这是一份ucl伦敦大学学院 PHAS0049作业代写的成功案
The state-dependent system mode set at time $k+1$ with respect to (w.r.t.) the previous hybrid state $\xi(k) \triangleq(x(k), m(k))$ is defined formally as
$$
S_{\xi}(k+1)={m(k+1): P{m(k+1) \mid \xi(k)}=\phi[k, \xi(k), m(k+1)]>0}
$$
where $P{m(k+1) \mid \xi(k)}$ was defined by $(3)$. The mode-dependent system mode set w.r.t. mode $m(k)$ is defined as
PHAS0049 COURSE NOTES ：
$$
\frac{\partial \ln L}{\partial \mathbf{R}}=-\frac{N}{2} \cdot \mathbf{R}^{-T}+\frac{1}{2} \cdot\left(\mathbf{R}^{-1} \mathbf{E}^{T} \mathbf{E R}^{-1}\right)^{T}
$$
To locate the zeros of this derivative, multiply the R.HS of Eq. (5), from right and left, by $\mathbf{R}^{T}$, and equate to zero; the maximum likelihood estimate of $\mathbf{R}$ is,
$$
\hat{\mathbf{R}}=\frac{1}{N} \cdot \mathbf{E}^{T} \mathbf{E}
$$