问题数据协方差矩阵估计rxx 09a.pdfVIP

Data:

{3.0,2.0,−0.5,1.5,−1.0}

Covariancematrixestimate:

xx=1{[2.0][2.03.0]+[−0.5][−0.52.0]+[1.5][1.5−0.5]+[−1.0][−1.01.5]}

43.02.0−0.51.5

=[1.87500.6875]

0.68753.8750

Frequency-quarterofsamplingfrequency

f

ω∆t=2π

fs

1

=2π

4

π

=

2

Fouriertransformvector:

1{[2.0]ȷ[−0.5]ȷ[1.5]ȷ[−1.0]ȷ}

=e+e+e+e

43.02.0−0.51.5

=[−0.5+0.5ȷ]

−0.5+3.8ȷ

matrix

=xx−H

=[1.87500.6875]−[−0.5+0.5ȷ][−0.5−0.5ȷ−0.5−3.8ȷ]

0.68753.8750−0.5+3.8ȷ

=[1.3750−1.3125−1.5000ȷ]

−1.3125+1.5000ȷ−8.6250

Inverse

−=[0.5448−0.0829−0.0947ȷ]

−0.0829+0.0947ȷ−0.0868

Steeringvector

=[1]

e−ȷ

Optimumweights

−=[0.5448−0.0829−0.0947ȷ][1]

−0.0829+0.09