Tracking and data association
Estimation with Applications to Tracking and Navigation
Estimation with Applications to Tracking and Navigation
Global Positioning Systems, Inertial Navigation, and Integration
Global Positioning Systems, Inertial Navigation, and Integration
Statistical Multisource-Multitarget Information Fusion
Statistical Multisource-Multitarget Information Fusion
The Gaussian Mixture Probability Hypothesis Density Filter
IEEE Transactions on Signal Processing
Square-Root Quadrature Kalman Filtering
IEEE Transactions on Signal Processing
Bayesian Filtering With Random Finite Set Observations
IEEE Transactions on Signal Processing
Automatica (Journal of IFAC)
Sparse-grid quadrature nonlinear filtering
Automatica (Journal of IFAC)
Gaussian filtering and smoothing for continuous-discrete dynamic systems
Signal Processing
International Journal of Information and Communication Technology
Adaptive ODE solvers in extended Kalman filtering algorithms
Journal of Computational and Applied Mathematics
Hi-index | 35.69 |
In this paper, we extend the cubature Kalman filter (CKF) to deal with nonlinear state-space models of the continuous-discrete kind. To be consistent with the literature, the resulting nonlinear filter is referred to as the continuous-discrete cubature Kalman filter (CD-CKF). We use the ItÔ-Taylor expansion of order 1.5 to transform the process equation, modeled in the form of stochastic ordinary differential equations, into a set of stochastic difference equations. Building on this transformation and assuming that all conditional densities are Gaussian-distributed, the solution to the Bayesian filter reduces to the problem of how to compute Gaussian-weighted integrals. To numerically compute the integrals, we use the third-degree cubature rule. For a reliable implementation of the CD-CKF in a finite word-length machine, it is structurally modified to propagate the square-roots of the covariance matrices. The reliability and accuracy of the square-root version of the CD-CKF are tested in a case study that involves the use of a radar problem of practical significance; the problem considered herein is challenging in the context of radar in two respects-high dimensionality of the state and increasing degree of nonlinearity. The results, presented herein, indicate that the CD-CKF markedly outperforms existing continuous-discrete filters.