| 1. |
- Ljung, Stefan, et al.
(författare)
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Error Propagation Properties of Recursive Least Squares Adaptation Algorithms
- 1985
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 21:2, s. 157-167
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Tidskriftsartikel (refereegranskat)abstract
- The numerical properties of implementations of the recursive least-squares identification algorithm are of great importance for their continuous use in various adaptive schemes. Here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates. It is shown that conventional LS algorithms, including Bierman's UD-factorization algorithm are exponentially stable with respect to such errors, i.e. the effect of the error decays exponentially. The base of the decay is equal to the forgetting factor. The same is true for fast lattice algorithms. The fast least-squares algorithm, sometimes known as the ‘fast Kalman algorithm’ is however shown to be unstable with respect to such errors.
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| 2. |
- Ljung, Stefan, et al.
(författare)
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Fast Numerical Solution of Fredholm Integral Equations with Stationary Kernels
- 1982
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Ingår i: BIT Numerical Mathematics. - : Kluwer Academic Publishers. - 0006-3835 .- 1572-9125. ; 22:1, s. 54-72
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Tidskriftsartikel (refereegranskat)abstract
- A fast recursive matrix method for the numerical solution of Fredholm integral equations with stationary kernels is derived. IfN denotes the number of nodal points, the complexity of the algorithm isO(N 2), which should be compared toO(N 3) for conventional algorithms for solving such problems. The method is related to fast algorithms for inverting Toeplitz matrices.Applications to equations of the first and second kind as well as miscellaneous problems are discussed and illustrated with numerical examples. These show that the theoretical improvement in efficiency is indeed obtained, and that no problems with numerical stability or accuracy are encountered.
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| 3. |
- Akcay, H., et al.
(författare)
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On the choice of norms in system identification
- 1996
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Ingår i: IEEE Transactions on Automatic Control. - Linköping : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286. ; 41:9, s. 1367-1372
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C > 0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all ℓp-norms, p ≀ 2 < ∞ for F(C). ©1996 IEEE.
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| 4. |
- Bauer, Dietmar, et al.
(författare)
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Some Facts about the Choice of the Weighting Matrices in Larimore Type of Subspace Algorithms
- 2002
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 38:5, s. 763-773
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Tidskriftsartikel (refereegranskat)abstract
- In this paper the effect of some weighting matrices on the asymptotic variance of the estimates of linear discrete time state space systems estimated using subspace methods is investigated. The analysis deals with systems with white or without observed inputs and refers to the Larimore type of subspace procedures. The main result expresses the asymptotic variance of the system matrix estimates in canonical form as a function of some of the user choices, clarifying the question on how to choose them optimally. It is shown, that the CCA weighting scheme leads to optimal accuracy. The expressions for the asymptotic variance can be implemented more efficiently as compared to the ones previously published.
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| 5. |
- Bergman, Niclas, et al.
(författare)
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Terrain Navigation using Bayesian Statistics
- 1999
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Ingår i: IEEE Control Systems. - : Institute of Electrical and Electronics Engineers (IEEE). - 1066-033X .- 1941-000X. ; 19:3, s. 33-40
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Tidskriftsartikel (refereegranskat)abstract
- The performance of terrain-aided navigation of aircraft depends on the size of the terrain gradient in the area. The point-mass filter (PMF) described in this work yields an approximate Bayesian solution that is well suited for the unstructured nonlinear estimation problem in terrain navigation. It recursively propagates a density function of the aircraft position. The shape of the point-mass density reflects the estimate quality; this information is crucial in navigation applications, where estimates from different sources often are fused in a central filter. Monte Carlo simulations show that the approximation can reach the optimal performance, and realistic simulations show that the navigation performance is very high compared with other algorithms and that the point-mass filter solves the recursive estimation problem for all the types of terrain covered in the test. The main advantages of the PMF is that it works for many kinds of nonlinearities and many kinds of noise and prior distributions. The mesh support and resolution are automatically adjusted and controlled using a few intuitive design parameters. The main disadvantage is that it cannot solve estimation problems of very high dimension since the computational complexity of the algorithm increases drastically with the dimension of the state space. The implementation used in this work shows real-time performance for 2D and in some cases 3D models, but higher state dimensions are usually intractable.
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| 6. |
- Björklund, Svante, et al.
(författare)
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An Improved Phase Method for Time-Delay Estimation
- 2009
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 45:10, s. 2467-2470
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Tidskriftsartikel (refereegranskat)abstract
- A promising method for estimation of the time-delay in continuous-time linear dynamical systems uses the phase of the all-pass part of a discrete-time model of the system. We have discovered that this method can sometimes fail totally and we suggest a method for avoiding such failures.
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| 7. |
- Chen, Tianshi, et al.
(författare)
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Decentralized Particle Filter with Arbitrary State Decomposition
- 2011
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Ingår i: IEEE Transactions on Signal Processing. - : IEEE Signal Processing Society. - 1053-587X .- 1941-0476. ; 59:2, s. 465-478
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, a new particle filter (PF) which we refer to as the decentralized PF (DPF) is proposed. By first decomposing the state into two parts, the DPF splits the filtering problem into two nested subproblems and then handles the two nested subproblems using PFs. The DPF has the advantage over the regular PF that the DPF can increase the level of parallelism of the PF. In particular, part of the resampling in the DPF bears a parallel structure and can thus be implemented in parallel. The parallel structure of the DPF is created by decomposing the state space, differing from the parallel structure of the distributed PFs which is created by dividing the sample space. This difference results in a couple of unique features of the DPF in contrast with the existing distributed PFs. Simulation results of two examples indicate that the DPF has a potential to achieve in a shorter execution time the same level of performance as the regular PF.
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| 8. |
- Chen, Tianshi, et al.
(författare)
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On the Estimation of Transfer Functions, Regularizations and Gaussian Processes - Revisited
- 2012
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 48:8, s. 1525-1535
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Tidskriftsartikel (refereegranskat)abstract
- Intrigued by some recent results on impulse response estimation by kernel and nonparametric techniques, we revisit the old problem of transfer function estimation from input-output measurements. We formulate a classical regularization approach, focused on finite impulse response (FIR) models, and find that regularization is necessary to cope with the high variance problem. This basic, regularized least squares approach is then a focal point for interpreting other techniques, like Bayesian inference and Gaussian process regression. The main issue is how to determine a suitable regularization matrix (Bayesian prior or kernel). Several regularization matrices are provided and numerically evaluated on a data bank of test systems and data sets. Our findings based on the data bank are as follows. The classical regularization approach with carefully chosen regularization matrices shows slightly better accuracy and clearly better robustness in estimating the impulse response than the standard approach - the prediction error method/maximum likelihood (PEM/ML) approach. If the goal is to estimate a model of given order as well as possible, a low order model is often better estimated by the PEM/ML approach, and a higher order model is often better estimated by model reduction on a high order regularized FIR model estimated with careful regularization. Moreover, an optimal regularization matrix that minimizes the mean square error matrix is derived and studied. The importance of this result lies in that it gives the theoretical upper bound on the accuracy that can be achieved for this classical regularization approach.
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| 9. |
- Enqvist, Martin, 1976-, et al.
(författare)
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Linear Approximations of Nonlinear FIR Systems for Separable Input Processes
- 2005
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Ingår i: Automatica. - Linköping : Elsevier. - 0005-1098 .- 1873-2836. ; 41:3, s. 459-473
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Tidskriftsartikel (refereegranskat)abstract
- Nonlinear systems can be approximated by linear time-invariant (LTI) models in-many ways. Here, LTI models that are optimal approximations in the mean-square error sense are analyzed. A necessary and sufficient condition on the input signal for the optimal LTI approximation of an arbitrary nonlinear finite impulse response (NFIR) system to be a linear finite impulse response (FIR) model is presented. This condition says that the in ut should be separable of a certain order, i.e., that certain conditional expectations should be,P linear. For the special case of Gaussian input signals, this condition is closely related to a generalized version of Bussgang's classic theorem about static nonlinearities. It is shown that this generalized theorem can be used for structure identification and for the identification of generalized Wiener-Hammerstein systems.
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| 10. |
- Fnaiech, Farhat, et al.
(författare)
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Recursive Identification of Bilinear Systems
- 1987
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Ingår i: International Journal of Control. - : Taylor & Francis. - 0020-7179 .- 1366-5820. ; 45:2, s. 453-470
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Tidskriftsartikel (refereegranskat)abstract
- Methods of identifying bilinear systems from recorded input-output data are discussed in this article. A short survey of the existing literature on the topic is given. ‘Standard’ methods from linear systems identification, such as least squares, extended least squares, recursive prediction error and instrumental variable methods are transferred to bilinear, input-output model structures and tested in simulation. Special attention is paid to problems of stabilizing the model predictor, and it is shown how a time-varying Kalman filter and associated parameter estimation algorithm can deal with this problem.
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