Showing papers on "Invariant extended Kalman filter published in 1992"

introduction to random signals and applied kalman filtering

Abstract: Probability and Random Variables Mathematical Description of Random Signals Response of Linear Systems to Random Inputs Wiener Filtering The Discrete Kalman Filter Applications and Additional Topics on Discrete Kalman Filtering The Continuous Kalman Filter Discrete Smoothing and Prediction Linearization and Additional Topics on Applied Kalman Filtering The Global Positioning System: A Case Study.

Forecasting, Structural Time Series and the Kalman Filter

Abstract: (1992). Forecasting, Structural Time Series and the Kalman Filter. Technometrics: Vol. 34, No. 4, pp. 496-497.

Using the Extended Kalman Filter with a Multilayer Quasi-Geostrophic Ocean Model

Abstract: The formulation of the extended Kalman filter for a multilayer nonlinear quasi-geostrophic ocean circulation model is discussed. The nonlinearity in the ocean model leads to an approximative equation for error covariance propagation, where the transition matrix is dependent on the state trajectory. This nonlinearity complicates the dynamics of the error covariance propagation, and effects which are nonexistent in linear systems contribute significantly. The transition matrix can be split into two parts, where one part results in pure evolution of error covariances in the model velocity field, and the other part contains a statistical correction term caused by the nonlinearity in the model. This correction term leads to a linear unbounded instability, which is caused by the statistical linearization of the nonlinear error propagation equation. Different ways of handling this instability are discussed. Further, nonlinear small-scale instabilities also develop, since energy is accumulated at wavelengths 2Δx, owing to the numerical discretization. These small-scale oscillations are removed with a Shapiro filter, and the effect they have on the error covariance propagation is discussed. Some data assimilation experiments are performed using the full extended Kalman filter, to examine the properties of the filter. An experiment where only the first part of the transition matrix is used to propagate the error covariances is also performed. This simplified experiment actually performs better than the full extended Kalman filter because the unbounded instability associated with the statistical correction term is avoided.

The Extended Kalman Filter as a Local Asymptotic Observer for Nonlinear Discrete-Time Systems

Abstract: The convergence aspects of the extended Kalman filter, when used as a deterministic observer for a nonlinear discrete-time system, are analyzed. The case of systems with nonlinear output maps as well as with linear maps is treated and the conditions needed to ensure the uniform boundedness of certain Riccati equations are related to the observability properties of the underlying nonlinear system. Furthermore, we show the convergence of the filter without any a priori boundedness assumptions on the error covariances as long as the states stay within a convex compact domain.

A real-time learning algorithm for a multilayered neural network based on the extended Kalman filter

Abstract: A novel real-time learning algorithm for a multilayered neural network is derived from the extended Kalman filter (EKF). Since this EKF-based learning algorithm approximately gives the minimum variance estimate of the linkweights, the convergence performance is improved in comparison with the backwards error propagation algorithm using the steepest descent techniques. Furthermore, tuning parameters which crucially govern the convergence properties are not included, which makes its application easier. Simulation results for the XOR and parity problems are provided. >

Training recurrent networks using the extended Kalman filter

Abstract: The author describes some relationships between the extended Kalman filter (EKF) as applied to recurrent net learning and some simpler techniques that are more widely used. In particular, making certain simplifications to the EKF gives rise to an algorithm essentially identical to the real-time recurrent learning (RTRL) algorithm. Since the EKF involves adjusting unit activity in the network, it also provides a principled generalization of the teacher forcing technique. Preliminary simulation experiments on simple finite-state Boolean tasks indicated that the EKF can provide substantial speed-up in number of time steps required for training on such problems when compared with simpler online gradient algorithms. The computational requirements of the EKF are steep, but scale with network size at the same rate as RTRL. >

Comparative analysis of backpropagation and the extended Kalman filter for training multilayer perceptrons

Abstract: The relationship between backpropagation and extended Kalman filtering for training multilayer perceptrons is examined. These two techniques are compared theoretically and empirically using sensor imagery. Backpropagation is a technique from neural networks for assigning weights in a multilayer perceptron. An extended Kalman filter can also be used for this purpose. A brief review of the multilayer perceptron and these two training methods is provided. Then, it is shown that backpropagation is a degenerate form of the extended Kalman filter. The training rules are compared in two examples: an image classification problem using laser radar Doppler imagery and a target detection problem using absolute range images. In both examples, the backpropagation training algorithm is shown to be three orders of magnitude less costly than the extended Kalman filter algorithm in terms of a number of floating-point operations. >

Optimal stochastic estimation with exponential cost criteria

Abstract: The expected value of the exponential of a weighted quadratic sum of the squares of the estimation error is minimized with respect to the state estimate subject to a Gauss-Markov system. The state estimates are assumed to be a function of the measurement history up to the stage time of the state vector. The estimator which optimizes this exponential cost criterion is linear but is not a conditional mean estimator such as the Kalman filter. This shows that the implications of Sherman's theorem are restricted to functions of the estimates which have access to the same measurement history such as in smoothing problems. In the solution process the expectation operation is replaced by an extremization operation allowing the formulation of a deterministic discrete time game. The saddle point estimator resulting from this game is the same as that obtained from the solution of an associated disturbance attenuation problem. This optimal stochastic estimator which generalizes the Kalman filter can feature the estimation error of certain states over others by the choice of the quadratic weighting matrices in the cost criterion. Correlation between the measurement and process noises is included. >

Constraining Kalman Filter and Smoothing Estimates to Satisfy Time-Varying Restrictions

Abstract: It sometimes happens that the unobservable state vector of a linear dynamic model expressed in the state space is subject to known restrictions. Incorporation of this information into the Kalman filter procedure will increase the efficiency of estimation. It is shown that a simple augmentation of the measurement equation constrains the estimated state vector to obey the restrictions. The method applies whether the restrictions are time-invariant, time-varying, linear, or nonlinear. Copyright 1992 by MIT Press.

A Kalman filter approach to catch-at-length analysis

Abstract: A state-space representation of a length-structured population under commercial harvest is described and a Kalman filter is used to develop the conditional likelihood equation needed for estimating the underlying system parameters. The state of the system is characterized using conventional fisheries theory with commercial harvest representing the observations taken on the population. The conditional likelihood framework embedded in the Kalman filter facilitates the incorporation of both system stochasticity as well as observation error in the development of the overall likelihood equation. Within this framework a maximum likelihood approach is used to estimate population parameters while taking into account both sources of error.

Game theory approach to state estimation of linear discrete-time processes and its relation to H∞ -optimal estimation

Abstract: A game theory approach to the state-estimation of linear discrete-time systems is presented. The resulting state estimation suggests an alternative to the Kalman filter, in cases where the exact statistics of the input and the measurement noise processes is not known. It turns out that the game-theoretic filter provides an H∞-optimal estimation. Moreover, it is shown that the covariance matrix of the estimation error is bounded, from above, by the solution of a modified Riccati equation.

Image estimation using fast modified reduced update Kalman filter

Abstract: The authors have proposed some modifications of the reduced update Kalman filter (RUKF) as applied to filtering of images corrupted by additive noise. They have reduced the computational complexity by reducing the state dimensionality. By doing so, it is shown that the computational requirement is reduced by an order of magnitude while the loss of performance is only marginal. Next, the RUKF is modified using the score function based approach to accommodate non-Gaussian noise. The image is modeled as a nonstationary mean and stationary variance autoregressive Gaussian process. It is shown that the stationary variance assumption is reasonable if the nonstationary mean is computed by an edge and detail preserving efficient estimator of local nonstationary mean. Such an estimator, called the hybrid multistage medium D (HMSMD) filter, is also described. Detailed experimental results are provided which indicate the success of the new filtering scheme. >

Frequency-domain characterization of Kalman filters as applied to power system protection

Abstract: So far, all tests on Kalman filters have been performed in the time domain. However, it is shown that conventional signal-processing tools such as frequency response can be successfully applied for the performance analysis. The concept of frequency response as applied to Kalman filters is based on its variation with time. Consequently, it is defined with respect to a definite observation window. It is also shown that the ratio of the initial error covariance matrix terms to the measurement noise variance, not the absolute values, is the relevant statistical quantity. The same principle applies to the ratio of the process noise covariance matrix diagonal terms to the noise measurement variance. >

A comparison between Kalman filters and recurrent neural networks

Abstract: The performance of a recurrent neural network signal estimator is compared to that of the basic discrete time Kalman filter for a number of simulated systems. The selected systems diverge from the assumptions upon which the Kalman filter is based. The architecture of the recurrent neural network is described. The training algorithm is based on the conjugate gradient optimization method. The neural network was found to provide improved performance over the Kalman filter in several cases. In all cases tried, the neural net was found to never perform significantly worse than the Kalman filter. >

A new state estimation algorithm-adaptive fading Kalman filter

Abstract: A novel adaptive state estimation algorithm, namely the adaptive fading Kalman filter (AFKF), is proposed to solve the divergence problem of the Kalman filter. A criterion function is constructed to measure the optimality of the Kalman filter. The forgetting factor in the adaptive fading Kalman filter is adaptively adjusted by minimizing the defined criterion function using measured outputs. The algorithm achieves optimality and convergence simultaneously. The filter uses a variable exponential weighting approach to compensate the model errors and unknown drifts. This algorithm has been successfully applied to the headbox of a paper-making machine for state estimation. >

The GPS filtering problem

Abstract: The authors explore the possibility of both improved navigation accuracy and computational simplification by using nonlinear filters based on direct solutions to the GPS (Global Positioning System) equations. After reviewing results concerning the existence of sufficient statistics for the nonlinear GPS filtering problem, they introduce the notion of a two-stage estimator in which a direct solution is combined with a time-series smoothing algorithm, such as a constant-gain Kalman filter. This method provides a means for decoupling, in a sense, the spatial and temporal aspects of the GPS filtering problem. Experiments using real data suggest that the method has advantages over the extended filter, in terms of both computational burden and accuracy. >

Using pseudo Kalman-filters in the presence of constraints application to sensing behaviors

Abstract: A new generalization of the linear Kalman-filter to non-linear equations is introduced. The deterministic interpretation of this mechanism is discussed. The proposed algorithm is an alternative to the well known extended Kalman filer. A small experimental illustration is given. An application to sensory-motor behaviors is proposed.

A stochastic perturbation analysis of bias in the extended Kalman filter as applied to bearings-only estimation

Abstract: Expressions for the range and range-rate biases encountered in the extended Kalman filter (EKF) applied to the bearings-only estimation problem are derived. The analysis generalizes earlier results obtained using a special case. An estimator is designed with reduced bias for the bearings-only estimation problem by using the estimates of the biases to remove the biases from the a posteriori estimates. This results in the formulation of a new estimator that performs well in scenarios where the EKF cannot function due to its inherent bias. >

A singular value decomposition based Kalman filter algorithm

Abstract: A novel Kalman filter algorithm for the discrete linear filtering problem has been developed. The crucial component of the algorithm involves the computation of the singular value decomposition of an unsymmetric matrix without explicitly forming its left factor which has a high dimension. The proposed algorithm has good numerical stability and can handle correlated measurement noise without any additional transformations. This algorithm is formulated in the form of vector-matrix and matrix-matrix operations, so that it is also useful for parallel computers. Details of the algorithm are provided, and a numerical example is given. >

A new estimator for passive tracking of maneuvering targets

Abstract: A method for reducing the range estimation bias inherent in the extended Kalman filter (EKF) when used for passive tracking is presented. Using a first-order approximation of the bias, the a posteriori state estimation is corrected in an attempt to remove most of the bias. Modifications based on empirical results are required but the resulting estimator is shown to be nearly unbiased and to function well in a stressing scenario where the EKF fails. >

Empirical evidence of bias in extended Kalman filters used for passive target tracking

Abstract: The bearings-only estimation problem and its application to the intercept of an aircraft target by an air-to-air missile are discussed. That is, how does one estimate the state of a system of a missile and a target (relative position, relative velocity, and target acceleration) in a plane with measurements of the line-of-sight (LOS) or bearing angle only? The ownship-to-target range is unobservable unless the LOS rate is nonzero. The range and range-rate estimates are biased for both the extended Kalman filter (EKF) and the modified gain EKF (MGEKF). Empirical evidence of this biasing is presented using a simple simulation. The bias is shown to be caused by a correlation between the gain and innovations sequences. It is further shown that this bias is not removed (though it is reduced and bounded) when the range is observable. >

Recursive state and parameter estimation of SISO singular systems

Abstract: In this paper, recursive algorithms are presented for the online state and parameter estimation of a linear time invariant single-input single-output (SISO) discrete-time singular system. The model considered is in the canonical observable form. The approach is based on the generalised Kalman filter and can be developed in two steps. First, the parameters are estimated by recursive least squares method. These parameters are then used to estimate the state by the generalised Kalman filter in the second step. The results are illustrated by a numerical example.

K-step ahead prediction in fuzzy decision space-application to prognosis

Abstract: The authors demonstrate the ability and the accuracy of a modified extended Kalman filter used as a k-step-ahead predictor to perform a predicted membership function's point in a fuzzy decision space based on fuzzy pattern recognition principles, instead of a predicted state in the feature space. Results obtained with this prediction procedure are presented. A scheme including both fuzzy decision and prediction procedures is proposed for prognosis. >