Related papers: The Hitchhiker's Guide to Nonlinear Filtering
The particle filter is a popular Bayesian filtering algorithm for use in cases where the state-space model is nonlinear and/or the random terms (initial state or noises) are non-Gaussian distributed. We study the behavior of the error in…
Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…
The distributed filtering problem sequentially estimates a global state variable using observations from a network of local sensors with different measurement models. In this work, we introduce a novel methodology for distributed nonlinear…
A Bayesian data assimilation scheme is formulated for advection-dominated or hyperbolic evolutionary problems, and observations. The method is referred to as the dynamic likelihood filter because it exploits the model physics to dynamically…
A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using…
Nonlinear adaptive filtering allows for modeling of some additional aspects of a general system and usually relies on highly complex algorithms, such as those based on the Volterra series. Through the use of the Kronecker product and some…
Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is…
Differentiable particle filters are an emerging class of sequential Bayesian inference techniques that use neural networks to construct components in state space models. Existing approaches are mostly based on offline supervised training…
Particle filters for data assimilation in nonlinear problems use "particles" (replicas of the underlying system) to generate a sequence of probability density functions (pdfs) through a Bayesian process. This can be expensive because a…
The use of Kalman filtering, as well as its nonlinear extensions, for the estimation of system variables and parameters has played a pivotal role in many fields of scientific inquiry where observations of the system are restricted to a…
In this tutorial we consider the non-linear Bayesian filtering of static parameters in a time-dependent model. We outline the theoretical background and discuss appropriate solvers. We focus on particle-based filters and present Sequential…
It is well known that the nonlinear filtering problem has important applications in both military and civil industries. The central problem of nonlinear filtering is to solve the Duncan-Mortensen-Zakai (DMZ) equation in real time and in a…
A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…
Particle filtering is a standard Monte-Carlo approach for a wide range of sequential inference tasks. The key component of a particle filter is a set of particles with importance weights that serve as a proxy of the true posterior…
A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical…
Unmanned vehicle navigation concerns estimating attitude, position, and linear velocity of the vehicle the six degrees of freedom (6 DoF). It has been known that the true navigation dynamics are highly nonlinear modeled on the Lie Group of…
In this thesis, we introduce Bayesian filtering as a principled framework for tackling diverse sequential machine learning problems, including online (continual) learning, prequential (one-step-ahead) forecasting, and contextual bandits. To…
Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines…
At the beginning of this century, a real time solution of the nonlinear filtering problem without memory was proposed in [1, 2] by the third author and his collaborator, and it is later on referred to as Yau-Yau algorithm. During the last…
In this paper, we study a non-linear filtering problem in the presence of signal model uncertainty. The model ambiguity is characterized by a class of probability measures from which the true one is taken. After interchanging the order of…