Download Estimation and Control with Quantized Measurements by Renwick E. Curry PDF

By Renwick E. Curry

The mathematical operation of quantization exists in lots of verbal exchange and regulate structures. The expanding call for on latest electronic amenities, reminiscent of conversation channels and knowledge garage, could be alleviated via representing the same quantity of data with fewer bits on the cost of extra subtle information processing. In Estimation and keep watch over with Quantized Measurements, Dr. Curry examines the 2 exact yet comparable difficulties of kingdom variable estimation and keep watch over whilst the measurements are quantized. attention is restricted to discrete-time difficulties, and emphasis is put on coarsely quantized measurements and linear, almost certainly time-varying structures. as well as reading the advance of the basic minimal variance or conditional suggest estimate, which lays the basis for different kinds of estimates, the writer additionally seems at easier-to-implement approximate nonlinear filters at the side of 3 communique structures, and so the ebook isn't constrained to idea by myself. subsequent, the functionality of optimal linear estimators is in comparison with the nonlinear filters. besides a brand new interpretation of the matter of producing estimates from quantized measurements. either optimum and suboptimal stochastic regulate with quantized measurements are taken care of for the 1st time in print through Dr. Curry. MIT study Monograph No. 60

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18) Thus, used, the quanlizer output computcd as though the quanlizcr output camc from two sourccs: a signal sourcc, which is [G(2k - G)) 1/2 timcs the quantizer input, and an additive, uncorrclatcd noi se sourcc 11,;. 3 47 A New Interpretation of the Describing Function The dilriculty in analysis and synthesis arises when the output autocorrelation function needs to be evaluated. Many times a quantizer is modeled as a unit gain (G I) and a white noise source (Widro\v, 1960; Ruchkin, 1961; Steiglitz.

72) The cond i t i o n a l mean of t he me�ls u rc­ rat i o of q u a n t u m i n t erval to sta n d a rd devia t i o n i s Ti l E CO:-; ( )ITlO:-;AJ. M EA N O F = . ment based on measu re­ of est imate o f Xk based o n mea su re­ ments at th • t k + = t". 28 NONL INEA R ESTlIII A TION IVITII Q UA NTIZED M EA S UREM EN TS given by Equation A. l 4 i n Appendix A. 73) Akr;;� kl'k o where l'1< is the geometric center o f the q u a n t u m region A • . I f the n o rm of rJ: � k

Be the region in which they )'11-\ = = fall. n +a J1,. _ . 13 ) p(L� -�) = .. ,IJ,,-. 14) This expression docs not require that {=,,] be derived from a 1\1arkov process. 13 call be solved by power-series approximations. 15 ) of midpoints of the quantum this equat i on is equivalent to where }'rI-1 is the collection A"_I' A,,-2 . . 16 ) which means that to the second-order approximation the optimal L" is the mode of the density function of : conditioned on unquantized measurements )',,_ [. If the : arc Gaussian random variables, then the conditional mode is t he conditional mean, and L� is a linear operation.

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