Showing papers on "Alpha beta filter published in 1999"

Adaptive Kalman Filtering for INS/GPS

Abstract: After reviewing the two main approaches of adaptive Kalman filtering, namely, innovation-based adaptive estimation (IAE) and multiple-model-based adaptive estimation (MMAE), the detailed development of an innovation-based adaptive Kalman filter for an integrated inertial navigation system/global positioning system (INS/GPS) is given. The developed adaptive Kalman filter is based on the maximum likelihood criterion for the proper choice of the filter weight and hence the filter gain factors. Results from two kinematic field tests in which the INS/GPS was compared to highly precise reference data are presented. Results show that the adaptive Kalman filter outperforms the conventional Kalman filter by tuning either the system noise variance–covariance (V–C) matrix `Q' or the update measurement noise V–C matrix `R' or both of them.

The extended Kalman filter as an exponential observer for nonlinear systems

Abstract: We analyze the behavior of the extended Kalman filter as a state estimator for nonlinear deterministic systems. Using the direct method of Lyapunov, we prove that under certain conditions, the extended Kalman filter is an exponential observer, i.e., the dynamics of the estimation error is exponentially stable. Furthermore, we discuss a generalization of the Kalman filter with exponential data weighting to nonlinear systems.

A receding horizon Kalman FIR filter for discrete time-invariant systems

Abstract: A receding horizon Kalman FIR filter is presented that combines the Kalman filter and the receding horizon strategy when the horizon initial state is assumed to be unknown. The suggested filter is a FIR filter form which has many good inherent properties. It can always be defined irrespective of singularity problems caused by unknown information about the horizon initial state. The suggested filter can be represented in either an iterative form or a standard FIR form. It is also shown that the suggested filter possesses the unbiasedness property and the remarkable deadbeat property irrespective of any horizon initial condition. The validity of the suggested filter is illustrated by numerical examples.

Vehicle Dynamics Estimation Using Kalman Filters

Abstract: This paper deals with the application of stochastic state estimators in vehicle dynamics control. It is often unrealistic to assume that all vehicle states and the disturbances acting on it can be measured. System states that cannot be measured directly, can be estimated by a Kalman Filter. The idea of the Kalman filter is to implement a model of the real system in an on-board computer in parallel with the system itself. This paper will give 3 examples of this principle applied to automotive systems.

Adaptive sliding mode observer for speed sensorless control of induction motors

Abstract: This paper presents an adaptive sliding-mode observer for the speed-sensorless field-oriented control of induction motors. The observer detects the rotor flux components in the two-phase stationary reference frame by the motor electrical equations. The motor speed is estimated by an additional relation obtained by a Lyapunov function. The analytical development of the sliding observer and the speed estimation algorithm is fully explained. Experimental results are presented, based on a TMS320F240 digital signal processor controller implementation. The system performance with different observer gains and the influence of the motor parameters deviations are shown and discussed.

Passivity-based versus disturbance observer based robot control : Equivalence and stability

Abstract: Disturbance observer based robot control algorithms provide good control performance while giving a straightforward method of gain selection Unfortunately the stability of these algorithms has not been shown rigorously for nonlinear systems such as robots. This paper demonstrates that a disturbance observer based algorithm can be made equivalent to the well-known passivity-based approaches of Sadegh and Horowitz, and Slotine and Li. This is accomplished by choosing a specific design of the Q(s) filter (described in the paper) of the disturbance observer. By doing so, the stability of the disturbance observer based approach can be proven rigorously. An additional benefit of the equivalence of the two approaches is the ability to combine an adaptive controller to the disturbance observer based approach.

Receding horizon recursive state estimation

Abstract: Describes a receding horizon discrete-time state observer using the deterministic least squares framework. The state estimation horizon, which determines the number of past measurement samples used to reconstruct the state vector, is introduced as a tuning parameter for the proposed state observer. A stability result concerning the choice of the state estimation horizon is established. It is also shown that the fixed memory receding horizon state observer can be related to the standard dynamic observer by using an appropriate end-point state weighting on the estimator cost function.

Comparison of extended and ensemble Kalman filters for data assimilation in coastal area modelling

Abstract: Data assimilation in a two-dimensional hydrodynamic model for bays, estuaries and coastal areas is considered. Two different methods based on the Kalman filter scheme are presented. These include (1) an extended Kalman filter in which the error covariance matrix is approximated by a matrix of reduced rank using a square root factorisation (RRSQRT KF), and (2) an ensemble Kalman filter (EnKF) based on a Monte Carlo simulation approach for propagation of errors. The filtering problem is formulated by utilising a general description of the model noise process related to errors in the model forcing, i.e. open boundary conditions and meteorological forcing. The performance of the two Kalman filters is evaluated using a twin experiment based on a hypothetical bay region. For both filters, the error covariance approximation sufficiently resolves the error propagation in the model at a computational load that is significantly smaller than required by the full Kalman filter algorithm. Furthermore, the Kalman filters are shown to be very robust with respect to defining the errors. Even in the case of a severely biased model error, the filters are able to efficiently correct the model. In general, the use of coloured model noise provides a numerically more efficient algorithm as well as a better performance of the filter. The error covariance approximation in the RRSQRT KF is shown to be more efficient than the error representation in the EnKF. For strongly non-linear dynamics, however, the EnKF is preferable. Copyright © 1999 John Wiley & Sons, Ltd.

Peak-seeking control with application to formation flight

Abstract: A new controller is proposed for linear systems with unknown optimal operating points. It is assumed that the desired operating point represents the maximum of a function of the states of the system. The controller uses a modified Kalman filter to estimate the derivatives of this function, and the controller drives the system to the optimum. The controller is derived in the context of the formation flight of aircraft for drag reduction, and a simulation is used to provide preliminary results.

A receding horizon Kalman FIR filter for linear continuous-time systems

Abstract: A receding horizon Kalman finite-impulse response (FIR) filter is suggested for continuous-time systems, combining the Kalman filter with the receding horizon strategy. In the suggested filter, the horizon initial state is assumed to be unknown. It can always be obtained irrespective of unknown information on the horizon initial state. The filter may be the first stochastic FIR form for continuous-time systems that may have many good inherent properties. The suggested filter can be represented in an iterative form and also in a standard FIR form. The suggested filter turns out to be a remarkable deadbeat observer. The validity of the suggested filter is illustrated by numerical examples.

Linear functional state observer for time-delay systems

Abstract: A new linear functional state observer for time-delay systems is introduced in this paper It is shown that the observer converges, with any prescribed stability margin, to any number of linear functionals when some conditions are met The design procedure is simple and can be easily implemented Numerical examples are given to illustrate the properties of the new observer and its advantages over existing observer design techniques in the literature

Design of Kalman filters for mobile robots; evaluation of the kinematic and odometric approach

Abstract: Kalman filters have for a long time been widely used on mobile robots as a location estimator. Many different Kalman filter designs have been proposed, using models of various complexity. In this paper, two different design methods are evaluated and compared. Focus is put on the common setup where the mobile robot is equipped with a dual encoder system supported by some additional absolute measurements. A common filter type for this setup is the odometric filter, where readings from the odometry system on the robot are used together with the geometry of the robot movement as a model of the robot. If additional kinematic assumptions are made, for instance regarding the velocity of the robot, an augmented model can be used instead. This kinematic filter has some advantages when used intelligently, and it is shown how this type of filter can be used to suppress noise on encoder readings and velocity estimates. The Kalman filter normally consists of a time update followed by one or more data updates. However, it is shown that when using the kinematic filter, the encoder measurements should be fused prior to the time update for better performance.

Nonlinear state observation using H/sub /spl infin//-filtering Riccati design

Abstract: The authors propose an observer for continuous-time nonlinear systems. The observer gain is computed by a Riccati differential equation similar to the extended Kalman filter. They prove that under certain conditions the proposed observer is an exponential observer by choosing an appropriate Lyapunov function. Furthermore, the authors explore some important relations of the proposed observer to robust control theory and H/sub /spl infin//-filtering. To examine the practical usefulness of the proposed observer they applied it to an induction motor for the estimation of the rotor flux and the angular velocity.

A Kalman filter approach to direct depth estimation incorporating surface structure

Abstract: The problem of depth-from-motion using a monocular image sequence is considered A pixel-based model is developed for direct depth estimation within a Kalman filtering framework A method is proposed for incorporating local surface structure into the Kalman filter Experimental results are provided to illustrate the effect of structural information on depth estimation

Reduced-order linear functional observer for linear systems

Abstract: A new reduced-order linear functional observer is introduced in this paper. The order of the observer is proportional to the ratio of the number of output measurements to the number of inputs. It is shown that the observer asymptotically converges to any number of linear functionals when some minor conditions are met. A simple observer construction procedure, which is easy to implement on MATLAB, is provided. Numerical examples are considered to illustrate the properties of the observer.

A hybrid asymptotic-Kalman observer for bioprocesses

Abstract: The exponential observers (extended Kalman or Luenberger observers, high gain observers) allow the use of a tuning parameter for managing the rate of convergence of the state estimate towards the true state. But their results are strongly dependent on the model quality (especially the kinetic model in bioprocesses). On the other hand, asymptotic observers (like the observer of Bastin and Dochain) have a rate of convergence which is a function of the experimental conditions (namely the dilution rate). However, this lack of tuning parameter is compensated by the absence of need for any kinetic model. In this paper, a hybrid technique is proposed which allows to jointly estimate the state and identify on-line the confidence on the kinetic model. The two limit cases (100 and 0 confidence) allow to recover rigorously the extended Kalman filter and the asymptotic observer of Bastin and Dochain. A simulation example (a fed-batch bacterial culture) is proposed and exhibits very satisfactory results.

Kalman Filters : A Tutorial

Abstract: A Kalman filter is a stochastic, recursive estimator, which estimates the state of a system based on the knowledge of the system input, the measurement of the system output, and a model of the relation between input and output. The Kalman filter equations are well known, but often little effort is spent to explain or understand how the Kalman filter really works, and what its assets and limitations are. This paper introduces the Kalman filter in a very intuitive way, and looks at its properties: what information can be extracted from it, and what are its limitations. This intuitive understanding should help to develop successful practical applications. The paper also points at further reading.

GPS-Based Optimal Kalman Estimation of Time Error, Frequency Offset, and Aging

Abstract: : Results are presented of studies of different types of optimal and quasi-optimal Kalman filters based on crystal and rubidium oscillators using reference timing signals from the Motorola GPS UT + Oncore Timing receiver. Filter equations are considered for different definitions of their coefficients, and the filter output signal and its statistics are investigated in time under real conditions. Various Kalman algorithms and corresponding optimal filter structures intended for crystal and rubidium oscillators are discussed. Three-dimensional Kalman filters intended for optimal estimation of time error, frequency offset, and frequency aging are considered based on the oscillator signal model. One application is the synchronization needs of digital communication networks and metrology. Results are given for the measured data and estimates are compared with respect to a quartz crystal oscillator. Practical results are considered of the Kalman filter's use in application to an oven-controlled quartz crystal oscillator (OCXO) with an AT-cut resonator. Plots of the original and filtered processes are discussed for the different approaches to definition of the Kalman filter coefficients. Estimates are also given for the filtering errors and the processing rate.

Information based estimation for both linear and nonlinear systems

Abstract: A new estimation algorithm is derived and appraised for nonlinear systems. The notion and measures of information are defined and this leads to a discussion of the algebraic equivalent of the Kalman filter, the linear information filter. Examples of dynamic systems are simulated to illustrate the algebraic equivalence of the Kalman and information filters. The benefits of information space are also explored. Estimation for systems with nonlinearities is then considered starting with the extended Kalman filter. Linear information space is extended to nonlinear information space by deriving the extended information filter. The advantages of the extended information filter over the extended Kalman filter are demonstrated for systems involving both nonlinear state evolution and nonlinear observations.

Stability of constrained linear moving horizon estimation

Abstract: We derive sufficient conditions for the stability of moving horizon state estimation with linear models subject to constraints on the estimate. The key result is that if the time-varying or steady-state Kalman filter covariance update is used to summarize the prior data, then the estimator is stable in the sense of an observer, even in the presence of constraints.

An adaptive Kalman filter with sequential rescaling of process noise

Abstract: An approach to adaptive Kalman filtering is presented. The filter utilizes a scale factor, which represents the target unpredictability at any time, as estimated from the available data. The performance of the algorithm is compared with that of an IMM algorithm and also with that of a standard Kalman filter. The proposed filter does not rely on a priori knowledge about the target motion and it produces better estimates than the IMM algorithm during manoeuvring periods.

Discrete time filters for doubly stochastic poisson processes and other exponential noise models

Abstract: The well-known Kalman filter is the optimal filter for a linear Gaussian state-space model. Furthermore, the Kalman filter is one of the few known finite-dimensional filters. In search of other discrete-time finite-dimensional filters, this paper derives filters for general linear exponential state-space models, of which the Kalman filter is a special case. One particularly interesting model for which a finite-dimensional filter is found to exist is a doubly stochastic discrete-time Poisson process whose rate evolves as the square of the state of a linear Gaussian dynamical system. Such a model has wide applications in communications systems and queueing theory. Another filter, also with applications in communications systems, is derived for estimating the arrival times of a Poisson process based on negative exponentially delayed observations. Copyright © 1999 John Wiley & Sons, Ltd.

Design of optimal gains for the proportional integral Kalman filter with application to single particle tracking

Abstract: In this paper, we introduce an optimal design strategy for the proportional-integral (PI) Kalman filter. The design of the PI Kalman filter involves the design of four matrices: The proportional and integral gains, the fading constant and the integral effect coefficient. The method in this paper provides optimal proportional and integral gains. Guidelines for the design of the fading constant and the integral effect coefficient are discussed as well. The suggested algorithm was tested as a single particle tracking system, for a maneuvering target.

Kalman filter implementation of self-organizing feature maps

Abstract: The self-organizing learning algorithm of Kohonen and most of its extensions are controlled by two learning parameters, the learning coefficient and the width of the neighborhood function, which have to be chosen empirically because neither rules nor methods for their calculation exist. Consequently, often time-consuming parameter studies precede neighborhood-preserving feature maps of the learning data. To circumvent those lengthy numerical studies, this article describes the learning process by a state-space model in order to use the linear Kalman filter algorithm training the feature maps. Then the Kalman filter equations calculate the learning coefficient online during the training, while the width of the neighborhood function needs to be estimated by a second extended Kalman filter for the process of neighborhood preservation. The performance of the Kalman filter implementation is demonstrated on toy problems as well as on a crab classification problem. The results of crab classification are compared to those of generative topographic mapping, an alternative method to the self-organizing feature map.

Estimation of fractional Brownian motion with multiresolution Kalman filter banks

Abstract: A filter bank design based on orthonormal wavelets and equipped with a multiscale Kalman filter was proposed for deconvolution of fractal signals. We use the same scheme for estimating fractional Brownian motion in noise considering (1) the effect of correlation in the sequence of wavelet coefficients; (2) the approximation term in the wavelet expansion; (3) aliasing effects; (4) the optimal number of scales in the filter bank. Considerations on the minimum number of filters in the bank are made, and comparisons between Wiener and Kalman filters are given. Explicit expressions of the mean-square error are given, and comparisons between theoretical and simulation results are shown.