# 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.

© BrainMass Inc. brainmass.com December 15, 2020, 9:54 pm ad1c9bdddfhttps://brainmass.com/statistics/ordinary-least-squares/observed-random-process-518518

#### Solution Preview

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.