Optimum quantization intervals by Chernoff information and deflection criterion in distributed sensing

A distributed system which comprises independent sensors and a fusion center is considered. Optimum quantization of sensor observations by Chernoff Information (CI) and deflection criterion (DC) for detection purpose is studied. Chernoff information of overall system is derived, and locally optimum quantization of sensor observations is proved to achieve global optimality. A relationship between DC and CI of quantized observations is established. A novel iterative algorithm which works similar to Lloyd-Max algorithm is proposed to find optimum quantization intervals. Results indicate that optimum 2-bit quantization gives detection performance that is close to what is achievable by collecting soft reports from sensors.