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Finally, set $$y = [y1, y2]$$. (a) Show (by reducing this to a problem that we already know how to solve - don't start from scratch!) (Hint: One approach to solving this is to use our recursive least squares formulation, but modified for the limiting case where one of the measurement sets - namely $$z = Dx$$ in this case - is known to have no error. While recursive least squares update the estimate of a static parameter, Kalman filter is able to update and estimate of an evolving state. Even though your estimation algorithms will assume that $$a$$ and $$b$$ are constant, we are interested in seeing how they track parameter changes as well. It does this by solving for the radial} \\ version 1.4.0.0 (4.88 KB) by Ryan Fuller. Aliases. Legal. Use $$f = .96$$, (iii) The algorithm in (ii), but with $$Q_{k}$$ of Problem 3 replaced by $$q_{k} = (1/n) \times trace(Q_{k})$$, where $$n$$ is the number of parameters, so $$n = 2$$ in this case. 1 m i=1 y i~a i I recursive estimation: ~a i and y i become available sequentially, i.e., m increases with time 23 Downloads. that the value $$\widehat{x}_{k}$$ of $$x$$ that minimizes the criterion, \[\sum_{i=1}^{k} f^{k-i} e_{i}^{2}, \quad \text { some fixed } f, \quad 0