Particle filtering for Quantized Innovations

In this paper, we re-examine the recently proposed distributed state estimators based on quantized innovations. It is widely believed that the error covariance of the Quantized Innovation Kalman filter follows a modified Riccati recursion. We present stable linear dynamical systems for which this is violated and the filter diverges. We propose a Particle Filter that approximates the optimal nonlinear filter and observe that the error covariance of the Particle Filter follows the modified Riccati recursion. We also simulate a Posterior Cramer-Rao bound (PCRB) for this filtering problem

An Optimal Transmission Strategy for Kalman Filtering over Packet Dropping Links with Imperfect Acknowledgements

This paper presents a novel design methodology for optimal transmission policies at a smart sensor to remotely estimate the state of a stable linear stochastic dynamical system. The sensor makes measurements of the process and forms estimates of the state using a local Kalman filter. The sensor transmits quantized information over a packet dropping link to the remote receiver. The receiver sends packet receipt acknowledgments back to the sensor via an erroneous feedback communication channel which is itself packet dropping. The key novelty of this formulation is that the smart sensor decides, at each discrete time instant, whether to transmit a quantized version of either its local state estimate or its local innovation. The objective is to design optimal transmission policies in order to minimize a long term average cost function as a convex combination of the receiver's expected estimation error covariance and the energy needed to transmit the packets. The optimal transmission policy is obtained by the use of dynamic programming techniques. Using the concept of submodularity, the optimality of a threshold policy in the case of scalar systems with perfect packet receipt acknowledgments is proved. Suboptimal solutions and their structural results are also discussed. Numerical results are presented illustrating the performance of the optimal and suboptimal transmission policies.Comment: Conditionally accepted in IEEE Transactions on Control of Network System

Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

An Upper Bound to Zero-Delay Rate Distortion via Kalman Filtering for Vector Gaussian Sources

We deal with zero-delay source coding of a vector Gaussian autoregressive (AR) source subject to an average mean squared error (MSE) fidelity criterion. Toward this end, we consider the nonanticipative rate distortion function (NRDF) which is a lower bound to the causal and zero-delay rate distortion function (RDF). We use the realization scheme with feedback proposed in [1] to model the corresponding optimal "test-channel" of the NRDF, when considering vector Gaussian AR(1) sources subject to an average MSE distortion. We give conditions on the vector Gaussian AR(1) source to ensure asymptotic stationarity of the realization scheme (bounded performance). Then, we encode the vector innovations due to Kalman filtering via lattice quantization with subtractive dither and memoryless entropy coding. This coding scheme provides a tight upper bound to the zero-delay Gaussian RDF. We extend this result to vector Gaussian AR sources of any finite order. Further, we show that for infinite dimensional vector Gaussian AR sources of any finite order, the NRDF coincides with the zero-delay RDF. Our theoretical framework is corroborated with a simulation example.Comment: 7 pages, 6 figures, accepted for publication in IEEE Information Theory Workshop (ITW

The Kalman Like Particle Filter: Optimal Estimation With Quantized Innovations/Measurements

We study the problem of optimal estimation using quantized innovations, with application to distributed estimation over sensor networks. We show that the state probability density conditioned on the quantized innovations can be expressed as the sum of a Gaussian random vector and a certain truncated Gaussian vector. This structure bears close resemblance to the full information Kalman filter and so allows us to effectively combine the Kalman structure with a particle filter to recursively compute the state estimate. We call the resulting filter the Kalman like particle filter (KLPF) and observe that it delivers close to optimal performance using far fewer particles than that of a particle filter directly applied to the original problem. We also note that the conditional state density follows a, so called, generalized closed skew-normal (GCSN) distribution

Active Classification for POMDPs: a Kalman-like State Estimator

The problem of state tracking with active observation control is considered for a system modeled by a discrete-time, finite-state Markov chain observed through conditionally Gaussian measurement vectors. The measurement model statistics are shaped by the underlying state and an exogenous control input, which influence the observations' quality. Exploiting an innovations approach, an approximate minimum mean-squared error (MMSE) filter is derived to estimate the Markov chain system state. To optimize the control strategy, the associated mean-squared error is used as an optimization criterion in a partially observable Markov decision process formulation. A stochastic dynamic programming algorithm is proposed to solve for the optimal solution. To enhance the quality of system state estimates, approximate MMSE smoothing estimators are also derived. Finally, the performance of the proposed framework is illustrated on the problem of physical activity detection in wireless body sensing networks. The power of the proposed framework lies within its ability to accommodate a broad spectrum of active classification applications including sensor management for object classification and tracking, estimation of sparse signals and radar scheduling.Comment: 38 pages, 6 figure

Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources

We deal with zero-delay source coding of a vector-valued Gauss-Markov source subject to a mean-squared error (MSE) fidelity criterion characterized by the operational zero-delay vector-valued Gaussian rate distortion function (RDF). We address this problem by considering the nonanticipative RDF (NRDF) which is a lower bound to the causal optimal performance theoretically attainable (OPTA) function and operational zero-delay RDF. We recall the realization that corresponds to the optimal "test-channel" of the Gaussian NRDF, when considering a vector Gauss-Markov source subject to a MSE distortion in the finite time horizon. Then, we introduce sufficient conditions to show existence of solution for this problem in the infinite time horizon. For the asymptotic regime, we use the asymptotic characterization of the Gaussian NRDF to provide a new equivalent realization scheme with feedback which is characterized by a resource allocation (reverse-waterfilling) problem across the dimension of the vector source. We leverage the new realization to derive a predictive coding scheme via lattice quantization with subtractive dither and joint memoryless entropy coding. This coding scheme offers an upper bound to the operational zero-delay vector-valued Gaussian RDF. When we use scalar quantization, then for "r" active dimensions of the vector Gauss-Markov source the gap between the obtained lower and theoretical upper bounds is less than or equal to 0.254r + 1 bits/vector. We further show that it is possible when we use vector quantization, and assume infinite dimensional Gauss-Markov sources to make the previous gap to be negligible, i.e., Gaussian NRDF approximates the operational zero-delay Gaussian RDF. We also extend our results to vector-valued Gaussian sources of any finite memory under mild conditions. Our theoretical framework is demonstrated with illustrative numerical experiments.Comment: 32 pages, 9 figures, published in IEEE Journal of Selected Topics in Signal Processin