Using the nonlinear programming (steepest decent) method, we want to estimate the parameters of an ARMAX model whose polynoomials are given in the following. A(q) = 1+qq¹ + a₂q² + a₂q B(q¹)=b₁q¹ C(q¹)=1+cq¹+c₂q² u(t) Assume that we have some parametric observations as B (q¹) U=[u (1),u (2),u (3),u (4),u (5),u (6),u (7),u (8) Y = [y (1),y (2), y (3), y (4), y (5), y (6), y (7), y (8) C (q-¹) A(q-¹) v(1) y (t) Considering whole steps of the mentioed method such as initial selection and updating of the parameters" value (one updating step is required in addition to the initialization step), write all the necessary relations and parameters in respect to the obserations in a parametric and simplified form as possible.

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Using the nonlinear programming (steepest decent) method, we want to estimate the parameters of an
ARMAX model whose polynoomials are given in the following.
A(q¹)=1+qq¹ + a₂q² + a²q³
B(q¹)=b₁q¹
C(q¹)=1+c₁q¹ +c₂q²
u(t)
Assume that we have some parametric observations as
B (q¹)
U = [u (1),u (2),u (3),u (4),u (5),u (6),u (7),u (8)]
Y = [y (1),y (2),y (3),y (4), y (5), y (6), y (7), y (8)
C(q-¹)
1
A(q¹)
V(1)
Considering whole steps of the mentioed method such as initial selection and updating of the parameters"
value (one updating step is required in addition to the initialization step), write all the necessary relations and
parameters in respect to the obserations in a parametric and simplified form as possible.
Transcribed Image Text:Using the nonlinear programming (steepest decent) method, we want to estimate the parameters of an ARMAX model whose polynoomials are given in the following. A(q¹)=1+qq¹ + a₂q² + a²q³ B(q¹)=b₁q¹ C(q¹)=1+c₁q¹ +c₂q² u(t) Assume that we have some parametric observations as B (q¹) U = [u (1),u (2),u (3),u (4),u (5),u (6),u (7),u (8)] Y = [y (1),y (2),y (3),y (4), y (5), y (6), y (7), y (8) C(q-¹) 1 A(q¹) V(1) Considering whole steps of the mentioed method such as initial selection and updating of the parameters" value (one updating step is required in addition to the initialization step), write all the necessary relations and parameters in respect to the obserations in a parametric and simplified form as possible.
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