Source localization using TDOA with erroneous receiver positions
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Source localization has been an active research for several years. It has applications in many areas such as geolocation and mobile user location. Various methodologies have been proposed to passively localize an emitting signal source. One of the most popular techniques is to use the Time Difference of Arrival (TDOA) measurements. TDOA localization technique determines the source position by examining the time differences at which the source signal arrives at multiple spatially separated sensors. There are several methods to solve the TDOA source location problem, and two of the widely known methods are the Maximum Likelihood method and the Taylor-series method. Those methods assume that the sensor positions are exactly known, and this assumption may not be the case in practice. The performance of these methods degrades significantly when the receiver positions have error. The estimation of the of the source location with sensor position uncertainty has been investigated for over a decade. While most of the previous research has been conducted on finding the bearing angle or the angle of arrival of multiple sources in the presence of sensor position noise, noise, in this research, the objective is to locate the exact position of a source in three dimensional space using TDOA measurements when there are random errors in the receiver positions. In this research, three methods are proposed to estimate the source position from TDOA measurements when the receiver positions have random errors. The first method is an extended work from Chan and Ho's work. Chan and Ho's method uses two-stage Least Square (LS) minimization. They introduce an auxiliary variable and solve the source position together with the auxiliary variable using linear LS minimization. The information in the auxiliary variable is then included to the location estimate through another LS minimization to improve accuracy. The first method includes the sensor position error power into a weighting matrix and uses it to improve the accuracy of the source location estimate. The second method consists of three steps. The first step is to estimate the source location with the noisy receiver positions. In the second step, the estimated source position is used to reduce the noise in the receiver positions in order to obtain more accurate positions of the receivers. And in the last step, the source is estimated again using the improved receiver positions from the second step. The source location estimate will be more precise due to better knowledge of receiver positions. The second and the third steps can be repeated several times to obtain even more accurate source location. The third method is based on the Taylor-series method and jointly estimates both source and receiver positions simultaneously. Both the first and the second proposed method utilize the weighted LS minimization to obtain the source and receiver positions and do not involve any linear approximation. Hence, they are computationally attractive and do not have the divergence and initialization problems. For the third method, one deficiency is that it requires a good initial solution guess close to the true solution to begin with in order to ensure convergence. In any case, the divergence behavior can often be detected so that reinitialization can be made. This researach also investigates the effect of receiver position errors to the accuracy of source location estimate in terms of the CRLB and the MSE. The observation confirms that the uncertainty in the receiver position did degrade an estimator's performance. In addition, this research also includes the study of the effect of the choice of reference receiver in the presence of unequal receiver noise power. The study indicates that CRLB is independent of the choice of the reference receiver. Nevertheless, the performance of the proposed closed form solutions is affected by choice of the reference receiver in near-field case, but not the far-field case.
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