Source localization in a wireless sensor network (WSN) is sensitive to the sensors' positions. In practice, due to mobility, the receivers' positions may be known inaccurately, leading to non-negligible degradation in source localization estimation performance. The goal of this paper is to develop a semidefinite programming (SDP) method using time-difference-of arrival (TDOA) and frequency-difference-of-arrival (FDOA) by taking the sensor position uncertainties into account. Specifically, we transform the commonly used maximum likelihood estimator (MLE) problem into a convex optimization problem to obtain an initial estimation. To reduce the coupling between position and velocity estimator, we also propose an iterative method to obtain the velocity and position, by using weighted least squares (WLS) method and SDP method, respectively. Simulations show that the method can approach the Cramér-Rao lower bound (CRLB) under both mild and high noise levels.

The issue of robust multi-input multi-output (MIMO) radar waveform design is investigated in the presence of imperfect clutter prior knowledge to improve the worst-case detection performance of space-time adaptive processing (STAP). Robust design is needed because waveform design is often sensitive to uncertainties in the initial parameter estimates. Following the min-max approach, a robust waveform covariance matrix (WCM) design is formulated in this work with the criterion of maximization of the worst-case output signal-interference-noise-ratio (SINR) under the constraint of the initial parameter estimation errors to ease this sensitivity systematically and thus improve the robustness of the detection performance to the uncertainties in the initial parameter estimates. To tackle the resultant complicated and nonlinear robust waveform optimization issue, a new diagonal loading (DL) based iterative approach is developed, in which the inner and outer optimization problems can be relaxed to convex problems by using DL method, and hence both of them can be solved very effectively. As compared to the non-robust method and uncorrelated waveforms, numerical simulations show that the proposed method can improve the robustness of the detection performance of STAP.

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.

We propose a novel approach to the target localization problem using Doppler frequency shift measurements. We first reformulate the maximum likelihood estimation (MLE) as a constrained weighted least squares (CWLS) estimation, and then perform the semidefinite relaxation to relax the CWLS problem as a convex semidefinite programming (SDP) problem, which can be efficiently solved using modern convex optimization methods. Finally, the SDP solution can be used to initialize the original MLE which can provide estimates achieve the Cramer-Rao lower bound accuracy. Simulations corroborate the good performance of the proposed method.

In this paper, we consider the problem of waveform optimization for multi-input multi-output (MIMO) radar in the presence of signal-dependent noise. A novel diagonal loading (DL) based method is proposed to optimize the waveform covariance matrix (WCM) for minimizing the Cramer-Rao bound (CRB) which improves the performance of parameter estimation. The resulting nonlinear optimization problem is solved by resorting to a convex relaxation that belongs to the semidefinite programming (SDP) class. An optimal solution to the initial problem is then constructed through a suitable approximation to an optimal solution of the relaxed one (in a least squares (LS) sense). Numerical results show that the performance of parameter estimation can be improved considerably by the proposed method compared to uncorrelated waveforms.