Browsing by Author "DeBrunner, Victor Earl"

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    Parameter sensitivity, estimation and convergence: an information approach
    DeBrunner, Victor Earl (Virginia Tech, 1990-04-18)
    Convergence rates are analyzed for Recursive Prediction (Output) Error Methods (RPEM) in the identification of linear state-space systems from (noisy) impulse response data) RPEM algorithms are derived which are suitable for the identification of the parameters in arbitrary state-space structures. Deterministic and stochastic versions of these identification algorithms are presented. These two classes indicate the number of realizations used in the identification, not the presence or absence of noise. The convergence analysis uses the eigen-information of the correlation matrix (really its inverse, the Fisher information matrix) for a chosen parameterization. This analysis explains why various state-space structures have different convergence properties, 1.e., why for the same system the estimation processes corresponding to different identification structures converge at different rates. The eigen-information of the parameter information matrix relates the system sensitivity and numerical conditioning in a manner which provides insight into the identification process. The relevant eigen-information is combined in the proposed scalar convergence time constant +. One important result is that identification of the usually identified direct form II parameters (the standard ARMA parameters) does not necessarily yield the fastest parameter set convergence for the system being identified. Identification from arbitrary input is also briefly considered, as is identification when the model order is different from the “true” system order.
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    Sensitivity analysis of digital filter structures
    DeBrunner, Victor Earl (Virginia Polytechnic Institute and State University, 1986)
    A coefficient sensitivity measure for state space recursive, finite wordlength, digital filters is developed and its relationship to the filter output quantization noise power is derived. The sensitivity measure is simply the sum of the L₂ norm of all first order partials of the system function with respect to the system parameters; alternatively, the measure may be viewed as the output variance of the error system created by the inherent parameter quantization. Since the measure uses only the first order partials, it is a lower bound approximation to the output quantization noise power. During analysis, numerically unstable conditions may occur because ideal filter characteristics imply system poles which are almost on the unit circle in the z-plane; therefore, it is proposed to scale the radii of the pole and zero magnitudes. Thus, the scaled system has the same frequency information as the original system, but performs better numerically. The direct II form sensitivity, which is shown to be inversely proportional to the product of the system pole and zero distances, can be reduced by the judicious placement of added pole/zero cancellation pairs which increase the order of the system but do not change the system function.