Adaptive Filters

CHAPTER 6 Constrained Estimation

In Sec. 5.1 we studied the problem of estimating a random variable x from a noisy observation y that is related to x via the linear model

(6.1)

where H is a known data matrix and v is some disturbance, with x and v satisfying

(6.2)

The linear least-mean-squares estimator of x given y was found to be given by either expression

(6.3)

with the right-most expression valid whenever R _x > 0 and R_v > 0.

In Sec. 5.5, we applied these results to a simple, yet revealing example. Given N measurements {y(0), y/(1), …, y(N – 1)} of a random variable x with variance ,

i.e., given

(6.4)

we estimated x from the {y(i)} and found that

(6.5)

where . In (6.4), the variable ...