# unscented kalman filter for non-linear state-space

I intend to use unscented kalman filter to estimate a non-linear state -space problem. latent factor $X_t$ in the formulation has usual VAR(1) specification

$$X_t = \phi X_{t-1} +\epsilon_t$$

where, $X_t$ is N-dimensional vector and $\epsilon_t$ ~N(0, $\Omega$)

but observed variable $Y_t$ is non linear function of $X_t$

$Y_t= f(X_t)+ \eta_t$

I have following questions in this regard

1. Is Unscented kalman filter is the right approach for this estimation
2. based on my understanding, in UKF you create sigma points around state vector and and try to approximate mean and variance of the state. But different papers seem to define state vectors differently. I this paper they augment state vector with few parameters they want to estimate and create sigma points around it (joint estimation approach). On the other hand, In the original paper they recommend augmenting state vector with the noise terms. While in this blog the create sigma points only around the original state verctor.. Which of these approach is correct, computaionally less intensive and suitable for my problem?