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

Sampling 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. Index Terms Additive white noise, autoregressive model, nonuniform sampling, signal reconstruction, signal sampling, wireless sensor networks.