Theory and design of multirate sensor arrays

This paper studies the basic design challenges associated with multirate sensor arrays. A multirate sensor array is a sensor array in which each sensor node communicates a low-resolution measurement to a central processing unit. The objective is to design the individual sensor nodes and the central processing unit such that, at the end, a unified high-resolution measurement is reconstructed. A multirate sensor array can be modeled as an analysis filterbank in discrete-time. Using this model, the design problem is reduced to solving the following two problems: a) how to design the sensor nodes such that the time-delay of arrival (TDOA) between the sensors can be estimated and b) how to design a synthesis filterbank to fuse the low-rate data sent by the sensor nodes given the TDOA? In this paper, we consider a basic two-channel sensor array. We show that it is possible to estimate the TDOA between the sensors if the analysis filters incorporated in the array satisfy specific phase-response requirements. We then provide practical sample designs that satisfy these requirements. We prove, however, that a fixed synthesis filterbank cannot reconstruct the desired high-resolution measurement for all TDOA values. As a result, we suggest a fusion system that uses different sets of synthesis filters for even and odd TDOAs. Finally, we use the H_∞ optimality theory to design optimal synthesis filters.