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UBC Theses and Dissertations

A parameter-estimation algorithm for small digital computers. Tapp, Robert James


An algorithm is developed for performing parameter estimation on a small-size digital computer. First principles of matrix algebra are used to derive a sequential estimator which computes an estimate of a general parameter array A from an array of measurements Z = HA+V where V is a matrix of zero-mean noise terms. At every stage a new row is adjoined to each of Z, H. and V and a new estimate of A is calculated recursively, with any one of three well-known filtering processes available from the same basic set of recursive equations: a least-squares filter to minimize [ Formula omitted ], a maximum-likelihood filter to maximize [ Formula omitted ] or a maximum- a-posteriori filter to maximize [ Formula omitted ]. Provision is made for starting the filter either with a-priori means and variances of the parameters or with a deterministic "minimum-norm" composition based on the first s measurement rows, s being the number of rows in the parameter array. The algorithm is applied to the problem of identifying the parameters of a discrete model for a linear time-invariant control system directly from sequential observations of the inputs and outputs. Results from computer tests are used to demonstrate properties of the algorithm and the important computer programs are included, along with suggestions for further applications.

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