In this work, the differential received signal strength based localization problem is addressed. Based on the measurement model, we present the constrained weighted least squares (CWLS) approach, which is difficult to be solved directly due to its nonconvex nature. However, by performing the semidefinite relaxation (SDR) technique, the CWLS problem can be relaxed into a semidefinite programming problem (SDP), which can be efficiently solved using modern convex optimization algorithms. Moreover, the SDR is proved to be tight, and hence ensures the corresponding SDP find the optimal solution of the original CWLS problem. Numerical simulations are included to corroborate the theoretical results and promising performance.

In this work, we address the stationary target localization problem by using Doppler frequency shift (DFS) measurements. Based on the measurement model, the maximum likelihood estimation (MLE) of the target position is reformulated as a constrained weighted least squares (CWLS) problem. However, due to its non-convex nature, it is difficult to solve the problem directly. Thus, in order to yield a semidefinite programming (SDP) problem, we perform a semidefinite relaxation (SDR) technique to relax the CWLS problem. Although the SDP is a relaxation of the original MLE, it can facilitate an accurate estimate without post processing. Simulations are provided to confirm the promising performance of the proposed method.

In this paper, the problem of target detection and tracking utilizing the single frequency network (SFN) is addressed. Specifically, by exploiting the characteristics of the signal in SFN, a novel likelihood model which avoids the measurement origin uncertain problem in the point measurement model is proposed. The particle filter based track-before-detect (PF-TBD) algorithm is adopted for the proposed SFN likelihood to detect and track the possibly existed target. The advantage of using TBD algorithm is that it is suitable for the condition of low SNR, and specially, in SFN, it can avoid the data association between the measurement and the transmitters. The performance of the adopted algorithm is examined via simulations.

In non-cooperative scenarios, the estimation of direct sequence spread spectrum (DS-SS) signals has to be done in a blind manner. In this letter, we consider the spreading sequence estimation problem for DS-SS signals. First, the maximum likelihood estimate (MLE) of spreading sequence is derived, then a semidefinite relaxation (SDR) approach is proposed to cope with the exponential complexity of performing MLE. Simulation results demonstrate that the proposed approach provides significant performance improvements compared to existing methods, especially in the case of low numbers of data samples and low signal-to-noise ratio (SNR) situations.