Showing papers on "Kalman filter published in 1969"

Adaptive filtering

Abstract: Applications of the Kalman filter in orbit determination problems have sometimes encountered a difficulty which has been referred to as divergence. The phenomenon is a growth in the residuals; the state and its estimate diverge. This problem can often be traced to insufficient accuracy in modeling the dynamics used in the filter. Although more accurate modeling is an obvious solution, it is often an impractical, and sometimes an impossible, one. Model errors are here approximated by a white, Gaussian noise input, and its covariance (Q) is determined so as to produce consistency between residuals and their statistics. In this way, realtime feedback is provided from the residuals to the filter gain. Onset of divergence produces an increase in the filter gain and the adaptive filter is able to continue tracking. This scheme has a probabilistic interpretation. Under certain conditions the estimate of Q produces the most probable finite sequence of residuals.

A cellular computer to implement the kalman filter algorithm

Abstract: The subject of this thesis is the development of the design for a specially-organized, general-purpose computer which performs matrix operations efficiently. The content of the thesis is summarized as follows: First, a review of the relevant work which has been done with microcellular and macrocellular techniques is made, Second, the discrete Kalman filter is described as an example of the type of problem for which this computer is efficient. Third, a detailed design for a cellular, array-structured computer is presented. Fourth, a computer program which simulates the cellular computer is described. Fifth, the recommendation is made that one cell and the associated control circuits be constructed to determine the feasibility of producing a hardware realization of the entire computer. A CELLL1TAR COMPUTER TO IMPLEMENT THE JLimAN FILTER ALGORITHM

Optimal control of linear systems with time-delay and observation noise

Abstract: The problem of controlling a linear system to minimize a quadratic cost criterion is investigated when the system output is a delayed linear combination of system states corrupted by additive observation noise. It is shown that the optimal control is generated by the cascade combination of a Kalman filter and a least mean-squared predictor. Expressions are derived for the minimum cost and for the state variances.

Consistent Estimates of the Parameters of a Linear System

Abstract: : The paper considers the identification of the transition matrix and statistical parameters of a discrete linear system excited by white noise. Estimates of these parameters are derived and shown to be strongly consistent. It is further shown that when strongly consistent estimates are used in the Kalman Filter equations that the Kalman Filter parameters and the state variable estimates so obtained are also strongly consistent. (Author)

Recursive algorithm for the calculation of the adaptive Kalman filter weighting coefficients

Abstract: The optimal discrete adaptive Kalman filter, as presented by Magill, necessitates the iterative calculation of a weighting coefficient for each value of the quantized parameter space. This correspondence proposes a new recursive algorithm for the calculation of the weighting coefficients and compares it to the weighting coefficient algorithm of Magill. When there are L elements in the a priori known parameter space, it is shown that the memory and computational savings include 1) L memory allocations, 2) L scalar additions per iteration, and 3) L scalar multiplications per iteration.

Stochastic differential games with constrained state estimators

Abstract: Attention is given to stochastic differential games in which the two controllers have available only noise-corrupted output measurements. Consideration is restricted to the case in which the system is linear, the cost functional quadratic, and the noises corrupting the output measurements are independent, white, and Gaussian. A solution to this problem is presented under the constraint that each controller is limited to a linear dynamic system of fixed dimension for the generation of his estimate of the system state. The optimal controls are shown to satisfy a separation theorem, the optimal estimators are shown to be closely related to Kalman filters, and the various terms in the optimal cost are shown to be readily assignable to the appropriate contributing sources.

Maximum-likelihood approach to the optimal filtering of distributed-parameter systems

Abstract: The maximum-likelihood approach to the lumped-parameter filtering estimation theory is extended to a general class of nonlinear distributed-parameter systems with additive Gaussian disturbances and measurement noise. The concept of conventional finite-dimensional-likelihood function is replaced by the likelihood functional which determines the statistical characteristics of an infinite-dimensional Gaussian random variable. First, the nonlinear filtering problem is considered. Using the differential dynamic-programming technique, an approximate nonlinear filter is derived which is shown to be the most natural nonlinear analogue of Kalman's linear distributed-parameter filter, presented in two recent papers. Secondly, the nonlinear prediction is treated by simple extrapolation. Thirdly, the smoothing problem is solved by the well known technique of decomposing the likelihood function(a1) in two parts. Finally, computational results are provided which show the effectiveness of the theory.

Simplified parameter quantization procedure for adaptive estimation

Abstract: Optimum Kalman filter design often requires estimation of the true value of an unknown parameter vector. In Magill's adaptive procedure, the parameter space must be quantized. An accurate estimate of the true value requires fine quantization, but this results in an unreasonable number of elemental filters. Iterative techniques that require only binary quantization of each unknown parameter are proposed. This reduces the number of elemental filters without sacrificing accuracy of the parameter estimate.

Identification of stochastic linear dynamic systems

Abstract: Using a new form of representation, a set of equations has been derived for the maximum likelihood identification of linear dynamic systems. These equations are shown to be directly related to the filtering and smoothing equations for linear dynamic systems. Numerical results are obtained for a fourth order system using Davidon's Conjugate Gradient Method which also gives the variances of the estimates.

An Evaluation of a Pilot Model Based on Kalman Filtering and Optimal Control

Abstract: A pilot model based on Kalman filtering and optimal control is given which, because of its structure, provides for estimation of the plant state variables, the forcing functions, the time delay, and the neuromuscular lag. The inverse filter and control problem is considered where the noise and cost function parameters yield a frequency response which is in close agreement with that found experimentally. A good correspondence with sine-wave tracking is shown including "eyes closed" tracking.

On the relative performance of the Kalman and Wiener filters

Abstract: Upper and lower bounds on the error covariance matrices of the Kalman and Wiener filters for linear finite state time-invariant system are derived. These bounds yield a measure of the relative estimation accuracy of these filters and provide a practical tool for determining when the implementational complexity of a Kalman filter can be justified. The calculation of these bounds requires little more than the determination of the corresponding Wiener filter.

On the linear smoothing problem

Abstract: The solution to the smoothing problem for a linear discrete-time system can be obtained directly from Kalman filtering theory by first converting it into a special case of the standard linear filtering problem. This conversion is accomplished by suitably defining a new state vector which contains all the relevant information about the past history of the system.

A Minimum Variance, Time Optimal, Control System Model of Human Lens Accommodation

Abstract: Experimental data relating ciliary nerve stimulation and lens motion are used to identify the open-loop plant dynamics of the lens accommodation system via a parameter identication variation of the Kalman filter equations. Using the resultant minimum variance plant model, experimental closed-loop responses of the human accommodative system are predicted by synthesizing the system closed-loop controller. The resultant control signals are shown to minimize the time required to change the refractive state of the eye. The plant dynamic model and the closed-loop model are further verified by comparing their frequency responses to experimental data. The optimal performance of the lens system is compared to analogous performance of another ocular control system, and a possible general theory of optimal control is discussed.

Modeling Nonstationary Random Processes with an Application to Gyro Drift Rate

Abstract: The problem of estimating the a priori statistics of a nonstationary process is considered using finite-time averages of experimental data. A model of the form of a linear time-invariant difference equation with a stationary independent random sequence driving function is proposed and investigated. Finite-time averages are calculated and then used in a steepest descent method to determine the coefficients of the difference nce equation. Methods are presented for transforming this model to the statespace pace format necessary for Kalman filtering, and an example is given using actual gyro drift-rate data.

Kalman Filtering and Its Application to Reliability

Abstract: The basic ideas of Kalman recursive filtering is explained in such a manner that the application of these ideas to reliability may be seen. The Bayesian viewpoint is adopted, and the explanation of Kalman filtering is broken into two parts: 1) the combination of an old estimate with data, and 2) the updating of estimates via the system model.

Region of Kalman filter convergence for several autonomous navigation modes.

Abstract: Autonomous navigation using a Kalman filter requires, in addition to an a priori knowledge of measurement data accuracy, an initial estimate of six orbit parameters and a six-by-six covariance matrix. If the initial estimates of the orbit parameters are too large, the filter fails to converge even though a large amount of data is processed. The limits of these estimates within which the filter converges is defined as the region of convergence. This characteristic is examined for navigational systems using combinations of star trackers, landmark telescopes, horizon sensors, and radar altimeters. A direct relationship between the accuracy of a system and the region of convergence is concluded, that is, the larger the system error the larger the region of convergence. For example, using a star tracker/horizon sensor system, a region of convergence of 1000 miles down range and 100 miles cross range is possible. Under these circumstances, the Kalman filter could be initialized by an astronaut making a visual estimate of geographic position and altitude. The region of convergence can be increased by selecting an initial co variance matrix representative of errors that are less than the expected errors or by using an a priori instrument-error covariance matrix that is larger than the expected error levels.

Optimal adaptive estimation: Structure and parameter adaptation-Part I: Linear models and continuous data

Abstract: A Bayesian approach to optimal adaptive estimation with continuous data is presented. Both structure and parameter adaptation are considered and specific recursive adaptation algorithms are derived for gaussian process models and linear dynamics. Specifically, for the class of adaptive estimation problems with linear dynamic models and gaussian excitations, a form of the "partition" theorem will be given that is applicable both for structure and parameter adaptation. The "partition" or "decomposition" theorem effects the partition of the essentially nonlinear estimation problem into two parts, a linear non-adaptive part consisting of ordinary Kalman estimators and a nonlinear part that incorporates the adaptive or learning nature of the adaptive estimator. In addition, a simple performance measure is introduced for the on-line performance evaluation of the adaptive estimator. The on-line performance measure utilizes quantities available from the adaptive estimator and hence a minimum of additional computational effort is required for evaluation.

Performance Analysis of Kalman Filter in Computed Tomography Thorax for Image Denoising

Abstract: Medical image processing is a very important field of study due to its large number of applications in human life. For diagnosis of any disease, several methods of medical image acquisition are possible such as Ultrasound (US), Magnetic Resonance Imaging (MRI) or Computed Tomography (CT). Depending upon the type of image acquisition, different types of noise can occur. The most common types of noises in medical images are Gaussian noise, Speckle noise, Poisson noise, Rician noise and Salt & Pepper noise. The related noise models and distributions are described in this paper. We compare several filtering methods for denoising the mentioned types of noise. The main purpose of this paper is to compare well-known filtering methods such as arithmetic mean, median and enhanced lee filter with only rarely used filtering methods like Kalman filter as well as with relative new methods like Non-Local Means (NLM) filter. To compare these different filtering methods, we use comparative parameters like Root Mean Square Error (RMSE), Peak Signal to Noise Ratio (PSNR), Mean Structural Similarity (MSSIM), Edge Preservation Index (EPI) and the Universal Image Quality Index (UIQI). The processed images are shown for a specific noise density and noise variance. We show that the Kalman filter performs better than Mean, Median and Enhanced Lee filter for removing Gaussian, Speckle, Poisson and Rician noise. Experimental results show that the Kalman filter provides better results as compared to other methods. It could be also a good alternative to NLM filter due to almost equal results and lower computation time.

A note on minimax estimation and Kalman filtering

Abstract: A minimax estimator for the state of a discrete time-varying linear plant with an a priori unknown control sequence is developed. No statistics for the sequence of control vectors are assumed to exist. It is assumed, however, that the a priori unknown control sequence can be measured in additive Gaussian noise with zero mean and known variance.

On the optimum colored noise Kalman filter

Abstract: A set of equations is presented for designing an optimum Kalman filter for a continuous linear dynamic system with colored measurement noise only. Included are the optimum Kalman filter variance, gain, and mechanization equations in a form which can be computerized easily and requires a minimum of engineering effort.

Error bounds in optimum smoothing

Abstract: Proper choice of prior statistics and mathematical models for optimum filtering and smoothing algorithms are essential for successful operation of control and communication systems in which estimation requirements are present. This letter presents the development of a set of relations which allows the determination of error bounds for the estimation error covariance matrix of fixed-point smoothing and fixed-interval smoothing algorithms for optimum linear estimation.

New proof for Kalman's criterion of state controllability

Abstract: A new proof is given for Kalman's criterion of state controllability in linear time-invariant dynamical systems. The proof is constructive, in that it may be used to generate control strategies.

Adaptive filtering in satellite orbit estimation.

Abstract: Adaptive filter for estimating system noise inputs from actual residuals developed to control Kalman filter in satellite orbit estimation

Comments on "Application of results from the absolute stability problem to the computation of finite stability domains"

Abstract: An error is corrected, and new material is added on maximizing the extent of the estimate of the stability region. In an example it is shown that the maximum-area estimate coincides with the estimate constructed by Kalman's method.