Research On Passive Localization And Tracking Algorithms Based On TDOA And FDOA

In the last decades, passive source localization and tracking has been widely used in the fields of radar, sonar, navigation, wireless communication, electronic warfare, sensor networks, and many others. Frequently used measurements for passive source localization and tracking tasks include angle of arrival(AOA), time difference of arrival(TDOA), phase rate of change(PRC) and frequency difference of arrival(FDOA). Nevertheless, it is not straightforward to compute the source state parameter since the localization and tracking problems based on these parameters are typically nonlinear. This dissertation mainly focuses on the source localization and tracking utilizing TDOA and FDOA measurements. It elaborates on the principle of TDOA and FDOA localization, system model, sensor location uncertainties, tracking algorithm, and develops some efficient solutions. The research strongly supports the passive localization and tracking engineering using multiple observers. Specifically, the major contributions of this thesis include the followings:1. A new modified Newton(Mod-Newton) algorithm is proposed to minimize the constrained weighted least-squares(CWLS) problem. Firstly, the nonlinear TDOA equations are transformed into a set of pseudo-linear ones of the emitter position, and then these pseudo-linear equations are exploited to formulate a constrained weighted least-squares minimization problem. The cost function in the CWLS minimization problem has a higher performance than the one based on the likelihood-function. Finally, the Mod-Newton method is applied to obtain the emitter position. On one hand, the Newton method is often unstable since its Hessian matrix is sometimes indefinite or close to singular, the Mod-Newton method utilizes the eigenvalue modification to address this problem. On the other hand, an appropriate iteration step size is obtained through using quadratic polynomial fitting technique for the one-dimensional optimization to reduce the number of iterations.2. When relative motion between the source and the observers exists, the passive source localization using TDOA measurements obtained from multiple time instants is studied. An efficient closed-form solution named two-step weighted least-squares(TSWLS) method is developed to calculate the source state parameter using TDOA measurements at different time instants simultaneously. The first step transforms the nonlinear TDOA equations into a set of pseudo-linear ones by introducing auxiliary variables and then uses the weighted least-squares(WLS) estimator to obtain the initial emitter state parameter estimation. The second stage refines the emitter state parameter estimation by exploiting the relationship between the emitter state parameter and the auxiliary parameters. Simulation study shows that the emitter state parameter estimation accuracy of the TSWLS method approaches the Cramer-Rao lower bounds(CRLB) for low TDOA measurement noise levels.3. Receiver positions generally include random errors, which can degrade significantly the source localization accuracy. The influence of the random sensor location errors on the source localization accuracy is investigated by comparing the CRLB of the source position with and without sensor location errors. Inspired by the idea of CWLS minimization, we construct two new cost functions and utilize the Gauss-Newton method to compute the source position in an iterative way. Simulation results demonstrate the effectiveness of the cost functions. Moreover, an efficient closed-form weighted multidimensional scaling analysis(WMDS) method based TDOA localization algorithm with sensor location errors is proposed to address the drawback of the conventional MDS method. The orthogonality between the column space of position coordinates matrix and the nullspace of the scalar product matrix is exploited to formulate the pseudo-linear equations and a novel weighting matrix is designed and used to suppress the sensor position errors, which makes the WMDS method robust to high receiver position error levels.4. The moving passive source localization using TDOA and FDOA measurements is studied. By introducing two auxiliary variables, the highly nonlinear TDOA and FDOA based source localization problem is converted into a CWLS minimization problem. The bi-iterative method is then used to estimate the source location and velocity alternately. This brings two benefits: firstly, it has a relatively low computational complexity in computing the matrix inversion; secondly, the linearity of the FDOA localization equation with respect to the source velocity is exploited. The proof of convergence of the bi-iterative method is provided. The extension of the bi-iterative method to the case where the sensor locations and velocities are subject to random errors is also presented. Furthermore, a weighted Multidimensional scaling(WMDS)-based source localization using TDOA and FDOA measurements with sensor location errors is proposed. A novel weighting matrix is formulated to suppress the sensor position and velocity errors, which enhances the robustness of the WMDS algorithm for high receiver location error levels.5. The problem of mobile target localization and tracking based on TDOA measurements is studied. By analyzing the defects of the Maximum Likelihood(ML) estimator and the extended Kalman filter(EKF), we propose several mobile target localization and tracking algorithms based on the combination of the ML estimator and the EKF. Two novel cost functions with respect to the emitter state parameter are formulated by combining the prediction step or the observation update of the EKF and the ML estimator, and the Gauss-Newton algorithm is applied to estimate the emitter state parameter. On one hand, the emitter state parameter estimates obtained from the prediction step and the observation update are closer to the true values than the WLS solution, therefore, they can be used as initial values for the Gauss-Newton algorithm. On the other hand, the emitter state parameter estimates obtained by minimizing the newly developed cost functions mitigate the error propagation in the EKF and enhance the localization and tracking performance. Simulation results show the superior performance of the proposed algorithms.