Discrete square root filtering: A survey of current techniques

Kamiński, P.; Bryson, Arthur E.; Schmidt, S. F.

doi:10.1109/tac.1971.1099816

Cited by 421 publications

(148 citation statements)

References 8 publications

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“…The predicted estimate recursion, (11)- (12), in information form can be written, after some algebra, as (15) and (16) The guidelines to obtain (16) can be seen in Appendix V-B.…”

Section: ) Predicted Information Estimatementioning

confidence: 99%

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Information Filtering and Array Algorithms for Descriptor Systems Subject to Parameter Uncertainties

Terra

Ishihara

Padoan

2007

IEEE Trans. Signal Process.

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Abstract-This paper presents information filters in Riccati recursions and in array algorithms for descriptor systems subject to parameters uncertainties. The filters are developed in filtered and predicted forms. The inversion of the state matrix is avoided in the new information recursive formulas. Therefore, it turns out clear that the invertibility of the state matrix, usually considered in the state-space information recursions, is not necessary. A numerical example is provided to illustrate the performance of the proposed robust array algorithms.Index Terms-Array algorithm, descriptor systems, information filter, Kalman filter.

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“…The predicted estimate recursion, (11)- (12), in information form can be written, after some algebra, as (15) and (16) The guidelines to obtain (16) can be seen in Appendix V-B.…”

Section: ) Predicted Information Estimatementioning

confidence: 99%

“…Fundamentally, array algorithms reduce the dynamic range in fixed-point implementations and assure better condition numbers than the conventional Kalman filter algorithm. More details on array algorithms can be found in [2], [9], [10], [14], [15], [24].…”

mentioning

confidence: 99%

Information Filtering and Array Algorithms for Descriptor Systems Subject to Parameter Uncertainties

Terra

Ishihara

Padoan

2007

IEEE Trans. Signal Process.

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“…The resulting post-array e n tries can be determined, by taking squares and using the orthogonality o f j , t o o b e y X X = R j + H j P j H j = R e j 2 By an orthogonal transformation, , we mean one for which, = = I. vi Y X = F j P j H j Z Z = F j P j F j + G j Q j G j ; Y Y = F j P j F j + G j Q j G j ; Y X (X X ) ;1 X Y = F j P j F j + G j Q j G j ; F j P j H j R ;1 e j H j P j F j = P j+1 :…”

Section: Square-root Arraysmentioning

confidence: 99%

“…We therefore exhibit here the necessary modi cations. This justi es the name hyperbolic rotation for , since the e ect of is to rotate a vector x along the hyperbola of equation x 2 ; y 2 = jaj 2 ; j bj 2 by an angle that is determined by the inverse of the above hyperbolic cosine and/or sine parameters, = tanh ;1 in order to align it with the appropriate basis vector. Note also that the special case jaj = jbj corresponds to a row vector x = a b with zero hyperbolic norm since jaj 2 ; j bj 2 = 0 : It is then easy to see that there does not exist a hyperbolic rotation that will rotate x to lie along the direction of one basis vector or the other.…”

Section: A3 Fast Givens Transformationsmentioning

confidence: 99%

“…The rst array forms for the Kalman lter are called the square-root array algorithms and were devised in the late 1960's 1, 2,3 ]. These algorithms are closely related to the (so-called) QR method for solving systems of linear equations 4,5,6,7], and have the properties of better conditioning, reduced dynamical range, and the use of orthogonal transformations, which typically lead to more stable algorithms.…”

Section: Introductionmentioning

confidence: 99%

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Array Algorithms for H 2 and H ∞ Estimation

Hassibi¹,

Kailath²,

Sayed³

1999

Applied and Computational Control, Signals, and Circuits

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Currently, the preferred method for implementing H 2 estimation algorithms is what is called the array form, and includes two main families: square-root array algorithms which a r e t ypically more stable than conventional ones, and fast array algorithms which, when the system is time-invariant, typically o er an order of magnitude reduction in the computational e ort. Using our recent o b s e r v ation that H 1 ltering coincides with Kalman ltering in Krein space, in this paper we d e v elop array algorithms for H 1 ltering. These can be regarded as natural generalizations of their H 2 counterparts, and involve propagating the inde nite square-roots of the quantities of interest. The H 1 square-root and fast array algorithms bothhave the interesting feature that one does not need to explicitly check for the positivity conditions required for the existence of H 1 lters. These conditions are built into the algorithms themselves so that an H 1 estimator of the desired level exists if, and only if, the algorithms can be executed. However, since H 1 square-root algorithms predominantly use Junitary transformations, rather than the unitary transformations required in the H 2 case, further investigation is needed to determine the numerical behaviour of such algorithms.

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Classification, Parameter Estimation and State Estimation

Heijden¹,

Duin²,

Ridder³

et al. 2004

352

122

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Discrete square root filtering: A survey of current techniques

Cited by 421 publications

References 8 publications

Information Filtering and Array Algorithms for Descriptor Systems Subject to Parameter Uncertainties

Information Filtering and Array Algorithms for Descriptor Systems Subject to Parameter Uncertainties

Array Algorithms for H 2 and H ∞ Estimation

Classification, Parameter Estimation and State Estimation

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