Showing papers on "Recursive least squares filter published in 1979"

A Kalman Filter Based Tracking Scheme with Input Estimation

Abstract: Beginning with the derivation of a least squares estimator that yields an estimate of the acceleration input vector, this paper first develops a detector for sensing target maneuvers and then develops the combination of the estimator, detector, and a "simple" Kalman filter to form a tracker for maneuvering targets. Finally, some simulation results are presented. A relationship between the actual residuals, assuming target maneuvers, and the theoretical residuals of the "simple" Kalman filter that assumes no maneuvers, is first formulated. The estimator then computes a constant acceleration input vector that best fits that relationship. The result is a least squares estimator of the input vector which can be used to update the "simple" Kalman filter. Since typical targets spend considerable periods of time in the constant course and speed mode, a detector is used to guard against automatic updating of the "simple" Kalman filter. A maneuver is declared, and updating performed, only if the norm of the estimated input vector exceeds a threshold. The tracking sclheme is easy to implement and its capability is illustrated in three tracking examples.

A study of algorithms for covariance structure analysis with specific comparisons using factor analysis

Abstract: Several algorithms for covariance structure analysis are considered in addition to the Fletcher-Powell algorithm. These include the Gauss-Newton, Newton-Raphson, Fisher Scoring, and Fletcher-Reeves algorithms. Two methods of estimation are considered, maximum likelihood and weighted least squares. It is shown that the Gauss-Newton algorithm which in standard form produces weighted least squares estimates can, in iteratively reweighted form, produce maximum likelihood estimates as well. Previously unavailable standard error estimates to be used in conjunction with the Fletcher-Reeves algorithm are derived. Finally all the algorithms are applied to a number of maximum likelihood and weighted least squares factor analysis problems to compare the estimates and the standard errors produced. The algorithms appear to give satisfactory estimates but there are serious discrepancies in the standard errors. Because it is robust to poor starting values, converges rapidly and conveniently produces consistent standard errors for both maximum likelihood and weighted least squares problems, the Gauss-Newton algorithm represents an attractive alternative for at least some covariance structure analyses.

A convergence proof for a hyperstable adaptive recursive filter (Corresp.)

Abstract: Hyperstability, a concept from nonlinear stability theory, is used to develop a real-time adaptive recursive filter useful in a nonstationary environment.

Fast Numerically Stable Computations for Generalized Linear Least Squares Problems

Abstract: The generalized linear least squares problem is treated here as a linear least squares problem with linear equality constraints. Advantage is taken of this formulation to produce a numerically stable algorithm based on plane rotations which is designed for fast computation, especially for large structured problems. The algorithm can be made to handle any rank deficiency in the matrices. A rounding error analysis and operation counts are given. The use of nonunitary transformations is considered.

Computer solution and perturbation analysis of generalized linear least squares problems

Abstract: A new formulation of the generalized linear least squares problem is given. This is based on some ideas in estimation and allows complete generality in that there are no restrictions on the matrices involved. The formulation leads directly to a numerical algorithm involving orthogonal decompositions for solving the problem. A perturbation analysis of the problem is obtained by using the new formulation and some of the decompositions used in the solution. A rounding error analysis is given to show that the algorithm is numerically stable.

On finite element methods of the least squares type

Abstract: A theoretical framework for the least squares solution of first order elliptic systems is proposed, and optimal order error estimates for piecewise polynomial approximation spaces are derived. Numerical examples of the least squares method are also provided.

A recursive approach to parameter estimation in regression and time series models

Abstract: In this paper we discuss the recursive (or on line) estimation in (i) regression and (ii) autoregressive integrated moving average (ARIMA) time series models. The adopted approach uses Kalman filtering techniques to calculate estimates recursively. This approach is used for the estimation of constant as well as time varying parameters. In the first section of the paper we consider the linear regression model. We discuss recursive estimation both for constant and time varying parameters. For constant parameters, Kalman filtering specializes to recursive least squares. In general, we allow the parameters to vary according to an autoregressive integrated moving average process and update the parameter estimates recursively. Since the stochastic model for the parameter changes will "be rarely known, simplifying assumptions have to be made. In particular we assume a random walk model for the time varying parameters and show how to determine whether the parameters are changing over time. This is illustrated wit...

Self-adaptive Kalman filter

Abstract: It is shown how the refined instrumental variable (r.i.v.) method of recursive parameter estimation can be modified simply so that it functions as an optimal adaptive filter and state-estimation algorithm.

A new form of the extended Kalman filter for parameter estimation in linear systems

Abstract: A well-known method for estimation of parameters in linear systems with correlated noise is the extended Kalman filter where the unknown parameters are estimated as a part of an enlarged state vector. To avoid the computational burden in determining the state estimates when only the parameter estimates are required, a new simple form of the extended Kalman filter, where the state consists only of the parameters to be estimated, is proposed. The algorithm is based on the inclusion of the computed residuals in the observation matrix of a state representation of the system, an idea first introduced in the so-called extended least squares or Panuska's method. Convergence properties of the proposed algorithm are studied and the algorithm is shown to perform a gradient-based minimization of the maximum likelihood loss function. Some special cases of the algorithm are also discussed and an extension to an estimator for randomly varying parameters is outlined.

Solutions to Weighted Least Squares Problems by Modified Gram-Schmidt with Iterative Refinement

Abstract: A Fortran Lmplementatlon of an algonthm for solving weighted least squares problems by modified Gram-Schmidt with iteratwe refmement is described. The algorithm is one known to prowde maximum accuracy in the case of ill-conditioned problems. The types of problems which can be solved include overdetermined and underdetermined systems of linear equations, and problems where the solution is subject to linear equality constraints. The covariance matrix of the solution vector is computed.

A short-term sequential regression algorithm

Abstract: A short-term sequential regression (STSER) formulation is introduced to facilitate adaptive filtering in nonstationary environments. A corresponding STSER algorithm for finite impulse response (FIR) filters is derived. Experimental results involving an STSER predictor are presented. For the purpose of comparison, corresponding results using other available adaptive algorithms are also included.

A Sampled Analog MOS LSI Adaptive Filter

Abstract: A novel realization of an adaptive filter using sampled analog MOS LSI techniques is described in this paper. The basic functional block of the adaptive filter is an electrically programmable transversal filter whose tap weights are modified according to the least mean square algorithm. A comparison has been made among different available approaches for implementing a programmable transversal filter. A rotating tap weight structure [1] has been used to realize a 32-tap programmable transversal filter with features for the adaptive operation included on an NMOS silicon-gate chip. The adaptive filter has been characterized as a parameter estimator which finds application in echo cancellation and noise cancellation. A wide range of magnitude and phase characteristics of the unknown system (to be modeled by the adaptive filter) have been used to test the performance of the present adaptive system. Results on the residual error and the convergence time under different conditions are reported. Some practical limitations of the system are also presented.

Applications of adaptive digital filtering to the data processing for the environmental system

Abstract: In this paper a least mean-square (LMS) adaptive digital filter (ADF) is used in order to detect the extraordinary levels of air pollution data, to predict the future air pollution levels, and to identify the unknown parameters in the environmental system. The technique used here is based on the recursive adaptive digital filtering method proposed by White, which is an extension of the usual ADF by Widrow. For the O x data developed at Sooka, Koshigaya, Kasukabe, and Kawaguchi, Japan, the extraordinary levels of the O x data are detected by using the recursive ADF. For the SO 2 data at Komatsushima, Japan, the predicted values of the SO 2 levels are obtained by using the ADF as the predictor. Finally, a new identification method is proposed to find the unknown parameters of the AR, MA, and ARMA processes and is applied to identify the environmental system.

Least Squares, Adaptive-Lattice Algorithms.

Abstract: : Recently, it has been shown by Morf, Lee and others that least squares, adaptive algorithms may be implemented in a lattice form. This result is of considerable interest due to the rapid convergence characteristics of least squares algorithms as well as the important properties of lattice structures (such as high insensitivity to round-off noise). This report provides an explicit derivation of the joint real process, scalar least squares lattice algorithm. Also, a Fortran subroutine listing of the algorithm is presented. (Author)

A study of the Kalman filter as a state estimator of deterministic and stochastic systems

Abstract: It is shown that the optimality of the Kalman filter prevents its application to estimate the state of deterministic; systems but that if the gain is slightly modified a deterministic filter is possible. Such a filter is subsequently used to explain some of the difficulties encountered in Kalman filter computations, from which it transpires that much Kalman filtering is essentially an application of a deterministic filter to stochastic problems. To reduce the order of the algorithm the concept of observer robustness is incorporated into the subsequent development of the deterministic filter. Exactly equivalent discrete- and continuous-time algorithms are derived and used for a new treatment of the problem of obtaining estimates of the state variables of a stochastic system when the measurements are free of noise.

Stabilization of two-dimensional recursive filters

Abstract: In this paper we present a new stabilization procedure based on the spectral factorization capability of PLSI (planar least square inverse) polynomials of semicausal form. It is not involved with an intermediate PLSI polynomial since stabilization of an unstable filter is directly obtained from its autocorrelation function. We also introduce a measure of amplitude distortion due to stabilization. The new procedure offers a remedy for flaws in Shanks' original procedure for stabilization.

Identification of multivariable systems in the transfer-function matrix form

Abstract: A recursive algorithm is presented for estimating the parameters of linear discrete-time multivariable systems using the transfer-function matrix representation. The proposed algorithm decomposes the system into sub systems such that the parameters of each subsystem are estimated independently by a recursive least squares method. Also, a technique is pro posed for determining the order of the system offline when it is unknown. Results of simulation are presented comparing this algorithm with an earlier method.

Convergence properties of "A method for the indentification of linear systems using the generalized least squares principle"

Abstract: In the above paper a new identification method was proposed. Here some analysis is added. It is shown theoretically by examples that the method, which is iterative, sometimes gives convergence in a finite number of steps and that the model so obtained can be false.

On the Routh approximation technique and least squares errors

Abstract: A new method for calculating the coefficients of the numerator polynomial of the direct Routh approximation method (DRAM) using the least square error criterion is formulated The necessary conditions have been obtained in terms of algebraic equations The method is useful for low frequency as well as high frequency reduced-order models

An algorithm for least squares analysis of spectroscopic data

Abstract: This paper describes a variant of the Gauss-Newton-Hartley algorithm for nonlinear least squares, in which aQR implementation is used to solve the linear least squares problem. We follow Grey's idea of updating variables at intermediate stages of the orthogonalization. This technique, applied in partitions identified with known or suspected spectral lines, appears to be especially suited to the analysis of spectroscopic data. We suggest that this algorithm is an attractive candidate for the optimization role in Ekenberg's interactive computer graphics curve fitting program.