Decentralized Bayesian Estimation with Quantized Observations: Theoretical Performance Bounds

The posterior Cramέr Rao lower bound (PCRLB) has recently been proposed as an effective selection criteria for sensor resource management in large, geographically distributed sensor networks. Existing algorithms (in particular the decentralized approaches with no central fusion centre) designed for computing the PCRLB are based on raw observations resulting in significant communication overhead from the sensor nodes to the associated local processing nodes. The paper derives distributive computational techniques for determining the PCRLB for quantized sensor networks configured using decentralized architectures. We refer to the distributed computation of the PCRLB as dPCRLB. The main contribution of the paper is extending the dPCRLB algorithm [1] to quantized observations that leads to significant savings in the communication overhead over its counterparts that use raw observations. In our Monte Carlo simulations, we show that the proposed dPCRLB closely follows the centralized bound based on quantized observations. As expected, there is potential performance loss with quantization as is illustrated by the difference between the dPCRLBs computed using raw and quantized observations. The drop in the estimator´s performance is, however, compensated for with an increase in the number of quantization levels associated with the observation quantizer.