Fundamental Limits of Self-localization for Cooperative Robotic Platforms Using Signals of Opportunity

Abstract

A fundamental problem in robotic applications is the localization of the robots. We consider the problem of global self-localization for a robotic platform with autonomous robots using signals of opportunity (SOOP). We first give a brief overview of the state-of-the-art in robotic localization using SOOP, and then propose a scheme that requires minimal prior environmental information, no pre-configuration, and only loose synchronization between the robots. To further analyze the potential for the use of SOOP in robotic localization and to investigate the effect of clock asynchronism, we derive an analytical expression for the equivalent Fisher information matrix of the Cramér-Rao lower bound (CRLB). The derivation is based on the received signal waveform, and allows us to analyze the contributions of various factors to the localization accuracy. The CRLB provides a valuable guideline for the design of a robotic platform in which a desired level of localization accuracy is to be achieved. We also analyze the distortions in the time difference of arrival and frequency difference of arrival measurements caused by different clock offsets and skews at the robots. We propose a robust algorithm to estimate robot location and velocity, which mitigates the clock biases. Simulation results suggest that our proposed algorithm approaches the CRLB when clock skews have small standard deviations.

Anchor-Aided Joint Localization and Synchronization Using SOOP: Theory and Experiments

“…(ii) After recording signal samples from the same set of beacons in each observation period, the anchor forwards its signal samples to the receiver, which utilizes them to compute TDOA and FDOA. A similar scheme was proposed in [17], which aims to localize a group of automated robots. In this paper, we focus on how to design a sequential algorithm to jointly track the receiver and estimate its clock drift parameters.…”

“…Substituting p y (l) x (l) and p x (l) x (l−1) into ( 17) and (18), we can obtain the estimation of the state x (l) in the lth time slot as x(l) = max x (l) p x (l) y (1:l) . The recursive relations (17) and (18) forms the basis for the optimal Bayesian solutions. When the integration cannot be obtained in closed form for general distributions, it can be solved by numerical methods such as particle filtering [45].…”