# Observed Random Process

Let {x_n} be an observed random process which is generated by the following nonlinear recursion

x_n = (theta_1)(x_n-1) + (theta_2g)(x_n-2, x_n-3) + w_n

where {w_n} is an i.i.d. zero-mean sequence and g(.,.) is a known deterministic function. We are interested in estimating the two parameters theta_1, theta_2. (a) Propose a fixed sample size and an adaptive estimator for the parameter vector [theta_1, theta_2] that does not require knowledge of the statistics of {w_n}. (b) Analyze the convergence properties of your adaptive estimator.

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The explanations are in the attached file.

Notations:

RLSE = Recursive least Squares Estimator

Patras Notes = http://www.ssp.ece.upatras.gr/courses/detest/noexternalweb/chapter4.pdf

IAState Notes = ...

#### Solution Summary

This solution discusses an observed random process.