Statistical Inference for Piecewise Affine System Identification

This short note studies the problem of piecewise affine system identification, being a special nonlinear system based on our previous contribution on it. Two different identification strategies are proposed to achieve our mission, such as centralized identification and distributed identification. More specifically, for centralized identification, the total observed input-output data are used to estimate all unknown parameter vectors simultaneously without any consideration on the classification process. But for distributed identification, after the whole observed input-output data are classified into their own right subregions, then part input-output data, belonging to the same subregion, are applied to estimate the unknown parameter vector. Whatever the centralized identification and distributed identification, the final decision is to determine the unknown parameter vector in one linear form, so the recursive least squares algorithm and its modified form with the dead zone are studied to deal with the statistical noise and bounded noise, respectively. Finally, one simulation example is used to compare the identification accuracy for our considered two identification strategies.

Zonotope Parameter Identification for Piecewise Affine System

This paper studies the identification problem for piecewise affine system, which is a special nonlinear system. As the difficulty in identifying piecewise affine system is to determine each separated region and each unknown parameter vector simultaneously, we propose a multi class classification process to determine each separated region. This multi class classification process is similar to the classical data clustering process, and the merit of our strategy is that the first order algorithm of convex optimization can be applied to achieve this classification process. Furthermore to relax the strict probabilistic description on external noise in identifying each unknown parameter vector, zonotope parameter identification algorithm is proposed to computes a set that contains the parameter vector, consistent with the measured output and the given bound of the noise. To guarantee our derived zonotope not growing unbounded with iterations, a sufficient condition for this requirement to hold may be formulated as one linear matrix inequality. Finally a numerical example confirms our theoretical results

Diffusion Logarithm-Correntropy Algorithm for Parameter Estimation in Non-Stationary Environments over Sensor Networks

This paper considers the parameter estimation problem under non-stationary environments in sensor networks. The unknown parameter vector is considered to be a time-varying sequence. To further promote estimation performance, this paper suggests a novel diffusion logarithm-correntropy algorithm for each node in the network. Such an algorithm can adopt both the logarithm operation and correntropy criterion to the estimation error. Moreover, if the error gets larger due to the non-stationary environments, the algorithm can respond immediately by taking relatively steeper steps. Thus, the proposed algorithm achieves smaller error in time. The tracking performance of the proposed logarithm-correntropy algorithm is analyzed. Finally, experiments verify the validity of the proposed algorithmic schemes, which are compared to other recent algorithms that have been proposed for parameter estimation.

Performance of Deconvolution Methods in Estimating CBOC-Modulated Signals

Multipath propagation is one of the most difficult error sources to compensate in global navigation satellite systems due to its environment-specific nature. In order to gain a better understanding of its impact on the received signal, the establishment of a theoretical performance limit can be of great assistance. In this paper, we derive the Cramer Rao lower bounds (CRLBs), where in one case, the unknown parameter vector corresponds to any of the three multipath signal parameters of carrier phase, code delay, and amplitude, and in the second case, all possible combinations of joint parameter estimation are considered. Furthermore, we study how various channel parameters affect the computed CRLBs, and we use these bounds to compare the performance of three deconvolution methods: least squares, minimum mean square error, and projection onto convex space. In all our simulations, we employ CBOC modulation, which is the one selected for future Galileo E1 signals.

Uniform Global Asymptotic Stability of Adaptively Controlled Nonlinear Systems via Strict Lyapunov Functions

We prove global uniform asymptotic stability of adaptively controlled dynamics by constructing explicit global strict Lyapunov functions. We assume a persistency of excitation condition that implies both asymptotic tracking and parameter identification. We also construct input-to-state stable Lyapunov functions under an added growth assumption on the regressor, assuming that the unknown parameter vector is subject to suitably bounded time-varying uncertainties. This quantifies the effects of uncertainties on the tracking and parameter estimation. We demonstrate our results using the Ro¨ssler system.

Effects of unstirred Disse fluid, nonequilibrium binding, and surface-mediated dissociation on hepatic removal of albumin-bound organic anions

Proceeding from the observation that organic anions bound to albumin have hepatic extraction fractions that are unexpectedly high, we have studied a distributed model that accounts for this phenomenon by invoking sites on the cell surface that catalyze the dissociation of albumin-anion complexes. The present report extends this model to include nonequilibrium binding and rate-limiting diffusion of bound anion to the cell surface. Simulation analysis of the extended model provides an unambiguous basis for interpreting the apparent intrinsic clearance of free anion. The model is fully consistent with the transport data that we obtained with rose bengal [Am. J. Physiol. 248 (Gastrointest. Liver Physiol. 11): G702-G708, 1985] but is suited to estimating only selected components of the unknown parameter vector. Uncertainties inherent in an alternate approach are discussed and illustrated.

Parametric estimators for stationary time series with missing observations

Three related estimators are considered for the parametrized spectral density of a discrete-time process X(n), n = 1, 2, · · ·, when observations are not available for all the values n = 1(1)N. Each of the estimators is obtained by maximizing a frequency domain approximation to a Gaussian likelihood, although they do not appear to be the most efficient estimators available because they do not fully utilize the information in the process a(n) which determines whether X(n) is observed or missed. One estimator, called M3, assumes that the second-order properties of a(n) are known; another, M2, lets these be known only up to an unknown parameter vector; the third, M1, requires no model for a(n). Under representative sets of conditions, which allow for both deterministic and stochastic a(n), the strong consistency and asymptotic normality of M1, M2, and M3 are established. The conditions needed for consistency when X(n) is an autoregressive moving-average process are discussed in more detail. It is also shown that in general M1 and M3 are equally efficient asymptotically and M2 is never more efficient, and may be less efficient, than M1 and M3.

Parametric estimators for stationary time series with missing observations

Three related estimators are considered for the parametrized spectral density of a discrete-time process X(n), n = 1, 2, · · ·, when observations are not available for all the values n = 1(1)N. Each of the estimators is obtained by maximizing a frequency domain approximation to a Gaussian likelihood, although they do not appear to be the most efficient estimators available because they do not fully utilize the information in the process a(n) which determines whether X(n) is observed or missed. One estimator, called M3, assumes that the second-order properties of a(n) are known; another, M2, lets these be known only up to an unknown parameter vector; the third, M1, requires no model for a(n). Under representative sets of conditions, which allow for both deterministic and stochastic a(n), the strong consistency and asymptotic normality of M1, M2, and M3 are established. The conditions needed for consistency when X(n) is an autoregressive moving-average process are discussed in more detail. It is also shown that in general M1 and M3 are equally efficient asymptotically and M2 is never more efficient, and may be less efficient, than M1 and M3.