Showing papers on "Alpha beta filter published in 1973"
TL;DR: In this paper, a full order adaptive observer is described for observing the state of a single-input single-output observable continuous differential system with unknown parameters, and convergence of the observer states to those of the system is accomplished by directly changing the observer parameters using an adaptive law based upon Lyapunov stability theory.
Abstract: A full order adaptive observer is described for observing the state of a single-input single-output observable continuous differential system with unknown parameters. Convergence of the observer states to those of the system is accomplished by directly changing the parameters of the observer using an adaptive law based upon Lyapunov stability theory. Observer eigenvalues may be freely chosen. Some restriction is placed upon the system input in that it must be sufficiently rich in frequencies in order to insure convergence.
238 citations
TL;DR: In this article, the stationary form of the discrete Kalman filter for state estimation in noisy process systems was demonstrated by simulated and experimental tests on a pilot plant evaporator, which resulted in good control despite process and/or measurement noise levels of 10%.
Abstract: The effectiveness of the stationary form of the discrete Kalman filter for state estimation in noisy process systems was demonstrated by simulated and experimental tests on a pilot plant evaporator. The filter was incorporated into a multivariable, computer control system and resulted in good control despite process and/or measurement noise levels of 10%. The results were significantly better than those obtained when the Kalman filter was omitted or replaced by conventional exponential filters. In this application the standard Kalman filter was reasonably insensitive to incorrect estimates of initial conditions or noise statistics and to errors in model parameters. The filter estimates were sensitive to unmeasured process disturbances. However this sensitivity could be reduced by treating the noise covariance matrices R and Q as design parameters rather than noise statistics and selecting values which result in increased weighting of the process measurements relative to the calculated model states.
30 citations
01 Feb 1973
TL;DR: The performance of the filter is considered, and, for state rather than signal estimation, the performance is found to depend on the details of the model, as distinct from its output statistics.
Abstract: The Kalman filter depends only on the output statistics of the message model; a technique for filter construction using only these statistics is given. The performance of the filter is considered, and, for state rather than signal estimation, the performance is found to depend on the details of the model, as distinct from its output statistics.
23 citations
TL;DR: A simple but effective method of divergence control for Kalman filters is described, which is in principle a considerable simplification of the type of divergence Control which is based on plant noise estimation.
Abstract: A simple but effective method of divergence control for Kalman filters is described. This is in principle a considerable simplification of the type of divergence control which is based on plant noise estimation.
21 citations
TL;DR: In this paper, the Gaussian second-order measurement equations appropriate for the nonlinear elongation of measured range were developed and demonstrated in a spacecraft rendezvous navigation simulation, where the required additions to a linearized Kalman filter are not complex.
Abstract: Advances in nonlinear filter theory have produced the Gaussian second-order filter. This extension of the Kalman filter compensates for measurement nonlinearity by appropriate bias compensation and a priori measurement variance increase. This paper develops the Gaussian second-order measurement equations appropriate for the nonlinear elongation of measured range. The required additions to a linearized Kalman filter are not complex. The performance improvement obtainable is demonstrated in a spacecraft rendezvous navigation simulation. Divergence of the standard linearized filter occurs if the initial error exceeds 1 km. Divergence in the second-order filter does not occur unless the initial error exceeds 10 km.
15 citations
01 Apr 1973
TL;DR: In this article, an application of the Kalmsn filter to equalization of a digital communication Chmnnel is described and the resultant modified Kalman equalizer (KE) is a nonlinear system in which the channel tap gain is estimated via a decision feedback approach and the state variable is estimated by a prediction process.
Abstract: An application of the Kalmsn filter to equalization of a digital communication Chmnnel is described. The resultant modified Kalman equalizer (KE) is a nonlinear system in which the channel tap gain are estimated via a decision feedback approach and the state variable is estimated by a prediction process.
13 citations
01 Dec 1973
TL;DR: In this article, a low-order observer design procedure is presented for multiple output systems, which does not require explicitly performing a change of basis on the system, and includes the construction of the linear transformation relating the system state to the asymptotic observer state.
Abstract: This paper discusses a well known change of co-ordinates for multiple output systems from a different viewpoint, and a new, simplified, low order observer design. The discussion of the transformation given here exhibits more of the system structure than previous presentations. The observer design procedure does not require explicitly performing a change of basis on the system, and includes the construction of the linear transformation relating the system state to the asymptotic observer state.
8 citations
TL;DR: In this article, a class of algorithms which are closely related to the Kalman filter is considered, and with an input signal of appropriate statistics these algorithms are easy to calculate and are characterized by a speed of convergence which is comparable to that of a KF given an imperfect, a priori knowledge of the error covariance matrix.
Abstract: In order to identify a linear system with a discrete non-parametric model a class of algorithms which is closely related to the Kalman filter is considered. With an input signal of appropriate statistics these algorithms are easy to calculate and are characterized by a speed of convergence which is comparable to that of a Kalman filter given an imperfect, a priori knowledge of the error covariance matrix.
5 citations
21 Mar 1973
TL;DR: In this paper, a procedure for determining the mean and covariance errors in an alpha-beta filter operating in cartesian coordinates was found, and closed-form solutions under steady-state conditions were found for the output covariances for the polar coordinate filter and for the cartesian coordinate filter when the target is stationary.
Abstract: : A procedure for determining the mean and covariance errors in an alpha-beta filter operating in cartesian coordinates was found. The results obtained from this procedure were compared to an alpha-beta filter operating in polar coordinates. Assuming that the input measurements in polar coordinates were Gaussian distributed, it was shown that at the output of the coordinate transformations the noise could be approximated accurately by a Gaussian distribution for typical radar data. Closed-form solutions under steady-state conditions were found for the output covariances for the polar coordinate filter and for the cartesian coordinate filter when the target is stationary. These covariances depended upon alpha, beta, and the measurement variances. For moving targets, the cartesian coordinate filter yielded output covariances which were nonstationary. Their values depended upon alpha, beta, measurement variances, target trajectory, target speed, and sampling time. The mean errors were discussed. Under fading conditions both the mean and covariance errors increased during the fading time.
4 citations
TL;DR: In this paper, the sensitivity of an observer to variations in the parameters of the system being observed is considered and an equation is developed for the error in the observer output caused by variations in system parameters.
Abstract: The sensitivity of an observer to variations in the parameters of the system being observed is considered. An equation is developed for the error in the observer output caused by variations in the system parameters. An analogue computer design procedure is utilized to minimize a quadratic performance index. An example is provided to illustrate this procedure.
2 citations
21 Dec 1973
TL;DR: In this article, a procedure for adjusting the gains in an alpha-beta filter used in tracking air targets by search radars is given for the case in which the track updates appear randomly in time.
Abstract: : A procedure for adjusting the gains in an alpha-beta filter used in tracking air targets by search radars is given for the case in which the track updates appear randomly in time.
TL;DR: In this article, a general recursive method for learning the optimal stationary Kalman filter Kopt was proposed, where the plant and measurement noise covariance kernels, denoted by Q and R, respectively, are unknown.
Abstract: It is the purpose of the letter to provide a short description of a general recursive method for learning the optimal stationary Kalman filter Kopt, when the plant and measurement noise covariance kernels, denoted by Q and R, respectively, are unknown. Experimental verification that confirms the theoretical expectations is presented.
TL;DR: Among several second-order approximations to the filter of a non-linear system, it is found that the extended Kalman filter is generally the most versatile as discussed by the authors, which can be further improved by using stochastic linear approximation as suggested by Sunahara.
Abstract: Among several second-order approximations to the filter of a non-linear system, it is found that the extended Kalman filter is generally the most versatile. The second-order likelihood filter, also known ns the Detchmendy—Sridhar filter is inferior to the ahove and at the same time involves more computation. In the special ease when analytical expressions For the gaussian expectation integrals of the non-linearities can be found, the extended Kalman filter can be further improved by using stochastic linear approximations as suggested by Sunahara. The third-order likelihood filter derived in this paper is more accurate than the above, but calls for considerable storage space and computing time.
01 Dec 1973
TL;DR: An adaptive observer is developed which will converge in mean square to the optimum filter asymptotically and can be improved by directly adjusting the gain of the observer adaptively.
Abstract: This paper considers the problem of estimating the state of a discrete linear time-invariant system when the noise statistics are unknown. In the absent of any knowledge of the noise statistics, an observer with a fixed gain can be used in estimating the state. When more observation information is accumulated, the estimation performance can be improved by directly adjusting the gain of the observer adaptively. An adaptive observer is developed which will converge in mean square to the optimum filter asymptotically.
TL;DR: It is shown that this state observer for a linear deterministic q-observable sequential machine has the structure of Kalman's linear estimator, i.e. it is a linear sequential machine driven by the measured outputs and inputs of the original machine.
Abstract: The problem of designing a state observer for a linear deterministic q-observable sequential machine is considered. It is shown that this observer has the structure of Kalman's linear estimator, i.e. it is a linear sequential machine driven by the measured outputs and inputs of the original machine. The main feature of this observer is that after q steps it gives the state of the original machine without error whatever the initial state estimate chosen. The theory is then applied for estimating the state of stochastic sequential machines. Observers are necessary when applying state feedback control to sequential machines, the state variables of which are not all accessible to direct measurement.
01 Dec 1973
TL;DR: A survey of algorithms for linear estimation of dynamical systems with time-invariant parameters can be found in this article, where the authors present several special cases of the algorithms that are closely related to certain early work in astrophysics by So Chandrasekhar and in estimation by Levinson.
Abstract: The paper is an outline of a talk that will survey some algorithms that have recently been developed for linear estimation in dynamical systems with time-invariant parameters. The algorithms have potential numerical advantages and in particular require less effort than the Kalman filter. Special cases of the algorithms are closely related to certain early (1947) work in astrophysics by So Chandrasekhar and in estimation by N. Levinson. The algorithms can be used to solve several other problems beside estimation. Furthermore, they are closely related to algorithms for minimal realization and for system inversion.
TL;DR: The structure of the innovations process is examined as the gain of a Kalman filter is allowed to deviate from its optimum structure in this article, and the state model of the resulting pseudo-innovations process is determined, and it is shown how the level of variance of the process depends on the difference between the desired Kalman gain and the gain actually being employed.
Abstract: The structure of the innovations process is examined as the gain of a Kalman filter is allowed to deviate from its optimum structure. The state model of the resulting pseudoinnovations process is determined, and it is shown how the level (or variance) of the process depends on the difference between the desired Kalman gain and the gain actually being employed. The model illustrates requirements on an arbitrary gain matrix to ensure stable filter performance.
TL;DR: In this article, the authors investigated the use of Luenberger's minimal-order observer as an alternate to the Kalman filter for obtaining state estimates in linear discrete-time stochastic systems.
Abstract: This chapter investigates the idea of using Luenberger's minimal-order observer as an alternate to the Kalman filter for obtaining state estimates in linear discrete-time stochastic systems. One of the major results presented in the chapter is the development of the general solution to the problem of constructing an optimal minimalorder observer for linear discrete-time stochastic systems where optimality is in the mean-square sense. The approach taken in the development which follows leads to a completely unified theory for the design of optimal minimum-order observers and is applicable to both time-varying and timeinvariant linear discrete systems.