I have a state-space model: $$ x_{t+1} = A x_{t} + \alpha_{t} \\ y_{t+1} = B y_{t} + \beta_{t} $$
The observation model is parameterized by a categorical exogenous variable, $$ a = M_1\ or \ M_2 $$ The observation equation: $$ z_{t}(M_{1}) = x_t + y_t + \epsilon_t \\ z_t(M_2) = x_t - y_t + \epsilon_t $$
Is this a valid space model where I can use a Kalman filter to generate state space estimators?
