| 1. |
- Friedlander, B, et al.
(författare)
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Extended Levinson and Chandrasekhar Equations for General Discrete-Time Linear Estimation Problems
- 1978
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE Control Systems Society. - 0018-9286 .- 1558-2523. ; 23:4, s. 653-659
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Tidskriftsartikel (refereegranskat)abstract
- Recursive algorithrms for the solution of linear least-squares estimation problems have been based mainly on state-space models. It has been known, however, that recursive Levinson-Whittle-Wiggins-Robinson (LWR) algorithms exist for stationary time-series, using only input-output information (i.e, covariance matrices). By introducing a way of classifying stochastic processes in terms of an "index of nonstationarity" we derive extended LWR algorithms for nonstationary processes We show also how adding state-space structure to the covariance matrix allows us to specialize these general results to state-space type estimation algorithms. In particular, the Chandrasekhar equations are shown to be natural descendants of the extended LWR algorithm.
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| 2. |
- Levy, Bernard, et al.
(författare)
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Fast Time-Invariant Implementations for Linear Least Squares Smoothing Filters
- 1979
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE Control Systems Society. - 0018-9286 .- 1558-2523. ; 24:5, s. 770-775
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Tidskriftsartikel (refereegranskat)abstract
- We present a new solution for the fixed interval linear least-squares smoothing of a random signal, finite dimensional or not, inadditive white noise. By using the so-called Sobolev identity of radiative transfer theory, the smoothed estimate for stationary processes is expressed entirely in terms of time-invariant causal and anticausal filtering operations; these are interpreted from a stochastic point of view as giving certain constrained (time-invariant) filtered estimates of the signal. Then by using a recently introduced notion of processes close to stationary, these results are extended in a natural way to general nonstationary processes. From a computational point of view, the representations presented here are particularly convenient, not only because time-invariant filters can be used to find the smoothed estimate, but also because a fast algorithm based on the so-called generalized Krein-Levinson recursions can be used to compute the time-invariant filters themselves.
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| 3. |
- Ljung, Lennart, 1946-
(författare)
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Analysis of Recursive Stochastic Algorithms
- 1977
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE Control Systems Society. - 0018-9286 .- 1558-2523. ; 22:4, s. 551-575
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Tidskriftsartikel (refereegranskat)abstract
- Recursive algorithms where random observations enter are studied in a fairly general framework. An important feature is that the observations my depend on previous "outputs" of the algorithm. The considered class of algorithms contains, e.g., stochastic approximation algorithm, recursive identification algorithm, and algorithms for adaptive control of linear systems. It is shown how a deterministic differential equation can be associated with the algorithm. Problems like convergence with probability one, possible convergence points and asymptotic behavior of the algorithm can all be studied in terms of this differential equation. Theorems stating the precise relationships between the differential equation and the algorithm are given as well as examples of applications of the results to problems in identification and adaptive control.
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| 4. |
- Ljung, Lennart, 1946-
(författare)
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Asymptotic Behaviour of the Extended Kalaman Filter as a Parameter Estimator for Linear Systems
- 1979
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE Control Systems Society. - 0018-9286 .- 1558-2523. ; 24:1, s. 36-50
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Tidskriftsartikel (refereegranskat)abstract
- The extended Kalman filter is an approximate filter for nonlinear systems, based on first-order linearization. Its use for the joint parameter and state estimation problem for linear systems with unknown parameters is well known and widely spread. Here a convergence analysis of this method is given. It is shown that in general, the estimates may be biased or divergent and the causes for this are displayed. Some common special cases where convergence is guaranteed are also given. The analysis gives insight into the convergence mechanisms and it is shown that with a modification of the algorithm, global convergence results can be obtained for a general case. The scheme can then be interpreted as maximization of the likelihood function for the estimation problem, or as a recursive prediction error algorithm.
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| 5. |
- Ljung, Lennart, 1946-
(författare)
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Consistency of the Least Squares Identification Method
- 1976
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE Control Systems Society. - 0018-9286 .- 1558-2523. ; 21:5, s. 779-781
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Tidskriftsartikel (refereegranskat)abstract
- Least-squares estimation of the parameters of a vector difference equation model of a dynamic system is studied. A theorem for the convergence and consistency of the least-squares estimate is given that is valid under general feedback conditions.
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| 6. |
- Ljung, Lennart, 1946-
(författare)
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Convergence Analysis of Parametric Identification Methods
- 1978
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 23:5, s. 770-783
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Tidskriftsartikel (refereegranskat)abstract
- A certain class of methods to select suitable models of dynamical stochastic systems from measured input-output data is considered. The methods are based on a comparison between the measured outputs and the outputs of a candidate model. Depending on the set of models that is used, such methods are known under a variety of names, like output-error methods, equation-error methods, maximum-likelihood methods, etc. General results are proved concerning the models that are selected asymptotically as the number of observed data tends to infinity. For these results it is not assumed that the true system necessarily can be exactly represented within the chosen set of models. In the particular case when the model set contains the system, general consistency results are obtained and commented upon. Rather than to seek an exact description of the system, it is usually more realistic to be content with a suitable approximation of the true system with reasonable complexity properties. Here, the consequences of such a viewpoint are discussed.
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| 7. |
- Ljung, Lennart, 1946-, et al.
(författare)
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Efficient Change of Initial Conditions , Dual Chandrasekhar Equations, and some Applications
- 1977
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE Control Systems Society. - 0018-9286 .- 1558-2523. ; 22:3, s. 443-447
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Tidskriftsartikel (refereegranskat)abstract
- We give simple proofs of formulas for converting linear least-squares filtered and smoothed estimates derived for one set of initial conditions to estimates valid for some other set. These are then used to study the possible advantages of first deliberately mischoosing the initial conditions so as to allow computational benefits to be obtained by using certain fast algorithms. In the course of this application we also obtain a new "dual" set of Chandrasekhar equations that provide a fast algorithm for fixed-point smoothing.
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| 8. |
- Ljung, Lennart, 1946-
(författare)
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On Positive Real Transfer Functions and the Convergence of some Recursive Schemes
- 1977
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE Control Systems Society. - 0018-9286 .- 1558-2523. ; 22:4, s. 539-551
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Tidskriftsartikel (refereegranskat)abstract
- The convergence with probability one of a recently suggested recursive identification method by Landau is investigated. The positive realness of a certain transfer function is shown to play a crucial role, both for the proof of convergence and for convergence itself. A completely analogous analysis can be performed also for the extended least squares method and for the self-tuning regulator of Åström and Wittenmark. Explicit conditions for convergence of all these schemes are given. A more general structure is also discussed, as well as relations to other recursive algorithms.
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| 9. |
- Söderström, Torsten, et al.
(författare)
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Identifiability Conditions for Linear Multivariable Systems Operating under Feedback
- 1976
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE Control Systems Society. - 0018-9286 .- 1558-2523. ; 21:6, s. 837-840
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Tidskriftsartikel (refereegranskat)abstract
- The possibility of estimating the parameters of a dynamic system when it is operating in closed loop is examined. Earlier considered ways of designing regulators to achieve desired identifiability properties are unified and generalized. The result of the analysis of this short paper gives a simple criterion, which contains earlier known conditions as simple special cases.
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| 10. |
- Wittenmark, Björn
(författare)
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A self-tuning predictor
- 1974
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286. ; 19:6, s. 848-851
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Tidskriftsartikel (refereegranskat)abstract
- An adaptive predictor for discrete time stochastic processes with constant but unknown parameters is described. The predictor which in real time tunes its parameters using the method of least squares is called a self-tuning predictor. The predictor has attractive asymptotic properties. If the parameter estimation converges and if the predictor contains parameters enough, then it will converge to the minimum square error predictor that could be obtained if the parameters of the process were known. The computations to be carried out at each sampling interval are very moderate and the algorithm is well suited for real-time applications. The self-tuning predictor can be used to predict processes which contain trends or periodic disturbances. Further, the algorithm can easily be modified in order to make it possible to predict processes with slowly time-varying parameters.
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