A Gaussian approximation recursive filter for nonlinear systems with correlated noises

Gaussian filter for nonlinear systems with correlated noises at the same epoch

“…Similar to the proof of the state correction of GASF in Wang et al (2012), based on Gaussian Assumption 1, the posterior PDF p(x k |Z k ) is updated as Gaussian, and (3)- (6) and (10)- (12) can be easily proved. The proofs of (7)-(9) are given in Appendix A.…”

“…The Gaussian assumption is reasonable for some applications with mild nonlinearity, such as target tracking (Arasaratnam & Haykin, 2009;Bar-Shalom et al, 2001) and ballistic target reentry (Chang, 2014b Similar to that in Wang et al (2012), in the case that process noise and measurement noise are correlated at the same epoch, we need to define the following augmented state vector ξ k = [x T k w T k ] T . If Gaussian approximations to p(x k |Z k ) and p(w k |Z k ) have been updated, the posterior probability density function (PDF) p(ξ k |Z k ) of the augmented state ξ k is also Gaussian, and its first two moments can be formulated as…”

“…There are two frameworks available to solve this problem including the decorrelating framework (Bar-Shalom, Li, & Kirubarajan, 2001) and Gaussian approximation recursive filter (GASF) framework (Wang, Liang, Pan, & Yang, 2012). For linear Gaussian system, these two frameworks are completely equivalent (Chang, 2014a), and for general nonlinear system, they are equivalent in the linear minimum mean square error (MMSE) sense (Wang, Liang, Pan, & Wang, 2014).…”

Gaussian sum approximation filter for nonlinear dynamic time-delay system

“…Further, GSF provides a feasible approach to meet both accuracy and real time required in the filtering problem of nonlinear time-delay systems. However, the existing literatures concerning GSF or GF have been limited to the research on the robust filter for dealing with the model error [13], on the adaptive filter with Gaussian sum refinement and coarsening [12,14], on the numerical technologies for approximating the nonlinear integrals [15][16][17][18][19][20], on the state smoothing framework design [10,[21][22][23], on the numerical and stability analyses [24][25][26][27][28], on the constrained estimation [29][30][31], and on the colored and correlated noises [9,10]. So far, there are seldom results paying adequate research attention on designing the GSF for the nonlinear time-delay systems despite GSF has been significantly shown to be good at both accuracy and real time.…”

Gain-Constrained Extended Kalman Filtering with Stochastic Nonlinearities and Randomly Occurring Measurement Delays

“…In the case that the nonlinearities contribute significantly in the systems and cannot be neglected, the appropriate algorithms to tackle nonlinearities are very necessary for the desired filtering performance. Up to now, various types of filtering schemes have been reported for nonlinear systems, such as extended Kalman filtering [15,17,21,29], H ∞ filtering [26,33], Gaussian filtering [25], and set-valued filtering [2]. Among them, the extended Kalman filtering has recently received particular research attention due to its effectiveness for multiplicative noises and wide application prospects in engineering, especially within the networked environment.…”