lecture16

lecture16 - 16.322 Stochastic Estimation and Control, Fall...

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16.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Page 1 of 5 Lecture 16 Last time: Wide band input Notice that 0 () () ( ) xy RS w xtyt τ = =+ so if t is the current time in a real time situation, we cannot compute xy R for 0 > which is necessary since x w is nonzero only for 0 > . But we showed earlier that ) xy yx RR ytxt = =− This can be computed in real time by averaging the product of the current output, yt , and the delayed input, xt , for 0 > . The Shaping Filter A shaping filter is a filter that produces an output process with a white noise input, which has a specified spectrum. If a given system is driven by a colored noise, we can precede it with the appropriate shaping filter and always treat the augmented system as driven by white noise. We usually work with rational spectra – so consider xx S ω to be a rational function. That is, it is a ratio of polynomials in . Since xx S is always an even function , it is a ratio of polynomials having only even powers of . 24 01 2 2 ... ... xx aa a S bb b ωω +++ = We wish to characterize the filter in terms of the Laplace variable s . The relation between s and is sj = .
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16.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Page 2 of 5 Rewrite xx S in terms of s . Since only even powers of ω appear there will be no imaginary terms.
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This note was uploaded on 11/07/2011 for the course AERO 16.322 taught by Professor Wallacevandervelde during the Fall '04 term at MIT.

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lecture16 - 16.322 Stochastic Estimation and Control, Fall...

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