Showing papers on "Kalman filter published in 1974"
TL;DR: A new tracking filter is developed that incorporates, in an a posteriori statistical fashion, all data available from sensor reports located in the vicinity of the track, and that provides both optimal performance and reliable estimates of this performance when operating in dense environments.
Abstract: When tracking targets in dense environments, sensor reports originating from sources other than the target being tracked (i.e., from clutter, thermal false alarms, other targets) are occasionally incorrectly used in track updating. As a result tracking performance degrades, and the error covariance matrix calculated on-line by the usual types of tracking filters becomes extremely unreliable for estimating actual accuracies. This paper makes three contributions in this area. First, a new tracking filter is developed that incorporates, in an a posteriori statistical fashion, all data available from sensor reports located in the vicinity of the track, and that provides both optimal performance and reliable estimates of this performance when operating in dense environments. The optimality of and the performance equations for this filter are verified by analytical and simulation results. Second, several computationally efficient classes of suboptimal tracking filters based on the optimal filter developed in this paper and on an optimal filter of another class that appeared previously in the literature are developed. Third, using an extensive Monte Carlo simulation, the various optimal and suboptimal filters as well as the Kalman filter are compared, with regard to the differences between the on-line calculated and experimental covariances of each filter, and with regard to relative accuracies, computational requirements, and numbers of divergences or lost tracks each produces.
282 citations
IBM1
TL;DR: This paper shows how a Kalman filter may be applied to the problem of setting the tap gains of transversal equalizers to minimize mean-square distortion, and its speed of convergence depending only on the number of taps.
Abstract: This paper shows how a Kalman filter may be applied to the problem of setting the tap gains of transversal equalizers to minimize mean-square distortion. In the presence of noise and without prior knowledge about the channel, the filter algorithm leads to faster convergence than other methods, its speed of convergence depending only on the number of taps. Theoretical results are given and computer simulation is used to corroborate the theory and to compare the algorithm with the classical steepest descent method.
271 citations
TL;DR: In this paper, the Chandrasekhar-type Riccati-type difference equation is replaced by another set of difference equations, which are then used for recursive estimation in constant continuous-time linear systems.
Abstract: Certain recently developed fast algorithms for recursive estimation in constant continuous-time linear systems are extended to discrete-time systems. The main feature is the replacement of the Riccati-type difference equation that is generally used for such problems by another set of difference equations that we call of Chandrasekhar-type. The total number of operations in the new algorithm is in general less than with the Riccati-equation based Kalman filter, with significant reductions being obtained in several important special cases. The algorithms are derived via a factorization of increments of the Riccati equation variable, a method that can be extended to nonsymmetric Riccati equations as well.
215 citations
TL;DR: In this paper, an algorithm for computing the gain matrices of the Kalman filter is presented, which does not involve the usual Riccati-type equation, and the number of nonlinear equations to be solved in each step is of order k rather than $k^2$ as by the usual procedure.
Abstract: An algorithm (which does not involve the usual Riccati-type equation) for computing the gain matrices of the Kalman filter is presented. If the dimension k of the state space is much larger than that of the observation process, the number of nonlinear equations to be solved in each step is of order k rather than $k^2$ as by the usual procedure.
96 citations
TL;DR: In this paper, an angle channel Kalman filter is configured which incorporates measures of range, range rate, and on-board dynamics, and theoretical performance results are given and a discussion of methods for reducing the complexity of the Kalman gain computation is presented.
Abstract: This paper studies the application of Kalman filtering to single-target track systems in airborne radar. An angle channel Kalman filter is configured which incorporates measures of range, range rate, and on-board dynamics. Theoretical performance results are given and a discussion of methods for reducing the complexity of the Kalman gain computation is presented. A suboptimal antenna controller which operates on the outputs of the angle Kalman filter is also described. In addition, methodological improvements are shown to exist in the design of range and range-rate trackers using the Kalman filter configuration.
77 citations
TL;DR: An expository derivation of the square-root information filter/smoother is given, based on the recursive least-squares method, which is easier to grasp, interpret and generalize than are the dynamic programming arguments previously used.
68 citations
TL;DR: The temperature‐dependent endogenous metabolism model of single species continuous culture dynamics is utilized in the computer simulation of the Kalman filter state estimation technique, and the state estimator is illustrated in the context of conventional control strategies.
Abstract: The temperature-dependent endogenous metabolism model of single species continuous culture dynamics is utilized in the computer simulation of the Kalman filter state estimation technique. Parameters of the nonlinear equations can be “tracked” while variance in measured states can be damped. The state estimator is illustrated in, the context of conventional control strategies.
49 citations
TL;DR: In this article, the authors developed an advection-diffusion model of air pollution over an urban area and the region is subdivided into a grid and the three-dimensional partial differential equation of the pollution concentration is reduced to a linear vector difference equation.
Abstract: The advection-diffusion model of air pollution over an urban area is developed. The region is subdivided into a grid and the three-dimensional partial differential equation of the pollution concentration is reduced to a linear vector difference equation. Along with this discrete equation, a stochastic model of air pollution is considered and pollution concentrations over the area are estimated from observed data generated by a few monitor points. High dimensionality of the resulting Kalman filter equation is avoided by using a discrete form of Chandrasekar-type equations. Diffusion coefficients in the advection-diffusion model, which are difficult to specify accurately, are also identified.
49 citations
TL;DR: A previously developed algorithm designed for use in the case of stationary noise is modified to allow estimation of an unknown Kalman gain and thus the system state in the presence of unknown time varying noise statistics.
Abstract: The problem of estimating the state of a linear dynamic system driven by additive Gaussian noise with unknown time varying statistics is considered. Estimates of the state of the system are obtained which are based on all past observations of the system. These observations are linear functions of the state contaminated by additive white Gaussian noise. A previously developed algorithm designed for use in the case of stationary noise is modified to allow estimation of an unknown Kalman gain and thus the system state in the presence of unknown time varying noise statistics. The algorithm is inherently parallel in nature and if implemented in a computer with parallel processing capability should only be slightly slower than the stationary Kalman filtering algorithm with known noise statistics.
42 citations
TL;DR: A two-dimensional x, y Kalman tracking filter is analyzed for a track-while-scan (TWS) operation when the radar sensor measures range and bearing at uniform sampling intervals T seconds apart and the steadystate components of the gain and error covariance matrixes are analytically determined under the assumption of a white noise maneuver acceleration model in two dimensions.
Abstract: A two-dimensional x, y Kalman tracking filter is analyzed for a track-while-scan (TWS) operation when the radar sensor measures range and bearing (r, ?) at uniform sampling intervals T seconds apart. This development explicitly considers the coupling between the quantities measured by the sensor (r, ?) and the Cartesian x, y coordinate system selected for the tracking operation. The steadystate components of the gain and error covariance matrixes are analytically determined under the assumption of a white noise maneuver acceleration model in two dimensions. These results are verified by computer calculation of the Kalman filter matrix equations.
38 citations
TL;DR: In this article, a suboptimal filter applicable to systems which have unknown impulses at unknown instances of time is described, and the minimum variance estimate of the input and the Bayes' decision rule is explained.
Abstract: This paper describes a suboptimal filter applicable to systems which have unknown impulses at unknown instances of time. The minimum variance estimate of the input and the Bayes' decision rule is explained. Computer results indicate the improvement over the standard Kalman filter.
TL;DR: In this article, a new approach based on both simple or weighted least squares is outlined and tested by Monte Carlo simulation, which is improved by noting the true statistical nature of the problem.
Abstract: The approach to the estimation of the optimum Kalman filter steady-state gain proposed by Mehra and modified by Carew and Belanger can be improved by noting the true statistical nature of the problem. A new approach based on both simple or weighted least squares is outlined and tested by Monte Carlo simulation.
TL;DR: In this article, the covariance-matching technique was used to estimate a scalar multiplier in the discrete Kalman filter (DKF) for the case of noise covariance matrices.
Abstract: In the application of the discrete Kalman filter, it occasionally happens that one of the noise covariance matrices is known except for a scalar multiplier. Algorithms are derived to estimate such a parameter using the covariance-matching technique.
TL;DR: In this paper, Bayesian recursion relations for the probability densities of the unknown random variables conditioned on all available data were developed for estimating the state of a linear dynamic system driven by white Gaussian noise with unknown covariance Q and observed by a linear function of the state contaminated by white gaussian noise R by using the steady state Kalman filter relations.
Abstract: The problem of estimation of the state of a linear dynamic system driven by white Gaussian noise with unknown covariance Q and observed by a linear function of the state contaminated by white Gaussian noise with unknown covariance R is considered. Bayesian recursion relations for the probability densities of the unknown random variables conditioned on all available data are developed. Initially a relation giving the a posteriori densities of Q and R conditioned on all available data is developed. However since the possible range of Q and R is generally unbounded and also because Q and R may have quite large dimension, a mechanization of the aforesaid algorithm by representing Q and R with a grid of possible values is considered unfeasible for any realistic problems. Therefore, the random variables Q and R are transformed to random variables representing the optimal gain and the covariance of the innovations process by use of the steady state Kalman filter relations. The resulting probability dens...
01 Jan 1974
TL;DR: A design method for digital self-reorganizing control systems which is optimally tolerant of failures in aircraft sensors and accomplished with software instead of the popular and costly technique of hardware duplication is presented.
Abstract: This paper presents a design method for digital self-reorganizing control systems which is optimally tolerant of failures in aircraft sensors. The functions of this system are accomplished with software instead of the popular and costly technique of hardware duplication. The theoretical development, based on M-ary hypothesis testing, results in a bank of M Kalman filters operating in parallel in the failure detection logic. A moving window of the innovations of each Kalman filter drives the detection logic to decide the failure state of the system. The detection logic also selects the optimal state estimate (for control logic) from the bank of Kalman filters. The design process is applied to the design of a self-reorganizing control system for a current configuration of the space shuttle orbiter at Mach 5 and 120,000 feet. The failure detection capabilities of the system are demonstrated using a real-time simulation of the system with noisy sensors.
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TL;DR: In this paper, auf den Arbeiten von Kalman beruhende Signalschatzung zeitdiskreter Prozesse betrachtet wurde.
Abstract: Wahrend im 4. Kapitel die auf den Arbeiten von Kalman beruhende Signalschatzung zeitdiskreter Prozesse betrachtet wurde, soll nun die Schatzung zeitkontinuierlicher Prozesse behandelt werden.
TL;DR: In this paper, the state and systematic error estimation are decoupled in the linear filter and the second-order filter, respectively, and the estimates are coupled in the discrete update stage of the two-stage filter.
Abstract: When recursively estimating the state of a nonlinear process using a second-order filter to process data from many sensors, the method of augmenting the state vector with those sensor systematic errors for which estimates are desired can result in a new vector of extremely large dimension. To avoid the computational problems arising from operations with large dimension matrices it is desirable to decouple the state and systematic error estimation. An efficient method of generating the estimates separately has been derived for the linear filter [1]. For the second-order filter [2] the separation can also be accomplished although unless the observation model is linear, the estimates are coupled during the discrete update stage of the two stage filter. If the observation model is linear, the estimates are completely decoupled just as in the linear filter.
TL;DR: A linear receiver that turns out to be practical and optimum in the mean-square sense is analyzed in detail, and some interesting features of this receiver are stressed; for instance, it is shown that in the absence of noise it becomes a zero-forcing equalizer, provided that stability can be achieved.
Abstract: Two main classes of receivers for data modems using linear modulation systems over time-dispersive channels have been investigated by many authors for both theoretical and practical purposes, 1) structure-constrained linear receivers, such as zeroforcing and mean-square-error tapped-delay-line equalizers, and 2) nonlinear receivers, such as decision-feedback equalizers and maximum likelihood sequence estimators. In this paper a linear receiver that turns out to be practical and optimum in the mean-square sense is analyzed in detail, and some interesting features of this receiver are stressed; for instance, it is shown that in the absence of noise it becomes a zero-forcing equalizer, provided that stability can be achieved. A comprehensive set of results is also presented, showing that conventional tapped-delay-line equalizers perform very close to the optimum.
TL;DR: In this article, an algorithm is developed for estimating a portion of the state of a linear dynamical system, where the dimensions of the filter used in the estimation procedure may be considerably smaller than the dimension of a Kalman filter used to estimate the entire state vector.
Abstract: An algorithm is developed for estimating a portion of the state of a linear dynamical system. The dimension of the filter used in the estimation procedure may be considerably smaller than the dimension of a Kalman filter used to estimate the entire state vector. Thus, an on line computational advantage is achieved. The savings may be significant if the dimension of the segment of the state vector which is of interest is much smaller than the dimension of the entire state vector.
TL;DR: In this paper, the problem of obtaining output feedback gains to minimize a quadratic performance criterion which includes sensitivity variables is discussed, and a set of non-linear matrix equations are obtained which constitute the necessary conditions that must be satisfied for an optimal solution.
Abstract: The problem of obtaining output feedback gains to minimize a quadratic performance criterion which includes sensitivity variables is discussed. The equivalent stochastic problems are also studied and when a Kalman filter is allowed, the minimum variance estimate of the state is employed to implement the control. A set of non-linear matrix equations are obtained which constitute the necessary conditions that must be satisfied for an optimal solution. For the deterministic case it is shown that when no sensitivity is considered and the matrix which relates output and input is invertible, the usual Riccati formulation is obtained. The problem is also reformulated using a compensator and it is shown that it can be cast into an instantaneous feedback form.
TL;DR: A new concept of observability based on the information set possessed by a local control station in decentralized dynamic system is introduced and an explicit expression for the required state vector is obtained as a by-product.
Abstract: This paper introduces a new concept of observability based on the information set possessed by a local control station in decentralized dynamic system. Necessary and sufficient conditions are presented for the initial state observability, present state reconstructibility, and strong observability by the local control station. When these conditions are satisfied, the local control station, who possesses no information on the control inputs generated by the other control station, can uniquely determine the required state vector. Furthermore, these conditions are stated in terms of the system coefficient matrices alone, and provide the structural information of the observable decentralized dynamic system. The derivation of the results is based on the properties of Penrose generalized inverse of partitioned matrix. An explicit expression for the required state vector is obtained as a by-product. The well-known observability condition ( Kalman, 1961 ) is also rederived from the results obtained in this paper. Examples are demonstrated to illustrate the theory.
TL;DR: In this article, it was shown that a Riccati equation of particular structure which arises in a number of singular optimal estimation and control processes can be reduced in order, leading directly to a procedure for the design of a class of minimal order observers, the structure of which can be interpreted as the limiting form of appropriate Kalman estimators with vanishing observation noise.
Abstract: It is shown that a Riccati equation of particular structure which arises in a number of singular optimal estimation and control processes can be reduced in order. This fact leads directly to a procedure for the design of a class of minimal order observers, the structure of which can be interpreted as the limiting form of appropriate Kalman estimators with vanishing observation noise.
TL;DR: In this paper, the joint plant and measurement control problem of linear, unknown, discrete time systems excited by white Ganssian noise is considered, and the performance criterion is quadratic in the state and is additive in the plant and control.
Abstract: In this paper, the joint plant and measurement control problem of linear, unknown, discrete time systems excited by white Ganssian noise is considered. The performance criterion is quadratic in the state and is additive in the plant and measurement control. The adaptive control solution is obtained by approximating the dynamic programming equation-the approximation amounts to replacing the optimal adaptive cost-to-go in the dynamic programming equation by the average value of the truly optimum cost-to-go for each admissible model. In our solution, the adaptive plant and measurement control schemes can be separated. The adaptive plant control is given by the product of the weighted integrals with the a posteriori probability of the parameter as weights. The adaptive measurement control scheme is obtained as the solution of a constrained nonlinear, optimization problem for each time; the constraint equations being the error covatiance matrix equations in the Kalman filter. An illustrative example of the optimum timing of measurements is discussed where the joint adaptive control scheme is simulated and its performance is compared with the optimum value of the performance if the system parameters were completely known.
TL;DR: The proposed spline-based estimator is readily implementable, its realization requiring essentially a bank of Kalman filters and integration of piece-wise polynomial functions, and should prove useful in practical applications of parameter estimation as well as of general nonlinear estimation.
TL;DR: In this paper, the problem of estimating the state of a linear system over a finite time interval in the presence of noise is considered, and the expected value of the integral of the quadratic error is taken as the performance index.
Abstract: The problem of estimating the state of a linear system over a finite time interval in the presence of noise is considered. The expected value of the integral of the quadratic error is taken as the performance index. A configuration of the same type as the Kaiman filter is assumed with the restriction that the gain must be constant. An integral equation is obtained as a necessary condition for the gain to be optimum, and an iterative procedure is suggested for its solution. Numerical results indicate that this filter can be significantly more accurate than one utilizing the steady-state gain of the Kalman filter.
TL;DR: In this paper, the g-h filter is used as a tracking filter and the target under track is modelled as a constant-velocity system with a correlated random acceleration, equations are derived for the covariances of the filtered and predicted estimates.
Abstract: The g-h filter is often used as a tracking filter. Assuming that the target under track is modelled as a constant-velocity system with a correlated random acceleration, equations are derived for the covariances of the filtered and predicted estimates. These equations are useful to predict the performance of the filter and to select suitable parameters so as to improve performance.
TL;DR: The real-time tracking and orbit determination program used on board the NASA tracking ship, the USNS Vanguard, is described in this article, which uses a variety of filtering algorithms, including an extended Kalman filter, to derive realtime orbit determinations (position-velocity state vectors) from shipboard tracking and navigation data.
Abstract: The real-time tracking and orbit determination program used on board the NASA tracking ship, the USNS Vanguard, is described in this paper The computer program uses a variety of filtering algorithms, including an extended Kalman filter, to derive real-time orbit determinations (position-velocity state vectors) from shipboard tracking and navigation data Results from Appolo missions are given to show that orbital parameters can be estimated quickly and accurately using these methods
TL;DR: The modified Bryson-Frazier fixed interval smoothing algorithm, is an addendem to the Kalman filter that when applied to the problem of fixed-lag smoothing is computationally more efficient than the algorithms recently reported.
01 Apr 1974
TL;DR: In this paper, the Kalman conjecture was verified for transfer functions with only negative real poles and no numerator dynamics based on the off-axis circle criterion of Cho and Narendra and a consideration of the curvature of the Nyquist locus of the transfer function.
Abstract: The Kalman conjecture is verified for certain transfer functions with only negative real poles and no numerator dynamics. The results are based on the off-axis circle criterion of Cho and Narendra and a consideration of the curvature of the Nyquist locus of the transfer function.