Showing papers on "Alpha beta filter published in 1998"

Analysis Scheme in the Ensemble Kalman Filter

Abstract: This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter. It is shown that the observations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the observations and generate an ensemble of observations that then is used in updating the ensemble of model states. Traditionally, this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low. This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach.

Tracking and Kalman Filtering Made Easy

Abstract: TRACKING, PREDICTION, AND SMOOTHING BASICS. g and g-h-k Filters. Kalman Filter. Practical Issues for Radar Tracking. LEAST-SQUARES FILTERING, VOLTAGE PROCESSING, ADAPTIVE ARRAY PROCESSING, AND EXTENDED KALMAN FILTER. Least-Squares and Minimum-Variance Estimates for Linear Time-Invariant Systems. Fixed-Memory Polynomial Filter. Expanding- Memory (Growing-Memory) Polynomial Filters. Fading-Memory (Discounted Least-Squares) Filter. General Form for Linear Time-Invariant System. General Recursive Minimum-Variance Growing-Memory Filter (Bayes and Kalman Filters without Target Process Noise). Voltage Least-Squares Algorithms Revisited. Givens Orthonormal Transformation. Householder Orthonormal Transformation. Gram--Schmidt Orthonormal Transformation. More on Voltage-Processing Techniques. Linear Time-Variant System. Nonlinear Observation Scheme and Dynamic Model (Extended Kalman Filter). Bayes Algorithm with Iterative Differential Correction for Nonlinear Systems. Kalman Filter Revisited. Appendix. Problems. Symbols and Acronyms. Solution to Selected Problems. References. Index.

Incorporation of time delayed measurements in a discrete-time Kalman filter

Abstract: In many practical systems there is a delay in some of the sensor devices, for instance vision measurements that may have a long processing time. How to fuse these measurements in a Kalman filter is not a trivial problem if the computational delay is critical. Depending on how much time there is at hand, the designer has to make trade offs between optimality and computational burden of the filter. In this paper various methods in the literature along with a new method proposed by the authors will be presented and compared. The new method is based on "extrapolating" the measurement to present time using past and present estimates of the Kalman filter and calculating an optimal gain for this extrapolated measurement.

Skewed approach to filtering

Abstract: The dynamics of many physical system are nonlinear and non- symmetric. The motion of a missile, for example, is strongly determined by aerodynamic drag whose magnitude is a function of the square of speed. Conversely, nonlinearity can arise from the coordinate system used, such as spherical coordinates for position. If a filter is applied these types of system, the distribution of its state estimate will be non-symmetric. The most widely used filtering algorithm, the Kalman filter, only utilizes mean and covariance and odes not maintain or exploit the symmetry properties of the distribution. Although the Kalman filter has been successfully applied in many highly nonlinear and non- symmetric system, this has been achieved at the cost of neglecting a potentially rich source of information. In this paper we explore methods for maintaining and utilizing information over and above that provided by means and covariances. Specifically, we extend the Kalman filter paradigm to include the skew and examine the utility of maintaining this information. We develop a tractable, convenient algorithm which can be used to predict the first three moments of a distribution. This is achieved by extending the sigma point selection scheme of the unscented transformation to capture the mean, covariance and skew. The utility of maintaining the skew and using nonlinear update rules is assessed by examining the performance of the new filter against a conventional Kalman filter in a realistic tracking scenario.

Robust Kalman filter for rank deficient observation models

Abstract: A robust Kalman filter is derived for rank deficient observation models. The datum for the Kalman filter is introduced at the zero epoch by the choice of a generalized inverse. The robust filter is obtained by Bayesian statistics and by applying a robust M-estimate. Outliers are not only looked for in the observations but also in the updated parameters. The ability of the robust Kalman filter to detect outliers is demonstrated by an example.

An adaptive Kalman filter for dynamic estimation of harmonic signals

Abstract: In electrical railway systems there is often a need of detecting or/and predicting harmonic signals contained in measurement data for vehicle control or monitoring purpose. An efficient on-line estimation method for such applications is the Kalman filter technique. However, the performance of a standard recursive Kalman algorithm is strongly dependent on the a priori information of the process and measurement noise which is either unknown or is known only approximately in practical situations. Furthermore, a Kalman filter often suffers from the problem of "dropping off" and loses then the ability to match abrupt parameter changes. In this paper an adaptive Kalman filter based on correlation analysis is proposed to help overcome these problems. The modelling and estimation technique is described in the paper. Simulation results using measured vehicle line current demonstrate the effectiveness of the proposed method.

H, Observer Design for Time-Delay Systems

Abstract: A method for H, observer design for linear time-delay systems based on the algebraic Riccati equation is proposed. A ”weak” sufficient condition for the existence of such an observer is given.

Separate-bias estimation with reduced-order Kalman filters

Abstract: This paper presents the optimal two-stage Kalman filter for systems that involve noise-free observations and constant but unknown bias. Like the full-order separate-bias Kalman filter, this new filter provides an alternative to state vector augmentation and offers the same potential for improved numerical accuracy and reduced computational burden. When dealing with systems involving accurate, essentially noise-free measurements, this new filter offers an additional advantage, a reduction in filter order. The optimal separate-bias reduced order estimator involves a reduced order filter for estimating the state, the order equalling the number of states less the number of observations.

A filter-bank-based Kalman filtering technique for wavelet estimation and decomposition of random signals

Abstract: In this work an effective algorithm is derived for optimal estimation and multiresolutional decomposition of noisy random signals. This algorithm performs the estimation and decomposition simultaneously, using the discrete wavelet transform implemented by a filter bank. The algorithm is developed based on the standard Kalman filtering scheme, and hence preserves the merits of the Kalman filter for random signal estimation in the sense that it produces an optimal (linear, unbiased, and minimum error variance) estimate of the unknown signal in a recursive manner. A set of Monte Carlo simulations was performed, and the statistical performance tests showed that the proposed estimation and decomposition approach outperforms the Kalman filter.

Properties of risk-sensitive filters/estimators

Abstract: Algorithms for risk-sensitive filters have been developed in literature and connections to H∞ filtering also established. The risk-sensitive filter differs from a conditional mean estimator (Kalman filter) and is either risk-prone or risk-averse depending on the sign of a scalar thetas that appears in the cost function. The RS filter exhibits many interesting properties. Statistical properties, parameter estimation and explicit bounds of estimation for these filters are presented in the paper.

Controllability and Observability: Tools for Kalman Filter Design

Abstract: Kalman’s optimum linear filter has proved to be immensely popular in the field of computer vision. A less often quoted contribution of Kalman’s to the control theory literature is that of the concepts of controllability and observability which may be used to analyse the state transition and observation equations and give insights into the filter’s viability. This paper aims to highlight the usefulness of these two ideas during the design stage of the filter and, as well as presenting the standard solutions for linear systems, uses a practical vision application (that of tracking plants for an autonomous crop protection vehicle) to illustrate a useful special case where these methods may be applied to a non-linear system. The application of tests for controllability and observability to the practical non-linear system give not only confirmation that the filter will be able to produce stable estimates, but also gives a lower bound on the number of features required from each image for it to do so.

State estimation under bit-rate constraints

Abstract: This paper considers the problem of estimating the state of a dynamic system from measurements obtained via a digital link with finite data rate R. The structures of the optimal coder and estimator for Markovian systems are derived. In particular, it is shown that the optimal coder for a Gauss-Markov system consists of a Kalman filter, followed by a stage which encodes the current Kalman estimate according to the symbols previously transmitted. A new suboptimal coder-estimator for linear systems is then constructed. Provided that a certain inequality linking the data rate to the dynamical parameters is satisfied, and under very mild assumptions on the noise distributions, this coder-estimator yields an expected absolute estimation error of the same order as in the classical situation with no data rate constraint. Hence if the classical estimation error approaches zero, then the rate-constrained error goes to zero at exactly the same speed.

Observer-based speed estimation method for sensorless vector control of induction motors

Abstract: The method is based on an adaptive flux observer in the rotor-speed reference frame, in which a second-order Kalman filter is employed to modify the estimated rotor flux to improve the performance of speed estimation. The Kalman filter modifies the estimated rotor flux based on the measured stator currents. The estimated speed is used in the speed feedback for vector control and in the co-ordinate transformation for current controller. The proposed method has the advantage of saving much computation time in comparison with the reduced-order extended Kalman filter. Compared with the conventional adaptive observer, the proposed method has the advantage of better accuracy to follow the speed command under heavy loads. Experimental results show the effectiveness of the proposed method.

Control effectiveness estimation using an adaptive Kalman estimator

Abstract: In this paper, an adaptive Kalman filtering algorithm is exploited for use to estimate the abrupt reduction of control effectiveness in dynamic systems. Control effectiveness factors are used to quantify faults entering control systems through actuators. A set of covariance-dependent forgetting factors is introduced into the filtering algorithm. As a result, the change in the control effectiveness is accentuated to help achieve a more accurate estimate more rapidly. The algorithm is applied to an aircraft model for the identification of impairment in its control surfaces.

An adaptive Kalman filter for the enhancement of noisy AR signals

Abstract: In this paper, we describe a new adaptive system for the enhancement of autoregressive (AR) signals which are disturbed by additive broadband noise. The system is comprised of an adaptive Kalman filter operating as a fixed-lag smoother and a subsystem for AR parameter estimation. As opposed to the conventional approach of employing an extended Kalman filter, we estimate the Kalman filter parameters using the enhanced signal and thus establishing a feedback between the Kalman filter output and the estimated parameters. Our system is capable of tracking short-time stationary signals. It is computationally efficient and can easily be implemented on today's integrated digital signal processors.

Comparison of Four Filtering Options for a Radar Tracking Problem

Abstract: : Four different filtering options are considered for the problem of tracking an exoatmospheric ballistic target with no maneuvers The four filters are an alpha-beta filter, an augmented alpha-beta filter, a decoupled Kalman filter, and a fully-coupled extended Kalman filter These filters are listed in the order of increasing computational complexity All of the filters can track the target with some degree of accuracy While the pure alpha-beta filter appreciably lags the other filters in performance for this problem, its augmented version is very competitive with the extended Kalman filter under benign conditions Perhaps the most surprising result is that under all conditions examined, the decoupled (linear) Kalman filter, which is at least an order of magnitude less computationally complex, performs nearly identical to the coupled, extended Kalman filter Four different filtering options are considered for the problem of tracking an exoatmospheric ballistic target with no maneuvers The four filters are an alpha-beta filter, an augmented alpha-beta filter, a decoupled Kalman filter, and a fully-coupled extended Kalman filter These filters are listed in the order of increasing computational complexity All of the filters can track the target with some degree of accuracy While the pure alpha-beta filter appreciably lags the other filters in performance for this problem, its augmented version is very competitive with the extended Kalman filter under benign conditions Perhaps the most surprising result is that under all conditions examined, the decoupled (linear) Kalman filter, which is at least an order of magnitude less computationally complex, performs nearly identical to the coupled, extended Kalman filter

Generalization of exponentially weighted RLS algorithm based on a state-space model

Abstract: We develop a generalized RLS (G-RLS) algorithm described by a state-space model through some modification of the procedure for Kalman filter derivation. It is shown that the G-RLS algorithm reduces to the conventional RLS when the state transition matrix is an identity matrix, and that the G-RLS algorithm without exponential weighting and Kalman filtering become identical when the state model is an unforced dynamical model. The G-RLS algorithm does not require model statistics, and can be implemented once the forgetting factor is chosen. The performances of the G-RLS and Kalman filtering are compared through computer simulation. Specifically, they are applied to the derivation of variable loop gains of a digital phase-locked loop (DPLL). The results indicate that the G-RLS algorithm can act like the Kalman filter if its forgetting factor is properly chosen.

Interrelationship of single-filter and multiple-model adaptive algorithms

Abstract: An equivalent filter bank structure for multiple model adaptive estimation (MMAE) is developed that uses the residual and state estimates from a single Kalman filter and linear transforms to produce equivalent residuals of a complete Kalman filter bank. The linear transforms, which are a function of the differences between the system models used by the various Kalman filters, are developed for modeling differences in the system input matrix, the output matrix, and the state transition matrix. The computational cost of this new structure is compared with the cost of the standard Kalman filter bank (SKFB) for each of these modeling differences. This structure is quite similar to the generalized likelihood ratio (GLR) structure, where the linear transforms can be used to compute the matched filters used in the GLR approach. This approach produces the best matched filters in the sense that they truly represent the time history of the residuals caused by a physically motivated failure model.

State estimation and fault detection by a bank of continuous finite-memory filters

Abstract: A continuous observer estimating the state vector of a linear time-invariant system from the measurements of the system's inputs and outputs passed through a bank of finite-memory filters is introduced. System observability is shown to guarantee the existence of the observer. An application of the observer to the problem of detecting and isolating sensor and actuator faults is discussed.

Disturbance estimation using sliding mode for discrete Kalman filter

Abstract: An approach to estimating disturbances using a sliding mode for an optimal Kalman filter is presented. We show that the disturbance estimation problem can be converted into a discrete tracking problem by using the difference of time update and measurement update of the Kalman filter. Disturbances cannot be modeled or measured previously, so the robustness of the sliding mode provides a very effective tool for disturbance estimation. We develop and improve a disturbance estimation algorithm using a discrete sliding mode for a discrete Kalman filter. The suggested algorithm can be easily implemented on real time applications.

Active control of combustion instabilities

Abstract: A novel active control strategy for unstable combustion systems is presented. It consists of three main parts: a mode observer, an output predictor and a feedback controller. The mode observer is established using neural networks to reconstruct the measured output. To overcome the time delay of the system, which is often very large relative to the necessary sampling period, an output predictor is developed based on the mode observer. Unlike a classical Luenberger type state observer only a measure of the output is required. An output-feedback controller is introduced which uses the output of the predictor. The approach described in this paper is demonstrated through its application to the control of an experimental combustor having two dominant modes.

Reconstructing nonlinear dynamics by extended Kalman filtering

Abstract: We investigate the use of the extended Kalman filter as a tool for the parameter estimation of radial basis function models. We show that the method is best used as an add-on to other estimation techniques such as subset selection of the centers using a minimum description length criterion rather than as a stand-alone method. We also show that the covariance matrix returned by the extended Kalman filter can be used to calculate Rissanen's minimum description length criterion more easily. Illustrative examples are given for data from the Ikeda map and two time series of real world experimental systems.

Asynchronous observer for a copier paper path

Abstract: A copier contains optical sensors along its paperpath to detect sheet positions and velocities. A measurement occurs when a sheet crosses a sensor. The measurement time may not coincide with the controller sample time. This paper presents an approach to more accurately process the asynchronous measurements without increasing the sampling frequency. An oversampled Kalman filter is used in between two controller sampling instants. The observer sampling rate remains equal to the controller sampling rate without loss in performance, since the Kalman filter equations can be evaluated in batch at the controller sampling instants. A look-up table reduces the computational load.

An extended Kalman filter for demodulation of polynomial phase signals

Abstract: This letter presents a new formulation of the extended Kalman filter (EKF) for use in frequency tracking. A brief summary of previous EKF approaches is given and the new approach detailed. Simulation studies of the standard and new algorithms show that a significant improvement in tracking and threshold performance is achieved.