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The stability of time-varying autoregressive (AR) models is an important issue in such applications as time-varying spectrum estimation and electroencephalography simulation and estimation. In some cases, such as time-varying spectrum estimation, the models that exhibit roots near unit moduli are difficult to use. Thus a tighter stability condition such as stability with a positive margin is needed. A time-varying AR model is stable with a positive margin if the moduli of the roots of the time-varying characteristic polynomial are somewhat less than unity for every time instant. Recently, a new method for the estimation of the time-varying AR models was introduced. This method is based on the interpretation of the underdetermined time-varying prediction equations as an ill-posed inverse problem that is solved by Tikhonov regularization. The method is referred to as the deterministic regression smoothness priors (DRSP) scheme. In this paper, a stabilization method in which the DRSP scheme is augmented with nonlinear stability constrainst is proposed. The problem is formulated so that stability with a positive margin can also be achieved. The problem is solved iteratively with an exterior point algorithm. The performance of the algorithm is studied with a simulation. It is shown that the proposed approach is well suited to stable modeling of signals containing narrowband transitions.

An alternative for root tracking algorithms that compute the roots explicitly is presented. The proposed method is first based on using any preferred algorithm to track the transversal model parameters and subsequently on the second-order perturbation expansion for the associated companion matrix to approximate a single root of interest. An application to EEG signal analysis is discussed and it is shown that the second-order approximation yields root location estimates that are more accurate than the first-order approximation.

Knowledge of the central-axis depth-dose curve and the dose profiles of a radiotherapy treatment unit are essential for setting up an external system for planning radiotherapy treatment. Estimates for these are usually found with the aid of a measurement probe with which the dose is measured at equally spaced measurement points. In this paper a strategy for selecting the measurement points for determination of the depth-dose curve and dose profile is proposed. The performance of the method is evaluated with real 6 MV photon depth-dose data and real 18 MV dose-profile data. The studies show that the proposed method allows the estimation of the depth-dose curve with adequate accuracy typically from 10 - 14 measurements at this energy instead of approximately 120 measurements, which is a common number of measurements. Thus the measurements protocol decreases about tenfold the number of measurements required. The studies also show that a fivefold decrease can be achieved in the dose-profile measurement.

The stability of autoregressive (AR) models is an important issue in many applications such as spectral estimation, simulation of EEG, and synthesis of speech. There are methods for AR parameter estimation that guarantee the stability of the model, that is, all roots of the characteristic polynomial of the model have moduli less than unity. However, in some situations, such as EEG simulation, the models that exhibit roots with almost unit moduli are difficult to use. In this paper we propose a method for estimating AR models that guarantees hyperstability, that is, the moduli of the roots are less than or equal to some arbitrary positive number. The method is based on an iterative minimization scheme in which the associated nonlinear constraints are linearized sequentially.

This paper presents a framework for parametrization, identification, and synthesis of brief time-varying sounds. The proposed scheme is based on a frequency-warped modification of Grenier's (1983) time-varying lattice algorithm. A new algorithm, which gives the optimal time-varying model for an ensemble of similar sounds, is introduced.

A method for estimation of the change point in event related desynchronization tests is presented. The method is based on tracking of a single system pole of the time-varying ARMA model. The pole is approximated using perturbation theory.

A method for the stabilization of time-varying autoregressive models is proposed. The method is based on the smoothness priors regularized prediction equations with nonlinear stability constraints. The problem is solved iteratively with a Gauss-Newton type algorithm in which the original constrained problem is approximated with a sequence of unconstrained problems by using appropriate penalty functions. The performance of the algorithm is studied with a simulation.

In this paper we propose a method for the estimation of time-varying autoregressive (TVAR) processes. The approach is essentially to regularize the heavily underdetermined unconstrained prediction equations with a smoothness priors type side constraint. The implementation of nonhomogeneous smoothness properties is straightforward. The method is compared to the usual deterministic regression approach (TVAR) in which the coefficient evolutions are constrained to a subspace. It is shown that the typical transient oscillations of TVAR can be avoided with the proposed method.

The inverse problem of the depth dose curve is formulated and a proposition for its solution is presented. The solution is based on the approximation of the observation equation with a numerical quadrature operator and the regularization of this inverse problem with a smoothness side constraint. The problem formulation is applicable for both the electron and the photon depth dose curve estimation. Moreover, the method is equivalent for, for example, all energies, field sizes and source-to-phantom distances. Simulations show that the estimation error is smaller with the proposed method than with direct linear interpolation. The main result of the paper, however, is the formulation of the problem that allows feasible extensions and modifications for different measurement situations.

The stability of time-varying autoregressive (TVAR) models is an important issue in many applications such as time-varying spectral estimation, EEG simulation and analysis, and time-varying linear prediction coding (TVLPC). For stationary AR models there are methods that guarantee stability, but the for nonadaptive time-varying approaches there are no such methods. On the other hand, in some situations, such as in EEG analysis, the models that temporarily exhibit roots with almost unit moduli are difficult to use. Thus we may need a tighter stability condition such as stability with margin 1??. In this paper we propose a method for the estimation of TVAR models that guarantees stability with margin 1??, that is, the moduli of the roots of the time-varying characteristic polynomial are less than or equal to some arbitrary positive number ? for every time instant. The model class is the Subba Rao-Liporace class, in which the time-varying coefficients are constrained to a subspace of the coefficient time evolutions. The method is based on sequential linearization of the associated nonlinear constraints and the subsequent use of a Gauss-Newton-type algorithm. The method is also applied to a simulated autoregressive process.

A method for the stabilization of stationary and time-varying autoregressive models is presented. The method is based on the hyperstability constrained LS-problem with nonlinear constraints. The problems are solved iteratively with Gauss-Newton type algorithm that sequentially linearizes the constraints. The proposed method is applied to simulated data in the stationary case and to real EEG data in the time-varying case.