A. T. Nelson. Nonlinear Estimation and Modeling of Noisy Time-Series by Dual Kalman Filtering Methods. PhD thesis, Oregon Graduate Institute, 2000.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Kalman filter (EKF) has probably had the most widespread use in nonlinear estimation and inference over the last 20 years. It has been applied successfully to problems in all areas of probabilistic inference, including state estimation, parameter estimation (machine learning) and dual estimation [29, 2, 15, 12, 10]. Even newer, more powerful inference frameworks such as sequential Monte Carlo methods sometimes makes use of extended Kalman filters as subcomponents [6] Unfortunately, the EKF is based on a suboptimal implementation of the recursive Bayesian estimation framework applied to Gaussian random ....

Alex T. Nelson. Nonlinear Estimation and Modeling of Noisy Time-Series by Dual Kalman Filtering Methods'. PhD thesis, Oregon Graduate Institute, 2000.

.... severely biased results [40] The dual EKF [40] is a nonlinear extension of the linear dual Kalman approach of [26] and recursive prediction error algorithm of [20] Application of the algorithm to speech enhancement appears in [41] while extensions to other cost functions have been developed in [25, 24]. The crucial, but often overlooked issue of sequential variance estimation is also addressed in [24] Overview The goal of this chapter is to present a uni ed probabilistic and algorithmic framework for nonlinear dual estimation methods. In the next section, we start with the basic Dual EKF ....

.... of [26] and recursive prediction error algorithm of [20] Application of the algorithm to speech enhancement appears in [41] while extensions to other cost functions have been developed in [25, 24] The crucial, but often overlooked issue of sequential variance estimation is also addressed in [24]. Overview The goal of this chapter is to present a uni ed probabilistic and algorithmic framework for nonlinear dual estimation methods. In the next section, we start with the basic Dual EKF prediction error method. This approach is the most intuitive, and involves simply running two EKF ....

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Alex T. Nelson. Nonlinear Estimation and Modeling of Noisy Time-Series by Dual Kalman Filter Methods. PhD thesis, Oregon Graduate Institute of Science and Technology, 2000.

....EM algorithm uses an extended Kalman smoother for the E step, in which forward and 1 backward passes are made through the data to estimate the signal. The model is updated during a separate M step. For a more thorough treatment and a theoretical basis on how these algorithms relate, see Nelson [6]. Rather than provide a comprehensive comparison between the different algorithms, the goal of this paper is to point out the assumptions and flaws in the EKF (Section 2) and offer a improvement based on the unscented transformation filter (Section 3) The unscented filter has recently been ....

....1 y k = 1 0 0] x k n k (10) In this context, the dual estimation problem consists of simultaneously estimating the clean signal x k and the model parameters w from the noisy data y k . 4. 1 Dual EKF Dual UF One dual estimation approach is the dual extended Kalman filter developed in [8, 6]. The dual EKF requires separate state space representation for the signal and the weights. A state space representation for the weights is generated by considering them to be a stationary process with an identity state transition matrix, driven by process noise u k : w k = w k 1 u k (11) y k = ....

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A. T. Nelson. Nonlinear Estimation and Modeling of Noisy Time-Series by Dual Kalman Filtering Methods. PhD thesis, Oregon Graduate Institute, 1999. In preparation.

....The EM algorithm uses an extended Kalman smoother for the E step, in which forward and backward passes are made through the data to estimate the signal. The model is updated during a separate M step. For a more thorough treatment and a theoretical basis on how these algorithms relate, see Nelson [6]. Rather than provide a comprehensive comparison between the di erent algorithms, the goal of this paper is to point out the assumptions and aws in the EKF (Section 2) and o er a improvement based on the unscented transformation lter (Section 3) The unscented lter has recently been proposed ....

....1 y k = 1 0 0] x k n k (10) In this context, the dual estimation problem consists of simultaneously estimating the clean signal x k and the model parameters w from the noisy data y k . 4. 1 Dual EKF Dual UF One dual estimation approach is the dual extended Kalman lter developed in [8, 6]. The dual EKF requires separate state space representation for the signal and the weights. A state space representation for the weights is generated by considering them to be a stationary process with an identity state transition matrix, driven by process noise u k : w k = w k 1 u k (11) y k = ....

[Article contains additional citation context not shown here]

A. T. Nelson. Nonlinear Estimation and Modeling of Noisy Time-Series by Dual Kalman Filtering Methods. PhD thesis, Oregon Graduate Institute, 1999. In preparation.

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A. T. Nelson. Nonlinear Estimation and Modeling of Noisy Time-Series by Dual Kalman Filtering Methods. PhD thesis, Oregon Graduate Institute, 2000.

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