Gaussian Smoothers for Nonlinear Systems With One-Step Randomly Delayed Measurements

Particle Smoother for Nonlinear Systems With One‐Step Randomly Delayed Measurements

“…In this paper, a new PS based on forward filtering backward simulation is developed to solve the nonlinear and non‐Gaussian smoothing problem when measurements are randomly delayed by one sampling time. The proposed PS has almost consistent computational complexity with existing Gaussian mixture UKS (GMUKS) when the numbers of both filter particles and smoother particles equal to the number of Gaussian mixture terms. Simulation results show that the proposed method has higher estimation accuracy than existing methods.…”

“…The computational complexities of both the proposed PS for nonlinear systems with one‐step randomly delayed measurements and existing standard PS based on forward filtering back simulation are O ( N s × N f × M ), and that of existing GMUKS is O ( L 2 × M ), where L is the number of Gaussian mixture terms .…”

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.…”

“…But such augmentation approach inevitably suffers from the enormous computation burdens. Here, we will show (16) for computing (18), (21) and (23) by CKF (17) for computing (20), (22) and (24) …”

Particle filter with one-step randomly delayed measurements and unknown latency probability

“…An improved extended Kalman filtering algorithm and an improved unscented Kalman filtering algorithm for nonlinear systems with one-step or two-step randomly delayed measurements have been proposed by Hermoso-Carazo & Linares-Pérez (2007, 2009. Wang et al proposed Gaussian approximate (GA) filter and smoother which give general and common frameworks for addressing the state estimation problem when the measurements are randomly delayed by one sampling time Wang, Pan, Liang, & Yang, 2013). A new GA filter with one-step randomly delayed measurements and correlated noises is proposed in Wang, Liang, Pan, Zhao, and Yang (2014).…”