Abstract
Source localization using RSS (received signal strength) measurements has received considerable attention recently. However, there are few works focusing on the problem of positioning multiple directional sources. To provide a benchmark for evaluating localization algorithms, this paper derives the Cramer-Rao lower bounds (CRLB) for estimating locations, orientations, transmit powers, beam widths of multiple directional sources and the path loss exponent (PLE) of the environment. Meanwhile, in order to facilitate the computation and expression, we also present the relationship of the CRLB among different quantities of sources when estimating their locations and orientations. Given that the maximum likelihood (ML) estimator for the localization problem is highly non-convex and non-linear, this paper proposes an Expectation Maximization (EM) like algorithm to estimate the multiple parameters of each of the sources iteratively. Moreover, the complexity of the presented ML-EM algorithm is significantly reduced via linear representation among the parameters to be estimated. Numerical and simulation results demonstrate the performance of the proposed methods and the derived bounds in terms of estimation error, noise robustness and number of sources.
Highlights
Source localization is a fundamental problem which has found many applications in the global positioning system, cognitive radio networks and wireless sensor networks (WSNs) [1]
On the other hand, considering that the sources and sensors may be randomly located in the region of interest (ROI) and the Cramer-Rao lower bounds (CRLB) results are averaged over multiple experiments, we have
As opposed to previous related work, this paper considered estimating unknown parameters of multiple directional sources based on received signal strength (RSS) measurements
Summary
Source localization is a fundamental problem which has found many applications in the global positioning system, cognitive radio networks and wireless sensor networks (WSNs) [1]. Less accurate than the localization adopting measurements of TOA, TDOA or AOA, the simple RSS based methods which have low requirements for devices are more suitable for WSNs, due to the fact that the inexpensive sensors in the WSNs could only collect the superimposed signal strength of the sources [3]. In our earlier work [27], three feasible methods were proposed for estimating the positions, orientations and transmit powers of multiple directional targets, with the derived Cramer-Rao lower bounds (CRLB) to characterize their estimation performance. This paper is the first to derive the CRLB for estimating parameters (i.e. locations, orientations, transmit powers, beam widths) of multiple directional sources in the region of interest (ROI) and the PLE of the environment;. Ωdenotes an estimate of ω. ρ, ρ, · · · , ρ means that the ω number of ρ in the vector/matrix is ω
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