Showing papers on "Invariant extended Kalman filter published in 1982"

Kalman Filtering for Spacecraft Attitude Estimation

Abstract: HIS report reviews the methods of Kalman filtering in attitude estimation and their development over the last two decades. This review is not intended to be complete but is limited to algorithms suitable for spacecraft equipped with three-axis gyros as well as attitude sensors. These are the systems to which we feel that Kalman filtering is most ap- plicable. The Kalman filter uses a dynamical model for the time development of the system and a model of the sensor measurements to obtain the most accurate estimate possible of the system state using a linear estimator based on present and past measurements. It is, thus, ideally suited to both ground-based and on-board attitude determination. However, the applicability of the Kalman filtering technique rests on the availability of an accurate dynamical model. The dynamic equations for the spacecraft attitude pose many difficulties in the filter modeling. In particular, the external torques and the distribution of momentum internally due to the use of rotating or rastering instruments lead to significant uncertainties in the modeling. For autonomous spacecraft the use of inertial reference units as a model replacement permits the circumvention of these problems. In this representation the angular velocity of the spacecraft is obtained from the gyro data. The kinematic equations are used to obtain the attitude state and this is augmented by means of additional state-vector components for the gyro biases. Thus, gyro data are not treated as observations and the gyro noise appears as state noise rather than as observation noise. It is theoretically possible that a spacecraft is three-axis stabilized with such rigidity that the time development of the system can be described accurately without gyro information, or that it is one-axis stabilized so that only a single gyro is needed to provide information on the time history of the system. The modification of the algorithms presented here in order to apply to those cases is slight. However, this is of little practical importance because a control system capable of such

Kalman filter models for network forecasting

Abstract: The Bell System has recently completed studies that are expected to result in substantially improved forecasts for use in network planning. These improved forecasts are achieved through the use of new forecasting algorithms that employ Kalman filter models. To motivate the selection of Kalman filter forecasting procedures, we describe the Bell System's special data characteristics and processing requirements in the network planning process. We also discuss the Kalman filter models, their statistical properties, the model identification process, and certain implementation considerations.

Two filter smoothing formulae by diagonalization of the Hamiltonian equations

Abstract: We present a new approach to two filter smoothing formulae via diagonalization of the general time variant hamiltonian equations of the linear estimation problem. This approach shows the special role of the famous Mayno-Fraser two filter formulae and also provides insight into certaini nvariance properties of backwards Kalman filter estimates.

A fast Kalman filter for images degraded by both blur and noise

Abstract: An optimal line-by-line recursive Kalman filter is derived for restoring images which are degraded in a deterministic way by linear blur and in a stochastic way by additive white noise. To reduce the computational and storage burden imposed by this line-by-line recursive Kalman filter circulant matrix approximations are made in order to diagonalize - by means of the fast Fourier transform (FFT) - both the model matrices and the distortion matrix in the dynamical model of the total image-recording system. Then the dynamical model reduces to a set of N decoupled equations and the line-by-line recursive Kalman filter based on this model reduces to a set of N scalar Kalman filters suitable for parallel processing of the data in the Fourier domain. Finally, via an inverse FFT the filtered data is presented in the data domain. The total number of computations for an N×N image reduces from the order of 0(N4) to 0(N^{2}\log_{2}N) .

Kalman filter preprocessor

Abstract: An optical signal preprocessor for computing the input functions required to utilize an extended Kalman filter algorithm. An incoming stream of time-varying images is integrated to form a reference image, which is then subtracted from each subsequently sampled image. The result is digitized for use with the extended Kalman filter algorithm. The reference image is also fed through a spatial filter and then input to two light valve image subtraction systems to produce difference image approximations of two partial derivatives. These derivative functions are then digitized and utilized as inputs to the extended Kalman filter algorithm.

Relationship between steady state Kalman filter gain and noise variances

Abstract: The Kalman filter requires an exact knowledge of the noise covariance matrices Theoretically, they may take arbitrary values under some restrictions ; positive semidefinite or positive definite. Values of the noise covariance matrices have direct effects upon the Kalman filter gain, and therefore affect the final result, of estimation. Practically, the noise covariance matrices are either unknown or are known only approximately, so they are often determined in a rule of trial and error. In this paper, we discover interesting relations between an index λ and the noise covariance matrices for multivariable identity transition systems and for general linear dynamic systems, through an algorithm of the exponential weighted least squares method. These relations are useful for determining the noise covariance matrices. New results are summarized into three points. The first main result is the relations between the steady state Kalman filter gain and the noise covariance matrices for multivariable identity trans...

Robust Kalman filter design for active flutter suppression systems

Abstract: Additional insight is provided into the use of the Doyle-Stein (1979, 1981) technique in aeroelastic control problems by examining the application of the method to a flutter control problem. The system to be controlled consists of a full-size wind tunnel model of a wing, plus an aileron, an actuator, and an accelerometer used to sense the motion of the wing. A full-state feedback controller was designed using linear optimal control theory, and a Kalman filter was used in the feedback loop for state estimation. The filter design procedure is explained along with that to improve closed-loop properties of the system. The locus of the poles of the filter is examined as a scalar design parameter is varied. The Doyle-Stein design procedure is shown to substantially improve the stability properties of an active flutter controller designed using the linear quadratic Gaussian control theory.

A Kalman filter procedure for the processing of the electroencephalogram

Abstract: In the present paper a Kalman filter procedure is illustrated for the reduction of muscular noise superimposed to the electroencephalografic traces (EEG). Such a noise, in fact, has a bandwidth which overlaps the signal carrying the information content useful for the clinical standpoint and, therefore, can not be removed by means of classical digital filtering. A Markov model is used for identifying the signal model (supposed generated by an ARMA process) and the noise model (conceived on the basis of experiments of neurophysiological evidence). The experimental results show a good performance of the filter on the discrete-time EEG signal which is also quantified by the spectral information and the values of the prediction error of the filter itself. Comparison is then carried on with a classical low-pass FIR filter (mostly used in practice) which can not be aggressive enough towards the noise contained in the signal bandwidth but which can undoubtly ameliorate the performance of the Kalman filter.

An exact solution of the time-invariant discrete Kalman filter

Abstract: An exact solution is presented of the matrix Riccati difference equation associated with a time-invariant discrete Kalman filter. The time-varying solution is expressed by means of the corresponding steady-state algebraic solution. An exact solution of the closed-loop transition matrix is also presented.

Real-Time Gravity Gradiometer Utilization to Improve INS Accuracy

Abstract: This paper details a method for deriving approximate low-order filters for estimation of velocity error in an inertial navigation system. The filter inputs are obtained from two sources—a gravity gradiometer and some external velocity reference. It is the intent here to show that these approximate filters are near-optimal. Covariance comparisons are used to evaluate filter performance. The first of these comparisons reveals that the approximate filter gives very nearly the same rms estimate error as the Kalman filter. This result, however, assumes a rational gravity perturbation model which, although unrealistic, is required to implement the Kalman filter. In addition, a multiple-measu rement scheme employing the external velocity reference appears to significantly improve estimation accuracy. A second covariance study compares the rms estimation accuracy of the approximate filters obtained analytically and numerically when an irrational but more realistic gravity perturbation model is assumed. Agreement of these numbers justifies the "Schuler Dominance" assumption used in all the filter derivations and therefore gives greater weight to the claim of filter near-optimality.

An invariant parameter in linear estimation and control

Abstract: This paper considers the implementation difficulty of the joint observer-controller design, the forward and backward Kalman Bucy (KB) filter, and the (estimator-controller) LQG solution, with respect to the choice of the realization. By establishing an invariant parameter, it is shown that the implementation difficulty for the joint design in each of the three problems is invariant. This invariant parameter is the inner product of the gain vectors for the observer (forward KB filter) and the controller (backward KB filter). Next the balancedness in balanced realizations is interpreted from the invariant parameter viewpoint. It is shown that in general a balanced realization does not lead to a balanced observer-controller design. Also the concept of continuous-time balanced stochastic realizations is developed.

Improved navigation accuracy through Kalman filtering

Abstract: Temporal and spatial variations in navigation data caused by deterministic and random phenomena can severely degrade integrated system accuracy unless suitable compensation is applied. An estimation procedure capable of modeling the statistical behavior of measurement and system error dynamics during real time operation has the capability of compensating measurements corrupted by stochastic effects. Several candidate estimators are investigated within a marine integrated system environment. A Kalman estimator is shown to provide the strongest benefits. A cautionary note is included concerning the effect modeling errors and numerical effects may have on estimation accuracy.

Adaptive filtering in structural dynamics

Abstract: The Kalman filter has been shown to be ideally suited to both the state and parameter estimation problems in structural dynamics. However these exploratory works on the application of Kalman filtering to structural engineering problems, in general only give suboptimal results, relying on assumed statistics to describe the noise sequences. Optimality however can be achieved by adapting onto these statistics (or the filter gain), using output from the filter equations to feed the adaptive algorithm. The present paper details one recently developed adaptive approach which exhibits good computational and convergence properties. This is coupled with a correlation test to show the optimality or nonoptimality of the results in any given application. A seismically excited structure is used to illustrate the required problem formulation and estimation results.

A discrete Kalman filter for a class of non-linear stochastic systemsf

Abstract: A class of non-linear systems of the form dx=A(x)x dl + σdW, t>0, XER m , A(x)ERm×m, where W is an Rm-valued standard Wiener process ; together with an observation process given by y(tk) = Mx(tk) + v(tk), y(tk)ERp, t0

Adaptive tracking of dynamic multiple hot-spot target IR images

Abstract: In the recent past, the capability of tracking dynamic targets from forward looking infrared (FLIR) measurements has been improved substantially by replacing standard correlation trackers with adaptive extended Kalman filters. This research investigates a tracker able to handle "multiple hot spot" targets, in which digital (or optical) signal processing is employed on the FLIR data to identify the underlying target shape. This identified shape is then used in the measurement model portion of the filter as it estimates target offset from the center of the field-of-view. In this algorithm, an extended Kalman filter processes the raw intensity measurements from the FLIR to produce target estimates. An alternative algorithm uses a linear Kalman filter to process the position indications of an enhanced correlator in order to generate tracking estimates; the enhancement is accomplished not only by thresholding to eliminate poor correlation information, but also by incorporating the dynamics information from the Kalman filter and the online identification of the target shape as a template instead of merely using previous frames of data. The performance capabilities of these two algorithms are evaluated under various tracking environment conditions and for a range of choices of design parameters.

Kalman filtering techniques applied to the dynamic ship positioning problem.

Abstract: The dynamic ship positioning problem using Kalman filtering techniques is considered. The main components of the system are discussed. The ship dynamics, based on a linearised model, are represented by state equations. These equations involve low and high frequency subsystems. A simplified design procedure for the implementation of a Kalman filter is described based on the linearised equations of motion. The Kalman filter involves a model of the system and is therefore particularly appropriate for separating the low and high frequency motions of the vessel. The filtering problem is one of estimating the low-frequency motions of the vessel so that control can be applied. An optimal feedback control system simulation based on optimal stochastic control theory is used. The optimal control performance criterion weighting matrices Q, R were pre-selected and the optimal feedback gain matrix was computed. This control scheme involves the low-frequency part of the ship model. The Kalman filter has been simulated on a digital computer for different modelled operating conditions. The computer simulation results showing the behaviour and responses of the Kalman filter applied to the dynamic ship positioning problem were investigated. The system dynamics vary as the weather conditions vary and can be classified from a calm sea condition (Beaufort number 5) to the worst condition (Beaufort number 9). Different tests involving systems modelling and filter mismatching have been carried out. Another field in which the robustness of a Kalman filter has been assessed involved a test in which the system observation noise covariance was increased keeping the filter with the usual noise information. Saving in both computation and computer storage requirement were achieved using a form of semi-constant filter gain and reduced-order Kalman filter respectively. System non-linearities have been considered and a non-linear control algorithm was proposed and implemented using an extended Kalman filter. These non-linearities involve the thruster dynamics and the associated low-frequency part of the system model. All data that have been used within this work for system implementation were obtained from two different models ("Wimpey Sealab" and "Star Hercules" vessels). Our system has been employed by GEC Electrical Projects Limited, Rugby, for a new vessel ("Star Hercules") and this has been commissioned and is currently operating successfully off Brazil.

An adaptive Kalman window filter to restore degraded images

Abstract: A semicausal model for image representation has been described which accounts for the correlated nature of the pixel data. The model is then used to develop a linear imaging system model suitable for Kalman algorithms. Since the blurring PSF is not known in practice, the system model is modified to include the estimation of the pixels while the noise characteristics are assumed to be known. For restoration, an adaptive Kalman filter is developed whose length of the state vector is shown to be a function of the PSF size resulting in significant savings in computational and storage requirements. Through examples, it is demonstrated that by carefully choosing the initial estimates of the PSF and error covariance terms, results comparable to the case when the PSF is fully known can be obtained. Two criteria to select such initial estimates have been described; one is based on the a priori knowledge about the dominant PSF coefficient and the other is based on the law of conservation of light flux.

Multichannel adaptive filtering with a feedback convergence function

Abstract: A new set of multichannel adaptive filtering algorithms containing a feedback convergence function is described The algorithms represent an extension of the Kalman filtering approach to the linearly constrained multichannel adaptive filtering In essence, the convergence function in the adaptive filtering algorithm, which is designed to control stability and rate of adaptation, is modified to fashion the Kalman gain structure Through adaptive feedback schemes, the algorithms are capable of tracking not only the prediction errors with respect to the input multichannel signals, but also the performance errors in the estimated filter weights by means of updating the error covariance matrix Thus, with double monitoring capability, the revised adaptive filtering algorithm is shown to be more effective in suppressing coherent noises than the previous one, and is well suited for processing the highly time-varying nonstationary data

On the Kalman-Bucy filter with specified input

Abstract: In a recent paper, Vathsal suggested that a new configuration had been obtained for linear filtering problems, which was distinctly different from the Kalman-Bucy filter. It is shown that this in fact is merely a special case of the filter with a specified input.