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lines changed Original file line number Diff line number Diff line change @@ -150,12 +150,45 @@ Available default models as :
150150* constant-acceleration
151151
152152This will automatically configure the ` dynamic.transition ` matrix.
153+ ##### constant-position
154+
155+ ``` math
156+ \begin{align}
157+ State :& \begin{bmatrix} x_t \end{bmatrix}\\
158+ Transition Equation :& x_t \sim x_{t-1} \\
159+ dynamic.transition :& \begin{bmatrix} 1 \end{bmatrix}
160+ \end{align}
161+ ```
162+
163+ ##### constant-speed
164+
165+ ``` math
166+ \begin{align}
167+ State :& \begin{bmatrix} x_t \\ speed_t \end{bmatrix} \\
168+ Transition Equation :&
169+ \begin{split}
170+ x_t &\sim x_{t-1} + speed_{t-1},\\
171+ speed_t &\sim speed_{t-1}
172+ \end{split} \\
173+ dynamic.transition :& \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}
174+ \end{align}
175+ ```
153176
154- | ` dynamic.name ` | State | Transition Equation | ` dynamic.transition ` |
155- | --| --| --| --|
156- | ` constant-position ` | $\begin{bmatrix} x_t \end{bmatrix}$ | $x_t \sim x_ {t-1}$ | $\begin{bmatrix} 1 \end{bmatrix}$ |
157- | ` constant-speed ` | $\begin{bmatrix} x_t \\\\ speed_t \end{bmatrix}$ | $\begin{split}x_t \sim x_ {t-1} + speed_ {t-1},\\\\ speed_t \sim speed_ {t-1}\end{split}$| $\begin{bmatrix} 1 & 1 \\\\ 0 & 1 \end{bmatrix}$ |
158- | ` constant-acceleration ` | $\begin{bmatrix} x \\\\ speed_t \\\\ acc_t \end{bmatrix}$ | $\begin{split}x_t \sim x_ {t-1} + speed_ {t-1} \\\\ speed_t \sim speed_ {t-1} + acc_ {t-1} \\\\ acc_t \sim acc_ {t-1}\end{split}$ | $\begin{bmatrix} 1 & 1 & 0 \\\\ 0 & 1 & 1 \\\\ 0 & 0 & 1\end{bmatrix}$ |
177+ ##### constant-acceleration
178+
179+ ``` math
180+ \begin{align}
181+ State :& \begin{bmatrix} x_t \\ speed_t \\ acc_t \end{bmatrix} \\
182+
183+ Transition Equation :&
184+ \begin{split}
185+ x_t &\sim x_{t-1} + speed_{t-1} \\
186+ speed_t &\sim speed_{t-1} + acc_{t-1} \\
187+ acc_t &\sim acc_{t-1}
188+ \end{split} \\
189+ dynamic.transition :& \begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1\end{bmatrix}
190+ \end{align}
191+ ```
159192
160193#### 'constant-position' on 2D data
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