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
Cubature kalman filtering for continuous-discrete systems: theory and simulations
IEEE Transactions on Signal Processing
A Numerical-Integration Perspective on Gaussian Filters
IEEE Transactions on Signal Processing
Particle Smoothing in Continuous Time: A Fast Approach via Density Estimation
IEEE Transactions on Signal Processing
Nonlinear filtering via generalized Edgeworth series andGauss-Hermite quadrature
IEEE Transactions on Signal Processing
A survey of data smoothing for linear and nonlinear dynamic systems
Automatica (Journal of IFAC)
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This paper is concerned with Bayesian optimal filtering and smoothing of non-linear continuous-discrete state space models, where the state dynamics are modeled with non-linear Ito-type stochastic differential equations, and measurements are obtained at discrete time instants from a non-linear measurement model with Gaussian noise. We first show how the recently developed sigma-point approximations as well as the multi-dimensional Gauss-Hermite quadrature and cubature approximations can be applied to classical continuous-discrete Gaussian filtering. We then derive two types of new Gaussian approximation based smoothers for continuous-discrete models and apply the numerical methods to the smoothers. We also show how the latter smoother can be efficiently implemented by including one additional cross-covariance differential equation to the filter prediction step. The performance of the methods is tested in a simulated application.