Received signal strength (RSS) measurements can be converted to the distance estimates between the emission source and the sensors to construct a system of linear equations, thereby allowing for the use of the weighted linear least squares (WLLS) estimators for location estimation. However, estimating the squared distances from the RSS measurements governed by the log-normal shadowing effect presents a major challenge in such approaches. In this paper, we propose a linear minimum mean square error (LMMSE) estimator of the squared distance between the emission source and the sensor first. Then a LMMSE-aided WLLS (LMMSE-WLLS) location estimator and its unbiased counterpart are presented for source localization. Furthermore, their estimation performance are analyzed in terms of mean square error (MSE) and covariance. It is found that the proposed LMMSE-aided WLLS location estimators have better estimation performance than existing WLLS estimators. Numerical examples also demonstrate the performance superiority of the proposed location estimators for source localization.

The problem of association of measurements acquired by passive bearings-only sensors in two dimensional (2D) plane is addressed in this paper. This problem can be formulated mathematically as a multidimensional assignment (MDA) problem with two steps of cost calculation and optimization. Compared with the optimization step, the cost calculation consumes more time (at least 80%; of the total time for solving the MDA problem). In order to reduce the computational requirements of the assignment costs of infeasible associations, a practical coarse gating strategy is proposed. First, two bearing measurements from different sensors are used to predict the bearing measurements of other sensors. Then, infeasible associations can be identified using gates centered on the predicted bearing measurements. This strategy is also extended to the measurement data association of heterogeneous sensors. Numerical examples verify the effectiveness of the proposed strategy.

Angle of arrival (AOA) and received signal strength (RSS) measurements have been commonly used in wireless localization due to easy access and simple implementation. In this paper, we investigate source localization using the AOA-only and hybrid RSS/AOA measurements, respectively. In AOA localization, we approximate the angle error using a range-related quantity. Then the optimization problem based on maximum likelihood (ML) is converted to a convex semidefinite programming (SDP) problem. In hybrid AOA/RSS localization, the ML estimator is decomposed into an RSS part and an AOA part. The AOA part follows a similar procedure as in the AOA localization. Taylor series expansion and relaxation are applied in optimizing the RSS part. These two parts are closely related through the range. The proposed methods avoid the nonconvexity in the original ML estimators for both AOA-only and hybrid AOA/RSS localization problems. Numerical examples show good performance of the proposed methods in both AOA and hybrid AOA/RSS localizations. They are close to or better than the LS methods in the literature.

Source localization is of great importance for wireless sensor network applications. Locating emission sources using received signal strength (RSS) measurements is investigated in this paper. As RSS localization is a non-convex optimization problem, it is difficult to achieve global optima. Many optimization methods have been proposed to relax it to a convex optimization problem. Unlike these methods, we propose a convex combination scheme. By introducing a highly accurate linear approximation of a logarithmic function, the source location is represented by a convex combination of a set of virtual anchors. Then the original problem is relaxed to be a convex optimization problem of finding the optimal combination coefficients, which can be solved efficiently using constrained least squares. To obtain the virtual nodes, we construct parallel lines and use their intersections to form a convex polygon, which covers the source location with certain probability. The vertices of the polygon are taken as the virtual nodes. Numerical examples verify the performance of the proposed method in both localization accuracy and computational efficiency.

A lot of performance evaluation metrics exist for nonlinear filters. At present, the most commonly used one is a single and incomprehensive metric of performance. This metric can continuously and quantitatively describe the performance of the nonlinear filters. But in many cases, we need to rank the performance of the filters. It is in general very hard to rank the filters just using a single metric. First, the rankings using a single metric at different times may be different. Then how to get a unique rank for all times? A typical existing solution is to average the single metric over all times. But it is easy to be dominated just by very large values at just some times. Second, a single metric is usually incomprehensive in measuring performance. To make the ranking more comprehensive, multiple metrics are usually needed. But how to get a comprehensive unique rank from the ranks, possibly conflicting with each other? In this paper, we propose a framework to rank multiple nonlinear filters using ranking vectors and voting fusion based on a single metric or multiple metrics. Illustrative examples show that this framework is very effective.

Emission source localization and sensor registration using received signal strength (RSS) measurements is investigated. Previous studies for RSS localization assume that the sensors receiving signals are bias free, which is not the case in practice. This issue is taken into consideration in this paper for the localization problem. To avoid non-convexity of the global optimization problem for the traditional maximum likelihood (ML) or least squares (LS) estimation, we present novel semidefinite programming methods, linear least squares (LLS) and constrained LS (CLS) methods by approximating and linearizing the original model. The methods are divided into two types: URSS and DRSS. The former estimates the source location and sensor bias simultaneously while the latter estimates the sensor bias after localizing the source. Numerical examples show that our proposed methods have good performance. Some of them are close to the Cramer-Rao Lower Bound (CRLB).