Asymptotic Optimality of Approximate Filters in Stochastic Systems with Colored Noises

In this report, a new interpretation of the main part of our study on asymptotic behaviour of reduced-order filters in [6] is given. Approximate filters are proposed for semi-linear and nonlinear stochastic systems with colored noises. Basically these filters are defined as those which are optimal when the noises are white. Their long time behavior is investigate- d and their asymptotic optimality is shown in two cases under some reasonable assumptions. At first the case of a system where the signal and observation dynamics are linear with respect to the state is considered; the approximate filter is a Kalman filter and the asymptotic analysis relies on a representati- on of the optimal filter which extends a formula known for a linear system with white noises and non-Gaussian initial condition. Then the case of a nonlinear system with limiting ergodic behavior is analyzed; here the approximate filter appears as the optimal filter corresponding to an incorrect prior distribution and the asymptotic study uses the results of Ocone and Pardoux on the asymptotic stability of optimal filters with respect to their initial condition

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

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

Robust recursive estimation in the presence of heavy-tailed observation noise

Includes bibliographical references (p. 33-41).Supported by the U.S. Army Research Office fellowship. ARO-DAAL03-86-G-0017 Supported by the U.S. Air Force Office of Scientific Research. AFOSR-85-0227 AFOSR-89-0276Irvin C. Schick and Sanjoy K. Mitter

Control optimization, stabilization and computer algorithms for space applications

Research of control optimization, stochastic stability, and air traffic control problem

On a stochastic control method for weakly coupled linear systems

The stochastic control of two weakly coupled linear systems with different controllers is considered. Each controller only makes measurements about his own system; no information about the other system is assumed to be available. Based on the noisy measurements, the controllers are to generate independently suitable control policies which minimize a quadratic cost functional. To account for the effects of weak coupling directly, an approximate model, which involves replacing the influence of one system on the other by a white noise process is proposed. Simple suboptimal control problem for calculating the covariances of these noises is solved using the matrix minimum principle. The overall system performance based on this scheme is analyzed as a function of the degree of intersystem coupling

Approximate Gaussian Conjugacy: Parametric Recursive Filtering Under Nonlinearity, Multimodal, Uncertainty, and Constraint, and Beyond

This is a post-peer-review, pre-copyedit version of an article published in Frontiers of Information Technology & Electronic Engineering. The final authenticated version is available online at: https://doi.org/10.1631/FITEE.1700379Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

A New Variable Regularized Transform Domain NLMS Adaptive Filtering Algorithm-Acoustic Applications and Performance Analysis

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Communicating over Filter-and-Forward Relay Networks with Channel Output Feedback

Relay networks aid in increasing the rate of communication from source to destination. However, the capacity of even a three-terminal relay channel is an open problem. In this work, we propose a new lower bound for the capacity of the three-terminal relay channel with destination-to-source feedback in the presence of correlated noise. Our lower bound improves on the existing bounds in the literature. We then extend our lower bound to general relay network configurations using an arbitrary number of filter-and-forward relay nodes. Such network configurations are common in many multi-hop communication systems where the intermediate nodes can only perform minimal processing due to limited computational power. Simulation results show that significant improvements in the achievable rate can be obtained through our approach. We next derive a coding strategy (optimized using post processed signal-to-noise ratio as a criterion) for the three-terminal relay channel with noisy channel output feedback for two transmissions. This coding scheme can be used in conjunction with open-loop codes for applications like automatic repeat request (ARQ) or hybrid-ARQ.Comment: 15 pages, 8 figures, to appear in IEEE Transactions on Signal Processin