Showing papers on "Alpha beta filter published in 1996"

Introduction to random signals and applied Kalman filtering : with MATLAB exercises and solutions

Abstract: Probability and Random Variables: A Review. Mathematical Description of Random Signals. Response of Linear Systems to Random Inputs. Wiener Filtering. The Discrete Kalman Filter, State-Space Modeling, and Simulation. Prediction, Applications, and More Basics on Discrete Kalman Filtering. The Continuous Kalman Filter. Smoothing. Linearization and Additional Intermediate-Level Topics on Applied Kalman Filtering. More on Modeling: Integration of Noninertial Measurements Into INS. The Global Positioning System: A Case Study. Appendices. Index.

Sliding mode observer for triangular input form

Abstract: This paper discusses the problem of designing an observer for nonlinear systems. In Drakunov and Utkin (1995) a new concept of sliding observers was introduced, where the key point is that the equivalent control concept is extensively used. Moreover, in Boukhobza, Djemai, and Barbot (1996) we use a classical sliding mode observer in order to design an observer for the largest class with the so-called output injection form. Here, our purpose is to discuss the observer design for a system in a triangular input observer form. For a system in a triangular input observer form there is no problem of singular input. The second purpose of this paper is to show how to use the anti-peaking sliding method in the case of successive equivalent vectors.

The Kalman filter in finance

Abstract: Preface. 1. Introduction. 2. Test for parameter stability. 3. Flexible Least Squares. 4. The Kalman filter. 5. Parameter estimation. 6. The estimates, reconsidered. 7. Modeling with the Kalman filter. A. Tables of references. B. The programs and the data. Bibliography. Index.

Incremental Least Squares Methods and the Extended Kalman Filter

Abstract: In this paper we propose and analyze nonlinear least squares methods which process the data incrementally, one data block at a time. Such methods are well suited for large data sets and real time operation and have received much attention in the context of neural network training problems. We focus on the extended Kalman filter, which may be viewed as an incremental version of the Gauss--Newton method. We provide a nonstochastic analysis of its convergence properties, and we discuss variants aimed at accelerating its convergence.

A new motor speed estimator using Kalman filter in low-speed range

Abstract: In this paper, a new machine drive technique using novel estimation strategy for the very low-speed operation to estimate both the instantaneous speed and disturbance load torque is proposed. In the proposed algorithm, a Kalman filter is incorporated to estimate both the motor speed and the disturbance torque. The Kalman filter is an optimal state estimator and is usually applied to a dynamic system that involves a random noise environment. The effects of parameter variations are discussed, and it is verified that the system is stable to the modeling error. Experimental results confirm the validity of the proposed estimation technique.

Dual Kalman Filtering Methods for Nonlinear Prediction, Smoothing and Estimation

Abstract: Prediction, estimation, and smoothing are fundamental to signal processing. To perform these interrelated tasks given noisy data, we form a time series model of the process that generates the data. Taking noise in the system explicitly into account, maximum-likelihood and Kalman frameworks are discussed which involve the dual process of estimating both the model parameters and the underlying state of the system. We review several established methods in the linear case, and propose several extensions utilizing dual Kalman filters (DKF) and forward-backward (FB) filters that are applicable to neural networks. Methods are compared on several simulations of noisy time series. We also include an example of nonlinear noise reduction in speech.

Elastically Adaptive Deformable Models

Abstract: We present a novel technique for the automatic adaptation of a deformable model's elastic parameters within a Kalman filter frame-work for shape estimation applications. The novelty of the technique is that the model's elastic parameters are not constant, but time varying. The model for the elastic parameter variation depends on the local error of fit and the rate of change of the error of fit. By augmenting the state equations of an extended Kalman filter to incorporate these additional variables and take into account the noise in the data, we are able to significantly improve the quality of the shape estimation. Therefore, the model's elastic parameters are initialized always to the same value and they subsequently modified depending on the data and the noise distribution. In addition, we demonstrate how this technique can be parallelized in order to increase its efficiency. We present several experiments to demonstrate the effectiveness of our method.

Nonlinear State Estimation in the Presence of Multiple Steady States

Abstract: This paper concerns the problem of state estimation in nonlinear deterministic processes. For moderately nonlinear deterministic processes, the inadequacy of full-order Luenberger observer and extended Luenberger observer with constant gain is shown analytically and through numerical simulation of a chemical reactor. The results indicate that the convergence of an extended Luenberger observer with constant gain may be poorer than that of a simple linear Luenberger observer. A nonlinear observer design method with varying gain is applied to a classical exothermic stirred-tank reactor with multiple steady states. Under significant observer-initialization errors and several observer gains, the global asymptotic convergence of the nonlinear observer is demonstrated through numerical simulations. In the presence of the multiple steady states, the nonlinear observer converges to the same steady-state operating point at which the reactor operates, irrespective of the observer initial conditions.

A nonlinear observer for the inverted pendulum

Abstract: This paper deals with the design of a nonlinear observer for the inverted pendulum. The observer uses the standard structure of the linear observer with the linear model replaced by a nonlinear model. Nominal observer gains are determined from a linearised model. This model is also used to find a compromise between robustness and performance. The stability of the observer is then discussed and conditions for the stability of the observer are given. The results are illustrated by simulation and experiments on a real pendulum.

Observer design and fault diagnosis for retarded dynamical systems

Abstract: In this paper, we propose a reduced order observer, for state estimation in a class of state delayed dynamical systems driven by known as well as unknown inputs. Conditions for existence of the proposed observer, plus the stability and convergence proof for the observer based on the Razumikhin theorem are given. Additionally, the proposed observer is utilized in an analytical redundancy based approach for sensor and actuator failure detection problem in the same class of time delay dynamical systems. Finally, the applicability and effectiveness of the proposed FDI scheme is illustrated by numerical examples.

Tutorial: The Likelihood Interpretation of the Kalman Filter.

Abstract: 1 This is only an extract from this work and contains references to material from other chapters in the larger document.

Order statistic fast Kalman filter

Abstract: This paper deals with the derivation of a new adaptive filtering algorithm, which takes into consideration the often encountered case of impulsive perturbations. The proposed method is a combination of a RLS-based algorithm and the Order Statistic (OS) filter, and can be seen as an extension of the LMS-type Order Statistic filter (OSLMS). In order to obtain a computational burden comparable to the OSLMS filter, our derivation is based on a fast version of the RLS algorithm-the Fast Kalman filter. We will show that the new algorithm is not a coarse extension of the OSLMS filter and that care should be taken when performing the order statistic filtering operation.

Initialization of the kalman filter with partially diffuse initial conditions

Abstract: The problem of computing estimates of the state vector when the Kalman filter is seeded with an arbitrarily large variance is considered To date the response in the literature has been the development of a number of relatively complex hybrid filters, usually involving additional quantities and equations over and above the conventional filter We show, however, that a certain square root covariance filter is capable of handling the complete range of variances (zero, positive and infinite) without modification to the filtering equations themselves and without additional computation loads Instead of the more conventional Cholesky factorization, our filter employs an alternative matrix factorization procedure based on a unit lower triangular matrix and a diagonal matrix This permits the use of a modified form of fast Givens transformations, central to the development of an efficient algorithm

Modification of the extended Kalman filter with an additive term of instability

Abstract: In this paper we propose an observer for nonlinear systems similar to the extended Kalman filter. The observer gain is computed by a Riccati differential equation assuming a more instable system. The purpose of this modification is two-fold: first the degree of stability can be assigned in advance and secondly this modification allows an effective treatment of the nonlinearities.

Kalman filter with hypothesis testing: A tool for estimating uncertain parameters

Abstract: In this paper we present a simple and practical algorithm for the estimation of uncertain parameters of linear systems. The uncertainty is twofold, involving random observation noise, and possible jumps in the parameter values. The jumps may occur at unknown points in time, and are of unknown magnitudes and directions. The algorithm is based on the Kalman filter, with a single-sample hypothesis test, which is used to employ a three-state decision rule (yes, no, maybe). The "maybe" choice invokes a fading memory Kalman filter. The overall algorithm contains the constant parameter filter, fading memory filter, and the set of tests and rules that enable it to switch back and forth between the two filters. Application examples are presented.

Filter coefficient selection using design criteria

Abstract: For tracking systems with a uniform data rate and stationary measurement noise, non-manoeuvring targets can be accurately tracked with a steady-state Kalman filter. The steady-state Kalman filter, which can be viewed as equivalent to an alpha-beta filter, has been widely applied to many different systems. A means of selecting the filter coefficients was proposed by Kalata (1984) using Kalman filter considerations. An alternative method based on noise reduction ratios is presented in this paper. Using a design criteria with the Kalata relation, optimal filter coefficients can be selected for specific applications. This method generalizes current methods for selecting the filter coefficients.

A fuzzy neural network based extended Kalman filter

Abstract: In this paper we construct a discrete extended Kalman filter by using fuzzy neural networks. The constructed filter makes it possible to estimate the states of a nonlinear dynamical system with unknown plant model. The unknown plant is identified by a fuzzy neural network and the modelling error can be compensated by a simple but efficient method that avoids the occurrence of divergence in state estimation. A computer simulation is presented to illustrate the performance and applicability of the proposed filter.

Estimating contact and grasping uncertainties using Kalman filters in force controlled assembly

Abstract: This paper presents a general approach for the identification of contact and grasping uncertainties, and the monitoring of contact situation changes in force controlled assembly operations. The identification problem is solved using virtual contact manipulators and Kalman filter techniques. Monitoring is solved by carrying out a statistical test on the sum of normalized and squared innovations of the Kalman filter, within a moving window, identification and monitoring are verified by experimental results. The paper explains how the error covariance matrix of the Kalman filter is interpreted to analyse the observability of the Kalman filter's states. Preliminary simulation results are presented for an ad hoc active sensing strategy to achieve complete state observability.

DSP based field-oriented control of induction motor with a nonlinear state observer

Abstract: The paper deals with the implementation of a standard field-oriented induction motor control with a rotor flux nonlinear state observer, similar in structure to the well known Luenberger observer for a linear system. The real time control hardware used to implement the field oriented control and the nonlinear observer consists of a data translation single board DSP data acquisition system based on a TMS 320C40. After a brief description of the observer features and the proposed system, the experimental set-up is presented and discussed in detail. Experimental results demonstrate its excellent low sensitivity to rotor resistance variation in comparison to a field-oriented control system based on conventional current model flux estimation.

Estimation of Tropical Sea Level Anomaly by an Improved Kalman Filter

Abstract: Kaiman filter theory and autoregressive time series are used to map sea level height anomalies in the tropical Pacific. Our Kalman filters are implemented with a linear state space model consisting of evolution equations for the amplitudes of baroclinic Kelvin and Rossby waves and data from the Pacific tide gauge network. In this study, three versions of the Kalman filter are evaluated through examination of the innovation sequences, that is, the time series of differences between the observations and the model predictions before updating. In a properly tuned Kalman filter, one expects the innovation sequence to be white (uncorrelated, with zero mean). A white innovation sequence can thus be taken as an indication that there is no further information to be extracted from the sequence of observations. This is the basis for the frequent use of whiteness, that is, lack of autocorrelation, in the innovation sequence as a performance diagnostic for the Kalman filter. Our long-wave model embodies the c...

Kalman filter incorporated model updating for real-time tracking

Abstract: This paper describes a real-time tracking system which detects an object entering into the field of view of a camera and executes the tracking of the detected object by controlling a servo device so that a target object always lies at the center of the image frame. In order to detect and track a moving object, we basically apply a model matching strategy. We allow the model to vary dynamically during the tracking process so that it can assimilate the variations of shape and intensities of the target object. We also utilize a Kalman filter so that a tracking history can be encoded into the state parameters of the Kalman filter. The estimated state parameters of the Kalman filter is then used to reduce the search areas for model matching and to control the servo device.

Kalman filter sensitivity with respect to parametric noises uncertainty

Abstract: The influence of the noises uncertainty on the Kalman filter performance is characterized by sensitivity functions. Relationships for computing these functions are derived and used both for synthesizing a Kalman filter with reduced sensitivity (KFRS) and a self-tuning Kalman filter (SKF). The results are illustrated by examples.

Parallel processing and stability analysis of the Kalman filter

Abstract: The paper presents an approach to implementing the parallel Kalman filter. The parallel Kalman filter is computationally intensive and hence complex due to the inherent matrix operations. Often, the filter cannot be computed in real time when the system has a large number of state variables. A method is discussed for achieving almost real-time performance. In addition, a method for determining stability of the Kalman filter is presented. This method involves the use a paradigm that achieves high performance and close to real time results while maintaining accuracy for the Kalman filter. In addition, the paradigm shows an improvement of the processor utilization over other implementations and provides flexibility in terms of the hardware used for implementation.