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

Multi-Tap Extended Kalman Filter for a Periodic Waveform with Uncertain Frequency and Waveform Shape, and Data Dropouts

Gait analysis presents the challenge of detecting a periodic waveform in the presence of time varying frequency, amplitude, DC offset, and waveform shape, with acquisition gaps from partial occlusions. The combination of all of these components presents a formidable challenge. The Extended Kalman Filter for this system model has six states, which makes it weakly identifiable within the standard Extended Kalman Filter network. In this work, a novel robust Extended Kalman Filter-based approach is presented and evaluated for clinical use in gait analysis. The novel aspect of the proposed method is that at each sample, the present and several past observations are used to update the system state, strengthening the state identification. These past observations are referred to as delay-line taps

Study of Kalman, Extended Kalman and Unscented Kalman Filter (An Approach to Design a Power System)

The accurate measurement of harmonics level is essential for designing harmonic filters,monitoring the stress to which the power system devices are subjected due to harmonics and specifying digital filtering techniques for phasor measurements for relaying. This project presents an integrated approach to design an optimal estimator of harmonic components of a power network in the presence of frequency variations. This has led to the study of Kalman, Extended Kalman and Unscented Kalman filter characteristics and a subsequent implementation of the study to design the optimal filter. We have employed the Extended Kalman filter and Unscented Kalman filter algorithms to estimate the power system voltage magnitude in the presence of random noise and distortions again taking into account the measurement noise. Kalman filter being an optimal estimator track the signal corrupted with noise and bearing harmonic distortion quite accurately. Adaptive tracking of harmonic components of a power system can easily be done using these algorithm. The proposed approaches are tested for only static signals. For a test signal both EKF and UKF algorithms are used and the results are compared

Power Allocation For Outage Minimization in State Estimation Over Fading Channels

This paper studies the outage probability minimization problem for state estimation of linear dynamical systems using multiple sensors, where an estimation outage is defined as an event when the state estimation error exceeds a pre-determined threshold. The sensors amplify-and-forward their measurements (using uncoded analog transmission) to a remote fusion center over wireless fading channels. For stable systems, the resulting infinite horizon problem can be formulated as a constrained average cost Markov decision process (MDP) control problem. A suboptimal power allocation that is less computationally intensive is proposed, and numerical results demonstrate very close performance to the power allocation obtained from the solution of the MDP based average cost optimality equation. Motivated by practical considerations, assuming that sensors can transmit with only a finite number of power levels, optimization of the values of these levels is also considered using a stochastic approximation technique. In the case of unstable systems, a finite horizon formulation of the estimation outage minization problem is presented and solved. An extension to the problem of minimization of the expected error covariance is also studied

Kalman filtering with faded measurements

This paper considers a sensor network where single or multiple sensors amplify and forward their measurements of a common linear dynamical system (analog uncoded transmission) to a remote fusion center via noisy fading wireless channels. We show that the expected error covariance (with respect to the fading process) of the time-varying Kalman filter is bounded and converges to a steady state value, based on some earlier results on asymptotic stability of Kalman filters with random parameters. More importantly, we provide explicit expressions for sequences which can be used as upper bounds on the expected error covariance, for specific instances of fading distributions and scalar measurements (per sensor). Numerical results illustrate the effectiveness of these bounds

On Kalman filtering with faded measurements

This paper considers a sensor network where single or multiple sensors amplify and forward their measurements of a common linear dynamical system (analog uncoded transmission) to a remote fusion centre via noisy fading wireless channels. We show that the expected error covariance (with respect to the fading process) of the time-varying Kalman filter is bounded and converges to a steady state value, based on some general earlier results on asymptotic stability of Kalman filters with random parameters. More importantly, we provide explicit expressions for sequences which can be used as upper bounds on the expected error covariance, for specific instances of fading distributions and scalar measurements (per sensor). Numerical results illustrate the effectiveness of these bounds