaustive grid search. Additionally, a detailed Cramér‐Rao bound (CRB) derivation is presented for the single‐step satellite geolocation of a non‐circular source on Earth with and without satellite orbit perturbations, and it is proved that these CRBs are lower than the associated CRBs for a circular source. The simulation results illustrate that the proposed method asymptotically attains the associated CRB, and shows greater performance robustness to signal‐to‐noise ratio (SNR) and satellite orbit errors compared with conventional two‐step satellite geolocation approaches.

Keywords

• alternating iteration
• Cramér‐Rao bound (CRB)
• non‐circular signal
• satellite geolocation
• single‐step geolocation