Showing papers on "Invariant extended Kalman filter published in 1988"
TL;DR: Two schemes for implementing systolic and pipelined processing on Kalman filters in real time are presented and the mathematical formulation of the Kalman filter algorithms is rearranged to be the type of the Faddeeva algorithm for generalizing matrix/vector manipulations.
Abstract: Two schemes for implementing systolic and pipelined processing on Kalman filters in real time are presented. In the first, a single two-dimensional systolic processor is used to perform a Kalman filtering process. In the second scheme, the utilization of the two-dimensional systolic processor is fully expanded and improves the speed of updating estimates, Kalman filter algorithms are implemented on two concurrent, identical systolic processors. In both schemes, the mathematical formulation of the Kalman filter algorithms is rearranged to be the type of the Faddeeva algorithm for generalizing matrix/vector manipulations. The corresponding data flow is easily mapped from algorithms into the computing structure which is of nearest neighbor type. The architecture of the processor cells is regular, simple, expandable, and suitable for VLSI implementation. The computing methodology and the two-dimensional systolic arrays are useful for Kalman filter applications as well as general matrix/vector algebraic computations. >
46 citations
TL;DR: In this article, the authors require only that M be invertible, although M~ 1 is not needed explicitly in subsequent development, and they require that M is symmetric positive definite and K symmetric nonnegative definite.
Abstract: where, usually, Mis symmetric positive definite and K is symmetric nonnegative definite. In this paper, we require only that M be invertible, although M~ 1 is not needed explicitly in our subsequent development. In some mechanical systems, for example, the constant matrices M,D,KtR are called the mass (or inertia), damping, and stiffness matrices, respectively, the state vector x€R" is called the displacement vector, and F=Bu is called the force vector, where u£R is a known input and B£R is a constant matrix. In most situations, a set of measurements, y£R, rather than the full state vector x, is available, where
37 citations
TL;DR: In this paper, the Kalman filter is generalized to cover state-space models in which the variance of the observation error depends on the state vector, and derived from two differing viewpoints: linear Bayes theory and Gauss-Markov theory.
Abstract: The Kalman filter is generalized to cover state-space models in which the variance of the observation error depends on the state vector. Derivations of the filter yielding minimum mean squared error linear estimators and associated error covariance matrices are obtained from two differing viewpoints: linear Bayes theory and Gauss—Markov theory. The results are applied to a model for which {y t: t = 1, 2, …, n} follow a Poisson distribution with corresponding intensities {θt: t = 1, 2, …,n} that are assumed to follow an autoregressive process of order 1, namely . The steady-state generalized Kalman filter algorithm in the case for which ρ = 1 gives a generalization of exponential smoothing for a Poisson process with time-varying intensity.
31 citations
TL;DR: In this paper, five algorithms for data analysis are evaluated for their abilities to discriminate against outliers in small data sets (4-10 points) and the conclusion is that the zero-lag adaptive Kalman filter and the least median of squares approaches are best suited for the detection of outliers.
28 citations
TL;DR: In this paper, the adaptive fading-memory Kalman filter is used to estimate rigid body motion from radar measurements, with emphasis on their interpretation in the frequency domain, and the stability analysis of an adaptive fading memory Kalman filters is performed.
Abstract: To resolve difficulties encountered in estimating rigid body motion from noisy radar measurements, the behavior of an adaptive fading-memory Kalman filter is studied. How adaptive fading-memory Kalman filters can be constructed to estimate rigid body motion from radar measurements is described. A review of fading-memory Kalman filters is contained, with emphasis on their interpretation in the frequency domain. The stability analysis of an adaptive fading-memory Kalman filter is performed. Sample behavior of the error state vector is also examined. The application of the adaptive fading-memory Kalman filters to rigid-body motion estimation is briefly described. >
25 citations
25 citations
TL;DR: In this article, the problem of finite-time, reduced-order, minimum variance full-state estimation of linear, continuous time-invariant systems is considered in cases where the output measurement is partially free of corrupting white-noise components.
Abstract: The problem of the finite-time, reduced-order, minimum variance full-state estimation of linear, continuous time-invariant systems is considered in cases where the output measurement is partially free of corrupting white-noise components. The structure of the optimal filter is obtained and a link between this structure and the structure of the system invariant zeros is established. Using expressions that are derived in closed form for the invariant zeros of the system, simple sufficient conditions are obtained for the existence of the optimal filter in the stationary case. The structure and the transmission properties of the stationary filter for general left-invertible systems are investigated. A direct relation between the optimal filter and a particular minimum-order left inverse of the system is obtained. A simple explicit expression for the filter transfer function matrix is also derived. The expression provides an insight into the mechanism of the optimal estimation. >
22 citations
07 Dec 1988
TL;DR: In this article, the tracking error bounds for the unknown parameters were established for the Kalman filter and it was shown that it has quite reasonable tracking properties even in the non-Gaussian case when it is not an optimal filter.
Abstract: Concerns the use of the Kalman filter as an algorithm for the parameter estimation of a linear stochastic system where the unknown parameters are randomly time-varying and can be represented by a Markov model. The authors develop asymptotic properties of the algorithm. In particular they establish the tracking error bounds for the unknown parameters. It is shown that the Kalman filter has quite reasonable tracking properties even in the non-Gaussian case when it is not an optimal filter. If the parameters are generated from a stable model, it is found that there is no restriction on the regressors to achieve tracking error bounds. The bounds obtained have application for adaptive controller analysis. >
20 citations
TL;DR: The Kalman filter as discussed by the authors is a recursive, digital filtering algorithm which has been used for state and parameter estimation in several areas of chemistry, including the determination of polyaromatic hydrocarbon compounds.
19 citations
TL;DR: The method is shown to be superior to ordinary autoregressive spectral estimation based on stationary theory in recognizing rapid changes in the frequencies of oscillations.
18 citations
01 Sep 1988
TL;DR: In this article, methods for the analysis of the performance of Kalman filters are considered, which are all based on the innovation sequence which has well defined statistical properties if the filter is optimal.
Abstract: Methods for the analysis of the performance of Kalman filters are considered in the paper. The methods are all based on the innovation sequence which has well defined statistical properties if the filter is optimal. Local and global test statistics are presented and discussed. A global slippage test statistic is introduced. This test, which has batch type properties, is given in a recursive form.
11 Apr 1988
TL;DR: A reduced-order model Kalman filter which reduces both the amount and the complexity of the computations is developed.
Abstract: The one-dimensional state-space representation of an image for restoration using a Kalman filter requires a relatively large state vector. For a typical autoregressive signal model with nonsymmetric half-plane support, the dimension of the state is approximately equal to the product of the image model order and the pixel width of the image. This state is large, particularly for practical images and would require excessive computation if the Kalman filter were used directly. Consequently, there have been various filtering approximations which reduce the amount of computation. An alternate approach is to reduce the dimension of the image model and use the corresponding optimal filter directly. To this effect a reduced-order model Kalman filter which reduces both the amount and the complexity of the computations is developed. >
TL;DR: In this paper, a one-dimensional Kalman filter algorithm is presented that resolves several overlapped liquid chromatographic peaks without algebraic operations of matrices, and the reliability is shown to be similar to that of the multi-dimensional filter for the resolution of overlapped Gaussian peaks with limited R s and S/N values.
TL;DR: The results presented in the paper help one to understand and be able to predict certain behavior of the Kalman filter when inexact values of noise covariances are used.
TL;DR: In this article, a reduced-order version of extended Kalman filtering is presented in which both the filtering equation and the associated Riccati equation have been reduced in dimension to allow for real-time processing.
Abstract: A reduced-order version of extended Kalman filtering is presented in which both the filtering equation and the associated Riccati equation have been reduced in dimension to allow for real-time processing. The procedure for designing the reduced-order filter is similar to that for designing the extended Kalman filter, the same approximations being applied. One technique useful for limiting the computational burden in a linearized filter design problems is presented and illustrated by an example. The primary limitation of the result is that the nonlinearity must be in terms of the vector to be estimated. >
05 Jun 1988
TL;DR: An optimized filtering method for deconvolution, based on Kalman filtering, is presented, and the results are significantly better than that of formerly published algorithms.
Abstract: An optimized filtering method for deconvolution, based on Kalman filtering, is presented. The results are significantly better than that of formerly published algorithms. After a brief survey of the literature, the new approach is described and its performance is illustrated. >
11 Apr 1988
TL;DR: Systolic Kalman (SK) filter designs are presented which are based on a triangular array (triarray) configuration, in order to facilitate the systolic design, the original algorithm for the Kalman filter estimation is reformulated in a new least-squares formulation.
Abstract: Systolic Kalman (SK) filter designs are presented which are based on a triangular array (triarray) configuration. In order to facilitate the systolic design, the original algorithm for the Kalman filter estimation is reformulated in a new least-squares formulation. The design has advantages in both numerical accuracy and computational efficiency. For the case of white additive noise, the SK-W filter design uses approximately n/sup 2//2 processors and provides a speed-up of n/sup 2//2, with a nearly 100% utilization rate. For the case of colored additive noise, the SK-C filter design also offers comparable speed-up performance. >
01 Jan 1988
TL;DR: In this article, a sequential square root method was proposed to solve the numerical problems of the conventional Kalman filter and a comparison with other square root methods was also provided, and a simple square root algorithm was derived for the Kalman covariance and information filters and for the smoothing equations.
Abstract: This paper describes a sequential square root method which is aimed at solving the numerical problems affecting the conventional Kalman filter. Simple square root algorithms are derived for the Kalman covariance and information filters and for the smoothing equations. A comparison with other square root methods is also provided.
15 Nov 1988
TL;DR: A novel Automatic Frequency Control loop based on an Extended Kalman Filter (EKF) is introduced and analyzed in detail and can easily be incorporated in the Advanced Receiver (ARX), requiring minimum software modifications.
Abstract: An Automatic Frequency Control (AFC) loop based on an Extended Kalman Filter (EKF) is introduced and analyzed in detail. The scheme involves an EKF which operates on a modified set of data in order to track the frequency of the incoming signal. The algorithm can also be viewed as a modification to the well known cross-product AFC loop. A low carrier-to-noise ratio (CNR), high-dynamic environment is used to test the algorithm and the probability of loss-of-lock is assessed via computer simulations. The scheme is best suited for scenarios in which the frequency error variance can be compromised to achieve a very low operating CNR threshold. This technique can easily be incorporated in the Advanced Receiver (ARX), requiring minimum software modifications.
07 Dec 1988
TL;DR: A simple algorithm is suggested to estimate, using a Kalman filter, the unknown process noise variance of an otherwise known linear plant, using the difference between the expected prediction error variance, computed in the Kalman Filter, and the measured predictionerror variance.
Abstract: A simple algorithm is suggested to estimate, using a Kalman filter, the unknown process noise variance of an otherwise known linear plant. The process noise variance estimator is essentially dead beat, using the difference between the expected prediction error variance, computed in the Kalman filter, and the measured prediction error variance. The estimate is used to adapt the Kalman filter. The use of the adaptive filter is demonstrated in a simulated example in which a wildly manoeuvring target is tracked. >
07 Dec 1988
TL;DR: A parallel algorithm for solving an n-state Kalman filter on an (n+1)-cell linear array is described, which is the basis for the mapping of an extended Kalmanfilter on the Warp computer.
Abstract: A parallel algorithm for solving an n-state Kalman filter on an (n+1)-cell linear array is described. The approach is to update the columns of the filter covariance matrix in parallel to balance the computations and minimize the communications. The algorithm is the basis for the mapping of an extended Kalman filter on the Warp computer. The Warp implementation is written in a high-level language and achieves a measured speedup of almost 300 over the same filter running on a Sun workstation. Efficient algorithm mapping is the key to achieve the high-speed filter performance. >
07 Jun 1988
TL;DR: An adaptive IIR (infinite-impulse response) filtering algorithm is proposed which combines advantages of two error criteria, and a steepest-descent form of the algorithm has been derived which uses a simple test to guarantee stability of the adaptive filter.
Abstract: An adaptive IIR (infinite-impulse response) filtering algorithm is proposed which combines advantages of two error criteria. The algorithm is termed master-slave, as an auxiliary adaptive filter (the slave) is used to assist the adaptation of the main adaptive IIR filter. By using an additional FIR (finite-impulse-response) filter to minimize the output error criterion, an IIR filter can be adapted using the preferred equation error criterion, while noise present in the desired filter response will not lead to biased parameter values. This enables IIR filters to converge much more rapidly than is possible with output error minimization alone. A steepest-descent form of the algorithm has been derived which uses a simple test to guarantee stability of the adaptive filter. >
23 May 1988
TL;DR: In this article, it was observed that in minimum MSE (mean square error) linear predictive transform (LPT) coding, a multivariable signal model of the Kalman type inherently arises.
Abstract: It is observed that in minimum MSE (mean square error) linear predictive transform (LPT) coding, a multivariable signal model of the Kalman type inherently arises. This is illustrated with a digital monochrome image example. It is proposed that the Kalman filter could make effective use of this signal model. It then follows that minimum MSE LPT modeling simultaneously addresses relevant coding and filtering problems. >
TL;DR: In this paper, a state estimator can be designed and implemented very easily if the system is output-decoupled, as is often the case in process monitoring and control applications.
Abstract: Most industrial processes are complex systems, characterized by nonlinearity, high order, and even implicit dynamics. The design of a Luenberger-type observer or an extended Kalman filter for state estimation of such systems presents, in general, considerable difficulties. The authors show that a state estimator can be designed and implemented very easily if the system is output-decoupled, as is often the case in process monitoring and control applications. Simulation study and experiments on an experimental water pipeline show that the proposed estimator works very well. Its estimation accuracy is nearly the same as that of an extended Kalman filter, while its computational expenditure is almost as small as the real-time system model. >
20 Mar 1988
TL;DR: In this article, the steady-state error of a version of the Kalman filter, called the alpha, beta filter, was analyzed under the assumption that missing data may occur.
Abstract: The Kalman filter provides a recursive least-mean-square estimate of parameters in a dynamic system. Because the initial variances of the measurements used in the estimation are uncertain in a practical situation, a tracking filter can be optimum only in steady-state. The steady-state error of a version of the Kalman filter, called the alpha , beta filter, is analyzed under the assumption that missing data may occur. The results are developed for a constant-scan-rate radar. The number of intervals between valid data is modeled as a geometric random variable with the probability of valid data as a parameter. It is shown that missing data can introduce large additional tracking error for slowly scanning radars. >
TL;DR: It is demonstrated that substantial decreases in the computational burden are possible without loss of filter accuracy, which makes possible the application of second‐order filters on large data sets, and they make real‐time filtering possible with a fast processor.
Abstract: The extended Kalman filter has been used to estimate initial reactant concentrations and rate constants for rate-based chemical assays employing a second-order chemical reaction. Application of first- and second-order models to data permits reaction order identification by examining either the filter innovations or the evolution of the filter states. Because of non-linearities in the second-order kinetic model, repetitive filtering is necessary for convergence to reliable state estimates. Reduction of the filter calculation burden is investigated through the use of information-based filter methods, and it is demonstrated that substantial decreases in the computational burden are possible without loss of filter accuracy. These decreases make possible the application of second-order filters on large data sets, and they make real-time filtering possible with a fast processor.
11 Apr 1988
TL;DR: 2D Kalman filtering for the restoration of stochastically blurred images is developed and the proposed filters are the best linear estimators for minimizing the mean-square error over the blur process ensemble and observation noise ensemble.
Abstract: 2D Kalman filtering for the restoration of stochastically blurred images is developed. Stochastic blur is treated as the combination of a deterministic blur and correlated random noise. For restoration from single-frame data, an augmented state-vector Kalman filter for stochastic blurs is derived. This filtering scheme is then extended to provide restoration from multiple-frame data also. Kalman filtering for both serial and parallel processing of the frames is proposed. The new filters can take into account the spatio-temporal correlations of the randomly varying blur. For the equivalent 1-D problem, the proposed filters are the best linear estimators for minimizing the mean-square error over the blur process ensemble and observation noise ensemble. Sample results are also provided to show the effectiveness of the proposed filters. >
23 May 1988
TL;DR: In this paper, the performance of a decoupled Kalman track filter is analyzed and a steady-state covariance analysis is discussed. But, the analysis is limited to the case where the root-mean-square tracking errors are unbounded.
Abstract: A steady-state covariance analysis is discussed in the study the performance of a six-state, decoupled Kalman track filter. Analytical and numerical results indicate that, for a considerable range of filter gains and target line-of-sight (LOS) rates, the decoupled filter is unstable, and its steady-state root-mean-square tracking errors are unbounded. >
20 Mar 1988
TL;DR: An estimator-subtractor-type line suppressor recently proposed by the author for pseudonoise (PN) spread-spectrum applications or as an adaptive line enhancer in acoustic applications is modeled as a combined discrete state-variable Kalman filter, one-step predictor and optimal linear smoother.
Abstract: An estimator-subtractor-type line suppressor recently (1986) proposed by the author for pseudonoise (PN) spread-spectrum applications or as an adaptive line enhancer in acoustic applications is modeled as a combined discrete state-variable Kalman filter, one-step predictor and optimal linear smoother. It is shown that the adaptive Kalman filter acts as the oscillator. However, the damping and the tuned frequency of this filter oscillator are influenced by the mean-square estimation error. Closed-form expressions are given for the estimation error of a sinusoidal process in the presence of additive broadband noise (the model of a discrete PN spread-spectrum signal). >
01 Jan 1988
TL;DR: In this article, the effects of the finite difference approximation on the performance of Kalman filtering for stochastic dynamic tidal models are investigated. And the degradation of the performance, in case an erroneous filter model is used, is investigated.
Abstract: Kalman filtering for stochastic dynamic tidal models, is a hyperbolic filtering problem. The questions of observability and stability of the filter as well as the effects of the finite difference approximation on the filter performance are studied. The degradation of the performance of the filter, in case an erroneous filter model is used, is investigated. In this paper we discuss these various practical aspects of the application of Kalman filtering for tidal flow identification problems. Filters are derived on the basis of the linear shallow water equations. Analytical methods are used to study the performance of the filters under a variety of circumstances.