Analysis of condition number and position estimation error for multiangulation position estimation system

A passive wireless positioning system could be used to detect the location of low-level airborne targets such as drones or unmanned aircraft systems from the electromagnetic emission detected at spatially deployed ground receiving stations (GRSs). The multiangulation system proposed in this paper makes use of the angle of arrival (AOA) of the transmitted signal from the target to estimate its position through a 2-stage process. The AOA is the position-dependent signal parameter (PDSP) obtained from the target emission in the first stage, and using the PDSP and GRSs, the target location is estimated in the second stage by the angulation algorithm. Noise in the received signal results in AOA estimation error and subsequently error in the position estimation (PE). This paper focuses on the angulation process, which is the second stage of the multiangulation target location estimation process. Analysis is conducted to determine the correlation between the PE error and the condition number of the coefficient matrix of a multiangulation position estimation system. The results based on Monte Carlo simulations show that both condition number and PE error distribution increase with the target range, where the higher condition number values correlate with higher PE error values appearing around 80◦ to 110◦ and 260◦ to 280◦ of both distributions