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# Programming Assignments

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Introduction   ::   System Model   ::   Expectation   ::   Part 1   ::   Filters   ::   Part 2   ::   Submission

## Estimating the expectations

The algorithm described above requires calculation of the autocorrelation matrices and the cross-correlation vectors. In practice, these are frequently estimated from sample averages. (In other words, we invoke an ergodic assumption.)

To illustrate this idea, suppose that we have a vector random process , and that we have vectors of measured sample data which we stack into columns as

Then the autocorrelation matrix may be estimated as

 (12)

Let be a random process, with measured sample values . The cross correlation vector between a random process and , can be estimated as

Exercise 5
Let

show that the estimated autocorrelation matrix in ( 12 ) can be written as

Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 13). Programming Assignments. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Stochastic_Processes/sysid_3.htm. This work is licensed under a Creative Commons License