随机过程IStochastic Processes MATH2012W1-01

这是一份southampton南安普敦大学MATH2012W1-01作业代写的成功案例

随机过程IStochastic Processes MATH2012W1-01
问题 1.

with measurement equation
$$
z(k)=\left[\begin{array}{ll}
1 & 0
\end{array}\right] x^{i}(k)+w(k)
$$
The models differ in the control gain parameter $b^{i}$. The process and measurement noises are mutually uncorrelated with zero mean and variances given by
$$
E[v(k) v(j)]=0.16 \delta_{k j}
$$
and
$$
E[w(k) w(j)]=\delta_{k j}
$$

证明 .

The control gain parameters were chosen to be $b^{1}=2$ and $b^{2}=0.5$.
The Markov transition matrix was selected to be
$$
\left[\begin{array}{ll}
0.8 & 0.2 \
0.1 & 0.9
\end{array}\right]
$$
For this example $N=7$, and the cost parameters $R(k)$ and $Q(k)$, were selected as
$$
R(k)=5.0 \quad k=1,2, \ldots, N-1
$$

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MATH2012W1-01 COURSE NOTES :

Proof: Since $f(d)$ is the minimal polynomial of $\boldsymbol{F}, p(d)$ can be factored as
$$
p(d)=g(d) . f(d)
$$
for some polynomial $g(d)=\sum_{i=0}^{s} b_{i} d^{s-i}$
Let $z_{k}$ and $\bar{z}{k}$ be linear combinations of $y{k}$ defined as in by using polynomials $f(d)$ and $p(d)$, respectively.
$\bar{z}{k} \quad$ can be expressed in terms of $z{k}$ as
$$
\bar{z}{k}=\sum{i=0}^{s} b_{i} z_{k-i}
$$










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