Quadratic Optimization and Linear Filtering

2013 ◽  
pp. 165-187
Author(s):  
Brigitte d’Andréa-Novel ◽  
Michel De Lara
Keyword(s):  
Quadratic Optimization ◽  
Linear Filtering

The Design of Optimal Lateral Motion Control of an UAV Using the Linear-Quadratic Optimization Method in the Complex Domain

2020 ◽  
Vol 13 (6) ◽  
pp. 217
Author(s):  
Vadim Kramar ◽  
Vasiliy Alchakov ◽  
Aleksey Kabanov ◽  
Sergey Dudnikov ◽  
Aleksandr Dmitriev
Keyword(s):  
Motion Control ◽  
Optimization Method ◽  
Quadratic Optimization ◽  
Complex Domain ◽  
Lateral Motion ◽  
Linear Quadratic

scholarly journals Unbiased estimation of the solution to Zakai’s equation

2020 ◽  
Vol 26 (2) ◽  
pp. 113-129
Author(s):  
Hamza M. Ruzayqat ◽  
Ajay Jasra
Keyword(s):  
Continuous Time ◽  
Unbiased Estimation ◽  
Finite Variance ◽  
Linear Filtering ◽  
Multilevel Monte Carlo ◽  
Zakai Equation ◽  
Unbiased Estimators ◽  
First Order ◽  
Multilevel Monte Carlo Method ◽  
Filtering Problem

AbstractIn the following article, we consider the non-linear filtering problem in continuous time and in particular the solution to Zakai’s equation or the normalizing constant. We develop a methodology to produce finite variance, almost surely unbiased estimators of the solution to Zakai’s equation. That is, given access to only a first-order discretization of solution to the Zakai equation, we present a method which can remove this discretization bias. The approach, under assumptions, is proved to have finite variance and is numerically compared to using a particular multilevel Monte Carlo method.

Embedding non-linear filtering in autonomous underwater vehicle dynamics via the Kolmogorov backward equation

2021 ◽  
pp. 014233122110196
Author(s):  
Ravish H. Hirpara ◽  
Shambhu N. Sharma
Keyword(s):  
State Vector ◽  
Autonomous Underwater Vehicle ◽  
Underwater Vehicle ◽  
Linear Filtering ◽  
Homogeneous Markov Process ◽  
Non Linear ◽  
Backward Equation ◽  
Noise Correction ◽  
Ito Process ◽  
Correction Terms

This paper revisits the state vector of an autonomous underwater vehicle (AUV) dynamics coupled with the underwater Markovian stochasticity in the ‘non-linear filtering’ context. The underwater stochasticity is attributed to atmospheric turbulence, planetary interactions, sea surface conditions and astronomical phenomena. In this paper, we adopt the Itô process, a homogeneous Markov process, to describe the AUV state vector evolution equation. This paper accounts for the process noise as well as observation noise correction terms by considering the underwater filtering model. The non-linear filtering of the paper is achieved using the Kolmogorov backward equation and the evolution of the conditional characteristic function. The non-linear filtering equation is the cornerstone formalism of stochastic optimal control systems. Most notably, this paper introduces the non-linear filtering theory into an underwater vehicle stochastic system by constructing a lemma and a theorem for the underwater vehicle stochastic differential equation that were not available in the literature.

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