Basis construction for range estimation by phase unwrapping

TL;DR

This paper introduces a new method for constructing a basis for range estimation via phase unwrapping using multiple wavelengths, improving accuracy without the need for pairwise relatively prime wavelengths.

Contribution

It provides an explicit basis construction for the lattice in range estimation that does not require the wavelengths to be pairwise relatively prime.

Findings

Significant accuracy improvements with non-relatively prime wavelengths

Explicit basis construction for a broader class of wavelengths

Enhanced range estimation precision through new basis methods

Abstract

We consider the problem of estimating the distance, or range, between two locations by measuring the phase of a sinusoidal signal transmitted between the locations. This method is only capable of unambiguously measuring range within an interval of length equal to the wavelength of the signal. To address this problem signals of multiple different wavelengths can be transmitted. The range can then be measured within an interval of length equal to the least common multiple of these wavelengths. Estimation of the range requires solution of a problem from computational number theory called the closest lattice point problem. Algorithms to solve this problem require a basis for this lattice. Constructing a basis is non-trivial and an explicit construction has only been given in the case that the wavelengths can be scaled to pairwise relatively prime integers. In this paper we present an explicit construction of a basis without this assumption on the wavelengths. This is important because the accuracy of the range estimator depends upon the wavelengths. Simulations indicate that significant improvement in accuracy can be achieved by using wavelengths that cannot be scaled to pairwise relatively prime integers.