An efficient one-dimensional search solution is proposed for single-sensor emitter localization based on signal periodicity. By introducing an intermediate variable, this single-sensor localization problem can be solved by solving a set of equations for classic multi-sensor time difference of arrival localization, whose algebraic solutions can be obtained by the well-known two-stage weighted least squares (TSWLS) algorithm. In this manner, the two-dimensional or three-dimensional search for the emitter location can be replaced by a one-dimensional search for the intermediate variable. Simulations indicate that, at the expense of a small loss of localization accuracy, the proposed method achieves a significant advantage in computation time, compared with the conventional maximum likelihood technique.

This paper focuses on passive emitter localization using moving sensors. The increase in observation time is beneficial to improve the localization accuracy, but it could cause deterioration of the relative motion between the emitter and the sensors, especially the nonlinear motion. The common localization algorithms typically have two steps: (1) parameter estimation and (2) position determination, where the parameters are assumed to be constant, and it is not applicable for long observation times. We proposed the time-varying delay-based direct position determination (DPD-TVD) method, regarding the variation in the propagation time delay during the observation time. Using one step, the proposed algorithm can obtain the emitter’s position directly from the received signals by calculating the cost function corresponding to the map grid. By better adapting to highly dynamic scenarios, the proposed algorithm can achieve better localization accuracy than that of constant parameters using one-step or two-step procedures, which is demonstrated by the simulation results.

To eliminate the bottleneck of computation and communication capability in classic direct position determination, recently several fast approximation methods have been proposed. However, the estimation accuracy of these methods is not satisfactory. In this letter, the common theoretical principle behind these fast approximation methods is analysed in depth. It is demonstrated that the maximum eigenvalue of a matrix can be approximated by the matrix norm. The performance of several commonly used matrix norms is then compared, and the Frobenius norm is preferable because of its great potential inferred from the analysis in this letter. Numerical simulations indicate that, compared with conventional methods, the proposed method can achieve better estimation accuracy with less computational complexity.