The truncated second-order nonlinear filter revisited

Henriksen, Rolf

doi:10.1109/tac.1982.1102840

Cited by 30 publications

(14 citation statements)

References 9 publications

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“…These approaches include the iterated EKF [24], the second order EKF [25], the Gaussian sum filter [26], the grid based filter [27,Chapter 6], and the more general particle filter [7]. However since the work presented in this paper indicates that the aircraft engine nonlinearities are mild enough that the UKF does not provide much better performance than the EKF, it is doubtful that these other higher order approaches will result in much improvement either.…”

Section: Resultsmentioning

confidence: 99%

A comparison of filtering approaches for aircraft engine health estimation

Simon

2008

Aerospace Science and Technology

110

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Different approaches for the estimation of the states of linear dynamic systems are commonly used, the most common being the Kalman filter. For nonlinear systems, variants of the Kalman filter are used. Some of these variants include the LKF (linearized Kalman filter), the EKF (extended Kalman filter), and the UKF (unscented Kalman filter). With the LKF and EKF, performance varies depending on how often Jacobians (partial derivative matrices) are updated. In other words, we see a tradeoff between computational effort and filtering performance. With the unscented Kalman filter, Jacobians are not calculated but computational effort is typically high due to the need for multiple simulations at each time step of the underlying dynamic system. Up to this point in time a number of filtering approaches have been used for aircraft turbofan engine health estimation, but a systematic comparison has not been published. This paper compares the estimation accuracy and computational effort of these filters for aircraft engine health estimation. We show in this paper that the EKF and UKF both outperform the LKF. The EKF computational effort is an order of magnitude higher than the LKF, and the UKF is another order of magnitude higher than the EKF. Overall we conclude that the EKF, with Jacobian calculations about every three flights, is the best choice for aircraft engine health estimation.

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Section: Resultsmentioning

confidence: 99%

A comparison of filtering approaches for aircraft engine health estimation

Simon

2008

Aerospace Science and Technology

110

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“…Based on this procedure, a version of the discrete Kalman filter, using discrete (in time) observations, is suggested for the estimation of {x(t k )} . The filtering algorithm proposed here, is, by its definition, more economical in the amount of computations and memory storage requirement than the linearized or extended Kalman filters or the truncated non-linear filters (for the construction of these filters see for example Jazwinski (1970), Sage and Melsa (1971), Henriksen (1982) and the references cited there). …”

Section: Discussionmentioning

confidence: 99%

A discrete Kalman filter for a class of non-linear stochastic systemsf

Yavin

1982

International Journal of Systems Science

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A class of non-linear systems of the form dx= A(x)x dt+ C1 dW, t » 0, xERm, A(x)EGlnlxm.where W is an Rm·valued standard Wiener process; together with an observation process given by y(lk) = .Mx(lk) +O(lk)' y(lk)ERP, I. < I, < ... < Ik < ... , is considered. A procedure for the discretization (in time) of the system's equation is introduced. Based on this procedure, a version of the discrete (in time) Kalman filter is suggested for the estimation of {x(t.~:)}. The filter proposed here proves to be more economical in the amount of computation and in memory storage requirements than the linearized or extended Kalman filters, or the truncated non-linear filters. Two examples are numerically solved.

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“…Next, substituting the above optimal gains in (17) and setting results in the following Hamilton-Jacobi-Bellman equation: (20) We then have the following result. Proposition 3.2: Consider the nonlinear discrete system (2) and the filtering problem for this system.…”

Section: Solution To the Filtering Problem Using Decomposition Fmentioning

confidence: 99%

“…Suppose the plant is locally asymptotically stable about the equilibrium-point and zero-input observable. Further, suppose there exist a local diffeomorphism that transforms the system to the partially decoupled form (4), a positive-semidefinite function locally defined in a neighborhood of the origin , and matrix functions , satisfying the DHJBE (20) together with the side-conditions (18), (19). Then the filter solves the filtering problem for the system locally in .…”

Section: Solution To the Filtering Problem Using Decomposition Fmentioning

confidence: 99%

“…In general, statistical discrete-time nonlinear filtering techniques developed using minimum-variance, Bayesian, and maximum-likelihood criteria [10], [30], [33] are too complicated, and approximations [20], [32] are still computationally intensive to implement. These filters require the solution of infinite-dimensional evolution equations such as the Kolmogorov equation, the Stratonovitch-Kushner equation or the Wong-Zakai equation [23].…”

Section: Introductionmentioning

confidence: 99%

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${\cal H}_{2}$ Filtering for Discrete-Time Nonlinear Singularly Perturbed Systems

Aliyu

Boukas

2011

IEEE Trans. Circuits Syst. I

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In this paper, we consider the 2 (or Kalman)-filtering problem for discrete-time singularly-perturbed (two time-scale) nonlinear systems. Two types of filters, namely, i) decomposition and ii) aggregate, are discussed, and sufficient conditions for the solvability of the problem in terms of new discrete-time Hamilton-Jacobi-Bellman equations (DHJBEs) are presented. For each type of filter above, first-order approximate filters are derived, and reduced-order filters are also derived in each case. The results are also specialized to linear systems, in which case the DHJBEs reduce to a system of linear-matrix-inequalities (LMIs) which are efficient to solve. Examples are also presented to illustrate the results.

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The truncated second-order nonlinear filter revisited

Cited by 30 publications

References 9 publications

A comparison of filtering approaches for aircraft engine health estimation

A comparison of filtering approaches for aircraft engine health estimation

A discrete Kalman filter for a class of non-linear stochastic systemsf

${\cal H}_{2}$ Filtering for Discrete-Time Nonlinear Singularly Perturbed Systems

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