Source localization for the nonlinear measurement model based on time difference of arrival (TDOA) measurements remains a vital research area and has been intensively studied for the past few decades. However, the localization accuracy decreases significantly as the random measurement noise becomes large. In addition, when sensors are mounted on moving platforms like vehicles or aircrafts, inevitable sensor position errors might pose more severe challenges on source localization accuracy. This paper proposes to construct a pseudo-linear measurement model that introduces both the TDOA measurement noise and the sensor position error firstly. Next, the constrained total least squares (CTLS) formulation is presented, and the iterative alternating direction method of multipliers (ADMM) is employed to solve the resulting optimization model. Simulation results show that the proposed method can approach Cramer Rao lower bound (CRLB) better and outperforms several existing methods when considering sensor position uncertainties and large TDOA measurement errors.

In many applications of wireless sensor networks (WSNs), sensor positions are often not known exactly. The existence of sensor position error (SPE) may significantly impact system performance if not appropriately modeled or considered. In this article, we address the important sensor selection problem in the presence of SPE for general nonlinear measurement models considering independent and correlated measurement noise cases. The sensor selection problem is formulated in the framework of sparse sensing, in which the number of activated sensors is minimized subject to certain predetermined performance constraints. To facilitate the challenging convex relaxation of nonconvex constraints for the case with independent measurement noise, we prove that the Fisher information matrix (FIM) remains additive even in the presence of SPE. For correlated measurement noise, quadratic inequality constraints are introduced and two suboptimal solvers are proposed. The first solver uses matrix decomposition to transform the quadratic constraint into linear matrix inequalities (LMIs), while the second solver iteratively performs a linearization procedure on the quadratic constraint to obtain a reduced dimension of LMI, thus decreasing the computational complexity significantly. The proposed algorithms are compared in terms of their computational complexity quantitatively and experimentally with suboptimal greedy approaches and existing algorithms ignoring SPE. The results show the importance and necessity of considering SPE when implementing sensor selection and demonstrate the effectiveness of the proposed three sensor selection solvers.

Time difference of arrival (TDOA) measurements, which are contaminated by large values of error, known as outliers, would have a significant impact on the accuracy of sound source localization (SSL) in wireless acoustic sensor networks (WASNs). Few techniques are reported in the literature to tackle SSL in WASNs by taking TDOA outliers into consideration. To mitigate the effect of outliers on the accuracy of SSL, we propose outlier-resistant robust sound source localization (RSSL) algorithms based on sparse regularization using an unsynchronized network of microphone arrays. The TDOA errors are divided into two components: a) energy-bounded inliers and b) outliers. Assuming that outliers are sparse in the measurement set, we formulate the RSSL problem as that of minimizing the number of outliers, mathematically, a $\ell _{0}$ (pseudo)-norm optimization problem with non-convex constraints. Five sub-optimal RSSL solvers are derived, among which the first two solvers are applicable to the scenario involving only outliers while the last three solvers concentrate on the scenario incorporating both outliers and inliers. In common, these solvers exploit a convex approximation technique called Concave Convex Procedure to dispose of the non-convex constraints. Differently, the first solver approximates the original $\ell _{0}$ (pseudo)-norm cost function with the $\ell _{1}$ norm while a concave surrogate function is adopted in the second solver to yield a tighter approximation to the $\ell _{0}$ (pseudo)-norm. Apart from the application of these two approximation techniques, the third and fourth solvers relax the non-convex $\ell _{2}$ norm constraint with the $\ell _{\infty }$ norm. The fifth solver is dedicated to the $\ell _{1}$ norm regularization problem with the Lasso formulation, which is equivalent to the M-estimator of Huber’s function solved via the iteratively reweighted least squares paradigm. Experimental results validate the effectiveness and robustness of the proposed algorithms.

This paper considers the localization problem of a mobile source based on time difference of arrival (TDOA) measurements and angle of arrival (AOA) measurements in the presence of random noises in both measurements and sensor location. We propose a sensor selection mechanism which aims to choose a subset of sensors to implement the multi-sensor passive localization. We use the covariance of the improved unscented Kalman filter (UKF) as a cost function where the dynamic model is augmented by incorporating the sensor positions into the state vector. Correspondingly, the number of sigma points in the improved UKF is also enlarged. Although the proposed method requires higher computational complexity, the selected subset achieves a better estimation performance in comparison with that of the linearization method EKF or classical UKF method which ignores the sensor position uncertainties. And the CEO (cross entropy optimization) is employed to solve the resulting complex combinatorial optimization model. Simulation experiments are conducted and simulation results demonstrate the efficiency of the proposed sensor selection scheme for multi-sensor passive localization.

In passive localization applications, the positioning accuracy for an emitter is highly dependent on the geometry between sensors and the target, the site error and measurement noise of sensors. We propose a sensor selection mechanism which aims to choose a subset of sensors to implement the multi-sensor passive localization. An optimization model is established by minimizing the GDOP (geometric dilution of precision), with or without the constraint on the cardinality of the selected sensor subset. The CEO (cross entropy optimization) is employed to solve the resulting complex combinatorial optimization model. Simulation experiments are conducted and simulation results demonstrate the efficiency of the proposed sensor selection scheme for multi-sensor passive localization.