SDP Relaxation Methods for RSS/AOA-Based Localization in Sensor Networks

Abstract

With the fast development of new array technology and intelligent antenna, it is easier to obtain angle of arrival (AOA) measurements. Hybrid received signal strength (RSS) and AOA measurement techniques are proposed for the position computing in sensor networks. By converting the measurement equations and relaxing the optimization function, range-based square semidefinite programming (RLS-SDP) and squared range-based square semidefinite programming (SRLS-SDP) algorithms are put forward to obtain the source position estimate by considering the transmit power to be known or unknown. The proposed RLS-SDP and SRLS-SDP algorithms provide accurate solution to the source position estimate and avoid the initialization process of numerical calculation. The simulations show that the proposed RLS-SDP and SRLS-SDP algorithms perform better than the linear estimator and provide the accuracy performance which is very close to the Cramér-Rao Lower Bound (CRLB) of position estimation. The proposed SRLS-SDP algorithm shows its advantages in the computational complexity compared with the RLS-SDP, since the complexity of SRLS-SDP is independent of the number of anchor nodes. INDEX TERMS Localization, received signal strength, angle of arrival, semidefinite programming.

An SOCP Estimator for Hybrid RSS and AOA Target Localization in Sensor Networks

“…Table 1 summarizes the complexity analysis for the considered methods. It is worth mentioning that the estimators in [ 24 , 27 ] are composed of two iterations, and therefore, their complexities double, which also affects their execution time. Note that the ECWLS method is included here for comparison since it is considered here as the state-of-the-art method for the problem of interest in the case of known transmit power, but its generalization to the case where the transmit power is unknown is not straightforward.…”

“…Many advances related to RSS-AOA-based localization have been made recently, in both non-cooperative [ 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 ] (where targets are allowed to communicate with anchors exclusively) and cooperative networks [ 22 , 29 ] (where targets can communicate with any sensor within their communication range). In [ 21 ], the authors employed an unbiased constant which takes advantage of the link quality through the path loss and angle noise variance to solve the non-cooperative problem by means of weighted linear least squares.…”

“…The authors employed quantized values of analogue RSS measurements to jointly estimate the location of the target and the two aforementioned channel components, by first setting the two parameters to fixed values and estimating the location, after which an update of the parameters was performed. In [ 27 ], the authors took two different approaches based on a range-based least squares (RLS) and a squared range-based least squares (SRLS) to derive two distinct estimators based on semidefinite programming (SDP) relaxation for both cases of known and unknown transmit power. Although the proposed SDP estimators work well even in noisy environments, their computation complexity is very high, and for the case of unknown transmit power, the authors actually solve two SDP problems, which results in an increased execution time of the algorithms.…”

“…The works in [ 12 , 15 , 21 , 22 , 23 , 24 , 26 , 27 , 28 , 30 ] considered angle measurement noise to be a Gaussian random variable. However, the von Mises distribution is a more appropriate distribution to model angular noise [ 31 ].…”

Unbalanced Hybrid AOA/RSSI Localization for Simplified Wireless Sensor Networks

“…While the ML algorithm achieves great accuracy, it suffers from severe computational complexity and the global solution is not guaranteed [6]. To reduce complexity while obtaining a comparable accuracy to ML, semidefinite programming and second-order cone programming relaxation techniques have been proposed in [12][13][14][15]. However, the computational complexity of these algorithms grows significantly with the network size [5].…”