Showing papers on "Invariant extended Kalman filter published in 1989"

Robustification of Kalman Filter Models

Abstract: Kalman filter models based on the assumption of multivariate Gaussian distributions are known to be nonrobust. This means that when a large discrepancy arises between the prior distribution and the observed data, the posterior distribution becomes an unrealistic compromise between the two. In this article we discuss a rationale for how to robustify the Kalman filter. Specifically, we develop a model wherein the posterior distribution will revert to the prior when extreme outlying observations are encountered, and we point out that this can be achieved by assuming a multivariate distribution with Student-t marginals. To achieve fully robust results of the kind desired, it becomes necessary to forsake an exact distribution-theory approach and adopt an approximation method involving “poly-t” distributions. A recursive mechanism for implementing the multivariate-t—based Kalman filter is described, its properties are discussed, and the procedure is illustrated by an example.

Training feed-forward networks with the extended Kalman algorithm

Abstract: It is shown that training feed-forward nets can be viewed as a system identification problem for a nonlinear dynamic system. For linear dynamic systems, the Kalman filter is known to produce an optimal estimator. Extended versions of the Kalman algorithm can be used to train feed-forward networks. The performance of the Kalman algorithm is examined using artificially constructed examples with two inputs, and it is found that the algorithm typically converges in a few iterations. Backpropagation is used on the same examples, and the Kalman algorithm invariably converges in fewer iterations. For the XOR problem, backpropagation fails to converge on any of the cases considered, whereas the Kalman algorithm is able to find solutions with the same network configurations. >

Mixture reduction algorithms for target tracking

Abstract: The paper is concerned with the development of practical filters for tracking a target when the origin of sensor measurements is uncertain. The full Bayesian solution to this problem gives rise to mixture distributions. From knowledge of the mixture distribution, in principle, an optimal estimate of the state vector for any criteria may be obtained. Also, if the problem is linear and Gaussian, the distribution becomes a Gaussian mixture in which each component probability density function is given by a Kalman filter. The author only considers this case. The methods presented are based on the premise that the number of mixture components should be minimized without modifying the 'structure' of the distribution beyond a specified limit. The techniques operate by merging similar components in such a way that the approximation preserves the mean and covariance of the original mixture. Also to allow the tracking filter to be implemented as a bank of Kalman filters, it is required that the approximated distribution is itself a Gaussian mixture.

Robust adaptive Kalman filtering with unknown inputs

Abstract: A method is proposed to adapt the Kalman filter to the changes in the input forcing functions and the noise statistics. The resulting procedure is stable in the sense that the duration of divergences caused by external disturbances are finite and short and, also, the procedure is robust with respect to impulsive noise (outlier). The input forcing functions are estimated by a running window curve-fitting algorithm, which concurrently provides estimates of the measurement noise covariance matrix and the time instant of any significant change in the input forcing functions. In addition, an independent technique for estimating the process noise covariance matrix is suggested which establishes a negative feedback in the overall adaptive Kalman filter. This procedure is based on the residual characteristics of the standard optimum Kalman filter and a stochastic approximation method. The performance of the proposed method is demonstrated by simulations and compared to the conventional sequential adaptive Kalman filter algorithm. >

An algorithmic approach to constructing the on-line estimation system for the specific growth rate.

Abstract: The objective of this article is to propose an algorithm for the on-line estimation of the specific growth rate in a batch or a fed-batch fermentation process. The algorithm shows the practical procedure for the estimation method utilizing the macroscopic balance and the extended Kalman filter. A number of studies of the on line estimation have been presented. However, there are few studies discussing about the selection of the observed variables and for the tuning of some parameters of the extended Kalman filter, such as covariance matrix and initial values of the state. The beginning of this article is devoted to explain the selection of the observed variable. This information is very important in terms of the practical know-how for using technique. It is discovered that the condition number is a practically useful and valid criterion for number is a practically useful and valid criterion for choosing the variable to be observed. Next, when the extended Kalman filter in applied to the online estimation of the specific growth rate, which is directly unmeasurable, criteria for judging the validity of the estimated value from the observed data are proposed. Based on the proposed criterial, the system equation of the specific growth rate is selected and initial value of the state variable and covariance matrix of the system noises are adjusted. From many experiments, it is certified that the specific growth rate in the batch or fed -batch fermentation can be estimated accurately by means of the algorithm proposed here. In these experiments, that is, when the cell concentration is measured directly, the extended Kalman filter using the convariance matrix with a constant element can estimate more accurately values of the specific growth rate than the adaptive extended Kalman filter does.

Application of an extended Kalman filter to parameter identification of an induction motor

Abstract: An extended Kalman filter is used to identify the parameters of an induction motor using measurements of the stator voltages, currents, and rotor speed. A model of the induction motor in the state space and the Kalman filter algorithm are shown. This filter is applied to the parameter identification of an inverter-fed induction motor. A simple and practical method of setting the covariance matrices of the noises, which are important in the Kalman filter algorithm, is proposed. The starting values of the state and parameter vectors as well as the covariance matrix of the estimation error are then shown, and, finally, the results of parameter identification are shown. The results demonstrate that the filter is capable of identifying the parameters. >

Stabilizing the fast Kalman algorithms

Abstract: The fast Kalman algorithms are stabilized by introducing a quantity that measures the accumulation of the roundoff errors. This quantity is used to correct the variables of the algorithm at every time step. The correction is defined as the solution of a specific minimization problem. The resulting algorithm still has the nice complexity properties of the original algorithm (linear in the number of parameters to be estimated), but it has a much more stable behavior. >

Estimating Dynamic Models Using Kalman Filtering

Abstract: The Kalman filter is useful to estimate dynamic models via maximum likelihood. To do this the model must be set up in state space form. This article shows how various models of interest can be set up in that form. Models considered are Auto Regressive-Moving Average (ARMA) models with measurement error and dynamic factor models. The filter is used to estimate models of presidential approval. A test of rational expectations in approval shows the hypothesis not to hold. The filter is also used to deal with missing approval data and to study whether interpolation of missing data is an adequate technique. Finally, a dynamic factor analysis of government entrepreneurial activity is performed. Appendices go through the mathematical details of the filter and show how to implement it in the computer language GAUSS.

On the properties of reduced order Kalman filters

Abstract: Several known results are unified by considering properties of reduced-order Kalman filters. For the case in which the number of noise sources equals the number of observations, it is shown that the reduced-order Kalman filter achieves zero steady-state variance of the estimation error if and only if the plant has no transmission zeros in the right-half plane, since these would be among the poles of the Kalman filter. The reduced-order Kalman filter cannot achieve zero variance of the estimation error if the number of independent noise sources exceeds the number of observations. It is also shown that the reduced-order Kalman filter achieves the generalized Doyle-Stein condition for robustness when the noise sources are colocated with the control inputs. When there are more observations than noise sources, additional noise sources can be postulated to improve the observer frequency response without diminishing robustness. >

Comments on "Tracking a maneuvering target using input estimation

Abstract: A best linear unbiased estimate (BLUE) of the input process which characterizes a pilot-induced maneuver is developed for the case of the one-dimensional Kalman filter. This approach is utilized to yield a recursive implementation of the adaptive Kalman filter that is identical to that obtained by P.L. Bogler in the above mentioned paper (see ibid., vol.AES-23, no.3, p.298-310, May 1987). >

Extended Kalman filter for attitude estimation of the earth radiation budget satellite

Abstract: The design and testing of an Extended Kalman Filter (EKF) for ground attitude determination, misalignment estimation and sensor calibration of the Earth Radiation Budget Satellite (ERBS) are described. Attitude is represented by the quaternion of rotation and the attitude estimation error is defined as an additive error. Quaternion normalization is used for increasing the convergence rate and for minimizing the need for filter tuning. The development of the filter dynamic model, the gyro error model and the measurement models of the Sun sensors, the IR horizon scanner and the magnetometers which are used to generate vector measurements are also presented. The filter is applied to real data transmitted by ERBS sensors. Results are presented and analyzed and the EKF advantages as well as sensitivities are discussed. On the whole the filter meets the expected synergism, accuracy and robustness.

The Discrete Kalman Filter

Abstract: In Chapter 6, we discussed the problem of making recursive estimates of a random vector X. The problem was static in the sense that every measurement was used to update or improve the estimate of the same random vector X. We now consider the case where the random vector changes in time, between measurements, according to a specified statistical dynamic.

Application Of The Extended Kalman Filter To Parameter And State Estimation Of Induction Motors

Abstract: This paper deals with the estimation of the state variables and the identification of some parameters of the model of an induction motor. A general algorithm, based on the Extended Kalman Filter te...

Improved understanding of the loss-of-symmetry phenomenon in the conventional Kalman filter

Abstract: An unclear treatment is corrected of the conventional Kalman filter implementation as presented by M. H. Verhaegen and P. van Dooren (1986). It shows that the habitual implementation of the Kalman filter makes it extremely sensitive to the so-called loss-of-symmetry phenomenon. Furthermore, it is also demonstrated that an exact implementation of the conventional Kalman filter removes this sensitivity. >

Analytical steady-state solution for a three-state Kalman filter

Abstract: A closed-form steady-state solution is presented for the discrete Kalman-Buch filter when only position is measured. The procedure is based on a comparison between the Wiener and Kalman approaches. The solution obtained is more straightforward than the one given by S.N. Gupta (see ibid., vol.AES-20, p.839-49, Nov. 1984), which is difficult to handle when the eigenvalues are complex. The results agree perfectly with those obtained by simulation of Kalman's recursive equations extended until the steady-state is reached. The results supply apriori tracking performances and are therefore useful for preliminary design. This approach is also applied to the Singer and Fitzgerald model, because of the latter's physical importance. >

Steady-state Kalman filter with correlated measurement noise-an analytical solution

Abstract: An analytical solution is presented for a discrete-time, steady-state Kalman filter with correlated measurement noise. The measurement model is a first-order Markov process, characterized by variance and correlation parameters. The analytical results are used to study the effect of a correlation on steady-state tracking accuracies. >

Fast Mapping Of A Kalman Filter On Warp

Abstract: A parallel algorithm for solving an n-state Kalman filter on an (n+2)-cell linear array is described. The algorithm is the basis for the mapping of a 9-state target tracking filter on the Warp computer. The Warp implementation is written in a high-level language and achieves a measured speedup of almost 300 over the same filter running on a Sun workstation.

New Kalman filter algorithms based on orthogonal transformations for serial and vector computers

Abstract: A new numerically stable Kalman filter algorithm based on a special Givens transformation is developed theoretically. The advantage of the new Kalman filter algorithm vs. conventional formulations is examined for the support of inertial navigation systems (simulation data). The conventional Kalman-Bucy filter, the Bierman formulation and the new Kalman filter algorithms are implemented on IBM 4381 and 3090 computers and vector processors CRAY-1S and CRAY-X-MP. A comparison of CPU-times of the algorithms on the different computers is shown.

Effects of modeling errors on the stability and innovations moments of kalman filters

Abstract: The effects of modeling errors on the performance of Kalman filters are classified and analyzed for the scalar time-invariant continuous-time case. Sufficient conditions for filter divergence are presented showing that process instability and unbounded deterministic control inputs usually cause the filter to go unstable if the dynamic parameters are incorrect. For stable processes and bounded control inputs errors in the dynamic parameters normally cause the filter innovations process to cease being zero mean. Errors in the noise covariances normally have no effect on the filter stability or the innovations mean, but such errors have impact on the innovations "whiteness" and covariance. The paper results may be applied for development of practical guidelines for Failure Detection and Diagnosis problems in dynamic systems.

Estimation of atmospheric and transponder survey errors with a navigation Kalman filter

Abstract: The Completely Integrated Reference Instrumentation System (CIRIS) is an aircraft inertial navigation system (INS) aided with range and range-rate measurements from precisely surveyed ground transponders. The full-ordered Kalman filter 'truth' model for this system is developed with the goal of increasing the error-estimation accuracy of the CIRIS Kalman filter. The authors present the basic structure of the 127-state 'truth' model Kalman filter. The random bias shaping filter model for the transponder positioon survey-errors and the first order Markov shaping filter model for the atmospheric propagation delays are developed. The full-ordered Kalman filter based on the CIRIS 'truth' model is used to process empirical data from a CIRIS flight. The time histories of selected correlated measurement errors' means, covariances, and range residuals are plotted and analyzed with respect to the filter's estimate of position and velocity errors, as well as the aircraft trajectory. The initial conclusions drawn from these data are presented. >

Instability of a decoupled Kalman tracking filter

Abstract: The performance of a decoupled Kalman tracking filter is studied by means of a suboptimal covariance analysis. Analytical and numerical results are presented that demonstrate filter instability over a range of target-sensor line-of-sight (LOS) rates. The instability is shown to occur only when the ratio of the decoupled filter gains exceeds a specific threshold value. >

Adaptive frequency shape Kalman filters

Abstract: A Kalman filter with adaptive frequency-shaped gains, suitable for operating in unknown colored noise environments, is described. The scheme uses least-squares parameter updates and is inherently stable. The adaptive loop enhances the performance of the filter under adverse operating conditions but evanesces under nominal designed condition, thereby preserving the desirable properties of an offline design. Simulation results show that the scheme is effective in enhancing Kalman filter performance when applied to other than nominal signal models. >

On applying the extended Kalman filter to nonlinear regression models

Abstract: In using an extended Kalman filter to estimate the parameters of a nonlinear regression model, the order in which the measurements are processed can be important, as the filter cannot always be expected to produce a satisfactory global fit when processing the measurements in the causal order in which they occur. To obtain a better fit, the possibility is explored of using a sequential state estimator in an offline mode to process the measurements in a random order rather than in the causal order in which they occur. >

Multivariate calibration as an identification method and its relationship to the extended Kalman filter

Abstract: Multivariate calibration (MC) constitutes a set of methods for establishing an estimator without considering prior knowledge of a dynamic process, noise properties or measurement functions. A short survey is presented of MC methods, and it is argued that the MC estimator is efficient for certain applications. The relationship between MC and the extended Kalman filter is established. >