Distributed sensor systems composed of spatially distributed micro sensor nodes have been proposed for large scale monitoring applications. In these systems, nodes aggregate their sensor data to provide real time information about the underlying state. To extend the lifetime each node of the system has to limit the complexity of the sequential fusion algorithm. In this paper we derive optimal likelihood quantization rules for maximizing sequential detection performance. The resulting sequential detection algorithm is in the form of a finite state machine ideal for implementation in low complexity/low power devices.Index Terms-Low power signal processing, Quantized Likelihood, Sequential tests with finite memory

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Sequential hypothesis testing is a desirable decision making strategy in any time sensitive scenario. Compared with fixed sample-size testing, sequential testing is capable of achieving identical probability of error requirements using less samples in average. For a binary detection problem, it is well known that for known density functions accumulating the likelihood ratio statistics is time optimal under a fixed error rate constraint. This paper considers the problem of learning a binary sequential detector from training samples when density functions are unavailable. We formulate the problem as a constrained likelihood ratio estimation which can be solved efficiently through convex optimization by imposing Reproducing Kernel Hilbert Space (RKHS) structure on the log-likelihood ratio function. In addition, we provide a computationally efficient approximated solution for large scale data set. The proposed algorithm, namely Wald-Kernel, is tested on a synthetic data set and two real world data sets, together with previous approaches for likelihood ratio estimation. Our empirical results show that the classifier trained through the proposed technique achieves smaller average sampling cost than previous approaches proposed in the literature for the same error rate.