INFERENCE IN STATE SPACE MODELS

I have the following state space model
$$x_{n}=x_{n-1}+cos(1.2n)$$
$$y_{n}=x_{n}^{2}+w_{n}$$
$$w_{n}\thicksim N(0,σ_{w}^{2})$$
For the observation pdf, we have $y_{n}\thicksim N(x_{n},{x_{n}σ_{w}}^{2})$ so we can use this to compute the observation pdf.
On the other hand, the transition equation dosent't have process noise. In this case, how am I supposed to compute the transition pdf $p(x_{n+1}|x_{n})$.