# w:EXP, P:VA


<!-- WARNING: THIS FILE WAS AUTOGENERATED! DO NOT EDIT! -->

------------------------------------------------------------------------

<a
href="https://github.com/SuzuSys/KalmanPaper/blob/main/KalmanPaper/wEXP_PVA.py#L21"
target="_blank" style="float:right; font-size:smaller">source</a>

### wEXP_PVA_out

``` python

def wEXP_PVA_out(
    args:VAR_POSITIONAL, kwargs:VAR_KEYWORD
):

```

\* \*\*
[`wEXP_PVA`](https://SuzuSys.github.io/KalmanPaper/wEXP_PVA/wexp_pva.html#wexp_pva)
関数の返り値

<table>
<colgroup>
<col style="width: 33%" />
<col style="width: 33%" />
<col style="width: 33%" />
</colgroup>
<thead>
<tr>
<th><span class="math inline"> </span></th>
<th>Type</th>
<th>Details</th>
</tr>
</thead>
<tbody>
<tr>
<td>W</td>
<td>Float[Array, ‘T N’]</td>
<td><span class="math inline">$\{\hat{\mathbf
w}_{t/t}\}_{t=0,\ldots,T-1}$</span></td>
</tr>
<tr>
<td>P</td>
<td>Float[Array, ‘T N N’]</td>
<td><span
class="math inline">{<strong>P</strong><sub><em>t</em>/<em>t</em></sub>}<sub><em>t</em> = 0, …, <em>T</em> − 1</sub></span></td>
</tr>
<tr>
<td>Xi</td>
<td>Float[Array, ‘T’]</td>
<td><span
class="math inline">{<em>ξ</em><sub><em>t</em></sub>}<sub><em>t</em> = 0, …, <em>T</em> − 1</sub></span></td>
</tr>
</tbody>
</table>

\* 

------------------------------------------------------------------------

<a
href="https://github.com/SuzuSys/KalmanPaper/blob/main/KalmanPaper/wEXP_PVA.py#L39"
target="_blank" style="float:right; font-size:smaller">source</a>

### wEXP_PVA

``` python

def wEXP_PVA(
    N:int, # $N$
    T:int, # $T$
    x:Float[Array, '{T} {N}'], # $\{ \mathbf x_t \}_{t=0,\ldots,T-1}$
    y:Float[Array, '{T}'], # $\{ y_t \}_{t=0,\ldots,T-1}$
    G:Float[Array, '{N} {N}'], # $\boldsymbol\Gamma$
    w0:Float[Array, '{N}'], # $\hat{\mathbf w}_{0/-1}$
    P0:Float[Array, '{N} {N}'], # $\mathbf P_{0/-1}$
)->wEXP_PVA_out:

```

\* \*\* **w**<sub>*t*/*t*</sub> を EKF
によって推論し、**P**<sub>*t*/*t*</sub> を VA によって推論する手法
*ξ*<sub>*t*</sub> には一段予測推定値 $\hat{\mathbf w}\_{t/t-1}$ を使う
$$\xi_t=\sqrt{\mathbf x_t^T\left(\mathbf P\_{t/t-1}+\hat{\mathbf w}\_{t/t-1}\hat{\mathbf w}\_{t/t-1}^T\right)\mathbf x_t}$$
\*