Delay and Doppler Induced Direct Tracking by Particle Filter

The geolocation and tracking of a moving transmitter using receivers mounted on stationary or moving platforms is considered. Two-step conventional methods measure time difference of arrivals (TDOA) and differential Doppler in the first step, and in the second step use these measurements for geolocation and tracking. We explore a particle filter that uses the received radio signal directly in order to determine the location and velocity of the transmitter. Two algorithms are derived for the case of unknown deterministic signals and for the case of unknown Gaussian signals. In addition we derive recursive performance bounds for the two cases. The proposed methods show better performance than two-step methods at low signal-to-noise ratio (SNR) values and achieve the performance bound at high SNR values.

[1]  Branko Ristic,et al.  Beyond the Kalman Filter: Particle Filters for Tracking Applications , 2004 .

[2]  Darko Musicki,et al.  Mobile Emitter Geolocation and Tracking Using TDOA and FDOA Measurements , 2010, IEEE Transactions on Signal Processing.

[3]  Calyampudi Radhakrishna Rao,et al.  Linear Statistical Inference and its Applications , 1967 .

[4]  John S. Baras,et al.  On the convergence of the inverses of Toeplitz matrices and its applications , 2003, IEEE Trans. Inf. Theory.

[5]  K. C. Ho,et al.  Geolocation of a known altitude object from TDOA and FDOA measurements , 1997, IEEE Transactions on Aerospace and Electronic Systems.

[6]  Benjamin Friedlander,et al.  On the Cramer-Rao bound for time delay and Doppler estimation , 1984, IEEE Trans. Inf. Theory.

[7]  M. Kupperman.  Linear Statistical Inference and Its Applications 2nd Edition (C. Radhakrishna Rao) , 1975 .

[8]  Thomas L. Marzetta,et al.  Detection, Estimation, and Modulation Theory , 1976 .

[9]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[10]  Simon J. Godsill,et al.  On sequential Monte Carlo sampling methods for Bayesian filtering , 2000, Stat. Comput..

[11]  H. V. Trees.  Detection, Estimation, And Modulation Theory , 2001 .

[12]  P. Chestnut.  Emitter Location Accuracy Using TDOA and Differential Doppler , 1982, IEEE Transactions on Aerospace and Electronic Systems.

[13]  Seymour Stein.  Differential delay/Doppler ML estimation with unknown signals , 1993, IEEE Trans. Signal Process..

[14]  D. Harville.  Matrix Algebra From a Statistician's Perspective , 1998 .

[15]  Jun S. Liu,et al.  Sequential Imputations and Bayesian Missing Data Problems , 1994 .

[16]  Nando de Freitas,et al.  The Unscented Particle Filter , 2000, NIPS.

[17]  Ehud Weinstein,et al.  Estimation of differential Doppler shifts , 1979 .

[18]  Thia Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation: Theory, Algorithms and Software , 2001 .

[19]  Carlos H. Muravchik,et al.  Posterior Cramer-Rao bounds for discrete-time nonlinear filtering , 1998, IEEE Trans. Signal Process..

[20]  K. C. Ho,et al.  An accurate algebraic solution for moving source location using TDOA and FDOA measurements , 2004, IEEE Transactions on Signal Processing.

[21]  S. Stein.  Algorithms for ambiguity function processing , 1981 .

[22]  Anthony J. Weiss,et al.  Localization of Narrowband Radio Emitters Based on Doppler Frequency Shifts , 2008, IEEE Transactions on Signal Processing.

[23]  Anthony J. Weiss,et al.  Tracking of a moving emitter based on delay and Doppler shift using a particle filter , 2010, 2010 IEEE 26-th Convention of Electrical and Electronics Engineers in Israel.

[24]  Robert M. Gray,et al.  Toeplitz and Circulant Matrices: A Review , 2005, Found. Trends Commun. Inf. Theory.