Showing papers on "Invariant extended Kalman filter published in 1981"

Kalman filtering in two dimensions: Further results

Abstract: The two-dimensional reduced update Kalman filter was recently introduced. The corresponding scalar filtering equations were derived for the case of estimating a Gaussian signal in white Gaussian noise and were shown to constitute a general nonsymmetric half-plane recursive filter. This paper extends the method to the deconvolution problem of image restoration. This paper also provides a more thorough treatment of the uniquely two-dimensional boundary condition problems. Numerical and subjective examples are presented.

An alternate derivation and extension of Friendland's two-stage Kalman estimator

Abstract: An alternate simplified derivation of Friedland's two-stage Kalman estimator is given for a somewhat more general class of problems than considered by Friedland. Friedland's result is also extended to encompass two variations on the basic idea which are of practical interest.

New results in two-dimensional Kalman filtering with applications to image restoration

Abstract: This paper describes the application of 2-D Kalman filtering to the restoration of images degraded by linear space invariant (LSI) blur and additive white Gaussian noise (WGN). The image restoration problem is formulated in the framework of the well-known Kalman strip filter. However, the Kalman filtering scheme assumes the availability of a statespace dynamic model for the image process as well as the blur. In the past, most researchers have sought to track the problem of image modeling by making the sometimes unrealistic assumption of separability of the image correlation. A new technique for image modeling which does not make this assumption is proposed. On-line, recursive methods for implementing the modeling algorithm are also presented. We then introduce a novel technique for the state-space realization of separable blurs, since separable 2-D blurs are often encountered in practice and constitute an important subset of 2-D blurs. This state-space model is rendered compatible with strip filtering by using a new recursive scheme which we call as pseudorecursion. An extension for estimating the blur when it is unknown, but can be parameterized, has also been indicated. Simulated experimental results using natural scenery are presented.

Statistically Linearized Estimation of Reentry Trajectories

Abstract: Several filters are applied to the problem of state estimation from inertial measurements of reentry drag. This is a highly nonlinear problem of practical significance. It is found that a filter based on the technique of statistical linearization performs better than the extended Kalman in this application. This is believed to be the first application of the statistically linearized filter to a practical dynamics problem. A sensitivity analysis is performed to demonstrate the relative insensitivity of this filter to modeling errors and approximations.

Inversion of ground‐based radiometric data by Kalman filtering

Abstract: Retrieval of atmospheric vertical temperature profiles from ground-based radiometric observations requires shrewdness and judicious choice of parameters to surmount the noxious effects of the ill-posed nature of the inversion. Kalman linear estimation, already successfully used in satellite microwave sounding of atmospheric temperature, can be also applied to infer the thermal state of the lower troposphere from ground-based infrared measurements. After a short survey of the relevant formalism the implementation of the Kalman filter is discussed with regard to the transition operator and to the error covariances. In particular, the measurement errors are considered in some detail, and their dependence on the atmospheric dynamics is pointed out. The attainable spatial resolution is compared with that of another commonly used inversion technique, and, finally, a set of temperature profiles estimated by the Kalman algorithm from a sequence of successive radiometric measurements is reported.

Performance Degradation in Digitally Implemented Kalman Filters

Abstract: A technique is presented for analyzing expected degradations in the performance of a fixed-point arithmetic implementation of a Kalman filter with precomputed gains. A quantitative approach is provided for comparing the relative degradations associated with different mechanizations of the same Kalman filter. The causes of divergence in digitally implemented filters are investigated. Finally, simulation studies are utilized to show how closely the analytical predictions agree with actual results.

Kalman type filter for models with stochastic regressors and applications to econometric models

Abstract: A discrete dynamic linear model is considered. In the Kalman filtering theory it has been usually assumed that the regressors are deterministic. In this paper the regressors are allowed to be stochastic, i.e. they can be functions of lagged observations and stochastic exogenous variables. For this model the Kalman type filter is derived, using conditional characteristic functions. It turns out that this filter is the same as the usual Kalman filter. Applications of the result to the filtering (or recursive estimation) of regression and simultaneous equation models are considered and for the latter models a two-stage Kalman filter method is introduced

The asymptotic minimum variance estimate of stationary linear single output processes

Abstract: The problem of minimum error variance estimation of single output linear stationary processes in the presence of weak measurement noise is considered. By applying s domain analysis to the case of single input systems and white observation noise, explicit and simple expressions are obtained for the error covariance matrix of estimate and the optimal Kalman gains both for minimum- and nonminimum-phase systems. It is found that as the noise intensity approaches zero, the error covariance matrix of estimating the output and its derivatives becomes insensitive to uncertainty, in the system parameters. This matrix depends only on the shape of the high frequency tail of the power-density spectrum of the observation, and thus it can be easily determined from the system transfer function. The theory developed is extended to deal with white measurement noise in multiinput systems where an analog- to the single input nonminimum-phase case is established. The results are also applied to colored observation noise problems and a simple method to derive the minimum error covariance matrices and the optimal filter transfer functions is introduced.

Nonlinear Filtering, the Link between Kalman and Extended Kalman Filters.

Abstract: The problem of developing practical suboptimal filters for non-linear systems is treated using a different, approach. The filter developed (El-F) is found to fill in the gap between Kalman and extended Kalman filters. A numerical experiment to test the performance of the developed filter is conducted and the results are shown,

Adaptive kalman filter for control of systems with unknown disturbances

Abstract: A canonical industrial filtering situation is considered whereby state estimates are required for feedback control purposes and parameter estimates are required because of an unknown and varying output disturbance. It is shown that the order of the extended Kalman filter may be reduced considerably by careful modelling. The disturbance is modelled using a modification to a technique proposed by Panuska. This modification allows parameters which can be assumed known tobe removed from the state equations. This latter method may also be applied to simplifying the identification algorithms used in self-tuning systems.

Alternative dynamics models and multiple model filtering for a short ranger tracker

Abstract: : The performance of three extended Kalman filter implementations that estimate target position, velocity, and acceleration states for a laser weapon system are compared using various target acceleration trajectories. Measurements available to the extended Kalman filters each update are taken directly from the outputs of a forward looking infrared (FLIR) sensor. Two dynamics models considered for incorporation into the filter are (1) a Brownian motion (BM) acceleration model and (2) a constant turn rate (CTR) target dynamics model. The CTR filter was compared against the BM filter to see if the more complex dynamics of the CTR filter gave it a significant improvement in tracking performance over the BM filter. These two simple extended Kalman filters were then compared to a multiple model adaptive filter consisting of a bank of three filters based on the Brownian motion acceleration model. All three filters are tested using three different flight trajectory simulations: a 2 g, a 10 g and a 20 g pull-up maneuver. All evaluations are accomplished using Monte Carlo simulation techniques. The constant turn rate extended Kalman filter was found to outperform the other two filters. The main advantage this filter had was the minimization of mean bias error in estimating position. The standard deviation of error was also slightly lower in most instances. (Author)

An alternative approach to the derivation of distributed-type partitioned filters

Abstract: In a recent paper Watanabe et al. (1980) considered the filtering for linear distributed-parameter systems with non-gaussian initial state via the ‘ partition theorem ’. It is shown here that the partitioned filtering equations for such systems are obtainable in a simpler manner by using the concept of the fundamental solution matrix for the distributed-type Kalman filter.

Linear prediction error filter design

Abstract: The design of a linear prediction error filter can be formulated as a four‐step procedure. These steps, in part, consist of a variational calculus approach that leads directly to the normal equations and an entropy conservation principle. From the normal equations, we obtain parameters called partial correlation coefficients that minimize the prediction error at the kth filter design step. Partial correlation coefficients determine the best prediction error filter for different seismic trace models (autoregressive, autoregressive‐moving average, and phase‐intercept‐shifted autoregressive traces). A result shows that simple phase distortion can increase the length of the prediction error filter and affect the estimates of the reflection sequence.

Simple derivation of discrete minimal-order optimal estimator

Abstract: A simple new derivation of the minimal-order discrete-time optimal estimator is presented. The method exploits the fact that the Kalman filter algorithm can be directly reduced in order by the number of noise-free system measurements.

Fault-Detection By Adaptive Non-Linear Filtering

Abstract: In a lintar iyitern perturbed by Gaussian noise, the state can be estimated from the observations by using Kalman filter. However, if a fault develops in the system at any random time, the Kalman filter will not be able to track the fault and large errors will develop in the state estimate. Consequently, the innovations process will no longer be white. If the random time of occurrence is coaiidered as a state then the system of state equations become nonlinear. In this paper, the Fujisaki, Killianpur arid Kunita nonlinear filtering results have been applied to obtain a representation for the stage estimite given the observations. The non-white nature of the innovations process has been modelled as an autoregressive process and an adaptive scheme has been proposed to improve the filter performance.