7.8 Let U(t) be a stationary process, t 2 with a covariance function ????(h) and an unknown mean ????. Consider n = 3 sites

7.8 Let U(t) be a stationary process, t ∈ ℝ2 with a covariance function ????(h) and an unknown mean ????. Consider n = 3 sites lying on an equilateral triangle with coordinates

⎡

⎢

⎢

⎣

t T

1 t

T 2

t T

3

⎤

⎥

⎥

⎦

=

⎡

⎢

⎢

⎢

⎣

−

√

3 2 −1 2

0 1

√

3 2 −1 2

⎤

⎥

⎥

⎥

⎦

.

The triangle is centered at the origin, and the three sides have length √

3.

Suppose noise-free measurements x = [x1 x2 x3]

T of the process are available at these three sites (i.e. no nugget effect).

The covariance vector of the process between the data sites and a new site t0, and the covariance matrix for the three data sites can be written as?