I'm working on tracking algorithm for radar system. I have 3 motion models with state vectors: $x_1=[x,y,v_x,v_y]$, $x_2=[x,y,v_x,v_y,a_x,a_y]$, $x_3=[x,y,v_{abs},\phi,\omega]$. The first two models are for straight motion (const. velocity, const. acceleration) and last is for turn rate motion. I would like to use interacting multiple model (IMM) algorithm for mixing these models but I found issues. The state interaction is described by the equation $$x_{0j}(k-1|k-1)=\sum_{i=1}^N x_{i}(k-1|k-1) \ u_{j|i}(k-1|k-1),$$
where
$$u_{j|i}(k-1|k-1)=\frac{1}{c_{j}} \ P_{i,j} \ u_{i}(k-1),$$
with
$$c_{j}=\sum_{i=1}^N P_{i,j} \ u_{i}(k-1).$$
I suppose that sum $x_{i}$,in the first equation, is definition of the sum for $x_1,x_2,x_3$ state vectors at the same time, but I don't understand how can I sum up state vectors with different degrees of dimension and different physical quantities.
Thank you in advance for your answer.