Fixed interval smoothing for nonlinear continuous time systems
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TLDR
The conditional Fokker Planck equation yielding the probability density of the state of a nonlinear dynamical system, conditioned on measurements over a fixed interval, is derived in a novel way.Abstract:
An equation is derived for the probability density of the state of a nonlinear dynamical system, conditioned on measurements over a fixed interval. In deriving the equation, the conditional Fokker Planck equation yielding the probability density of the filtering problem is used several times in a novel way.read more
Citations
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Journal ArticleDOI
Reverse-time diffusion equation models
TL;DR: Reverse-time stochastic diffusion equation models are defined in this article and it is shown how most processes defined via a forward-time or conventional diffusion equation model have an associated reverse-time model.
Book
Applied Stochastic Differential Equations
Simo Särkkä,Arno Solin +1 more
TL;DR: The topic of this book is stochastic differential equations (SDEs), which are differential equations that produce a different “answer” or solution trajectory each time they are solved, and the emphasis is on applied rather than theoretical aspects of SDEs.
Journal ArticleDOI
Smoothing algorithms for nonlinear finite-dimensional systems
TL;DR: In this article, the state evolves either as a diffusion process or a finitestate Markov process, and the measurement process consists either of a nonlinear function of the state with additive white noise or as a counting process with intensity dependent on the state.
Journal ArticleDOI
Projection smoothing for continuous and continuous-discrete stochastic dynamic systems
TL;DR: A differential geometric approach is adopted to construct finite-dimensional algorithms for solving the filtering and smoothing problems associated with continuous and continuous-discrete time nonlinear stochastic dynamic systems conditioned on noisy measurements.
Book ChapterDOI
Equations du lissage non lineaire
TL;DR: Le but de cette note est d'etablir trois couples d'equations, chacun des trois permettant de caracteriser la loi conditionnelle d'un probleme de lissage non lineaire as discussed by the authors.
References
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Book
Stochastic Processes and Filtering Theory
TL;DR: In this paper, a unified treatment of linear and nonlinear filtering theory for engineers is presented, with sufficient emphasis on applications to enable the reader to use the theory for engineering problems.
Journal ArticleDOI
Approximations to optimal nonlinear filters
TL;DR: In this article, the signal and noise processes are given as solutions to nonlinear stochastic differential equations and several methods of obtaining possibly useful finite dimensional approximations are considered, and some of the special problems of simulation are discussed.
Journal ArticleDOI
On the Differential Equations Satisfied by Conditional Probablitity Densities of Markov Processes, with Applications
Journal ArticleDOI
Nonlinear Smoothing Theory
TL;DR: Approximations to these equations are developed for the smoothed expectation of the state and the smoothing covariance matrix for linear systems and an iterative technique is suggested for even greater accuracy in approximations for severely nonlinear systems.
Journal ArticleDOI
Nonlinear interpolation
TL;DR: The nonlinear interpolation problem is formulated in state variable form and an exact solution is obtained that a partial differential equation for the evolution of the conditional probability density of the state vector at a fixed point in time is derived.