更改

where [math]\displaystyle{ p_{Z\mid X}(\cdot\mid x;\theta ) }[/math] is the conditional distribution of the unobserved data given the observed data [math]\displaystyle{ x }[/math] and [math]\displaystyle{ D_{KL} }[/math] is the Kullback–Leibler divergence.

where [math]\displaystyle{ p_{Z\mid X}(\cdot\mid x;\theta ) }[/math] is the conditional distribution of the unobserved data given the observed data [math]\displaystyle{ x }[/math] and [math]\displaystyle{ D_{KL} }[/math] is the Kullback–Leibler divergence.

 

<nowiki>其中 {\displaystyle p_{Z\mid X}(\cdot \mid x;\theta )}{\displaystyle p_{Z\mid X}(\cdot \mid x;\theta )} 是在给定观察数据{\displaystyle x}x前提下未观察到数据的条件分布， {\displaystyle D_{KL}}{\displaystyle D_{KL}} 是 Kullback–Leibler 散度。</nowiki>Then the steps in the EM algorithm may be viewed as:

Then the steps in the EM algorithm may be viewed as:

那么EM算法的步骤可以看成：

那么EM算法的步骤可以看成：

Operate a Kalman filter or a minimum-variance smoother designed with current parameter estimates to obtain updated state estimates.

Operate a Kalman filter or a minimum-variance smoother designed with current parameter estimates to obtain updated state estimates.

操作一个 Kalman 滤波器或一个最小方差平滑设计与当前的参数估计，以获得更新的状态估计。

操作一个 Kalman 滤波器或一个最小方差平滑设计与当前的参数估计，以获得更新的状态估计。

Use the filtered or smoothed state estimates within maximum-likelihood calculations to obtain updated parameter estimates.

Use the filtered or smoothed state estimates within maximum-likelihood calculations to obtain updated parameter estimates.

使用最大似然计算中的滤波或平滑状态估计来获得更新的参数估计。

使用最大似然计算中的滤波或平滑状态估计来获得更新的参数估计。

where [math]\displaystyle{ \widehat{x}_k }[/math] are scalar output estimates calculated by a filter or a smoother from N scalar measurements [math]\displaystyle{ z_k }[/math]. The above update can also be applied to updating a Poisson measurement noise intensity. Similarly, for a first-order auto-regressive process, an updated process noise variance estimate can be calculated by

where [math]\displaystyle{ \widehat{x}_k }[/math] are scalar output estimates calculated by a filter or a smoother from N scalar measurements [math]\displaystyle{ z_k }[/math]. The above update can also be applied to updating a Poisson measurement noise intensity. Similarly, for a first-order auto-regressive process, an updated process noise variance estimate can be calculated by

其中 < math > widehat { x } _ k <nowiki></math ></nowiki> 是由过滤器计算的标量输出估计值，或者由 n 个标量测量值计算得到的平滑器。上述更新也可以应用于泊松测量噪声强度的更新。同样，对于一阶自回归过程，更新后的过程噪声方差估计可以通过

<nowiki>其中 {\displaystyle {\widehat {x}}_{k}}{\displaystyle {\widehat {x}}_{k}} 是由滤波器或平滑器从 N 个标量测量 {\displaystyle z_ {k}}z_{k}。 上述更新也可以应用于更新泊松测量噪声强度。 类似地，对于一阶自回归过程，更新的过程噪声方差估计可以计算为</nowiki>

 

<nowiki>{\displaystyle {\widehat {\sigma }}_{w}^{2}={\frac {1}{N}}\sum _{k=1}^{N}{({\widehat {x} }_{k+1}-{\widehat {F}}{\widehat {x}}_{k})}^{2},}{\displaystyle {\widehat {\sigma }}_{w}^ {2}={\frac {1}{N}}\sum _{k=1}^{N}{({\widehat {x}}_{k+1}-{\widehat {F}}{ \widehat {x}}_{k})}^{2},}</nowiki>

where [math]\displaystyle{ \widehat{x}_k }[/math] and [math]\displaystyle{ \widehat{x}_{k+1} }[/math] are scalar state estimates calculated by a filter or a smoother. The updated model coefficient estimate is obtained via

where [math]\displaystyle{ \widehat{x}_k }[/math] and [math]\displaystyle{ \widehat{x}_{k+1} }[/math] are scalar state estimates calculated by a filter or a smoother. The updated model coefficient estimate is obtained via

其中 < math > 和 < math > <nowiki></math ></nowiki> > > > > > > > x }{ k + 1} <nowiki></math ></nowiki> 是由过滤器或平滑器计算的标量状态估计。通过对模型参数的估计，得到了修正后的模型参数估计

<nowiki>其中 {\displaystyle {\widehat {x}}_{k}}{\displaystyle {\widehat {x}}_{k}} 和 {\displaystyle {\widehat {x}}_{k+1}}{ \displaystyle {\widehat {x}}_{k+1}} 是由过滤器或平滑器计算的标量状态估计。 更新后的模型系数估计是通过</nowiki>

 

<nowiki>{\displaystyle {\widehat {F}}={\frac {\sum _{k=1}^{N}({\widehat {x}}_{k+1}-{\widehat {F}}{ \widehat {x}}_{k})}{\sum _{k=1}^{N}{\widehat {x}}_{k}^{2}}}.}{\displaystyle {\widehat {F}}={\frac {\sum _{k=1}^{N}({\widehat {x}}_{k+1}-{\widehat {F}}{\widehat {x}} _{k})}{\sum _{k=1}^{N}{\widehat {x}}_{k}^{2}}}</nowiki>

The convergence of parameter estimates such as those above are well studied.

The convergence of parameter estimates such as those above are well studied.