The Extended Parameter Filter

The parameters of temporal models, such as dynamic Bayesian networks, may be modelled in a Bayesian context as static or atemporal variables that influence transition probabilities at every time step. Particle filters fail for models that include such variables, while methods that use Gibbs sampling of parameter variables may incur a per-sample cost that grows linearly with the length of the observation sequence. Storvik devised a method for incremental computation of exact sufficient statistics that, for some cases, reduces the per-sample cost to a constant. In this paper, we demonstrate a connection between Storvik's filter and a Kalman filter in parameter space and establish more general conditions under which Storvik's filter works. Drawing on an analogy to the extended Kalman filter, we develop and analyze, both theoretically and experimentally, a Taylor approximation to the parameter posterior that allows Storvik's method to be applied to a broader class of models. Our experiments on both synthetic examples and real applications show improvement over existing methods

A modified extended kalman filter as a parameter estimator for linear discrete-time systems

This thesis presents the derivation and implementation of a modified Extended Kalman Filter used for Joint state and parameter estimation of linear discrete-time systems operating in a, stochastic Gaussian environment. A novel derivation for the discrete-time Extended Kalman Filter is also presented. In order to eliminate the main deficiencies of the Extended Kalman Filter, which are divergence and biasedness of its estimates, the filter algorithm has been modified. The primary modifications are due to Ljung, who stated global convergence properties for the modified Extended Kalman Filter, when used as a parameter estimator for linear systems. Implementation of this filter is further complicated by the need to initialize the parameter estimate error covariance inappropriately small, to assure filter stability. In effect, due to this inadequate initialization process the parameter estimates fail to converge. Several heuristic methods have been developed to remove the effects of the inadequate initial parameter estimate covariance matrix on the filter\u27s convergence properties. Performance of the improved modified Extended Kalman Filter is compared with the Recursive Extended Least Squares parameter estimation scheme

Online Natural Gradient as a Kalman Filter

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.Comment: 3rd version: expanded intr

Improved Distributed Estimation Method for Environmental\ud time-variant Physical variables in Static Sensor Networks

In this paper, an improved distributed estimation scheme for static sensor networks is developed. The scheme is developed for environmental time-variant physical variables. The main contribution of this work is that the algorithm in [1]-[3] has been extended, and a filter has been designed with weights, such that the variance of the estimation errors is minimized, thereby improving the filter design considerably\ud and characterizing the performance limit of the filter, and thereby tracking a time-varying signal. Moreover, certain parameter optimization is alleviated with the application of a particular finite impulse response (FIR) filter. Simulation results are showing the effectiveness of the developed estimation algorithm

Subsonic flight test evaluation of a propulsion system parameter estimation process for the F100 engine

Integrated engine-airframe optimal control technology may significantly improve aircraft performance. This technology requires a reliable and accurate parameter estimator to predict unmeasured variables. To develop this technology base, NASA Dryden Flight Research Facility (Edwards, CA), McDonnell Aircraft Company (St. Louis, MO), and Pratt & Whitney (West Palm Beach, FL) have developed and flight-tested an adaptive performance seeking control system which optimizes the quasi-steady-state performance of the F-15 propulsion system. This paper presents flight and ground test evaluations of the propulsion system parameter estimation process used by the performance seeking control system. The estimator consists of a compact propulsion system model and an extended Kalman filter. The extended Laman filter estimates five engine component deviation parameters from measured inputs. The compact model uses measurements and Kalman-filter estimates as inputs to predict unmeasured propulsion parameters such as net propulsive force and fan stall margin. The ability to track trends and estimate absolute values of propulsion system parameters was demonstrated. For example, thrust stand results show a good correlation, especially in trends, between the performance seeking control estimated and measured thrust

Step response of a second-order digital filter with two’s complement arithmetic

It is well known that the autonomous response of a second-order digital filter with two’s complement arithmetic may exhibit chaotic behaviors [1]. In this paper, results of the step response case are presented. Even though in the presence of the overflow nonlinearity, it is found that the step response behaviors can be related to some corresponding autonomous response behaviors by means of an appropriate affine transformation. Based on this method, some differences between the step response and the autonomous response are explored. The effects of the filter parameter and input step size on the trajectory behaviors are presented. Some previous necessary conditions for the trajectory behaviors, initial conditions and symbolic sequences are extended and strengthened to become necessary and sufficient conditions. Based on these necessary and sufficient conditions, some counter-intuitive results are reported. For example, it is found that for some sets of filter parameter values, the system may exhibit the type I trajectory even when a large input step size is applied and overflow occurs. On the other hand, for some sets of filter parameter values, the system will not give the type I trajectory for any small input step size, no matter what the initial conditions are

Online identification of a two-mass system in frequency domain using a Kalman filter

Some of the most widely recognized online parameter estimation techniques used in different servomechanism are the extended Kalman filter (EKF) and recursive least squares (RLS) methods. Without loss of generality, these methods are based on a prior knowledge of the model structure of the system to be identified, and thus, they can be regarded as parametric identification methods. This paper proposes an on-line non-parametric frequency response identification routine that is based on a fixed-coefficient Kalman filter, which is configured to perform like a Fourier transform. The approach exploits the knowledge of the excitation signal by updating the Kalman filter gains with the known time-varying frequency of chirp signal. The experimental results demonstrate the effectiveness of the proposed online identification method to estimate a non-parametric model of the closed loop controlled servomechanism in a selected band of frequencies