Algorithm development for source localization in wireless sensor networks
Student thesis: Doctoral Thesis
Related Research Unit(s)
Source localization has been one of the fundamental and important problems in a variety of fields ranging from radar, sonar, and, navigation, to telecommunications, mobile communications, and wireless sensor networks. A sensor with a known position is called the anchor and a sensor with an unknown position is named the source. In this thesis, several algorithms are devised to locate the source(s) with the use of the noisy distance measurements between the source(s) and anchors. Locating a source with time-difference-of-arrival (TDOA) measurements, which is one of the standard measurements for positioning, is investigated in many research works. One of the TDOA-based positioning algorithms, the linear least squares (LLS) technique, is widely used because of its computational efficiency. Two-step weighted least squares (WLS) and constrained WLS (CWLS) are two common LLS schemes where an additional variable is introduced to obtain linear equations. However, they both have the same measurement matrix that becomes ill-conditioned when the sensor geometry is a uniform circular array and the source is close to the array center. In this thesis, a new CWLS estimator is proposed to circumvent this problem. The main strategy is to separate the source coordinates and the additional variable to different sides of the linear equations where the latter is first solved via a quadratic equation. In doing so, the matrix to be inverted has a smaller condition number than that of the conventional LLS approaches, so that it can provide a superior performance in different geometry settings. Numerical examples are also included to evaluate the proposed location estimator by comparing with the existing two-step WLS and CWLS algorithms as well as the Cramér-Rao lower bound (CRLB). Employing received signal strength (RSS) measurements, which utilizes the signal strength received at an array of spatially separated sensors, is considered to be more cost effective than other measurements in hardware. Therefore, being able to locate a source using RSS measurements in an accurate and low-complexity manner is desirable. Assuming that the source transmit power is known, a two-step WLS estimator for RSS-based positioning is devised by utilizing the mean and variance of the squared distance estimates according to the RSS measurements. The first step estimator is a best linear unbiased estimator without considering the relationship between unknown parameters while the second one is its improved version by exploiting the known relationship between the parameter estimates. This algorithm is then extended to unknown path-loss factor case with relaxation technique. Furthermore, given that the transmit power is unknown, the differential RSS information is employed to devise a computationally attractive localization method based on the two-step WLS approach. The main ingredients in the first step development are to obtain the unbiased estimates of the ratios of squared ranges and the second step is to exploit the relationship between the extra variable and the source location. Theoretical performance analysis of the proposed algorithms is also produced to evaluate their statistical properties. In many scenarios, there is more than one source to be located, so it is desirable to investigate algorithms to estimate the positions of multiple sources for RSS-based positioning problems. Assuming that the transmit powers are unknown, a two-step WLS algorithm is devised with non-collaborative RSS measurements in which only the one-way distances between sources and anchors are used. This two-step WLS method is different from the proposed one in the single source case; the former utilizes the RSS measurements directly while the latter employs the differential RSS information. Moreover, when the path-loss factors are unknown, two nonlinear least squares (NLS) algorithms are devised. The first one is the maximum-likelihood (ML) method which is directly devised for all unknown parameters while the second algorithm is a combination of the LLS and ML techniques. The nuisance parameters, transmit powers and path-loss factors, are first removed from the RSS measurements using the separable LLS technique, then the resulting problem is a non-linear function of the source positions and can be handled by the ML principle. Numerical examples show that the second algorithm has a better performance than the first one. Multidimensional scaling (MDS) algorithm, which transforms the pair-wise distance information into the relative coordinates of sensors, is one of the collaborative schemes in which all pair-wise distances between sources and sources, sources and anchors, anchors and anchors are employed. Two weighted MDS (WMDS) methods are proposed to locate the sources for the scenarios of known and unknown transmit power assuming that the path loss factors are known. By utilizing the unbiased estimates of the squared ranges, a WMDS algorithm is devised for known transmit power case, while the other WMDS algorithm is devised for unknown transmit power case with the use of unbiased estimates of the ratios of squared distances and of the selected reference squared distance. Simulation results show that these two proposed WMDS algorithms are comparable to their corresponding CRLBs at sufficiently small noise conditions.
- Wireless localization, Wireless sensor networks