Asymptotic expansions and Lie algebras for some nonlinear filtering problems

Blankenship, G. L.; Liu, Chang-Huan; Marcus, Solomon

doi:10.1109/tac.1983.1103307

Cited by 17 publications

(9 citation statements)

References 17 publications

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“…But it is still true that ( 11.6) gives an asymptotic expansion (Blankenschip-Liu-Marcus [4]). The Lie algebras being solvable one can of course implement these approximate filters, using the Wei-Nonnan technique.…”

Section: Proposition I 13 [I 5)mentioning

confidence: 99%

“…The Lie algebras being solvable one can of course implement these approximate filters, using the Wei-Nonnan technique. This was done in [4] and also the results were compared with the extended Kalman filter (EKF). The zero-th order approximation (of course) performed worse than EKF but the first order approximation performed better!…”

Section: Proposition I 13 [I 5)mentioning

confidence: 99%

“…First however let me point out that the procedures based on Wei-Norman techniques as described in sections 11 and 12 above clearly indicate that existence, uniqueness and regularity results for solutions of the DMZ-equation have a lot to do with the existence of asymptotic expansions ( [2,4] [25,8,22,2] and references in these papers).…”

Section: Asymptotic Expansions and Approximate Homomorphismsmentioning

confidence: 99%

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Lie Algebraic Method in Filtering and Identification

Hazewinkel¹

1988

Stochastic Processes in Physics and Engineering

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ABSTRACT. These lectures concern (nonlinear) filtering. Very roughly the art of obtaining best estimates for some stochastic time-varying variable x on the basis of observations of another process y. The more concrete object under consideration being a stochastic dynamical system dx=f(x)dt+G(x)dw, where w is Wiener noise, with observations dy=h(x)dt+dv, corrupted by further noise. The subject as presented here involves ideas and techniques from Lie algebra theory, stochastics, differential topology, approximation theory and partial differential equations and has relations with quantum theory and stochastic physics. The lectures are adressed to practitioners in any one of these areas assuming that as a rule they are not experts in the other ones.

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Section: Proposition I 13 [I 5)mentioning

confidence: 99%

Section: Proposition I 13 [I 5)mentioning

confidence: 99%

Section: Asymptotic Expansions and Approximate Homomorphismsmentioning

confidence: 99%

See 1 more Smart Citation

Lie Algebraic Method in Filtering and Identification

Hazewinkel¹

1988

Stochastic Processes in Physics and Engineering

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“…In addition, the disturbance attenuation property of the approximate guidance schemes as derived in [l, 2 , 31 has not been studied. To the authors' knowledge, the only stochastic approximate optimal estimator using a power series expansion technique is found in [4] and valid only for a scalar system. In [4] , for a specific polynomial nonlinearity of order 3 , an approximate estimation scheme is derived by calculating the approximate conditional density function using a perturbation method.…”

Section: Introductionmentioning

confidence: 99%

“…To the authors' knowledge, the only stochastic approximate optimal estimator using a power series expansion technique is found in [4] and valid only for a scalar system. In [4] , for a specific polynomial nonlinearity of order 3 , an approximate estimation scheme is derived by calculating the approximate conditional density function using a perturbation method. Furthermore, in [4] , explicit formula to determine the expansion terms of the conditional density is obtained only for a very simple example.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear approximate game-theoretic estimation

Jang¹,

Speyer²

Proceedings of 35th IEEE Conference on Decision and Control

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Over a finite-time interval, for a class of linear timevarying dynamical systems with a small nonlinearity, a n approximate nonlinear optimal estimation scheme is derived based on a deterministic game-theoretic criterion. Using t h e calculus of variation approach, this game-theoretic criterion is first maximized by t h e process disturbance and initial state vectors. T h e resulting optimality condition is expanded with respect t o a small parameter E and t h e expression of t h e worst case state and t h e La-

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Lectures on Linear and Nonlinear Filtering

Hazewinkel

1988

Analysis and Estimation of Stochastic Mechanical Systems

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Asymptotic expansions and Lie algebras for some nonlinear filtering problems

Cited by 17 publications

References 17 publications

Lie Algebraic Method in Filtering and Identification

Lie Algebraic Method in Filtering and Identification

Nonlinear approximate game-theoretic estimation

Lectures on Linear and Nonlinear Filtering

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