The forward-backward averaging technique applied to TLS-ESPRITprocessing

Certain array geometries greatly simplify and enhance high resolution array processing. Two techniques are used-the ESPRIT algorithm, which employs two shifted but otherwise identical subarrays, and forward-backward averaging, which can be applied to axis-symmetrical arrays. The former has been shown to provide an efficient solution to bearing estimation while the latter incorporates the a priori knowledge about the symmetry, effectively increasing the number of data vectors available and decorrelating coherent or highly correlated signals. A combination of the two techniques implies a special array geometry that includes uniformly spaced linear arrays. The resulting algorithm yields parameter estimates that are constrained on the unit circle, satisfying the postulated data model provided merely that the arguments of these estimates are distinct. However, if the arguments of some parameter estimates coincide in a given scenario, the ESPRIT algorithm does not yield different results for distinct signals and these estimates can be rejected. Perhaps the most significant advantage of combining forward-backward averaging with ESPRIT parameter estimation is the substantial reduction in computational complexity that can be achieved. Based on the centro-Hermitian property of the data and noise covariance matrices, the computational complexity of the ESPRIT solution is reduced almost by a factor of four and the algorithm can be formulated entirely over the field of real numbers     

Statistical Measures of Parameter Estimates from Models Fit to Respiratory Impedance Data: Emphasis on Joint Vanabilities

To describe respiratory mechanical impedance data, many investigators have proposed electromechanical models and then fit them to data using formal parameter estimation techniques. This approach has resulted in confusion as to how to interpret the resulting estimated values, and hence as to which model is most appropriate. A key cause of this confusion is that most studies rely on the quality of fit between the model and the data as the only measure of model validity rather than performing adequate statistical analysis of the parameter estimates themselves. This paper describes several statistical measures that should be applied to parameter estimates obtained from forced oscillation data. Specifically, we describe standard errors of the parameter estimates, confidence intervals for each parameter estimate, and the joint confidence region for the parameters. Much emphasis is placed on the joint confidence region which, unlike the interval, allows for simultaneous variations in parameters. The measures are applied to an often used six-element model for respiratory impedance data of dogs from 4 to 64 Hz. This application indicated that even when fitting data over this frequency range, parameter estimates are not well defined and the parameter estimated with least accuracy is airway resistance.     

A combined order selection and parameter estimation algorithm forundamped exponentials

We propose an approximate maximum likelihood parameter estimation algorithm, combined with a model order estimator for superimposed undamped exponentials in noise. The algorithm combines the robustness of Fourier-based estimators and the high-resolution capabilities of parametric methods. We use a combination of a Wald (1945) statistic and a MAP test for order selection and initialize an iterative maximum likelihood descent algorithm recursively based on estimates at higher candidate model orders. Experiments using simulated data and synthetic radar data demonstrate improved performance over MDL, MAP, and AIC in places of practical interest     

Maximum likelihood estimation of Burr XII distribution parameters under Type II censoring

The mathematical theory for the point estimation of the parameters of the Burr Type XII distribution by maximum likelihood (ML) is developed for Type II censored samples. Also derived are necessary and sufficient conditions on the sample data that guarantee the existence, uniqueness and finiteness of the ML parameter estimates for all possible permissible parameter combinations. The asymptotic theory of ML is invoked to obtain approximate confidence intervals for the ML parameter estimates. An application to reliability data arising in a life test experiment is discussed.     

Uniqueness of maximum likelihood estimators of the 2-parameterWeibull distribution

We present a simple statistic, calculated from either complete failure data or from right-censored data of type-I or -II. It is useful for understanding the behavior of the parameter maximum likelihood estimates (MLE) of a 2-parameter Weibull distribution. The statistic is based on the logarithms of the failure data and can be interpreted as a measure of variation in the data. This statistic provides: (a) simple lower bounds on the parameter MLE, and (b) a quick approximation for parameter estimates that can serve as starting points for iterative MLE routines; it can be used to show that the MLE for the 2-parameter Weibull distribution are unique     

Parameter estimation for the 3-parameter Gamma distribution usingthe continuation method

This paper shows a maximum-likelihood (ML) parameter estimation algorithm for the 3-parameter Gamma distribution. The algorithm, a combination of the continuation method and the extended Gamma distribution model, can find the local ML estimates of the parameters without a careful selection of the starting point in the iterative process. This algorithm is more efficient than previous algorithms, and can find the multiple local ML estimates     

Confidence bounds on respiratory mechanical properties estimatedfrom transfer versus input impedance in humans versus dogs

Using parameters typical of a dog, we have shown that estimates for the parameters in the six-element model of Dubois et al. would be very unreliable if either input (Z(in)) or transfer (Ztr) data from only 2-32 Hz were fit. It has subsequently been shown that this model is not appropriate for human Z(in) from 2-320 Hz. However, several studies have continued to apply the model to human Ztr data from only 2-32 Hz. In this study a sensitivity analysis is used to determine whether and why the six-element model could be applicable to lower frequency (less than 64 Hz) Ztr data in humans, but not Z(in) data over any frequency range. We first predicted the joint parameter uncertainty bounds assuming a fit to either 2-32 Hz Z(in) or Ztr data created from literature based mean parameter values. Consistent with previous studies, we predicted that the estimates will be very unreliable if obtained from Z(in) data for humans or dogs, or from Ztr data from dogs. Surprisingly, however, the reliability of several parameter estimates from human Ztr data from only 2-32 Hz are reasonable. We next evaluated the variability in 2-64 Hz based Ztr parameter estimates by comparing experimental variability in two healthy human subjects (over 10 and 13 trials) to theoretical and Monte Carlo numerical predictions based on a single trial. Again, the Ztr parameters were reliable. A simulation study was used to describe the reasons for enhanced reliability when using human Ztr data. It is shown that this reliability is largely dependent on alveolar gas compressibility, Cg.(ABSTRACT TRUNCATED AT 250 WORDS)     

Asymptotically convergent modified recursive least-squares with data-dependent updating and forgetting factor for systems with bounded noise

Continual updating of estimates required by most recursive estimation schemes often involves redundant usage of information and may result in system instabilities in the presence of bounded output disturbances. An algorithm which eliminates these difficulties is investigated. Based on a set theoretic assumption, the algorithm yields modified least-squares estimates with a forgetting factor. It updates the estimates selectively depending on whether the observed data contain sufficient information. The information evaluation required at each step involves very simple computations. In addition, the parameter estimates are shown to converge asymptotically, at an exponential rate, to a region around the true parameter.     

Estimation problems in rate-augmented learning curves

In situations where production rate is variable, the learning curve can provide unreliable results. One proposed solution to the “production rate” problem is to multiplicatively augment the learning curve with a production rate explanatory variable, while widely used by cost analysts, the rate-augmented learning curve has not proved reliable. It has been assumed, but not demonstrated, that data and measurement problems lead to unreliable parameter estimates. In this paper we demonstrate that the parameter estimates are a function of the units in which the cost and delivery data are measured; hence, the estimates are always arbitrary. We propose a procedure for obtaining meaningful estimates, but it requires assigning weights to the cost and delivery time data. We use a simple dynamic program to demonstrate that proper estimates of sign and magnitude can only be obtained when the learning and rate equations are estimated simultaneously and the sum-of-squares for the rate equation receives a higher weighting in the estimation. These results have major implications for cost analysts. Since accurate parameter estimation requires weighting, estimation by unweighted ordinary least squares is a futile effort     

Linear Homeomorphic Model for Human Movement

The parameter values for this model are specific to the human eye movement systems; however, the form of the model is applicable to other neurological motor control systems. The muscle length-tension diagram was modeled with an ideal spring. The muscle force-velocity relationship was linearized in a manner that produced a linear model. Initial parameter estimates were based on physiological data, human when possible. Then a function minimization program was used to fine tune model parameters. These parameter values were compared to the original physiological data to ensure that they were within the range of variability of the data. The antagonist dashpot value was selected to minimize the mean squared error between human and model responses; the value produced suggested a unique simplified representation for the original physiological data. The parameter estimation routine was applied to make the model match atypical human eye movements; these simulations suggested that glissades in normals are caused by pulsewidth, not pulse height errors.     

Endothelial cell electrical impedance parameter artifacts produced by a gold electrode and phase sensitive detection

Frequency dependent cellular micro-impedance estimates obtained from a gold two-electrode configuration using phase sensitive detection have become increasingly used to evaluate cellular barrier model parameters. The results of this study show that cellular barrier function parameter estimates optimized using measurements obtained from this biosensor are highly susceptible to both time dependent and systematic instrumental artifacts. Based on a power spectral analysis of experimentally measured microelectrode voltages, synchronous, 60 Hz, and white Gaussian noise were identified as the most significant time dependent instrumental artifacts. The reduction of these artifacts using digital filtering produced a corresponding reduction in the optimized model parameter fluctuations. Using a series of instrumental circuit models, this study also shows that electrode impedance voltage divider effects and circuit capacitances can produce systematic deviations in cellular barrier function parameter estimates. Although the implementation of an active current source reduced the voltage divider effects, artifacts produced by coaxial cable and other circuit capacitive elements at frequencies exceeding 1 kHz still remained. Reducing time dependent instrumental fluctuations and systematic errors produced a significant reduction in cellular model barrier parameter errors and improved the model fit to experimental data.     

Data Filtering-Based Multi-innovation Stochastic Gradient Algorithm for Nonlinear Output Error Autoregressive Systems

This paper discusses the parameter estimation problems of nonlinear output error autoregressive systems and presents a data filtering-based multi-innovation stochastic gradient algorithm for improving the parameter estimation accuracy of the stochastic gradient algorithm by combining the multi-innovation identification theory and the data filtering technique. The proposed algorithm is effective and can generate highly accurate parameter estimates compared with the multi-innovation stochastic gradient algorithm. The simulation results confirm this conclusion.     

Parameter Estipiates in a Five-Element Respiratory Mechanical Model

Using four sets of forced random noise impedance data from each of five normal subjects and five patients with obstructuve lung disease, we computed parameter estimates for a three-element series model and a five-element parallel compartment model. For normal subjects, the five-element model provided no better fit to the impedance data than did the simple series model. Estimates obtained from normal subjects using this three-element model were reasonable and reproducible within 25 percent. For all subjects with lung disease, the five-element model provided a significantly (p 0.05) better fit than the three-element model. Estimates for parameters representing central inertance and resistance, airway compliance, and peripheral resistance were reasonable and reproducible-within 18 percent. However, estimates for the compliance of the lung and chest wall were more variable since measured impedance appeared to be insensitive to this parameter in the frequency range used.     

一种基于多模板的超宽带信道估计算法

该文针对码片率抽头间隔的脉冲超宽带(IR-UWB)系统离散信道,提出一种基于帧(frame)级采样速率的多模板信道估计算法。在该算法中引入了若干个复合信道参数,每个复合信道参数都是几个独立信道参数的线性组合。利用极大似然准则和从多个模板中获得的帧级采样数据,可以先获得所有复合信道参数的极大似然估计值。然后联合由不同模板得到的复合信道参数估计值,得到每个独立的信道参数的极大似然估计。通过仿真,验证了该方法的可行性。     

Estimating lung mechanics of dogs with unilateral lung injury

Extended least-squares algorithms using transpulmonary pressure and airway flow data from ventilatory waveforms were studied for their ability to track parameters of one- and two-compartment models of lung mechanics. A recursive extended least-squares algorithm with discounted measures estimated parameters of discrete-time models during synchronized intermittent mandatory ventilation. In tests on seven dogs developing oleic acid-induced unilateral hemorrhagic pulmonary edema, the one-compartment estimator responded rapidly and appropriately to changes in mechanics: compliance fell to 0.55 +/- 0.15 of its initial value and resistance rose by a factor of 1.8 +/- 0.5 in 3 h following injection of oleic acid. One-compartment parameter estimates revealed a difference between the airway resistance of inspiration and expiration. Two-compartment estimates were seldom physiologically plausible. The difference between inspiratory and expiratory resistance may have caused the two-compartment estimator to fail when applied to data from the entire respiratory cycle; when only expiratory data were used for estimation, the two-compartment estimates were meaningful. These estimates demonstrated increasing lung inhomogeneity after oleic acid was injected; at the end of 3 h, the ratio of the time constants of the two compartments ranged from 5 to 20 in six of the seven dogs. We conclude that the one- and two-compartment estimates may be combined to provide a meaningful assessment of lung mechanics.     

Online system identification using matrix pseudoinverse

Recursive algorithms for online identification of discrete-time systems have been described. These provide minimum-norm estimates of the parameter vector when insufficient data are available, and least-squares estimates with sufficient data. Matrix inversion is not required; nor is the a priori knowledge of noise statistics or probability densities of the parameters.     

Minimum test chip sample size selection for characterizing process parameters

A method for determining a test-chip sample size to estimate effectively the electrical parameter distributions on an integrated circuit wafer is presented. This method gives relations among sample size and the figure of merit for four statistical techniques (trimmed mean, biweighted mean, median, and arithmetic mean) by which estimates are calculated. To demonstrate its use, the method has been applied to the evaluation of a CMOS fabrication process. Measurements on wafers completely patterned with identical test chips were used to determine actual parameter distributions for an entire wafer (true parameter values). Estimates of true parameters were determined using a site-selection plan which is representative of sampling plans used in industry. The four statistical techniques were used to compute estimates for electrical parameters and their respective figures of merit. These estimates were compared with the true parameter values determined from testing all test chips on the wafer.     

Maximum likelihood estimation of K distribution parameters for SARdata

The K distribution has proven to be a promising and useful model for backscattering statistics in synthetic aperture radar (SAR) imagery. However, most studies to date have relied on a method of moments technique involving second and fourth moments to estimate the parameters of the K distribution. The variance of these parameter estimates is large in cases where the sample size is small and/or the true distribution of backscattered amplitude is highly non-Rayleigh. The present authors apply a maximum likelihood estimation method directly to the K distribution. They consider the situation for single-look SAR data as well as a simplified model for multilook data. They investigate the accuracy and uncertainties in maximum likelihood parameter estimates as functions of sample size and the parameters themselves. They also compare their results with those from a new method given by Raghavan (1991) and from a nonstandard method of moments technique; maximum likelihood parameter estimates prove to be at least as accurate as those from the other estimators in all cases tested, and are more accurate in most cases. Finally, they compare the simplified multilook model with nominally four-look SAR data acquired by the Jet Propulsion Laboratory AIRSAR over sea ice in the Beaufort Sea during March 1988. They find that the model fits data from both first-year and multiyear ice well and that backscattering statistics from each ice type are moderately non-Rayleigh. They note that the distributions for the data set differ too little between ice types to allow discrimination based on differing distribution parameters     

Optimal selection of frequencies for estimating parameters fromrespiratory impedance data

The goal of this study was to evaluate whether optimal selection of a reduced number of frequency points would still result in statistically reliable parameter estimates. A direct-search technique is described which optimally places a small number of frequencies so that the volume of the parameter joint confidence region is minimized. The accuracy of the parameters estimated from a full data set (50 evenly spaced points) is compared to that achievable with optimal designs using 20, 10, or 5 frequency points. The techniques were applied to parameters obtained from healthy dogs and humans. Results indicated that with ten optimally chosen frequencies most parameter uncertainties are only slightly higher than that achievable with 50 frequencies while parameter uncertainties increase greatly when only five optimal points are used. This suggests that the technique of forced oscillation permits identification of the distribution of respiratory system properties without the need for extensive data acquisition     

A new model for step-stress testing

The mathematical intractability of the Weibull cumulative exposure model (CE-M) has impeded the development of statistical procedures for step-stress accelerated life tests. Our new model (KH-M) is based on a time transformation of the exponential CE-M. The time-transformation enables the reliability engineer to use known results for multiple-step, multiple-stress models that have been developed for the exponential step-stress model. KH-M has a realistically appealing proportional-hazard property. It is as flexible as the Weibull CE-M for fitting data, but its mathematical form makes it easier to obtain parameter estimates and standard deviations. Maximum likelihood estimates are given for test plans with unknown shape parameter. The mathematical similarity to the constant-stress Weibull model is shown. Chi-square goodness of fit tests are performed on simulated data to compare the fit of the models