Recursive Estimation and Time-Series Analysis: An by Peter C. Young

By Peter C. Young

This can be a revised model of the 1984 e-book of an identical identify yet significantly transformed and enlarged to deal with the entire advancements in recursive estimation and time sequence research that experience happened over the past area century. additionally over this time, the CAPTAIN Toolbox for recursive estimation and time sequence research has been built by way of my colleagues and that i at Lancaster, to be used within the MatlabTM software program setting (see Appendix G). as a result, the current model of the booklet is ready to make the most the various computational exercises which are contained during this extensively to be had Toolbox, in addition to a number of the different exercises in Matlab and its different toolboxes.

The ebook is an introductory one concerning recursive estimation and itdemonstrates how this method of estimation, in its a variety of varieties, should be a magnificent reduction to the modelling of stochastic, dynamic structures. it truly is meant for undergraduate or Masters scholars who desire to receive a grounding during this topic; or for practitioners in who could have heard of issues handled during this e-book and, whereas they need to understand extra approximately them, can have been deterred via the quite esoteric nature of a few books during this tough quarter of research.

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Young, 1965a) multiple col linearity can also be interpreted as a tendency towards the development of valley-like phenomena in the hypersurface associated with the cost function J 2 in the parameter-cost function hyperspace. Thus there is no clearly defined minimum in the surface and the estimates wander along the elongated, valley-like bottom in some partial relationship with each other: this leads to low residual errors but some ambiguity about the parameter values, as indicated by the high estimation error variance.

111(4) is not, however, a particularly satisfactory estimate of 0 2 if e k is replaced by ~k,as we see later in Chapter 5 (page 64). The algorithm 111(1) to (3) is a very powerful and elegant one: it not only supplies the parameter estimates at each sampling instant but also an indication of the accuracy of these estimates through the error-covariance matrix P*k. It is not difficult to see that P*k behaves like Pk except for the scale factor 0A2 and is a strictly decreasing function of the sample size.

That the RLS algorithm can be considered as a naturally occurring SA algorithm with optimum properties. There is. perhaps. 3) no estimates of the second statistical moment (or variance) of the estimation errors are generated. And more generally. in multi-parameter algorithms such as the recursive least squares (RLS) procedures (II). no estimates of second moment or covariance matrix of the estimation errors are obtained. 39 optimization problem in which a non-recursive analytic solution already exists, we may do better to look for a recursive version of this solution, in which the stochastic approximation properties are implicit, rather than concocting an SA algorithm and then attempting to make it optimal in some manner.

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