Some Study Projects on Applied Signal Processing Remarks About Related Contributions of Scientists
Harish Parthasarathy · 2022
[1] Linear models: Time series models like AR, MA, ARMA, casting these models in the form https://www.w3.org/1998/Math/MathML"> X ( n ) = H ( n ) θ + V ( n ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003353447/33d45e82-2e44-4e42-8180-04a739205e5f/content/math3_133_1_B.tif" xmlns:xlink=" https://www.w3.org/1999/xlink "/> where X ( n ), H ( n ) are data vectors and data matrices. V ( n ) is noise. H ( n ) ∈ ℝ n × p , X ( n ), V ( n ) ∈ ℝ n . If R υ = Coυ ( V ( n )) and V ( n ) are iid zero mean Gaussian, then the MLE of θ based on data collected upto time n is given by https://www.w3.org/1998/Math/MathML"> θ ^ ( n ) = ( ∑ k = 1 n H ( k ) T R υ H ( k ) ) − 1 ( ∑ k = 1 n H ( n ) T R υ X ( k ) ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003353447/33d45e82-2e44-4e42-8180-04a739205e5f/content/math3_133_2_B.tif" xmlns:xlink=" https://www.w3.org/1999/xlink "/>