A Mathematical Algorithm of Locomotive Source Localization Based on Hyperbolic Technique

Abstract

Recent trend shows that sensors situated on an axis in two-dimensional scenario measuring the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) of the emitting signal from a moving source can estimate the emitting signal’s position and velocity from the intersection point of hyperbola, which derives from TDOA and FDOA. However, estimating the location of an emitter based on hyperbolic measurements is a highly nonlinear problem with inconsistent data, which are created due to the measurement noise, the deviation between assumption model and actual field of the velocity, and so forth. In addition, the coefficient matrix of TDOA and FDOA equations set is singular in the linear sensor array network (LSAN). In this paper, a noniterative and simpler method is proposed to locate the instantaneous position of the moving source in LSAN by estimating the position and velocity based on TDOA and FDOA which does not have the convergence problem. In addition, the method avoids the singularity problem of LSAN by introducing the nuisance variables. The proposed method achieved the theoretical lower bound for near to far field with same and different velocity and different baseline of sensors in low to moderate noise.