Abstract
Received-signal-strength (RSS)-based localization has received widespread attention recently. Due to the simple acquisition of the RSS measurements, the adequate inexpensive sensors in sensor networks are capable of providing the information needed for the positioning of multiple target sources. However, few studies have focused on the RSS-based localization of multiple directional sources that are common in reality. Based on the deduced parametric Optimal Maximum Likelihood (OML) solution, this paper proposes three new grid search-based algorithms, namely Alternating Projection (i.e., OMLAP) algorithm, Expectation-Maximization like (i.e., OMLEM) algorithm, and Particle Swarm Optimization (i.e., OMLPSO) algorithm. They can be utilized for estimating the transmit powers, locations, and orientations of multiple directional sources. Combining the interpolation process and proposed power threshold setting method, the search space is obviously reduced. Moreover, the corresponding Cramer-Rao lower bounds (CRLB) are also derived to characterize the estimation accuracy of the algorithms. Both the scenarios with different Signal-to-Noise Ratios (SNRs) and the scenarios with different sensor quantities are considered in the simulation, and the results demonstrate the effectiveness of the proposed algorithms and indicate that they are suitable for the parameter estimation of multiple directional sources.
Highlights
Localization plays an important role in many systems, such as wireless networks, cognitive radio networks, the global positioning system and wireless sensor networks (WSNs) [1], [4]
As typically we have N < IAP · LOnum · ORnum · K 2, the complexity of Algorithm 1 can be expressed as O(IAP · LOnum · ORnum · K 2M 2), which is significantly lower than the complexity of the aforementioned brute-force search method especially when the number (i.e. K ) of directional sources is large
For quick and easy estimation of the parameters of the directional sources, we propose to use the Particle Swarm Optimization (PSO) algorithm [28] which exerts the correlation characteristics between the randomly initialized solutions, it has a faster solving speed compare to the brute-force method under the premise of obtaining satisfactory estimation results
Summary
Localization plays an important role in many systems, such as wireless networks, cognitive radio networks, the global positioning system and wireless sensor networks (WSNs) [1], [4]. This assumption may lack rationality, as many devices nowadays adopt spatial diversity through non-uniform antenna gain patterns [11] This paper removes this assumption, and considers estimating multiple parameters including the locations, transmit powers and orientations of multiple directional sources in the ROI. Towards this end, we first formulate the parametric Optimal ML solution to the estimation problem, based on which we respectively propose the AP algorithm, EM like algorithm and Particle Swarm Optimization (PSO) algorithm (we separately call them as OMLAP, OMLEM and OMLPSO algorithms).
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