A Closed-form Localization Method Utilizing Pseudorange Measurements from Two Non-synchronized Positioning Systems

TL;DR

This paper introduces a low-complexity, closed-form dual-system localization method that effectively handles clock offsets between two non-synchronized GNSS systems, achieving near-optimal accuracy and outperforming existing approaches.

Contribution

The paper presents a novel closed-form localization technique for dual GNSS systems that simplifies computation, handles clock offsets, and attains CRLB accuracy without requiring initialization.

Findings

Achieves CRLB in far-field conditions with small noise

Outperforms iterative methods in accuracy and complexity

Validated with real GPS and BDS data

Abstract

In a time-of-arrival (TOA) or pseudorange based positioning system, user location is obtained by observing multiple anchor nodes (AN) at known positions. Utilizing more than one positioning systems, e.g., combining Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS), brings better positioning accuracy. However, ANs from two systems are usually synchronized to two different clock sources. Different from single-system localization, an extra user-to-system clock offset needs to be handled. Existing dual-system methods either have high computational complexity or sub-optimal positioning accuracy. In this paper, we propose a new closed-form dual-system localization (CDL) approach that has low complexity and optimal localization accuracy. We first convert the nonlinear problem into a linear one by squaring the distance equations and employing intermediate variables. Then, a weighted least squares (WLS) method is used to optimize the positioning accuracy. We prove that the positioning error of the new method reaches Cramer-Rao Lower Bound (CRLB) in far field conditions with small measurement noise. Simulations on 2D and 3D positioning scenes are conducted. Results show that, compared with the iterative approach, which has high complexity and requires a good initialization, the new CDL method does not require initialization and has lower computational complexity with comparable positioning accuracy. Numerical results verify the theoretical analysis on positioning accuracy, and show that the new CDL method has superior performance over the state-of-the-art closed-form method. Experiments using real GPS and BDS data verify the applicability of the new CDL method and the superiority of its performance in the real world.