State estimation of a moving frequency source from observations at multiple receivers

TL;DR

This paper introduces a direct, polynomial-based method using homotopy continuation to estimate the position and velocity of a moving frequency source from multiple receiver observations, applicable to acoustic and electromagnetic signals.

Contribution

It presents a novel polynomial equation approach for source localization that works without prior frequency knowledge, using data from six or seven receivers.

Findings

Six receivers suffice for known frequency estimation.

Seven receivers are needed when the frequency is unknown.

Method successfully applied to acoustic and satellite signal scenarios.

Abstract

The task of position and velocity estimation of a moving transmitter (with either a known or unknown frequency) is a common problem arising in many different application domains. Based on the Doppler effect, this work presents a direct solution using only the frequency measured by a multitude of receivers with a known state. A natural rewriting of the problem as a system of polynomial equations allows for the use of homotopy continuation to find the global solution without any a priori information about the frequency source. We show that the data from six or seven receivers is sufficient in case of known or unknown frequency, respectively. After a brief development of the mathematics, two simple examples are provided: (1) position and velocity estimation of a vocalizing dolphin emitting an acoustic signal and (2) initial orbit determination of a satellite emitting an electromagnetic signal.