Showing papers on "Alpha beta filter published in 2009"

Direct Yaw-Moment Control of an In-Wheel-Motored Electric Vehicle Based on Body Slip Angle Fuzzy Observer

Abstract: A stabilizing observer-based control algorithm for an in-wheel-motored vehicle is proposed, which generates direct yaw moment to compensate for the state deviations. The control scheme is based on a fuzzy rule-based body slip angle (beta) observer. In the design strategy of the fuzzy observer, the vehicle dynamics is represented by Takagi-Sugeno-like fuzzy models. Initially, local equivalent vehicle models are built using the linear approximations of vehicle dynamics for low and high lateral acceleration operating regimes, respectively. The optimal beta observer is then designed for each local model using Kalman filter theory. Finally, local observers are combined to form the overall control system by using fuzzy rules. These fuzzy rules represent the qualitative relationships among the variables associated with the nonlinear and uncertain nature of vehicle dynamics, such as tire force saturation and the influence of road adherence. An adaptation mechanism for the fuzzy membership functions has been incorporated to improve the accuracy and performance of the system. The effectiveness of this design approach has been demonstrated in simulations and in a real-time experimental setting.

Kalman filtering for positioning and heading control of ships and offshore rigs

Abstract: In this article, we have described the main components of a ship motion-control system and two particular motion-control problems that require wave filtering, namely, dynamic positioning and heading autopilot. Then, we discussed the models commonly used for vessel response and showed how these models are used for Kalman filter design. We also briefly discussed parameter and noise covariance estimation, which are used for filter tuning. To illustrate the performance, a case study based on numerical simulations for a ship autopilot was considered. The material discussed in this article conforms to modern commercially available ship motion-control systems. Most of the vessels operating in the offshore industry worldwide use Kalman filters for velocity estimation and wave filtering. Thus, the article provides an up-to-date tutorial and overview of Kalman-filter-based wave filtering.

Large sample asymptotics for the ensemble Kalman filter

Abstract: The ensemble Kalman filter (EnKF) has been proposed as a Monte Carlo, derivative-free, alternative to the extended Kalman filter, and is now widely used in sequential data assimilation, where state vectors of huge dimension (e.g. resulting from the discretization of pressure and velocity fields over a continent, as considered in meteorology) should be estimated from noisy measurements (e.g. collected at sparse in-situ stations). Even if the state and measurement equations are linear with additive Gaussian white noise, computing and storing the error covariance matrices involved in the Kalman filter is practically impossible, and it has been proposed to represent the filtering distribution with a sample (ensemble) of a few elements and to think of the corresponding empirical covariance matrix as an approximation of the intractable error covariance matrix. Extensions to nonlinear state equations have also been proposed. Surprisingly, very little is known about the asymptotic behaviour of the EnKF, whereas on the other hand, the asymptotic behaviour of many different classes of particle filters is well understood, as the number of particles goes to infinity. Interpreting the ensemble elements as a population of particles with mean-field interactions (and not merely as an instrumental device producing the ensemble mean value as an estimate of the hidden state), we prove the convergence of the EnKF, with the classical rate 1/\sqrt{N}, as the number N of ensemble elements increases to infinity. In the linear case, the limit of the empirical distribution of the ensemble elements is the usual (Gaussian distribution associated with the) Kalman filter, as expected, but in the more general case of a nonlinear state equation with linear observations, this limit differs from the usual Bayesian filter. To get the correct limit in this case, the mechanism that generates the elements in the EnKF should be interpreted as a proposal importance distribution, and appropriate importance weights should be assigned to the ensemble elements.

Adaptive Two-Stage Extended Kalman Filter for a Fault-Tolerant INS-GPS Loosely Coupled System

Abstract: The well-known conventional Kalman filter requires an accurate system model and exact stochastic information. But in a number of situations, the system model has an unknown bias, which may degrade the performance of the Kalman filter or may cause the filter to diverge. The effect of the unknown bias may be more pronounced on the extended Kalman filter (EKF), which is a nonlinear filter. The two-stage extended Kalman filter (TEKF) with respect to this problem has been receiving considerable attention for a long time. Recently, the optimal two-stage Kalman filter (TKF) for linear stochastic systems with a constant bias or a random bias has been proposed by several researchers. A TEKF can also be similarly derived as the optimal TKF. In the case of a random bias, the TEKF assumes that the information of a random bias is known. But the information of a random bias is unknown or partially known in general. To solve this problem, this paper proposes an adaptive two-stage extended Kalman filter (ATEKF) using an adaptive fading EKF. To verify the performance of the proposed ATEKF, the ATEKF is applied to the INS-GPS (inertial navigation system-Global Positioning System) loosely coupled system with an unknown fault bias. The proposed ATEKF tracked/estimated the unknown bias effectively although the information about the random bias was unknown.

Consideration of time-correlated errors in a Kalman filter applicable to GNSS

Abstract: An algorithm for considering time-correlated errors in a Kalman filter is presented. The algorithm differs from previous implementations in that it does not suffer from numerical problems; does not contain inherent time latency or require reinterpretation of Kalman filter parameters, and gives full consideration to additive white noise that is often still present but ignored in previous implementations. Simulation results indicate that the application of the new algorithm yields more realistic and therefore useful state and covariance information than the standard implementation. Results from a field test of the algorithm applied to the problem of kinematic differential GPS demonstrate that the algorithm provides slightly pessimistic covariance estimates whereas the standard Kalman filter provides optimistic covariance estimates.

Lyapunov-Based Nonlinear Disturbance Observer for Serial n-Link Robot Manipulators

Abstract: In this paper we extend the work done by Chen et al. (IEEE Trans Ind Electron 47(4):932---938, 2000) which proposed a nonlinear disturbance observer for two-link robot manipulators to n-link robot manipulators. A general form of dynamic equations of serial n-link robot manipulator is considered, and the stability analysis of the proposed observer is performed by using Lyapunov's direct method. Although it seems that the formulation of disturbance observer is easy to derive, choosing the disturbance observer gain to guarantee stability is really hard. In this paper it is shown that the design parameter can be selected depends on the maximum velocity and physical parameters of robot manipulator to guarantee the global asymptotic stability of the disturbance observer. Using this nonlinear disturbance observer, no accurate dynamic model is required to achieve high precision motion control, because it makes the system robust against internal disturbances such as unmodeled dynamics and external disturbances such as friction in joints. The effectiveness of the proposed observer is investigated by numerical simulation for three-Dofs robot manipulator. In fact, controller with disturbance observer has more superior tracking performance, with a wide range of payloads and in the presence of friction in joints. It is also found that, although the proposed observer is designed for slow varying disturbances, it can estimate rapid time varying disturbances very well.

Digital Implementation of Stator and Rotor Flux-Linkage Observers and a Stator-Current Observer for Deadbeat Direct Torque Control of Induction Machines

Abstract: Properly formed discrete-time recursive models of a stator and rotor flux-linkage observer are presented. A model delay in the flux-linkage observer, which hindered previous work, is identified. To remove this delay, a new stationary frame current observer is developed and experimentally verified. With this new observer system, the flux linkages are properly estimated for the next sample instant, thus removing the computational delay. The improved and the delayed flux observer are evaluated in a deadbeat direct torque control algorithm.

Unscented Kalman Filters for Multiple Target Tracking With Symmetric Measurement Equations

Abstract: The symmetric measurement equation approach to multiple target tracking is revisited using the unscented Kalman filter. The performance of this filter is compared to the original symmetric measurement equation implementation using an extended Kalman filter. Counterintuitive results are presented and explained for two sets of symmetric measurement equations. We find that the performance of the SME approach is dependent on the interaction of the SME equations and filter used. Furthermore, an SME/unscented Kalman filter pairing is shown to have improved performance versus previous approaches while possessing simpler implementation and equivalent computational complexity.

A comparative study of Luenberger observer, sliding mode observer and extended Kalman filter for sensorless vector control of induction motor drives

Abstract: Observer-based sensorless techniques are becoming more and more popular and universal. This paper presents a comparative study of three kinds of observers for direct field oriented controlled (DFOC) induction motor (IM) drive: Luenberger observer (LO), sliding mode observer (SMO) and extended Kalman filter (EKF). Each kind of observer employs the dynamic full-order IM model and mechanical equation is introduced to improve the performance of speed estimation. Theoretical principles of the three observers are illustrated. Not only computer simulations, but also a series of experimental results are presented to evaluate the performances of the three observers. A comprehensive analysis and comparisons are given from several aspects, such as steady state accuracy, dynamic performance, low speed operation, parameter sensitivity, noise sensitivity and complexity. The advantages and disadvantages of each observer are summarized and a comprehensive conclusion is given.

Particle Filtering for State Estimation in Nonlinear Industrial Systems

Abstract: State estimation is a major problem in industrial systems, particularly in industrial robotics. To this end, Gaussian and nonparametric filters have been developed. In this paper, the extended Kalman filter, which assumes Gaussian measurement noise, is compared with the particle filter, which does not make any assumption on the measurement noise distribution. As a case study, the estimation of the state vector of an industrial robot is used when measurements are available from an accelerometer that was mounted on the end effector of the robotic manipulator and from the encoders of the joints' motors. It is shown that, in this kind of sensor fusion problem, the particle filter outperforms the extended Kalman filter, at the cost of more demanding computations.

Particle and Kalman filtering for state estimation and control of DC motors.

Abstract: State estimation is a major problem in industrial systems. To this end, Gaussian and nonparametric filters have been developed. In this paper the Kalman Filter, which assumes Gaussian measurement noise, is compared to the Particle Filter, which does not make any assumption on the measurement noise distribution. As a case study the estimation of the state vector of a DC motor is used. The reconstructed state vector is used in a feedback control loop to generate the control input of the DC motor. In simulation tests it was observed that for a large number of particles the Particle Filter could succeed in accurately estimating the motor's state vector, but at the same time it required higher computational effort.

Comparison of several space target tracking filters

Abstract: In this paper, we present a comparative study of several nonlinear filters, namely, extended Kalman Filter (EKF), unscented KF (UKF), particle filter (PF), and recursive linear minimum mean square error (LMMSE) filter for the problem of satellite trajectory estimation. We evaluate the tracking accuracy of the above filtering algorithms and obtain the posterior Cramer-Rao lower bound (PCRLB) of the tracking error for performance comparison. Based on the simulation results, we provide recommendations on the practical tracking filter selection and guidelines for the design of observer configurations.

A Brief Tutorial on the Ensemble Kalman Filter

Abstract: The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models. The EnKF originated as a version of the Kalman filter for large problems (essentially, the covariance matrix is replaced by the sample covariance), and it is now an important data assimilation component of ensemble forecasting. EnKF is related to the particle filter (in this context, a particle is the same thing as an ensemble member) but the EnKF makes the assumption that all probability distributions involved are Gaussian. This article briefly describes the derivation and practical implementation of the basic version of EnKF, and reviews several extensions.

The stability analysis of the adaptive fading extended Kalman filter using the innovation covariance

Abstract: The well-known conventional Kalman filter gives the optimal solution but to do so, it requires an accurate system model and exact stochastic information. However, in a number of practical situations, the system model and the stochastic information are incomplete. The Kalman filter with incomplete information may be degraded or even diverged. To solve this problem, a new adaptive fading filter using a forgetting factor has recently been proposed by Kim and co-authors. This paper analyzes the stability of the adaptive fading extended Kalman filter (AFEKF), which is a nonlinear filter form of the adaptive fading filter. The stability analysis of the AFEKF is based on the analysis result of Reif and co-authors for the EKF. From the analysis results, this paper shows the upper bounded condition of the error covariance for the filter stability and the bounded value of the estimation error. Keywords: Adaptive Kalman filter, forgetting factor, nonlinear filter, stability analysis.

A SLAM algorithm based on the central difference Kalman filter

Abstract: This paper presents an central difference Kalman filter (CDKF) based Simultaneous Localization and Mapping (SLAM) algorithm, which is an alternative to the classical extended Kalman filter based SLAM solution (EKF-SLAM). EKF-SLAM suffers from two important problems, which are the calculation of Jacobians and the linear approximations to the nonlinear models. They can lead the filter to be inconsistent. To overcome the serious drawbacks of the previous frameworks, Sterling's polynomial interpolation method is employed to approximate nonlinear models. Combined with the Kanlman filter framework, CDKF is proposed to solve the probabilistic state-space SLAM problem. The proposed approach improves the filter consistency and state estimation accuracy. Both simulated experiments and bench mark data set are used to demonstrating the superiority of the proposed algorithm.

Process monitoring and parameter estimation via unscented Kalman filtering

Abstract: Nonlinear estimation techniques play an important role in process monitoring since some states and most of the parameters cannot be directly measured. This paper investigates the use of several estimation algorithms such as linearized Kalman filter (LKF), extended Kalman filter (EKF), unscented Kalman filter (UKF) and moving horizon estimation (MHE) for nonlinear systems with special emphasis on UKF as it is a relatively new technique. Detailed case studies show that UKF has advantages over EKF for highly nonlinear unconstrained estimation problems while MHE performs better for systems with constraints.

Bayesian filtering techniques: Kalman and extended Kalman filter basics

Abstract: Bayesian filters provide a statistical tool for dealing with measurement uncertainty. Bayesian filters estimate a state of dynamic system from noisy observations. These filters represent the state by random variable and in each time step probability distribution over random variable represents the uncertainty. If estimate is needed with every new measurement, it is suitable to use recursive filter. Unfortunately optimal Bayesian solution exists in a restrictive set of cases, e.g. Kalman filters which assume Gaussian PDF or we need to use suboptimal solution, e.g. extended Kalman filters which use local linearization to approximate PDF to be Gaussian.

Fault detection in sensor information fusion Kalman filter

Abstract: An approach to the test of the sensor information fusion Kalman filter is proposed. It is based on the introduced statistics of mathematical expectation of the spectral norm of a normalized innovation matrix. The approach allows for simultaneous test of the mathematical expectation and the variance of innovation sequence in real time and does not require a priori information on values of the change in its statistical characteristics under faults. Using this approach, fault detection algorithm for the sensor information fusion Kalman filter is developed.

Adaptive Unscented Kalman Filter with multiple fading factors for pico satellite attitude estimation

Abstract: Thus far, Kalman filter based attitude estimation algorithms have been used in many space applications. When the issue of pico satellite attitude estimation is taken into consideration, general linear approach to Kalman filter becomes insufficient and Extended Kalman Filters (EKF) are the types of filters, which are designed in order to overrun this problem. However, in case of attitude estimation of a pico satellite via magnetometer data, where the nonlinearity degree of both dynamics and measurement models are high, EKF may give inaccurate results. Unscented Kalman Filter (UKF) that does not require linearization phase and so Jacobians can be preferred instead of EKF in such circumstances. Nonetheless, if the UKF is built with an adaptive manner, such that, faulty measurements do not affect attitude estimation process, accurate estimation results even in case of measurement malfunctions can be guaranteed. In this study an Adaptive Unscented Kalman Filter with multiple fading factors based gain correction is introduced and tested on the attitude estimation system of a pico satellite by the use of simulations.

A Low-Complexity Kalman Approach for Channel Estimation in Doubly-Selective OFDM Systems

Abstract: In this letter, we propose a vector state-scalar observation (VSSO) Kalman filter for channel estimation in doubly-selective orthogonal frequency division multiplexing (OFDM) systems. Vector state-vector observation (VSVO) Kalman filters have been reported before in the literature for this purpose. The proposed VSSO Kalman filter achieves the same performance as the VSVO Kalman filter and results in 92% complexity savings. The Kalman filter outperforms a recently proposed linear minimum mean square error (LMMSE) estimator and achieves a high spectral efficiency of 93% as compared to the LMMSE estimator of 68%. A key aspect of this paper is that we show how the observed pilot symbol vector can be decorrelated or decoupled into uncorrelated multipath scalars. This aspect (and the proposed Kalman filter) is similar in spirit to that of a quasi-static channel.

Unscented Kalman Filter with Application to Bearings- Only Target Tracking

Abstract: The unscented transformation coupled with certain parts of the classic Kalman Alter, provides a more accurate method than the Extended Kalman Filter for nonlinear state estimation. Using bearings-only measurements, the unscented Kalman Filter algorithm estimates target motion parameters and detects target maneuver, using zero mean chi-square distributed random sequence residuals, in a sliding window format. During target maneuvering, the co-variance of the process noise is sufficiently increased in such a way that the disturbance in the solution is minimized. When target maneuver is completed, the covariance of process noise is lowered. The performance of this algorithm is evaluated using Monte Carlo simulation and results are presented.

Comments on “Sigma-Point Kalman Filter Data Assimilation Methods for Strongly Nonlinear Systems”

Abstract: Ambadan and Tang (2009, hereinafter AT09) recently performed a study of several varieties of a ‘‘sigma-point’’ Kalman filter (SPKF) using two strongly nonlinear models, Lorenz (1963, hereinafter L63) and Lorenz (1996, hereinafter L96). In this comparison, a reference benchmark was the performance of a standard ensemble Kalman filter (EnKF) of Evensen (1994, 2003), presumably with perturbed observations following Houtekamer and Mitchell (1998) and Burgers et al. (1998). We have identified problems in the description of the EnKF as well as its application with the L63 and L96 models.