Multisubaperture Backward Projection Positioning Algorithm for Radiation Sources by Single Satellite

High-accuracy localization of radiation sources is a prominent research area in the field of passive positioning technology. Synthetic aperture positioning (SAP) outperforms traditional methods in low signal-to-noise ratio environments due to the persistent and coherent accumulation of Doppler signals along the flight path. However, SAP is a challenge in slant scenarios and is susceptible to residual frequency offset (RFO) resulting from noncooperative operation between transceivers. In this study, we propose a multisubaperture backward projection positioning (MSBPP) method. Leveraging the backward projection of the Doppler history, a cost function for the slant angle and slant range of the target is formulated to produce a backward projection positioning (BPP) image for the radiation source position in the region of interest. Nonlinear equations for the target position, RFO, and the slant angle obtained by BPP method are derived at different subapertures, and these equations are solved using the Newton method to obtain the target position and RFO. The influence of factors, such as the slant angle error, satellite position error, satellite velocity error, and subaperture distribution, on the positioning results is meticulously analyzed, and the error matrix of MSBPP method is obtained. Our theoretical formulations and Monte Carlo experiments indicate that the positioning accuracy of BPP method closely approaches the Cramer-Rao lower bound in the SAP model, surpassing traditional methods by an order of magnitude. Actual satellite experiments validate the RFO removal capability of MSBPP method, demonstrating positioning accuracy that exceeds that of traditional frequency of arrival by an order of magnitude.