Showing papers on "Alpha beta filter published in 2001"

Stochastic Methods for Sequential Data Assimilation in Strongly Nonlinear Systems

Abstract: This paper considers several filtering methods of stochastic nature, based on Monte Carlo drawing, for the sequential data assimilation in nonlinear models. They include some known methods such as the particle filter and the ensemble Kalman filter and some others introduced by the author: the second-order ensemble Kalman filter and the singular extended interpolated filter. The aim is to study their behavior in the simple nonlinear chaotic Lorenz system, in the hope of getting some insight into more complex models. It is seen that these filters perform satisfactory, but the new filters introduced have the advantage of being less costly. This is achieved through the concept of second-order-exact drawing and the selective error correction, parallel to the tangent space of the attractor of the system (which is of low dimension). Also introduced is the use of a forgetting factor, which could enhance significantly the filter stability in this nonlinear context.

Better proposal distributions: object tracking using unscented particle filter

Abstract: Tracking objects involves the modeling of non-linear non-Gaussian systems. On one hand, variants of Kalman filters are limited by their Gaussian assumptions. On the other hand, conventional particle filter, e.g., CONDENSATION, uses transition prior as the proposal distribution. The transition prior does not take into account current observation data, and many particles can therefore be wasted in low likelihood area. To overcome these difficulties, unscented particle filter (UPF) has recently been proposed in the field of filtering theory. In this paper, we introduce the UPF framework into audio and visual tracking. The UPF uses the unscented Kalman filter to generate sophisticated proposal distributions that seamlessly integrate the current observation, thus greatly improving the tracking performance. To evaluate the efficacy of the UPF framework, we apply it in two real-world tracking applications. One is the audio-based speaker localization, and the other is the vision-based human tracking. The experimental results are compared against those of the widely used CONDENSATION approach and have demonstrated superior tracking performance.

Model-based 3D tracking of an articulated hand

Abstract: This paper presents a practical technique for model-based 3D hand tracking. An anatomically accurate hand model is built from truncated quadrics. This allows for the generation of 2D profiles of the model using elegant tools from projective geometry, and for an efficient method to handle self-occlusion. The pose of the hand model is estimated with an Unscented Kalman filter (UKF), which minimizes the geometric error between the profiles and edges extracted from the images. The use of the UKF permits higher frame rates than more sophisticated estimation methods such as particle filtering, whilst providing higher accuracy than the extended Kalman filter The system is easily scalable from single to multiple views, and from rigid to articulated models. First experiments on real data using one and two cameras demonstrate the quality of the proposed method for tracking a 7 DOF hand model.

Sliding mode observer for nonlinear uncertain systems

Abstract: A new sliding mode observer for a class of nonlinear uncertain systems is proposed in this article. The proposed sliding mode observer works under much less conservative conditions than previous nonlinear unknown input observers. Also, a functional version of the observer is proposed in certain cases where it may not be possible to design an observer capable of estimating the entire state of the system.

A nonlinear state observer for the sensorless control of a permanent-magnet AC machine

Abstract: This paper presents a sensorless speed regulation scheme for a permanent-magnet synchronous motor (PMSM) based solely on the motor line currents measurements. The proposed scheme combines an exact linearization-based controller with a nonlinear state observer which estimates the rotor position and speed. Moreover, the stability of the closed-loop system, including the observer, is demonstrated through Lyapunov stability theory. The proposed observer has the advantage of being insensitive to rotation direction. It is shown how a singularity at zero velocity appears in the scheme and how it can be avoided by switching smoothly from the observer-based closed-loop control to an open-loop control at low velocity. The system performance is tested with an experimental setup consisting of a PMSM servo drive and a digital-signal-processor-based controller for both unidirectional and bidirectional speed regulation.

Finite-horizon robust Kalman filter design

Abstract: We study the problem of finite-horizon Kalman filtering for systems involving a norm-bounded uncertain block. A new technique is presented for robust Kalman filter design. This technique involves using multiple scaling parameters that ran be optimized by solving a semidefinite program. The use of optimized scaling parameters leads to an improved design. A recursive design method that can be applied to real-time applications is also proposed.

Efficient derivative-free Kalman filters for online learning.

Abstract: The extended Kalman filter(EKF) is considered one of the most ef- fective methods for both nonlinear state estimation and parameter estimation(e.g., learning the weights of a neural network). Recently, a number of derivative free alternatives to the EKF for state estimation have been proposed. These include the Unscented Kalman Filter(UKF) (1, 2), the Central Difference Filter(CDF) (3) and the closely related Divided Difference Filter(DDF) (4). These filters consistently outperform the EKF for state estimation, at an equal computational complexity of . Extension of the UKF to parameter estimation was presented by Wan and van der Merwe in (5, 6). In this paper, we further develop these techniques for parameter estimation and neural network training. The extension of the CDF and DDF filters to parameter estimation, and their relation to UKF parameter estimation is presented. Most significantly, this paper introduces efficient square-root forms of the different filters. This enables an implementation for parameter esti- mation (equivalent to the EKF), and has the added benefit of improved numerical stability and guaranteed positive semi-definiteness of the Kalman filter covariances.

State Estimation Using a Reduced-Order Kalman Filter

Abstract: Minimizing forecast error requires accurately specifying the initial state from which the forecast is made by optimally using available observing resources to obtain the most accurate possible analysis. The Kalman filter accomplishes this for a wide class of linear systems, and experience shows that the extended Kalman filter also performs well in nonlinear systems. Unfortunately, the Kalman filter and the extended Kalman filter require computation of the time-dependent error covariance matrix, which presents a daunting computational burden. However, the dynamically relevant dimension of the forecast error system is generally far smaller than the full state dimension of the forecast model, which suggests the use of reduced-order error models to obtain near-optimal state estimators. A method is described and illustrated for implementing a Kalman filter on a reduced-order approximation of the forecast error system. This reduced-order system is obtained by balanced truncation of the Hankel operator ...

Robust fault detection using Luenberger-type unknown input observers-a parametric approach

Abstract: A new parametric observer-based approach for robust fault detection in multivariable linear systems with unknown disturbances is proposed. The residual is generated through utilizing a Luenberger function observer. By using a parametric solution to a class of generalized Sylvester matrix equations, a parametrization is proposed for the residual generator on the basis of a Luenberger function observer. By further properly constraining the design parameters provided in the Luenberger observer design, the effect of the unknown disturbance is decoupled from the residual signal. The proposed approach provides all the degrees of freedom and is demonstrated to be simple and effective.

Improved Kalman filter design for three-dimensional radar tracking

Abstract: The problem of three-dimensional (3D) radar tracking is considered. The usual tracking filter design relying on first-order (or linear) approximations leads to poor convergence and erratic filter behavior in highly nonlinear situations. Simple filter algorithms that can overcome these ill effects are developed for two different types of 3D radar measurement. For each type of radar measurement, an accurate expression for the measurement covariance is obtained by evaluating inherent nonlinearities of radar measurements via coordinate transformation. Then algebraic manipulations and reasonable approximations are employed to yield a simple filter formulation based on the expression. The resulting filter equations are similar to the extended Kalman filter (EKF) and provide some useful insights into the behavior of linearized Kalman filters designed with radar measurements. Finally, simulation results show that the proposed approach is very effective in accounting for the measurement nonlinearities.

An asymptotic state observer for a class of nonlinear delay systems

Abstract: The problem of state reconstruction from input and output measurements for nonlinear time delay systems is studied in this paper and a state observer is proposed that is easy to implement and, under suitable assumptions on the system and on the input function, gives exponential observation error decay. The proposed observer is itself a delay system and can be classified as an identity observer, in that it is such that if at a given time instant the system and observer states coincide, on a suitable Hilbert space, the observation error remains zero in all following time instants. The computation of the observer gain is straightforward. Computer simulations are reported that show the good performance of the observer.

Fully-coupled positioning system

Abstract: A positioning system is disclosed for measuring a position of a vehicle on land, air, and space, using measurements from a global positioning system receiver and an inertial measurement unit. In the present invention, an integrated Kalman filter processes the all-available measurements of the global positioning system: pseudorange, delta range, carrier phase, and the solution of an inertial navigation system. The integrated Kalman filter is a multi-mode, robust kalman filter, in which optimal integrated mode is selected based on the measurement availability and filter stability. The high accurate solution of the inertial navigation system, which is corrected by the Kalman filter, is used to aid on-the-fly resolution of the carrier phase integer ambiguity of global positioning system in order to incorporate the carrier phase measurements into the Kalman filter, and to aid the carrier phase and code tracking loops of the receiver of the global positioning system to improve the receiver jamming and high dynamic resistance.

Detection of the EEG Artifacts by the Means of the (Extended) Kalman Filter

Abstract: This paper presents a new approach for detection of artifacts in sleep electroencephalogram (EEG) recordings. The proposed approach is based on Kalman filter. The idea of this approach consist in embedding the AR model into the Kalman Filter which makes possible to use such KF AR (Kalman Filter AR) models for linear prediction of non-stationary signals. Such model can be set up to detect and follow discrete dynamic changes of the signal. For detection of the EEG artifacts we have exploited the evolution of the state noise - increase in state noise indicate the dynamic change of the signal. The evaluation of the results was done by the Receiver-Operator Characteristics (ROC) curves in terms of the specificity and the sensitivity. For 90% of the specificity the best achieved value of the sensitivity using KF AR model was 33%. In order to achieve better results we have tried the following modification: instead of the Kalman Filter we have used extended Kalman Filter and instead of the AR model a neural network. The preliminary results look promissing: for 90% of the specificity we have achieved 65% of the sensitivity.

End-point sensing and state observation of a flexible-link robot

Abstract: This paper presents an end-point sensor system and the development of an observer to reconstruct the states of a flexible-link robot. The sensor system includes a tip displacement sensor and an accelerometer. Based on the assumed-models method, an observer is developed using the Kalman filtering algorithm. Experimental results are given to demonstrate the effectiveness of the observer.

Sensor fusion based on fuzzy Kalman filter

Abstract: We present a fuzzy Kalman filter, which is based on fuzzy logic theory and a Kalman filter. It is similar to a Kalman filter when a linear system with Gaussian noise is considered. However, when non-Gaussian noise is introduced, it is shown that the fuzzy Kalman filter outperforms the Kalman filter and the Kalman filter does not work well. We demonstrate the performances of the Kalman filter and the fuzzy Kalman filter for a position estimation application under different circumstances. Comparisons are made to draw conclusions.

Nonlinear estimation of aircraft models for on-line control customization

Abstract: This paper describes a new nonlinear estimation procedure used to estimate and track the parameters of a nonlinear aircraft. The Unscented Kalman Filter (UKF) is developed and compared to the more traditional Extended Kalman Filter (EKF). State and parameters are estimated on the F-15 for both a complex maneuver and a maneuver with failure. The algorithms have access to the nonlinear dynamic equations, but not the aircraft engine models, aerodynamic models, or atmospheric models. Parameters describing these unknown dynamics are estimated in the EKF and UKF algorithms. Results show the UKF to be more accurate than the EKF, and track all parameters very well at all times, even after a 50% failure of the stabilator. The aerodynamic forces and moments, while difficult to track immediately after the failure because of the discontinuous nonlinearity, did recover quickly and stay within the predicted bounds.

Global adaptive observer for a class of nonlinear systems

Abstract: The problem considered is the joint estimation of state and some parameters for a class of truly nonlinear systems. The proposed method is constructive and guarantees global convergence. It has been inspired by the technique of high gain observer and by a recent result on linear adaptive observer. A numerical example is presented for illustration.

A general purpose observer architecture with application to failure detection and isolation

Abstract: Proposes a general observer structure which can be employed in various estimation and control problems. The starting point is the proportional integral (PI) observer which has been shown to be effective not only in loop transfer recovery (LTR) but also in estimating and accommodating disturbances. The connections of the PI observer to a disturbance observer (DO) and an unknown input observer (UIO) are established. We show that the PI structure can be further generalized to a PI adaptive observer and a PI observer with fading property. The PI adaptive (PIA) observer expands the applicability of integral action to systems with unknown parameters, while the PI fading (PIF) observer can also accommodate transitory disturbances of unknown origin. It is also shown that, when process and sensor noises are present, a PI Kalman filter can be used to achieve the same goal. A systematic design procedure is developed for estimating both the state and the unknown inputs of a dynamic system. The results presented are applicable directly to fault detection and isolation (FDI) of systems under sensor and/or actuator failures.

Improved rotor speed estimation using two Kalman filter-based algorithms

Abstract: This paper proposes the application of two new Kalman filter-based algorithms to realise a speed-sensorless vector control of induction motor drives. The first one is a linear Kalman filter (LKF)-based algorithm that estimates the equivalent disturbance torque, which is compensated by the injection of a feedforward signal. The latter is an extended Kalman filter (EKF)-based algorithm used to obtain a correct implementation of sensorless vector control, since it estimates both the rotor flux components and speed. The mathematical EKF-model is accurate because of the equivalent-disturbance compensation obtained from the LKF-based observer. The rotor speed estimate is very good in the whole velocity range including zero value. The results show the effectiveness of the proposed control scheme.

Development of a fuzzy logic-based adaptive Kalman filter

Abstract: In this paper, after reviewing the traditional Kalman filter formulation, a development of a fuzzy logic-based adaptive Kalman filter is outlined. The adaptation is in the sense of adaptively tuning, on-line, the measurement noise covariance matrix R or the process noise covariance matrix Q. This improves the Kalman filter performance and prevents filter divergence when R or Q are uncertain. Based on the whiteness of the filter innovation sequence and employing the covariance-matching technique the tuning process is carried out by a fuzzy inference system. If a statistical analysis of the innovation sequence shows discrepancies with its expected statistics then a fuzzy inference system adjusts a factor through which the matrices R or Q are tuned on line. This fuzzy logic-based adaptive Kalman filter is tested on a numerical example. The results are compared with these obtained using a conventional Kalman filter and a traditionally adapted Kalman filter. The fuzzy logic-based adaptive Kalman filter showed better results than its traditional counterparts.

Kalman filter with adaptive measurement variance estimator

Abstract: A Kalman filtering technique employing an adaptive measurement variance estimator is disclosed. The Kalman filtering technique includes a signal filtering mechanism, the signal filtering mechanism futher includes a Kalman filter and a variance estimator. The variance estimation used in the filtering includes estimating the variance of the measured quantity signal and generating the variance estimate signal for use in filtering the input signal and the measured quantity signal, wherein estimating the variance of the measured quantity signal includes determining a smoothed estimate of the measured quantity's variance from the measured quantity signal. The invention also manifests itself as a method for filtering and estimating, a program storage medium encoded with instructions that, when executed by a computer, performs such a method, an electronic computing device programmed to perform such a method, and a transmission medium over which the method is performed.

State-Dependent Pseudo-Linear Filter for Spacecraft Attitude and Rate Estimation

Abstract: This paper presents the development and performance of a special algorithm for estimating the attitude and angular rate of a spacecraft. The algorithm is a pseudo-linear Kalman filter, which is an ordinary linear Kalman filter that operates on a linear model whose matrices are current state estimate dependent. The nonlinear rotational dynamics equation of the spacecraft is presented in the state space as a state-dependent linear system. Two types of measurements are considered. One type is a measurement of the quaternion of rotation, which is obtained from a newly introduced star tracker based apparatus. The other type of measurement is that of vectors, which permits the use of a variety of vector measuring sensors like sun sensors and magnetometers. While quaternion measurements are related linearly to the state vector, vector measurements constitute a nonlinear function of the state vector. Therefore, in this paper, a state-dependent linear measurement equation is developed for the vector measurement case. The state-dependent pseudo linear filter is applied to simulated spacecraft rotations and adequate estimates of the spacecraft attitude and rate are obtained for the case of quaternion measurements as well as of vector measurements.

Observer-type Kalman innovation filter for uncertain linear systems

Abstract: An observer-type of Kalman innovation filtering algorithm to find a practically implementable "best" Kalman filter, and such an algorithm based on the evolutionary programming (EP) optima-search technique, are proposed, for linear discrete-time systems with time-invariant unknown-but-hounded plant and noise uncertainties. The worst-case parameter set from the stochastic uncertain system represented by the interval form with respect to the implemented "best" filter is also found in this work for demonstrating the effectiveness of the proposed filtering scheme. The new EP-based algorithm utilizes the global optima-searching capability of EP to find the optimal Kalman filter and state estimates at every iteration, which include both the best possible worst case Interval and the optimal nominal trajectory of the Kalman filtering estimates of the system state vectors. Simulation results are included to show that the new algorithm yields more accurate estimates and is less conservative as compared with other related robust filtering schemes.

Multiple-model multiple-hypothesis filter for tracking maneuvering targets

Abstract: In this paper a new method is presented to deal with multiple model filtering The method is the so called Multiple Model Multiple Hypothesis Filter (MMMH filter) For each hypothesis a Kalman filter is running This hypothesis represents a specific model mode sequence history The proposed method has a high level of genericity and is highly flexible The main feature is that the number of hypotheses that are maintained varies with the "difficulty" of a scenario It is shown that the MMMH performs better than the widely used Interacting Multiple Model (IMM) filter

Full-order Perfect Observers for Continuous-time Linear Systems

Abstract: A new concept of the full-order perfect observer for continuous-time linear systems is presented. Conditions for the existence of the perfect observer are established and its design procedure is derived.