Communications in Information and Systems

Volume 14 (2014)

Number 1

A novel efficient homotopy continuation method in tracking

Pages: 57 – 78



Yueh-Cheng Kuo (Department of Applied Mathematics, National University of Kaohsiung, Taiwan)

Wen-Wei Lin (Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)


Tracking a moving object by Doppler effect is an important tool to locate the position and to estimate the velocity of a moving object. Suppose that we have $N(N \geqslant 6)$ observation stations which measure the relative speed of the moving object by Doppler effect. Theoretically, the corresponding movement of the moving object can be formulated by a system of $2N$ polynomials in $N+6$ unknowns. In this paper, we propose a novel simplification to reduce the original system to a system of $N-2$ polynomials in $4$ unknowns. Then using this simplified system we develop an efficient homotopy continuation method to trace the moving object. Numerical experiments show that the position and the velocity of the moving object can be solved efficiently and reliably by the homotopy continuation method.

Full Text (PDF format)