G.C. Goodwin and K.S. Sin. Adaptive Filtering, Prediction and Control. Prentice-Hall, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... is T T FG G O = U FG J q U BG q (6) 8 S # G # T KG J G T U BG G 7 U BG and = q c v T G T and we have KG J G O = U FG q U BG q and therefore [GS84] q q KG q G O = FG FG q U BG q O q U KG q q U BG q KG q G O = 7 Hs U BG J q O q U BG J q q U BG q KG q O G = 7 ....

Graham C. Goodwin and Kwai Sang Sin. Adaptive Filtering, Prediction and Control. Prentice Hall, Englewood Cliffs, New Jersey 07632, 1984.

.... 51570 M 51570 c 510 c 150 (6) 0 a 910 550 b 00 46640 c 30 466 c 436 ; 0 n Define 740 bU 399 and we have 690 20 354 M 35470 c 630 c 270 and therefore [14] 6 9 610 V M 310 430 c 710 (7) Two conclusions can be drawn from inequality (7) i) 0 is a non increasing sequence, hence b is bounded. Moreover, ii) y=z p y= y= S; a T Q y SUT o . It then ....

G. C. Goodwin and K. S. Sin. Adaptive Filtering, Prediction and Control. Prentice Hall, Englewood Cliffs, New Jersey 07632, 1984. 12

....estimate and predict T c values. A linear model is maintained for the time to contact in each of the three windows: 13) where t = 0, 1, 2, For each measurement of time to contact, model parameters and are updated by a weighted recursive least squares computation with exponential decay [5][9][13] 19] This involves determining and such that the residual is minimized: 14) where ; is the present; is the forgetting factor; and is the confidence of the measurement (the number of flow data points in the window) In order to solve for a , a , the square root information filter ....

G. Goodwin and K. Sin. Adaptive Filtering, Prediction and Control. Prentice-Hall. Englewood Cliffs, New Jersey, 1984.

....can be written as: 3.8) where and are given by: By following the methods in [15] the new form is: 3.9) The vectors and are known every instant of time, while the scalar is continuously estimated. The details of the estimation equations are presented in [12] Further analysis is given in [7] and [15] Manipulator control for grasping Manipulator motions are effected by a control law similar to that in the previous sections: We use this control law during both the object centering and gripper alignment phase, and the object approach and grasping phase. We can also extend the use of ....

G. Goodwin and K. Sin, Adaptive filtering, prediction and control, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1984.

....parameters. Such techniques will be called, following the current literature, recursive parameter estimations. Classical methods belonging to this class are least square estimation and its variants. A comprehensive discussion of this approach is out of the scope of this paper and can be found in [16, 9]. The basic idea is the following. At every step, the current measurements for the inputs and the outputs are used to update the = y(k 1) y(k m)u(k d 1) u(k d m) T vector; then the following equation is applied: K(k) P (k) k) k) k 1) K(k) y(k) T (k) k ....

G. C. Goodwin and K. S. Sin. Adaptive Filtering, Prediction and Control. Prentice Hall, Englewood Clis, N.J, 1984.

....Varianten treten bei der Modellierung von IIR Filtern auf. 1 1 Introduction This paper provides a time domain feedback analysis of the class of Gauss Newton recursive schemes, which have been employed in several areas of identification, control, signal processing, and communications (e.g. [6, 14, 16, 17, 19, 31]) These are recursive methods that are based on gradient descent ideas and employ sample covariance matrices to control the update directions. Their descriptions involve two update relations: one for the update of the weight estimate and the other for the update of the inverse of the sample ....

G. C. Goodwin and K. S. Sin, Adaptive Filtering, Prediction and Control, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1984.

....error, can be associated with such recursive schemes. I. INTRODUCTION This paper provides a time domain feedback analysis of the class of Gauss Newton (GN) recursive schemes, which have been employed in several areas of identification, control, signal processing, and communications (e.g. 1] [4]) These are recursive estimators that are based on gradientdescent ideas and which involve two update relations: one updates the weight estimate while the other updates the inverse of the sample covariance matrix. Several free parameters are also included in the filter description, which allows ....

G. C. Goodwin and K. S. Sin, Adaptive Filtering, Prediction and Control, Prentice-Hall, Englewood Cliffs, NJ, 1984.

....the standard LMS algorithm is applied on one data pair (input vector and desired) for an infinite number of times, the same solution as for an LS estimator on the same data pair is obtained. This property has been shown by Nitzberg [6] and from a different point of view already by Goodwin and Sin [7]. An open question, however, is what solution is obtained when the updates are performed over a set of data pairs and then repeated anumber of times, i.e. the operation of the UNDR LS algorithm. For normalized regression vectors, the Kaczmarz s row projection method (see [3] and references ....

....is best for achieving the LS solution. So far, only a constant step size has been used, 0 (l) 20) In gradient type approximation theory it is wellknown that a decreasing step size of the form 1 (l) c 1 l # l =1# 2: 21) can achieve the Wiener solution without errors (see for example [7]) Another decreasing sequence of great practical importance is given by 2 (l) c 2 2 (l ; 1) 22) since a simple multiplication can derive the following step size value. Yet, another interesting choice is 3 (l) c 2 3 (l ; 1) c 3 : 23) For all sequences it can be shown that given the ....

G.C. Goodwin, K.S. Sin, Adaptive Filtering, Prediction and Control, Prentice--Hall, 1984.

....to exploit the averaging properties of the disturbance. This allows it to provide better performance in terms of disturbance rejection. The mathematical foundation of this field was laid by Goodwin, Ramadge and Caines [2] and Solo [3] and the various ramifications were explored in Goodwin and Sin [4]. Also, for identification, Lai and Wei [5, 6] and Chen and Guo [7] have determined sharp estimates of the rate of convergence of several parameter estimation algorithms. The research reported here has been supported in part by the U.S.A.R.O. under Contract No. DAAL 0391 G 0182, and by the ....

.... (t Gamma 1) r(t Gamma s) 2 1 A O 0 n X t=1 kOE(t Gamma s)k 2 r(t Gamma s)r(t Gamma s Gamma 1) 2 v 2 (t) 1 A (from (33) o 0 N X t=1 OE T (t Gamma s) e (t) r(t Gamma s Gamma 1) 2 1 A O(1) From (23) and the SPR assumption (27) we have (see [3, 4]) S(N) N X t=1 [ GammaOE T (t Gamma s) e (t) b v(t) Gamma v(t) Gamma ffl( b v(t) Gamma v(t) 2 ] S(0) 0 ; 36) for some constant ffl 0, and random variable S(0) 1 a.s. Summing by parts, we have N X t=1 S(t) Gamma S(t Gamma 1) r(t Gamma s Gamma 1) S(N) r(N ....

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G. C. Goodwin and K. S. Sin. Adaptive Filtering, Prediction and Control. Prentice-Hall, Englewood Cliffs, NJ, 1984.

....here we choose the RLS algorithm for the on line bandwidth prediction of video traffic. Since each bandwidth adaptation requires computation of the predictions fx L (n D) xL (n D 1) x L (n D M )g, the so called indirect prediction approach is used to avoid redundant computation [9]. That is, instead of directly constructing (M 1) RLS prediction filters, we construct a single RLS filter to perform parameter estimation of a given autoregressive (AR) model of the time series. The (M 1) predictions are then obtained by converting the model into the required predictor ....

G.C. Goodwin and K.S. Sin, Adaptive Filtering, Prediction and Control, Prentice-Hall, Englewood Cliffs, N.J., 1984.

....here we choose the RLS algorithm for the on line bandwidth prediction of video traffic. Since each bandwidth adaptation requires computation of the predictions fxL(n D 0) xL(n D 1) xL(n D M)g, the so called indirect prediction approach is used to avoid redundant computation [9]. That is, instead of directly constructing (M 1) RLS prediction filters, we construct a single RLS filter to perform parameter estimation of a given autoregressive (AR) model of the time series. The (M 1) predictions are then obtained by converting the model into the required predictor ....

G.C. Goodwin and K.S. Sin, Adaptive Filtering, Prediction and Control, Prentice-Hall, Englewood Cliffs, N.J., 1984.

....adaptive control of discretetime nonlinear systems remains a largely unsolved problem. The few existing results [2]can only guarantee global stability under restrictive growth conditions on the nonlinearities, because they use techniques from the literature on adaptive control of linear systems [3].The only available result which guarantees global stability without imposing any such growth restrictions is found in [4] but it only deals with a scalar nonlinear system which contains a single unknown parameter. The backstepping methodology [1] which provided a crucial ingredient for the ....

G. C. Goodwin and K. S. Sin, Adaptive Filtering, Prediction and Control, Prentice-Hall, Englewood Cliffs, 1984.

....nonlinear systems remains a largely unsolved problem. The few existing results [3, 4, 5, 6] can only guarantee global stability under restrictive growth conditions on the nonlinearities, because they use techniques from the literature on adaptive control of linear discrete time systems [7, 8]. The only available result which guarantees global stability without imposing any such growth restrictions is found in [9] but it only deals with a scalar nonlinear system which contains a single unknown parameter. The backstepping methodology [1] which provided a crucial ingredient for the ....

G. C. Goodwin and K. S. Sin, Adaptive Filtering, Prediction and Control, Prentice-Hall, Englewood Cliffs, 1984.

....can be detected and used to predict the future over time scales relevant to congestion control. Time series analysis and prediction theory has a long history with techniques spanning a number of domains from estimation theory to regression theory to neural network based techniques to mention a few [3, 17, 22, 40]. In many senses, it is an art form with different methods giving variable performance depending on the context and modeling assumptions. Our goal is not to perform optimal time series prediction but rather to choose a simple, easy to implement scheme and use it as a reference for studying ....

G. C. Goodwin and K. S. Sin. Adaptive Filtering, Prediction and Control. Prentice Hall, 1984.

....condition on the inverse to exist. Definition 1: The input is said to be persistently exciting (PE) of order k at time n if T k (a n ) has full (column) rank. That is, to determine the channel, the input must be PE of order q. This definition is quite common in adaptive control, see e.g. [3], although a similar asymptotic condition is more common in system identification. However, the main purpose of this paper is to identify the input, and generally it is easier to estimate the input to a linear, time invariant system than to identify the coefficients in the system. Definition 2: ....

G.C. Goodwin and K.S. Sin. Adaptive filtering, prediction and control. Prentice-Hall, Englewood Cliffs, N.J., 1984. 10

....w : f(x) g(x)u Gamma Phi(x; u) is bounded and square integrable. Under these conditions, we want to design an identifier that insures lim t 1 e = 0, where e : x Gamma x, with all signals remaining bounded. From any standard textbook on systems identification or adaptive control, e.g. [12], we can see that the estimator x = Gammaa(x Gamma x) Phi ; a 0 with the parameter update = Gamma Phie solves the problem. There are several ways to prove this well known fact. The simplest one uses the Lyapunov function jej 2 j Gamma j 2 , and some signal chasing. ....

Goodwin, G. and K. Sin, Adaptive filtering, prediction and control, Prentice-Hall, NJ, 1984.

....0 denotes the transpose of a vector. Note that if we introduce a shift operator q 01 z(t) 4 = z(t 0 1) then equation (3) can be written equivalently as follows AE = 2 1 q 01 : q 0 1 3 0 x(t) 5) Equation (5) is sometimes referred to as the regression vector in the literature [21]. Equation (4) can also be expressed in a regression vector form quite easily. It is noted that the performance of the TDNN as a signal model for time varying signals is dependent on the parameters and , as well as the weights. The parameters and express the dependence of the output signal on ....

G.C. Goodwin and K.S. Sin. Adaptive Filtering, Prediction and Control. Prentice-Hall, Englewood Cliffs, NJ, 1984.

....2 ) In chapter 3, we investigate both regressors and provide robust ways of adapting their parameters. Also in the same chapter, the steps of the adaptation algorithms for both regressors are tabulated. In chapter 4, the well known extended Kalman filter algorithm is tailored to our application [11 13]. It is shown that since the resultant algorithm requires no matrix inversions, system parameters can be estimated by computing O(N 2 ) multiplications. Also, a robust way of updating the required covariance matrices is provided. CHAPTER 1. INTRODUCTION 3 In chapter 5, we provide extensive ....

.... beneficial features of the OE and EE formalism in one algorithm [1 4, 6, 7, 19] Notably, the bias remedy least mean square equation error (BRLE) 2] and the composite regressor algorithms (CRA) 3] are proposed to obtain low biased parameter estimates by using gradient descent type adaptation [11, 16 18]. However, since the corresponding cost functions of these algorithms are not designed to be quadratic with respect to the parameters, recursive least squares techniques cannot be utilized to obtain fast converging estimates to the parameters. In the first part of our work, we also try to combine ....

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G. Goodwin and K. Sin. Adaptive Filtering, Prediction and Control. Prentice Hall, Englewood Cliffs, NJ, 1984. BIBLIOGRAPHY 34

....and noise variables can be stochastic, the exact value of k cannot be determined. What we require, instead, is that k , the predictor of k , be optimal in some sense. 2 Classical approach The standard solution to this problem is to use a Kalman predictor or one of its many variants [1] [3]. This is optimal in the sense that the expected squared error in k is zero. However, the system perturbation and observation noise variables must be from a zero mean, gaussian, white noise distribution and the observer must supply the variances of the system perturbation and the observation ....

G.C. Goodwin, K.S. Sin, Adaptive Filtering, Prediction and Control, Prentice Hall, 1984

....1 and 2 above. See, among many references, e.g. 19] 21] 5] and [13] These schemes, seemingly, do not address step 3 explicitly. Iterative control design is closely related to adaptive control, which in a sense is the limit as the experiment time decreases down to one sample. See, e.g. 2] [6] and [10] for basic treatments of adaptive control. Step 3 above concerns model validation. This is a classical topic in statistics, but has also been the subject of intense, renewed interest in the control community again due to its importance for identification for control. In particular, ....

G.C. Goodwin and K.S. Sin. Adaptive Filtering, Prediction and Control. Prentice-Hall, Englewood Cliffs, N.J., 1984.

....excess mean squared error step size u u opt total excess MSE lag error term gradient noise term Fig. 3: misadjustment of the LMS algorithm in a non stationary environment in dependency of the step size parameter . which adjusts the step size by an estimate x T k x k of the input signal power [7, 1, 15]. For ANC applications, the filtered X LMS can also be normalised to improve convergence speed [3, 13] 3.5. Convergence and Tracking Behaviour The tracking behaviour of the LMS can be viewed in terms of the mean square deviation of the filter coefficients from the optimum and the excess means ....

Goodwin, G. C. and Sin, K. S.: Adaptive Filtering, Prediction and Control. Prentice Hall, Englewood Cliffs,N.J., 1984.

....like [5] for its treatment of linear filters, Wiener filters, Lattice Filters, and of course Kalman filters. Horn s book [6] has a nice short section on optimal image restoration that is related to the math that comes up in Wiener filtering. Another classic you should know about is Goodwin and Sin [4]. When do you want to use a (predictive or smoothing or filtering) filter Whenever your problem fits nicely into a state estimation formalism: you need a plant model, a gaussian noise model, and you are estimating some plant parameters or state varibles from noisy data. KFs or their kin should ....

G. C. Goodwin and K. S. Sin. Adaptive Filtering, Prediction and Control. PrenticeHall, 1984.

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G.C. Goodwin and K.S. Sin. Adaptive Filtering, Prediction and Control. Prentice-Hall, 1984.

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Goodwin G.C., Sin K.S., Adaptive Filtering, Prediction and Control, Prentice-Hall, Englewood Cliffs, 1984. 33

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G.C. Goodwin and K.S. Sin, Adaptive filtering, prediction and control, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1984.

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G. C. Goodwin and K. W. Sin. Adaptive Filtering, Prediction and Control. Prentice-Hall, Englewood Cli#s, New

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G. C. Goodwin and K. S. Sin. Adaptive Filtering, Prediction and Control. Prentice-Hall,, Englewood Cliffs, NJ, 1984.

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GOODWIN, G.C. and SIN, K.S. 'Adaptive Filtering, Prediction and Control' (Prentice Hall, Englewood Cliffs, 1984). 31

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G.C. Goodwin, K. Sin, Adaptive Filtering, Prediction and Control, Prentice-Hall, Englewood Cli#s, NJ, 1984.

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Goodwin, G.C., and Sin, K.S., Adaptive Filtering, Prediction and Control, Prentice Hall, Englewood Cliffs, NJ, 1984, Chapter 6.

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G. C. Goodwin and K. S. Sin, Adaptive Filtering, Prediction and Control, Prentice-Hall, Englewood Cliffs, 1984.

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G. C. Goodwin and K. S. Sin, Adaptive Filtering, Prediction and Control. Prentice-Hall, Englewood Cliffs, NJ, 1984.

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