On Distributed Linear Estimation With Observation Model Uncertainties - 2018


We contemplate distributed estimation of a Gaussian supply during a heterogenous bandwidth constrained sensor network, where the supply is corrupted by freelance multiplicative and additive observation noises. We tend to assume the additive observation noise is zero-mean Gaussian with known variance, however, the system designer is unaware of the distribution of multiplicative observation noise and solely is aware of its first- and second-order moments. For multibit quantizers, we tend to derive an correct closed-kind approximation for the mean-square error (MSE) of the linear minimum MSE) estimator at the fusion center. For both error-free and erroneous Communication channels, we tend to propose many rate allocation methods named as longest root to leaf path, greedy, integer relaxation, and individual rate allocation to attenuate the MSE given a network bandwidth constraint, and minimize the required network bandwidth given a target MSE. We conjointly derive the Bayesian Cramér-Rao lower bound (CRLB) for an arbitrarily distributed multiplicative observation noise and compare the MSE performance of our proposed ways against the CRLB. Our results corroborate that, for the low-power multiplicative observation noise and adequate network bandwidth, the gaps between the MSE of greedy and integer relaxation ways and therefore the CRLB are negligible, while the MSE of individual rate allocation and uniform methods isn't satisfactory. Through analysis and simulations, we conjointly explore why maximum likelihood and maximum a posteriori estimators based on one-bit quantization perform poorly for the low-power additive observation noise.

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