2023/08/09 by Michela Mancini, Mancini, Michela, Anton Leykin +3
Computer Science · Engineering · #14Q00 #65H20 #Advanced Adaptive Filtering Techniques #Algebraic Geometry (math.AG) #Control Systems and Identification #FOS: Electrical engineering #FOS: Mathematics #Signal Processing (eess.SP) #Target Tracking and Data Fusion in Sensor Networks #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2308.05223
openalex publication_date 2023/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.