Sequential signal encoding from noisy measurements using quantizers with dynamic bias control

Abstract

Signal estimation from a sequential encoding in the form of quantized noisy measurements is considered. As an example context, this problem arises in a number of remote sensing applications, where a central site estimates an information-bearing signal from low-bandwidth digitized information received from remote sensors, and may or may not broadcast feedback information to the sensors. We demonstrate that the use of an appropriately designed and often easily implemented additive control input before signal quantization at the sensor can significantly enhance overall system performance. In particular, we develop efficient estimators in conjunction with optimized random, deterministic, and feedback-based control inputs, resulting in a hierarchy of systems that trade performance for complexity.

Distributed inference in wireless sensor networks

“…For one-bit quantization at the sensors, it has been shown that the maximum likelihood estimate achieves the Cramér-Rao lower bound (CRLB) asymptotically when the number of sensors is large [76]. When the observation noise is small, adding a Gaussian dithering noise or some deterministic signals at the local sensors may lower the CRLB [77]. It has also been shown that using onebit uniformly dithered samples instead of the unquantized, full-precision data only suffers a logarithm rate loss, for single-and multiple-parameter estimation [78,79].…”

Adjustable quantizers for joint estimation of location and scale parameters

“…Asymptotic results for adaptive algorithms with decreasing gains presented in [6, pp. 110-113] can be applied to (3) to get the asymptotic performance of the estimator. It can be shown under all the assumptions above that the estimation error ǫ k tends in distribution to a zero mean Gaussian random variable as follows…”

“…Main results on estimation from quantized measurements can be found in [3], where the behavior of the Cramér-Rao lower bound (CRB) on the variance of estimation of a constant parameter based on uniformly quantized noisy measurements was studied for different types of quantizer input offset, it was shown that a good type of offset should be…”

“…Also, as a main difference from [3], where location parameter estimation is studied, the problem treated here includes the joint estimation of the scale parameter.…”

Asymptotic approximation of optimal quantizers for estimation

“…Analysis of the performance of location parameter estimation based on multiple bit quantized measurements is presented in [3], where the effect of the quantizer input offset on the Cramér-Rao bound is studied. In [4], the same problem is analyzed, but in a binary quantization context.…”