Spatial Field estimation from Samples taken at Unknown Locations generated by an Unknown Autoregressive Process

TL;DR

This paper proposes a method for estimating spatially bandlimited fields from noisy samples taken at unknown locations generated by an autoregressive process, demonstrating that the mean squared error decreases as the number of samples increases.

Contribution

It introduces a novel approach to field estimation using samples from an autoregressive model of intersample distances, accounting for correlated sampling locations in mobile sensing.

Findings

Mean squared error decreases as O(1/n) with the number of samples.

Sampling at unknown locations modeled by an autoregressive process is feasible for accurate field estimation.

The method effectively handles measurement noise and location uncertainty.

Abstract

Sampling of physical fields with mobile sensors is an upcoming field of interest. This offers greater advantages in terms of cost as often just a single sensor can be used for the purpose and this can be employed almost everywhere without sensing stations and has nominal operational costs. In a mobile sensing setup, the accurate knowledge of sampling locations may lead to a manifold increase in the costs. Moreover, the inertia of the moving vehicle constrains the independence between the intersample distances, making them correlated. This work, thus, aims at estimating spatially bandlimited fields from samples, corrupted with measurement noise, collected on sampling locations obtained from an autoregressive model on the intersample distances. The autoregressive model is used to capture the correlation between the intersample distances. In this setup of sampling at unknown sampling locations obtained from an autoregressive model on intersample distances, the mean squared error between the field and its estimated version has been shown to decrease as O($1/n$), where $n$ is the average number of samples taken by the moving sensor.