Localization of a Moving Source by Frequency Measurements

• Published in: IEEE transactions on signal processing Vol. 68; p. 1
• Main Authors: Ahmed, Musaab M., Ho, Dominic K. C., Wang, Gang
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-01-2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Closed form solutions; Computer simulation; Cramer-Rao bounds; Doppler effect; Exact solutions; Localization; Lower bounds; Optimization; Polynomials; Random noise
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2020.3016133

This paper investigates the localization of a moving source in position and velocity, by observing the emitted frequency from the source that is subject to the Doppler shift effect at a number of stationary sensors. Previous attempts rely on exhaustive grid search or numerical polynomial optimization to obtain a solution. We shall propose a constrained optimization to formulate the localization problem, which enables the problem to be solved efficiently using the linear optimization method to reach a closed-form solution or the semi-definite relaxation technique to achieve a noise resilient estimate. The algorithms are developed for the single-time and multiple-time observations. The presence of errors in the source frequency and the sensor positions are considered. The non-cooperative scenario where the source frequency is completely not known is also addressed. Analysis validates the proposed closed-form solution in reaching the Cramer-Rao Lower Bound accuracy under Gaussian noise over the small error region. Simulations support the performance of the proposed solutions.