Distributed signal processing techniques for classification of objects are studied assuming knowledge of sensor measurement statistics. The spatio-temporal signal field generated by an object is modeled as a bandlimited stationary ergodic Gaussian field. The model suggests a simple abstraction of correlation between node measurements: it partitions the network into disjoint spatial coherence regions over which the signal remains strongly correlated, whereas the signal in distinct coherence regions is approximately uncorrelated. The size of coherence regions is determined by spatial signal bandwidths. It is shown that this partitioning imposes a structure on optimal distributed classification algorithms that is naturally suited to the communication constraints of the network: local high-bandwidth exchange of feature vectors within each coherence region to improve the measurement signal-to-noise ratio (SNR), and global low-bandwidth exchange of local decisions across coherence regions to stabilize the inherent variability in the signal. Classifier performance is analyzed for both soft and hard decision fusion across coherence regions assuming noise-free, as well as noisy communication links between nodes. Under mild conditions, the probability of error of all classification schemes (soft, hard, noisy) decays exponentially to zero with the number of independent node measurements-the error exponent depends on both the measurement and communication SNRs and decreases from soft to hard to noisy fusion. Numerical results based on real data illustrate the remarkable advantage of multiple sensor measurements in distributed decision making.

Sensor networks provide virtual snapshots of the physical world via distributed wireless nodes that can sense in different modalities, such as acoustic and seismic. Classification of objects moving through the sensor field is an important application that requires collaborative signal processing (CSP) between nodes. Given the limited resources of nodes, a key constraint is to exchange the least amount of information between them to achieve the desired performance. Two main forms of CSP are possible. Data fusion - exchange of low dimensional feature vectors - is needed between correlated nodes, in general, for optimal performance. Decision fusion $exchange of likelihood values - is sufficient between independent nodes. Decision fusion is generally preferable due to its lower communication burden. We study the CSP of multiple node measurements, each modeled as a Gaussian signal vector (corresponding to the target class) corrupted by additive white Gaussian noise. The measurements are partitioned into groups. The signal components within each group are perfectly correlated whereas they vary independently between groups. Three classifiers are compared: the optimal maximum likelihood classifier; a data averaging classifier that treats all measurements as correlated; a decision fusion classifier that treats them all as independent. The performances of the three CSP classifiers are compared using analytical and numerical results based on real data. These indicate that the sub-optimal decision fusion classifier, that is most attractive in the context of sensor networks, is also a robust choice from a decision theoretic viewpoint.