where \(x_{k}\in R^{n_{x}}\) is an \(n_{x}\)-dimensional vector representing the system states at time step \(t_{k}\) (k = 0, 1, 2, …). \(R^{n_{x}}\) represents \(n_{x}\)-dimensional real space; variable \(v_{k}\) is an\(n_{v}\)-dimensional vector representing a white noise sequence with independent and identical distribution; \(f_{k}\)\(R^{n_{x}}\times R^{n_{v}}\)represents a nonlinear function transiting the system from time\(t_{k}\) to time \(t_{k+1}\) in response to the model input vector.
The general measurement equation can be written as: