Estim, Filter&Detect EECS 564
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This 1 page Class Notes was uploaded by Ophelia Ritchie on Thursday October 29, 2015. The Class Notes belongs to EECS 564 at University of Michigan taught by Staff in Fall. Since its upload, it has received 37 views. For similar materials see /class/231538/eecs-564-university-of-michigan in Engineering Computer Science at University of Michigan.
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Date Created: 10/29/15
EEOS 564 ESTIMATORS Winter 1999 GOAL NEED WANT COST Estimate a from observation R of random variable 7quot Conditional pdf prlaRA and a priorz pdf paA for a If we knew a we would know pdf for random variable 7 min E ce where random variable e a arerror Different gtdifferent estimators 39 66 i 0 if e lt 6 compare to detection criterion 39 i 1 if e gt E amiss is as good as amile 1430 g mm AdA dR 1 26 ff pnaR mama minimized when pmR aR maximized for each R 7 ARGMAX A I ampMAPltR 1773a prapa Often use logprlaRA logpaA 0 As in detection MEP criterion gtMAP solution LSE LSE Ce e2 Least Squares Estimation criterion A i 7 7 f Apr aRApaAdA denominator SW EW R pr aRlA gtpaA gtdA isjustprR PROOF Stark and Woods page 298 che moment of inertia of a body is minimized around its center of mass parallel axis theorem of mechanics MLE What if we don t have a priorz paA non Bayesian Use Maximum Likelihood Estimator MLE zzMLEltRgt ARCl4 mama Often use ongMRlA 0 Maximizes likelihood of what actually happened rR i A Let a be a parameter paA 6A Aact am is unbiased if mam Aact H Ee 0 A AactdR dA faRpTaRAactdR aR unbiased gt Ear Aact2 03m MSEVariance
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