In the nonlinear Bayesian Tracking problem, if we consider the noise exists only in the state equation : x[k] = f(x[k-1],v[k-1]) where vk-1 here is an iid process noise sequence

And we suppose that the measurement is directly and noise free observed, that means z[k] = h(x[k])

What is the likelihood function p( z[k] | x[k] ) in this case?