*2.2. Model Filtering*

$$
\hat{X}\_i(k+1|k) = H\_i(k+1|k)\hat{X}\_{0i}(k)\tag{10}
$$

$$P\_i(k+1\middle|k) = A\_i(k+1\middle|k)P\_{0i}(k)A\_i^T(k+1\middle|k) + B\_i(k)Q(k)B\_i^T(k) \tag{11}$$

$$K\_{i}(k+1) = P\_{i}(k+1|k)H\_{i}^{T}(k+1)\left[H\_{i}(k+1)P\_{i}(k+1|k)H\_{i}^{T}(k+1) + \mathcal{R}\_{i}(k+1)\right]^{-1} \tag{12}$$

$$\mathbf{P}\_{i}(k+1) = \left[\mathbf{I} - \mathbf{K}\_{i}(k+1)\mathbf{H}\_{i}(k+1)\right]\mathbf{P}\_{i}(k+1|k) \tag{13}$$

$$\dot{\mathbf{X}}\_{i}(k+1) = \dot{\mathbf{X}}\_{i}(k+1|k) + \mathbf{K}\_{i}(k+1) \Big[ \mathbf{Z}\_{i}(k+1) - H\_{i}(k+1)\mathbf{\hat{X}}\_{i}(k+1|k) \Big] \tag{14}$$

where *Q*(*k*) is the covariance of the process noise and *R*(*k*) is the covariance of the observation noise.

*2.3. Updating Model Probability*

$$
\mu\_i(k+1) = \frac{\Lambda\_i(k+1)\overline{c}\_i(k+1)}{\sum\_{i=1}^m \overline{c}\_i \Lambda\_i(k+1)}\tag{15}
$$

$$\Lambda\_{i}(k+1) = \frac{\exp\left\{-\frac{1}{2} (\boldsymbol{\sigma}\_{i}(k+1))^{T} (\boldsymbol{S}\_{i}(k+1))^{-1} \boldsymbol{\sigma}\_{i}(k+1)\right\}}{\sqrt{2\pi \det(\mathbf{S}\_{i}(k+1))}}\tag{16}$$

where *v* is measurement residuals and *S* is the residual covariance matrix.
