A new iterative algorithm for geolocating a known altitude target using TDOA and FDOA measurements in the presence of satellite location uncertainty

AbstractThis paper considers the problem of geolocating a target on the Earth surface whose altitude is known previously using the target signal time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements obtained at satellites. The number of satellites available for the geolocation task is more than sufficient and their locations are subject to random errors. This paper derives the constrained Cramér-Rao lower bound (CCRLB) of the target position, and on the basis of the CCRLB analysis, an approximately efficient constrained maximum likelihood estimator (CMLE) for geolocating the target is established. A new iterative algorithm for solving the CMLE is then proposed, where the updated target position estimate is shown to be the globally optimal solution to a generalized trust region sub-problem (GTRS) which can be found via a simple bisection search. First-order mean square error (MSE) analysis is conducted to quantify the performance degradation when the known target altitude is assumed to be precise but indeed has an unknown but deterministic error. Computer simulations are used to compare the performance of the proposed iterative geolocation technique with those of two benchmark algorithms. They verify the approximate efficiency of the proposed algorithm and the validity of the MSE analysis

Source localization using TDOA with erroneous receiver positions

The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.Title from title screen of research.pdf file viewed on (May 22, 2006)Includes bibliographical references.Vita.Thesis (Ph. D.) University of Missouri-Columbia 2005.Dissertations, Academic -- University of Missouri--Columbia -- Electrical engineering.[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