Topic
Alpha beta filter
About: Alpha beta filter is a research topic. Over the lifetime, 5653 publications have been published within this topic receiving 128415 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: It is proved that the joint Kalman filter over states and parameters is a natural gradient on top of real-time recurrent learning (RTRL), a classical algorithm to train recurrent models.
Abstract: We cast Amari’s natural gradient in statistical learning as a specific case of Kalman filtering. Namely, applying an extended Kalman filter to estimate a fixed unknown parameter of a probabilistic model from a series of observations, is rigorously equivalent to estimating this parameter via an online stochastic natural gradient descent on the log-likelihood of the observations. In the i.i.d. case, this relation is a consequence of the “information filter” phrasing of the extended Kalman filter. In the recurrent (state space, non-i.i.d.) case, we prove that the joint Kalman filter over states and parameters is a natural gradient on top of real-time recurrent learning (RTRL), a classical algorithm to train recurrent models. This exact algebraic correspondence provides relevant interpretations for natural gradient hyperparameters such as learning rates or initialization and regularization of the Fisher information matrix.
40 citations
12 Dec 2005
TL;DR: In this article, a hybrid scheme for angle tracking observer (ATO) design is introduced, in which a closed-loop LTI observer is combined with a quadrature encoder.
Abstract: Resolvers are absolute angle transducers that are usually used for position and speed measurement in permanent magnet motors. An observer that uses the sinusoidal signals of the resolver for this measurement is called an Angle Tracking Observer (ATO). Current designs for such observers are not stable in high acceleration and high-speed applications. This paper introduces a novel hybrid scheme for ATO design, in which a closed-loop LTI observer is combined with a quadrature encoder. Finite gain stability of the proposed design is proven based on the circle theorem in input-output stability theory. Simulation results show that the proposed ATO design is stable in two cases where an LTI observer and an extended Kalman filter are unstable due to high speed and acceleration,. In addition, the tracking accuracy of our hybrid scheme is substantially higher than a single quadrature encoder.
40 citations
TL;DR: The efficacy of the observer is demonstrated in two examples; namely, a synchronous generator connected to an infinite bus and a Translating Oscillator with a Rotating Actuator system.
40 citations
TL;DR: In this article, the Tobit Kalman filter was extended to discrete-time linear systems with time-correlated multiplicative measurement noise, which can be implemented in a recursive manner.
Abstract: Kalman filters for discrete-time linear systems with censored measurements have been developed, of which the Tobit Kalman filter has been shown an effective candidate. In this study, the authors expand the Tobit Kalman filter to discrete-time linear systems with time-correlated multiplicative measurement noise. By introducing several new terms including the estimates for the products of multiplicative measurement noise and the state as well as their error covariance matrices, the proposed filter can be implemented in a recursive manner. A numerical example involving radar tracking is provided to show the effectiveness of the proposed filter.
40 citations
TL;DR: This work proposes a new method, by designing an unknown input type state observer, to stabilize an unstable 1-d heat equation with boundary uncertainty and external disturbance, and achieves a first result on active disturbance rejection control for a PDE with both boundary uncertaintyand external disturbance.
40 citations