Passive source localization in wireless sensor networks (WSNs) is an important field of research with numerous applications in signal processing and wireless communications. One purpose of a WSN is to determine the position of a signal emitted from a source. This position is estimated based on received noisy measurements from sensors (anchor nodes) that are distributed over a geographical area. In most cases, the sensor positions are assumed to be known exactly, which is not always reasonable. Even if the sensor positions are measured initially, they can change over time. Due to the sensitivity of source location estimation accuracy with respect to the a priori sensor position information, the source location estimates obtained can vary significantly regardless of the localization method used. Therefore, the sensor position uncertainty should be considered to obtain accurate estimates. Among the many localization approaches, signal strength based methods have the advantages of low cost and simple implementation. The received signal energy mainly depends on the transmitted power and path loss exponent which are often unknown in practical scenarios. In this dissertation, three received signal strength difference (RSSD) based methods are presented to localize a source with unknown transmit power. A nonlinear RSSD-based model is formulated for systems perturbed by noise. First, an effective low complexity constrained weighted least squares (CWLS) technique in the presence of sensor uncertainty is derived to obtain a least squares initial estimate (LSIE) of the source location. Then, this estimate is improved using a computationally efficient Newton method. The Cramer-Rao lower bound (CRLB) is derived to determine the effect of sensor location uncertainties on the source location estimate. Results are presented which show that the proposed method achieves the CRLB when the signal to noise ratio (SNR) is sufficiently high. Least squares (LS) based methods are typically used to obtain the location estimate that minimizes the data vector error instead of directly minimizing the unknown parameter estimation error. This can result in poor performance, particularly in noisy environments, due to bias and variance in the location estimate. Thus, an efficient two stage estimator is proposed here. First, a minimax optimization problem is developed to minimize the mean square error (MSE) of the proposed RSSD-based model. Then semidefinite relaxation is employed to transform this nonconvex and nonlinear problem into a convex optimization problem. This can be solved e ciently to obtain the optimal solution of the corresponding semidefinite programming (SDP) problem. Performance results are presented which con rm the e ciency of the proposed method which achieves the CRLB. Finally, an extended total least squares (ETLS) method is developed for blind localization which considers perturbations in the system parameters as well as the constraints imposed by the relation between the observation matrix and data vector. The corresponding nonlinear and nonconvex RSSD-based localization problem is then transformed to an ETLS problem with fewer constraints. This is transformed to a convex semidefinite programming (SDP) problem using relaxation. The proposed ETLS-SDP method is extended to the case with an unknown path loss exponent. The mean squared error (MSE) and corresponding CRLB are derived as performance benchmarks. Performance results are presented which show that the RSSD-based ETLS-SDP method attains the CRLB for a sufficiently large SNR. / Graduate / 0544 / lohrasbi@uvic.ca

HMK Geodesi, GPS publicerades år 1996 och är fortfarande det regelverk som idag tillämpas vid statisk mätning med GNSS. Studien genomförs för att bidra med rekommendationer till nya HMK-Stommätning för statisk GNSS-mätning.   Studiens syfte var att undersöka baslinje- och sessionslängdens påverkan på lägesosäkerheten vid mätning av korta baslinjer. Eftersom studien skulle efterlikna mätning under praktiska förhållanden undersöktes baslinjelängder 0,7–100 km och sessionstider 20 min–6 h. Syftet var också att undersöka om lägesosäkerheten påverkas olika vid beräkning med de olika frekvenserna, L1, L1+L2 eller L3.   Två delstudier genomfördes i två olika geografiska områden. I Gävleområdet användes data från egna mätningar i kombination med data från en SWEPOS-station för beräkning av spridningen i position för korta baslinjer. I Göteborgsområdet har data erhållits från och beräknats mellan 14 SWEPOS-stationer. En felvektor har beräknats mellan stationens beräknade position i studien och en given position beräknad av SWEPOS.   I Gävleområdet var skillnaden i standardosäkerhet för koordinaterna mellan olika sessionstider mindre än 3 och 7 mm i plan respektive i höjd. För baslinjer upp till 5 km är spridningen i höjd i hälften av fallen mindre än i plan för frekvenserna L1, L1+L2 och L3. Vid längre sessioner gav frekvenserna likvärdiga resultat. I Göteborgsområdet ökade höjddifferensen i samband med baslinjelängden. Den tredimensionella avvikelsen för baslinjerna var 1–71 mm.   Lägesosäkerheten i plan påverkas inte nämnvärt av ökad baslinjelängd. Lägesosäkerheten i höjd blir större när baslinjelängden ökar. Till skillnad från tidigare studier ses ingen tydlig förbättring när sessionstiden ökar. / HMK Geodesy, GPS was published in 1996 and is still the regulations that currently apply to static measurement with GNSS. The study is conducted to provide recommendations for new HMK Control networks for static GNSS surveying.   The purpose of the study was to investigate how the baseline and session length influence the position uncertainty when measuring short baselines. A second purpose was to investigate whether there will be any difference in the position uncertainty when using different frequencies: L1, L1 + L2 or L3. The study investigates baseline lengths 0,7–100 km and session lengths 20 min–6 h. The study was designed to mimic measurements during practical conditions and investigate the position uncertainties that can be expected to be achieved by users.   Two sub-studies were conducted in two different geographical areas. In the Gävle area self-produced data was used combined with data from a SWEPOS station for calculating the spread in the position for short baselines. In the Gothenburg area the data was obtained from observations of known SWEPOS reference stations. An error vector was calculated between the station's estimated position of the study and a given position calculated by SWEPOS.   In the Gävle area the differences in standard uncertainty between different session lengths for the coordinates were less than 3 mm and 7 mm in plane and height. For baselines up to 5 km the spread in height in half of the cases was lower than in plane for the frequencies L1, L1+L2 and L3. During longer sessions the results for the different frequencies are equal. In the Gothenburg area the height differences increased when associated/combined/correlated with baseline length. The three-dimensional deviations of the base lines were 1–71 mm.   The position uncertainty in plane is not affected significantly by increased baseline length. Location Uncertainty in height becomes larger when baseline length increases. Unlike previous studies our study showed no clear improvement in position uncertainty when session length increases.