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Nonlinear Robust Estimation Problem Research and Application on Krien Space

Author: ZhangPengYu
Tutor: YuFei
School: Harbin Engineering University
Course: System theory
Keywords: Kalman filtering Nonlinear system Krein space SINS initial alignment Robust
CLC: O231
Type: Master's thesis
Year: 2012
Downloads: 36
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With the development of technology,more and more engineering problems and it arisessome theoretical issues will be put in front of people.One of them which is the robust filteringproblem with parameter uncertainty and bias of nonlinear discrete-time stochastic systemsbecome more attractive.In the past several years people try different ways to solve theproblem,one of the most representative is Kalman filtering method,a type of very importantsignal estimation method. And because this method is robusts, it’s able to overcome thesystem model parameter perturbation Robust filtering,and also it makes Kalman filteringmethod very important. But despite the Kalman filter with high accuracy and simplerecursive form, but it may also be difficult to draw the desired results in the case of thesystem model is inaccurate.The paper major work is aimed at filtering problem at a class of nonlinear system. Bythe transformation in Krein space interpretation in the form of systems of nonlinear systemswith uncertainty, combined with Krein space linear estimation theory to derive the extendedKrein space estimation theory and the formula. Krein space talking about here is a specialsense of space model, Krein space topology on a Hilbert space H is defined as the normtopology, and then by the Krein space conjugate bilinear mapping to construct a Hilbert space,making it a space with Krein space. Because space on the form system in Krein and theuncertainty of standard Kalman filtering is the consistency under certain conditions. Theoptimal state estimation is in an ellipsoid region to achieve the effect of the standard Kalmanfilter. Nonlinear systems is given in Krein space measurement equation and according to theof determ residentinant of Graeme in Krein space and deterministic quadratic constraintshave the same the recursive formula of measurement error estimates are given.SINS initial alignment has been the existence of navigation can not be ignored,nonlineardiscrete-time stochastic system which has been a hot topic in this area.Combined with Kreinspace Kalman filtering theory, we can use Krein space under the heuristic Kalman filter tosolve practical engineering problems of this type. Numerical examples given in this paper andsimulation results verify the feasibility and advantages of this theory.

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