Showing papers on "Alpha beta filter published in 2004"

Optimal Estimation of Dynamic Systems

Abstract: LEAST SQUARES APPROXIMATION A Curve Fitting Example Linear Batch Estimation Linear Least Squares Weighted Least Squares Constrained Least Squares Linear Sequential Estimation Nonlinear Least Squares Estimation Basis Functions Advanced Topics Matrix Decompositions in Least Squares Kronecker Factorization and Least Squares Levenberg-Marquardt Method Projections in Least Squares Summary PROBABILITY CONCEPTS IN LEAST SQUARES Minimum Variance Estimation Estimation without a Prior State Estimates Estimation with a Prior State Estimates Unbiased Estimates Maximum Likelihood Estimation Cramer-Rao Inequality Nonuniqueness of the Weight Matrix Bayesian Estimation Advanced Topics Analysis of Covariance Errors Ridge Estimation Total Least Squares Summary REVIEW OF DYNAMICAL SYSTEMS Linear System Theory The State Space Approach Homogeneous Linear Dynamical Systems Forced Linear Dynamical Systems Linear State Variable Transformations Nonlinear Dynamical Systems Parametric Differentiation Observability Discrete-Time Systems Stability of Linear and Nonlinear Systems Attitude Kinematics and Rigid Body Dynamics Attitude Kinematics Rigid Body Dynamics Spacecraft Dynamics and Orbital Mechanics Spacecraft Dynamics Orbital Mechanics Aircraft Flight Dynamics Vibration Summary PARAMETER ESTIMATION: APPLICATIONS Global Positioning System Navigation Attitude Determination Vector Measurement Models Maximum Likelihood Estimation Optimal Quaternion Solution Information Matrix Analysis Orbit Determination Aircraft Parameter Identification Eigen-system Realization Algorithm Summary SEQUENTIAL STATE ESTIMATION A Simple First-Order Filter Example Full-Order Estimators Discrete-Time Estimators The Discrete-Time Kalman Filter Kalman Filter Derivation Stability and Joseph's Form Information Filter and Sequential Processing Steady-State Kalman Filter Correlated Measurement and Process Noise Orthogonality Principle The Continuous-Time Kalman Filter Kalman Filter Derivation in Continuous Time Kalman Filter Derivation from Discrete Time Stability Steady-State Kalman Filter Correlated Measurement and Process Noise The Continuous-Discrete Kalman Filter Extended Kalman Filter Advanced Topics Factorization Methods Colored-Noise Kalman Filtering Consistency of the Kalman Filter Adaptive Filtering Error Analysis Unscented Filtering Robust Filtering Summary BATCH STATE ESTIMATION Fixed-Interval Smoothing Discrete-Time Formulation Continuous-Time Formulation Nonlinear Smoothing Fixed-Point Smoothing Discrete-Time Formulation Continuous-Time Formulation Fixed-Lag Smoothing Discrete-Time Formulation Continuous-Time Formulation Advanced Topics Estimation/Control Duality Innovations Process Summary ESTIMATION OF DYNAMIC SYSTEMS: APPLICATIONS GPS Position Estimation GPS Coordinate Transformations Extended Kalman Filter Application to GPS Attitude Estimation Multiplicative Quaternion Formulation Discrete-Time Attitude Estimation Murrell's Version Farrenkopf's Steady-State Analysis Orbit Estimation Target Tracking of Aircraft The a-b Filter The a-b-g Filter Aircraft Parameter Estimation Smoothing with the Eigen-system Realization Algorithm Summary OPTIMAL CONTROL AND ESTIMATION THEORY Calculus of Variations Optimization with Differential Equation Constraints Pontryagin's Optimal Control Necessary Conditions Discrete-Time Control Linear Regulator Problems Continuous-Time Formulation Discrete-Time Formulation Linear Quadratic-Gaussian Controllers Continuous-Time Formulation Discrete-Time Formulation Loop Transfer Recovery Spacecraft Control Design Summary APPENDIX A MATRIX PROPERTIES Basic Definitions of Matrices Vectors Matrix Norms and Definiteness Matrix Decompositions Matrix Calculus APPENDIX B BASIC PROBABILITY CONCEPTS Functions of a Single Discrete-Valued Random Variable Functions of Discrete-Valued Random Variables Functions of Continuous Random Variables Gaussian Random Variables Chi-Square Random Variables Propagation of Functions through Various Models Linear Matrix Models Nonlinear Models APPENDIX C PARAMETER OPTIMIZATION METHODS C.1 Unconstrained Extrema C.2 Equality Constrained Extrema C.3 Nonlinear Unconstrained Optimization C.3.1 Some Geometrical Insights C.3.2 Methods of Gradients C.3.3 Second-Order (Gauss-Newton) Algorithm APPENDIX D COMPUTER SOFTWARE Index

Kalman filters for non-linear systems: a comparison of performance

Abstract: The Kalman filter is a well-known recursive state estimator for linear systems. In practice, the algorithm is often used for non-linear systems by linearizing the system's process and measurement models. Different ways of linearizing the models lead to different filters. In some applications, these ‘Kalman filter variants’ seem to perform well, while for other applications they are useless. When choosing a filter for a new application, the literature gives us little to rely on. This paper tries to bridge the gap between the theoretical derivation of a Kalman filter variant and its performance in practice when applied to a non-linear system, by providing an application-independent analysis of the performances of the common Kalman filter variants. Correlated uncertainties can be dealt with by augmenting the state vector, this is the original formulation of the KF (Kalman 1960). Expressed in this new state vector, the process and measurement models are of the form (1) and (2) with uncorrelated uncertainties...

Sigma-Point Kalman Filters for Integrated Navigation

Abstract: Core to integrated navigation systems is the concept of fusing noisy observations from GPS, Inertial Measurement Units (IMU), and other available sensors. The current industry standard and most widely used algorithm for this purpose is the extended Kalman filter (EKF) [6]. The EKF combines the sensor measurements with predictions coming from a model of vehicle motion (either dynamic or kinematic), in order to generate an estimate of the current navigational state (position, velocity, and attitude). This paper points out the inherent shortcomings in using the EKF and presents, as an alternative, a family of improved derivativeless nonlinear Kalman filters called sigma-point Kalman filters (SPKF). We demonstrate the improved state estimation performance of the SPKF by applying it to the problem of loosely coupled GPS/INS integration. A novel method to account for latency in the GPS updates is also developed for the SPKF (such latency compensation is typically inaccurate or not practical with the EKF). A UAV (rotor-craft) test platform is used to demonstrate the results. Performance metrics indicate an approximate 30% error reduction in both attitude and position estimates relative to the baseline EKF implementation.

Robust observer-based control of systems with state perturbations via LMI approach

Abstract: In this note, the observer-based control for a class of uncertain, linear systems is considered. Exponential stabilizability for the systems is studied and the convergence rate of the system is estimated. A linear matrix inequality (LMI) approach is used to design the observer-based control. The control and observer gains are given from LMI feasible solution. A numerical example is given to illustrate our results.

Comparison between the unscented Kalman filter and the extended Kalman filter for the position estimation module of an integrated navigation information system

Abstract: An integrated navigation information system must know continuously the current position with a good precision. The required performance of the positioning module is achieved by using a cluster of heterogeneous sensors whose measurements are fused. The most popular data fusion method for positioning problems is the extended Kalman filter. The extended Kalman filter is a variation of the Kalman filter used to solve non-linear problems. Recently, an improvement to the extended Kalman filter has been proposed, the unscented Kalman filter. This paper describes an empirical analysis evaluating the performances of the unscented Kalman filter and comparing them with the extended Kalman filter's performances.

Estimation of nonstationary EEG with Kalman smoother approach: an application to event-related synchronization (ERS)

Abstract: An adaptive spectrum estimation method for nonstationary electroencephalogram by means of time-varying autoregressive moving average modeling is presented The time-varying parameter estimation problem is solved by Kalman filtering along with a fixed-interval smoothing procedure Kalman filter is an optimal filter in the mean square sense and it is a generalization of other adaptive filters such as recursive least squares or least mean square Furthermore, by using the smoother the unavoidable tracking lag of adaptive filters can be avoided Due to the properties of Kalman filter and benefits of the smoothing the time-frequency resolution of the presented Kalman smoother spectra is extremely high The presented approach is applied to estimation of event-related synchronization/desynchronization (ERS/ERD) dynamics of occipital alpha rhythm measured from three healthy subjects With the Kalman smoother approach detailed spectral information can be extracted from single ERS/ERD samples

Estimation of parameters in a linear state space model using a Rao-Blackwellised particle filter

Abstract: A Rao-Blackwellised particle filter is used in the estimation of the parameters of a linear stochastic state space model. The proposed method combines the particle filtering technique with a Kalman filter using marginalisation so as to make full use of the analytically tractable structure of the model. Simulation studies are performed on a simple illustrative example and the results demonstrate the effectiveness of the proposed method in comparison with the conventional extended-Kalman-filler-based method. The proposed method is then applied in the estimation of the parameters in a railway vehicle dynamic model for condition monitoring and the desired results have been obtained.

Closed-loop neural control of cursor motion using a Kalman filter

Abstract: Recently, we proposed a Kalman filter method to model the probabilistic relationship between neural firing in motor cortex and hand kinematics. In this paper, we demonstrate on-line, closed-loop, neural control of cursor motion using the Kalman filter. In this task a monkey moves a cursor on a computer monitor using either a manipulandum or their neural activity recorded with a chronically implanted micro-electrode array. A number of advantages of the Kalman filter were explored during the on-line tasks and we found that the Kalman filter had superior performance to previously reported linear regression methods. While the results suggest the applicability of the Kalman filter for neural prosthesis applications, we observed the decoded cursor position was noisier under brain control as compared with manual control using the manipulandum. To smooth the cursor motion without decreasing accuracy we propose a method that smoothes the neural firing rates. This smoothing method is described and its validity is quantitatively evaluated with recorded data.

Use of the Kalman filter for inference in state-space models with unknown noise distributions

Abstract: The Kalman filter is frequently used for state estimation in state-space models when the standard Gaussian noise assumption does not apply. A problem arises, however, in that inference based on the incorrect Gaussian assumption can lead to misleading or erroneous conclusions about the relationship of the Kalman filter estimate to the true (unknown) state. This note shows how inequalities from probability theory associated with the probabilities of convex sets have potential for characterizing the estimation error of a Kalman filter in such a non-Gaussian (distribution-free) setting.

Unscented Kalman Filtering of a Simulated pH System

Abstract: Recently, the unscented Kalman filter (UKF) algorithm, which is a new generalization of the Kalman filter for nonlinear systems, was proposed in the literature. It has significant advantages over its widely used predecessor, the extended Kalman filter (EKF). These include better accuracy and simpler implementation and the dispensability of system and measurement model differentiability. In this work, we compare the performance of the two approaches in a simulated pH process with three situations considered. The first one evaluates the performance differences between the unscented transform and the EKF linearization, as applied to the nonlinear pH output equation. In the second simulation, the complete filter algorithms are compared in a state estimation framework. The third case concerns parameter estimation. In all three cases, the UKF produced more-accurate results.

Remarks on the existence of a Kazantzis-Kravaris/Luenberger observer

Abstract: We state sufficient conditions for the existence, on a given open set, of the extension, to nonlinear systems, of the Luenberger observer as it has been proposed by Kazantzis and Kravaris. To weaken these conditions, the observer is modified in a way which induces a time rescaling and which follows from a forward unboundedness observability property. Also, we state it is sufficient to choose the dimension of the dynamic system, giving the observer, less than or equal to 2 + twice the dimension of the state to be observed. Finally we show how approximation is allowed and we establish a link with high gain observers.

An adaptive speed observer based on a new total least-squares neuron for induction machine drives

Abstract: This paper proposes a new observer that computes the rotor speed of an induction motor by employing on-line a least-square algorithm implemented by an original neuron (total least squares (TLS) EXIN). It minimizes the estimation error from the equation of the Luenberger observer considering the rotor flux linkage estimation uncertainty. Experimental results show the goodness of this algorithm that outperforms the Matsuse observer in speed estimation accuracy at very low speed and zero-speed operations at no-load and at load. Moreover, it has been verified both numerically and experimentally that this observer works properly even at very low speeds in regenerating mode without any instability.

New natural observer applied to speed-sensorless DC servo and induction motors

Abstract: A simple observer design technique with parameter adaptation is proposed for bounded-input bounded-output nonlinear systems. In this technique, no feedback is used in the observer but parameter estimations are considered as if they are observer inputs. The proposed technique is successfully applied to speed-sensorless dc servomotors and speed-sensorless induction motors with load torque adaptation schemes. The observer is robust to noise and parameter uncertainty. Excellent experimental and simulation results have been obtained.

Introduction to Kalman filters

Abstract: This chapter discusses recursive least square (RLS) estimation and the underlying idea of Kalman filters. When it comes to filtering of stochastic (random) signals, it is difficult to extract or reject the desired parts of the spectra to obtain the required filtering action. In such a situation, a Kalman filter is very helpful as signals are filtered according to their statistical properties, rather than their frequency contents. The Kalman filter has other interesting properties. The filter contains a signal model, a type of “simulator” that produces the output signal. When the quality of the input signal is good, the signal is used to generate the output signal and the internal model is adjusted to follow the input signal. When, on the other hand, the input signal is poor, it is ignored and the output signal from the filter is mainly produced by the model. In this way, the filter can produce a reasonable output signal even during drop out of the input signal. Further, once the model has converged well to the input signal, the filter can be used to simulate future output signals, i.e., the filter can be used for prediction. Kalman filters are often used to condition transducer signals and in control systems for satellites, aircraft and missiles. The filter is also used in applications dealing with examples, such as economics, medicine, chemistry, and sociology.

An unscented particle filter for GMTI tracking

Abstract: Ground moving target indicator (GMTI) tracking is often carried out using extended Kalman filters, as in the variable-structure interacting multiple-model (VS-IMM) filter. In some scenarios, however, this is considered to be inadequate. It has been shown that in this case, a particle filter can give better performance. Such a filter, the variable-structure multiple-model particle filter (VS-MMPF), is given in the literature. In this paper we present a new approach to solving the GMTI tracking problem using a particle filter. We have developed an unscented particle filter, where the particles model the uncertainty over the motion model while, conditional upon the model, the target state is modelled using an unscented Kalman filter. Simulation results show that the UPF-based filter gives performance similar to the VS-MMPF with significantly fewer particles and better results than the standard VS-IMM approach.

SLAM based on Kalman filter for multi-rate fusion of laser and encoder measurements

Abstract: In this paper, extended Kalman and unscented Kalman filters are developed for multi-rate systems in the context of the SLAM problem. These multi-rate filters have been extensively compared and tested with experimental data taken from a parking lot. Both multi-rate filters have improved the estimation with respect to the conventional single-rate Kalman filter. A performance index is introduced, showing that EKF gives better performance than UKF. In order to complete the SLAM solution, well-known techniques for feature extraction, data association and map building have been also implemented.

Robust Kalman filtering via Krein space estimation

Abstract: A robust Kalman filter is proposed for the discrete-time system with norm-bounded parametric uncertainties. The uncertainties are described by the energy bound constraint, i.e. the sum quadratic constraint (SQC). It is shown that the SQC can be converted into an indefinite quadratic cost function to be minimised in the Krein space, and it is found that the Krein space Kalman filter is a solution of the minimisation problem. After introducing a Krein space state-space model, which includes the uncertainty, one can easily write a robust version of the Krein space Kalman filter by modifying the measurement matrix and the variance of measurement noises in the original Krein space Kalman filter. Since the resulting robust Kalman filter has the same recursive structure as a conventional Kalman filter, a robust filtering scheme can be readily designed using the proposed method. A numerical example demonstrates that the proposed filter achieves robustness against parameter variation and improvement in performance when compared with a conventional Kalman filter and an existing robust Kalman filter, respectively.

Nonlinear robust observer design for strapdown INS in-flight alignment

Abstract: A nonlinear observer is proposed for a strapdown inertial navigation system (SDINS) in-flight alignment problem using an H/sub /spl infin// filter Riccati equation and a freedom parameter. The proposed observer improves the filtering stability, convergence, and performance. The characteristics of the observer are analyzed using a Lyapunov function. Simulation results demonstrate a significant reduction in alignment errors by employing the proposed nonlinear observer. The observer is developed in general such that it can be applied to estimating nonlinear systems other than the SDINS in-flight alignment.

Powerful nonlinear observer associated with field-oriented control of an induction motor

Abstract: In this paper, we associate field-oriented control with a powerful nonlinear robust flux observer for an induction motor to show the improvement made by this observer compared with the open-loop and classical estimator used in this type of control We implement this design strategy through an extension of a special class of nonlinear multivariable systems satisfying some regularity assumptions We show by an extensive study that this observer is completely satisfactory at low and nominal speeds and it is not sensitive to disturbances and parametric errors It is robust to changes in load torque, rotational speed and rotor resistance The method achieves a good performance with only one easier gain tuning obtained from an algebraic Lyapunov equation Finally, we present results and simulations with concluding remarks on the advantages and perspectives for the observer proposed with the field-oriented control

A new approach to time-dependent inversion of geodetic data using a Monte Carlo mixture Kalman filter

Abstract: SUMMARY In the last decade, continuous Global Positioning System (GPS) networks have observed transient crustal deformation associated with various types of aseismic fault-slip event in many subduction zones. It is important to precisely clarify the entire time history of these events to understand the physical process of earthquake generation. For this purpose, we have developed a new time-dependent inversion method for imaging transient fault slips from geodetic data. Segall & Matthews (1997) presented a time-dependent inversion method to infer the spatiotemporal distribution of fault slip from geodetic data. They modelled a transient crustal deformation associated with fault-slip events using a linear Gaussian state space model and employed a Kalman filter. They introduced a scaling parameter that represents the temporal smoothness of the fault slip, and assumed that the scaling parameter is constant over the observation period. Under this assumption, abrupt changes of slip have been overly smoothed, whereas estimated slips in a ‘quiet’ steady-state period have been oscillatory. To improve the method, we developed a new filtering technique, a Monte Carlo mixture Kalman filter (MCMKF), and apply it to time-dependent inversion. The MCMKF allows variations of the temporal smoothness of slips by regarding it as a stochastic variable. The MCMKF is based on a Monte Carlo method in which conditional probability density functions of the stochastic variable are estimated recursively. We examine the validity of the introduced MCMKF-based inversion scheme through numerical experiments using simulated displacement time-series. Then, the results are compared with those obtained by a conventional Kalman filter-based scheme. In all cases, MCMKF gives a significantly smaller Akaike information criterion (AIC) values than the Kalman filter. This indicates that MCMKF yields better state estimates than the Kalman filter. We also find that MCMKF is capable of imaging the initiation process of transient slip events in cases with a high signal-to-noise ratio, while the Kalman filter is not. Furthermore, MCMKF is superior to the Kalman filter in detecting small signals from noisy data sets. From all of the results above, we conclude that the new filtering approach introduced here may provide a powerful tool for imaging the time history of fault slips.

Adaptive observer and related method

Abstract: A disclosed apparatus comprises an adaptive observer that has an adaptive element to augment a linear observer to enhance its ability to control a nonlinear system. The adaptive element comprises a first, and optionally a second, nonlinearly parameterized neural network unit, the inputs and output layer weights of which can be adapted on line. The adaptive observer generates the neural network units' teaching signal by an additional linear error observer of the nominal system's error dynamics. The adaptive observer has the ability to track an observed system in the presence of unmodeled dynamics and disturbances. The adaptive observer comprises a delay element incorporated in the adaptive element in order to provide delayed values of an actual output signal and a control signal to the neural network units.

Covariance profiling for an adaptive Kalman filter to suppress sensor quantization effects

Abstract: This paper presents a generic approach to model the noise covariance associated with discrete sensors such as incremental encoders and low resolution analog to digital converters. The covariance is then used in an adaptive Kalman filter that selectively and appropriately carries out measurement updates. The temporal as well as system state measurements are used to predict the quantization error of the measurement signal. The effectiveness of the method is demonstrated by applying the technique to incremental encoders of varying resolutions. Simulation of an example system with varying encoder resolutions is presented to show the performance of the new filter. Results show that the new adaptive filter produces more accurate results while requiring a lower resolution encoder than a similarly designed conventional Kalman filter, especially at low velocities.

Application of the Kalman-Levy filter for tracking maneuvering targets

Abstract: In target tracking algorithms using Kalman filtering-like approaches, the standard assumptions are Gaussian process and measurement noise models. Based on these assumptions, the Kalman filter is widely used in single or multiple filter versions (e.g., in an Interacting Multiple Model-IMM-estimator). The over-simplification resulting from the above assumptions can cause severe degradation in tracking performance. Of particular concern is the simplistic white noise or Wiener process acceleration models used to handle maneuvering targets. Presence of heavy-tailed noise in the observation process is another concern. In this paper we explore the application of Kalman-Levy filter to handle maneuvering targets. This filter assumes a heavy tailed noise distribution known as the Levy distribution. Unlike in the case of Gaussian distribution, the existence of the covariance is not guaranteed in this case. Due to the heavy tailed nature of the assumed distribution, the Kalman-Levy filter is more effective in the presence of large errors that can occur, for example, due to the onset of acceleration or deceleration. However, for the same reason, the performance of Kalman-Levy filter in non-maneuvering portion of track is worse than a Kalman filter's. This motivates us to develop an IMM estimator incorporating a Kalman filter and a Kalman-Levy filter. The performance of this filter is compared with an IMM estimator with two standard Kalman filters in a scenario from the 4th Navy tracking benchmark problem. It is found that the IMM estimator with a Kalman-Levy filter performs better than the other IMM estimator in both maneuvering and non-maneuvering portion of target flight.© (2004) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A color-based tracking by Kalman particle filter

Abstract: In this paper, a method for real-time tracking of moving objects is proposed. We applied Kalman particle filter (KPF) to color-based tracking. This KPF is a particle filter including the principle of Kalman filter, and it was adopted to the object contour tracking. We modified this KPF for color-based tracking. This modified KPF can approximate the probabilistic density of the position of the tracked object properly and needs fewer particles for tracking than conventional particle filters. We made experiments to confirm the effectiveness of this method.

Predict chaotic time-series using unscented Kalman filter

Abstract: Although the extended Kalman filter is a widely used estimator for nonlinear systems, it has two drawbacks: linearization can produce unstable filters and it is hard to implement the derivation of the Jacobian matrices. This work presents a new method of predicting Mackey-Glass equation based on unscented Kalman filter. The principle of unscented transform is analyzed and the algorithm of UKF is discussed And then EKF and UKF methods are used to estimate the noisy chaotic time-series, and the estimation errors between two different algorithms are compared. Simulation results show this filter can predict chaotic time-series more effectively and accurately than extended Kalman filter.