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At least 19 records

Correlation autoregressive processes with application to helicopter noise

This paper introduces a new class of random processes X(t), the autocorrelations R sub x (t1, t2) of which satisfy a linear relation for all t1 and t2 in some interval of the time axis. Such random processes are denoted as 'correlation-autoregressive'. This class is shown to include the familiar stationary and periodically correlated processes as well as many other, both harmonizable and nonharmonizable, nonstationary processes. When a process is correlation-autoregressive for all times and harmonizable, its two-dimensional power spectral density is shown to take a particularly simple form. The relationship of such processes to the class of stationary processes is examined. In addition, the application of such processes in the analysis of typical helicopter noise signals is described.

Hardin, J. C.↗

The effects of correlation on goodness of fit

Autocorrelated normal random variates were generated via computer and the effects of various levels of correlation on goodness of fit problems were studied. The results are useful in determining the distribution or estimating the parameters of populations that correlate observations such as wind speeds and temperature. The model used to generate the autocorrelated data is an autoregressive process of order 1. The Kolmogorov-Smirnov and chi-square statistics are used in the analysis. It was observed in the simulation that high positive correlations tend to shift the sample mean away from the population mean and negative correlations tend to shift the sample mean towards the population mean. In many cases, it was observed that positive and negative correlations tend to decrease the standard deviation. However, since this did not occur in all cases, no definite conclusion can be made regarding the standard deviation. Since the autoregressive process is a linear transformation, it is not surprising that normality was preserved. However, a possible extension of this problem could be to generate non-normal data and observe how the distribution is affected by correlation. Another extension might utilize another model such as autoregressive of order k or a moving average process of order k.

Kitchens, L. J.↗

Linear and nonlinear trending and prediction for AVHRR time series data

The variability of AVHRR calibration coefficient in time was analyzed using algorithms of linear and non-linear time series analysis. Specifically we have used the spline trend modeling, autoregressive process analysis, incremental neural network learning algorithm and redundancy functional testing. The analysis performed on available AVHRR data sets revealed that (1) the calibration data have nonlinear dependencies, (2) the calibration data depend strongly on the target temperature, (3) both calibration coefficients and the temperature time series can be modeled, in the first approximation, as autonomous dynamical systems, (4) the high frequency residuals of the analyzed data sets can be best modeled as an autoregressive process of the 10th degree. We have dealt with a nonlinear identification problem and the problem of noise filtering (data smoothing). The system identification and filtering are significant problems for AVHRR data sets. The algorithms outlined in this study can be used for the future EOS missions. Prediction and smoothing algorithms for time series of calibration data provide a functional characterization of the data. Those algorithms can be particularly useful when calibration data are incomplete or sparse.

Smid, J.↗

Methods and software for cosmic ray scintillation studies

The principal instrument used in cosmic ray scintillation studies is the spectra constructed from intensive observation. This method has its drawbacks in that the statistical characteristics of the process undergo essential reconstruction, i.e., the process becomes nonstationary from the viewpoint of such phenomena as Forbush decrease and during solar flares. The software used to process the above includes the direct Fourier transform and its modifications, autoregressive processes, and instantaneous spectrum methods. Used in various combinations, they prove helpful in handling the time series.

Gulinsky, O. V.↗

Real-time processing of radar return on a parallel computer

NASA is working with the FAA to demonstrate the feasibility of pulse Doppler radar as a candidate airborne sensor to detect low altitude windshears. The need to provide the pilot with timely information about possible hazards has motivated a demand for real-time processing of a radar return. Investigated here is parallel processing as a means of accommodating the high data rates required. A PC based parallel computer, called the transputer, is used to investigate issues in real time concurrent processing of radar signals. A transputer network is made up of an array of single instruction stream processors that can be networked in a variety of ways. They are easily reconfigured and software development is largely independent of the particular network topology. The performance of the transputer is evaluated in light of the computational requirements. A number of algorithms have been implemented on the transputers in OCCAM, a language specially designed for parallel processing. These include signal processing algorithms such as the Fast Fourier Transform (FFT), pulse-pair, and autoregressive modelling, as well as routing software to support concurrency. The most computationally intensive task is estimating the spectrum. Two approaches have been taken on this problem, the first and most conventional of which is to use the FFT. By using table look-ups for the basis function and other optimizing techniques, an algorithm has been developed that is sufficient for real time. The other approach is to model the signal as an autoregressive process and estimate the spectrum based on the model coefficients. This technique is attractive because it does not suffer from the spectral leakage problem inherent in the FFT. Benchmark tests indicate that autoregressive modeling is feasible in real time.

Aalfs, David D.↗

Adaptive clutter rejection filters for airborne Doppler weather radar applied to the detection of low altitude windshear

An optimum adaptive clutter rejection filter for use with airborne Doppler weather radar is presented. The radar system is being designed to operate at low-altitudes for the detection of windshear in an airport terminal area where ground clutter returns may mask the weather return. The coefficients of the adaptive clutter rejection filter are obtained using a complex form of a square root normalized recursive least squares lattice estimation algorithm which models the clutter return data as an autoregressive process. The normalized lattice structure implementation of the adaptive modeling process for determining the filter coefficients assures that the resulting coefficients will yield a stable filter and offers possible fixed point implementation. A 10th order FIR clutter rejection filter indexed by geographical location is designed through autoregressive modeling of simulated clutter data. Filtered data, containing simulated dry microburst and clutter return, are analyzed using pulse-pair estimation techniques. To measure the ability of the clutter rejection filters to remove the clutter, results are compared to pulse-pair estimates of windspeed within a simulated dry microburst without clutter. In the filter evaluation process, post-filtered pulse-pair width estimates and power levels are also used to measure the effectiveness of the filters. The results support the use of an adaptive clutter rejection filter for reducing the clutter induced bias in pulse-pair estimates of windspeed.

Keel, Byron M.↗

Interdecadal Variations in the Alaska Gyre

Climatic dynamic topography variations in the Alaska gyre during the period 1968-1990 are described with an objective analysis of more than 12000 STD and XBT stations, and COADS wind stress data Interannual the dynamic height and SST variations were correlated and were consistent with recently described large-scale climatic shifts in the North Pacific. The gyre was centered more to the east, circulation appeared stronger, and SST was lower during the early to mid-1970s than during the 1980s. The Aleutian low (NP and PNA indices) intensified during the interim, but the response did not appear as a gyre spinup. Instead, the associated wind stress anomalies forced a slowly varying dynamic height anomaly across the eastern and northern part of the gyre through Ekman convergence, which had the effect of displacing the gyre's low somewhat to the WSW in the 1980s. The wind curl spectrum was white, and the slow oceanic response was modeled as stochastic-forced climate variability with a simple first-order Markov autoregression process. Forcing was assumed to be Ekman pumping of the pycnocline, and the damping coefficient was estimated from the data to be approx. 1 yr. A hindcast with observed winds gave estimated dynamic height patterns similar to those observed, with a canonical correlation of 0.79 at 99% confidence. This response was weak in the western half of the gyre, where slow baroclinic variability may have been influenced by long Rossby wave propagation. A simple autoregression simulation using artificial white noise forcing shows the evolution of decadal variations similar in nature to those observed. This result, along with the low frequency correlation between dynamic height and SST, suggests that the upper-ocean climatic variability in this region is primarily wind forced.

Lagerloef, Gary S.E.↗

Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics

We postulated that aging is associated with disruption in the fractallike long-range correlations that characterize healthy sinus rhythm cardiac interval dynamics. Ten young (21-34 yr) and 10 elderly (68-81 yr) rigorously screened healthy subjects underwent 120 min of continuous supine resting electrocardiographic recording. We analyzed the interbeat interval time series using standard time and frequency domain statistics and using a fractal measure, detrended fluctuation analysis, to quantify long-range correlation properties. In healthy young subjects, interbeat intervals demonstrated fractal scaling, with scaling exponents (alpha) from the fluctuation analysis close to a value of 1.0. In the group of healthy elderly subjects, the interbeat interval time series had two scaling regions. Over the short range, interbeat interval fluctuations resembled a random walk process (Brownian noise, alpha = 1.5), whereas over the longer range they resembled white noise (alpha = 0.5). Short (alpha s)- and long-range (alpha 1) scaling exponents were significantly different in the elderly subjects compared with young (alpha s = 1.12 +/- 0.19 vs. 0.90 +/- 0.14, respectively, P = 0.009; alpha 1 = 0.75 +/- 0.17 vs. 0.99 +/- 0.10, respectively, P = 0.002). The crossover behavior from one scaling region to another could be modeled as a first-order autoregressive process, which closely fit the data from four elderly subjects. This implies that a single characteristic time scale may be dominating heartbeat control in these subjects. The age-related loss of fractal organization in heartbeat dynamics may reflect the degradation of integrated physiological regulatory systems and may impair an individual's ability to adapt to stress.

NASA Discipline Cardiopulmonary↗

Classification results using spacially correlated Landsat data

Tubbs and Coberly (1978) demonstrated that Landsat multispectral scanner data are not independent random observations, but, are in fact highly correlated. They also demonstrated that the correlation structure for the data is similar to that of a stationary autoregressive process of order one. This paper investigates the effect that serially correlated training data have upon both the estimation of parameters and the classification problem. Results are included for both the Bayesian and maximum likelihood classification procedures.

Tubbs, J. D.↗

Short-term fluctuations in the eddy heat flux and baroclinic stability of the atmosphere

National Meteorological Center data from midlatitudes for three Januaries is used in calculating time series of the zonal mean meridional eddy heat flux and the zonal mean baroclinic stability, as measured by the difference between the zonal wind shear and the critical value of the shear in two-level models. Time-lagged correlations between the two series reveal a highly significant negative correlation for short time lags, peaking at approximately -0.4 when the stability parameter lags one half day behind the eddy flux. They also reveal that strongly unstable conditions are not followed by significant increases in the eddy flux. These results are seen as indicating that the synoptic variations of the zonal mean eddy flux are not closely related to the degree of baroclinic instability of the zonal mean flow. The autocorrelation of the eddy flux is then compared with those expected for autoregressive processes. A Bayesian information criterion suggests that the behavior is represented best by a damped oscillation, with a damping time of 0.8 day and a period of five days.

Stone, P. H.↗

A statistical model of the human core-temperature circadian rhythm

We formulate a statistical model of the human core-temperature circadian rhythm in which the circadian signal is modeled as a van der Pol oscillator, the thermoregulatory response is represented as a first-order autoregressive process, and the evoked effect of activity is modeled with a function specific for each circadian protocol. The new model directly links differential equation-based simulation models and harmonic regression analysis methods and permits statistical analysis of both static and dynamical properties of the circadian pacemaker from experimental data. We estimate the model parameters by using numerically efficient maximum likelihood algorithms and analyze human core-temperature data from forced desynchrony, free-run, and constant-routine protocols. By representing explicitly the dynamical effects of ambient light input to the human circadian pacemaker, the new model can estimate with high precision the correct intrinsic period of this oscillator ( approximately 24 h) from both free-run and forced desynchrony studies. Although the van der Pol model approximates well the dynamical features of the circadian pacemaker, the optimal dynamical model of the human biological clock may have a harmonic structure different from that of the van der Pol oscillator.

NASA Discipline Regulatory Physiology↗

Representing the Sub-Grid Heterogeneity of Surface Precipitation in A General Circulation Model

Precipitation variability on spatial scales smaller than a typical general circulation model (GCM) grid box is often neglected, with the grid-mean precipitation rate being applied uniformly to underlying surface tiles. This reduces the extrema seen by the surface, with corresponding reductions in surface runoff and altered land-atmosphere fluxes. Here we present a novel approach to stochastically distribute precipitation across sub-grid surface tiles within a GCM. Based on 4 km Stage IV precipitation data, the scheme parameterizes the dry area fraction as a function of grid mean precipitation rate, and defines the relative distribution of intensities across non-dry surface tiles. To incorporate memory and mimic the persistence of precipitating storms, the relative intensity assigned to each sub-grid tile is determined by an autoregressive process. Using single column experiments, the scheme is shown to reproduce observed precipitation statistics at the scale of model surface tiles. We also document impacts on surface hydrology and energy partitioning, with notable increases in precipitation runoff, surface temperature variance, and the Bowen ratio.

GCM↗

Random Process Simulation for stochastic fatigue analysis

A simulation technique is described which directly synthesizes the extrema of a random process and is more efficient than the Gaussian simulation method. Such a technique is particularly useful in stochastic fatigue analysis because the required stress range moment E(R sup m), is a function only of the extrema of the random stress process. The family of autoregressive moving average (ARMA) models is reviewed and an autoregressive model is presented for modeling the extrema of any random process which has a unimodal power spectral density (psd). The proposed autoregressive technique is found to produce rainflow stress range moments which compare favorably with those computed by the Gaussian technique and to average 11.7 times faster than the Gaussian technique. The autoregressive technique is also adapted for processes having bimodal psd's. The adaptation involves using two autoregressive processes to simulate the extrema due to each mode and the superposition of these two extrema sequences. The proposed autoregressive superposition technique is 9 to 13 times faster than the Gaussian technique and produces comparable values for E(R sup m) for bimodal psd's having the frequency of one mode at least 2.5 times that of the other mode.

Larsen, Curtis E.↗

Stratospheric ozone profile and total ozone trends derived from the SAGE I and SAGE II data

Global trends in both stratospheric column ozone and as a function of altitude are derived on the basis of SAGE I/II ozone data from the period 1979-1991. A statistical model containing quasi-biennial, seasonal, and semiannual oscillations, a linear component, and a first-order autoregressive noise process was fit to the time series of SAGE I/II monthly zonal mean data. The linear trend in column ozone above 17-km altitude, averaged between 65 deg S and 65 deg N, is -0.30 +/-0.19 percent/yr, or -3.6 percent over the time period February 1979 through April 1991. The data show that the column trend above 17 km is nearly zero in the tropics and increases towards the high latitudes with values of -0.6 percent/yr at 60 deg S and -0.35 percent/yr at 60 deg N. Both these results are in agreement with the recent TOMS results. The profile trend analyses show that the column ozone losses are occurring below 25 km, with most of the loss coming from the region between 17 and 20 km. Negative trend values on the order of -2 percent/yr are found at 17 km in midlatitudes.

Mccormick, M. P.↗

Modeling methodology for MLS range navigation system errors using flight test data

Flight test data was used to develop a methodology for modeling MLS range navigation system errors. The data used corresponded to the constant velocity and glideslope approach segment of a helicopter landing trajectory. The MLS range measurement was assumed to consist of low frequency and random high frequency components. The random high frequency component was extracted from the MLS range measurements. This was done by appropriate filtering of the range residual generated from a linearization of the range profile for the final approach segment. This range navigation system error was then modeled as an autoregressive moving average (ARMA) process. Maximum likelihood techniques were used to identify the parameters of the ARMA process.

Karmali, M. S.↗

The application of time series models to cloud field morphology analysis

A modeling method for the quantitative description of remotely sensed cloud field images is presented. A two-dimensional texture modeling scheme based on one-dimensional time series procedures is adopted for this purpose. The time series procedure used is the seasonal autoregressive, moving average (ARMA) process in Box and Jenkins. Cloud field properties such as directionality, clustering and cloud coverage can be retrieved by this method. It has been demonstrated that a cloud field image can be quantitatively defined by a small set of parameters and synthesized surrogates can be reconstructed from these model parameters. This method enables cloud climatology to be studied quantitatively.

Chin, Roland T.↗

Digital spectral estimation and modeling of Space Shuttle flight data

Application of the digital signal processing technique of autoregressive-moving-average (ARMA) modeling to the estimation of power spectra and shock spectra from Space Shuttle lift-off flight accelerograms is described in this paper. The background for application to ARMA of lift-off accelerograms which are non-stationary in nature is exemplified through a step-by-step discussion of actual numerical results. Included is a discussion of pertinent mathematical background for the ARMA approximations. Potential areas for application of ARMA modeling in payload integration activities are suggested.

Spanos, P. D.↗

Condition Monitoring for Helicopter Data

In this paper the classical "Westland" set of empirical accelerometer helicopter data is analyzed with the aim of condition monitoring for diagnostic purposes. The goal is to determine features for failure events from these data, via a proprietary signal processing toolbox, and to weigh these according to a variety of classification algorithms. As regards signal processing, it appears that the autoregressive (AR) coefficients from a simple linear model encapsulate a great deal of information in a relatively few measurements; it has also been found that augmentation of these by harmonic and other parameters can improve classification significantly. As regards classification, several techniques have been explored, among these restricted Coulomb energy (RCE) networks, learning vector quantization (LVQ), Gaussian mixture classifiers and decision trees. A problem with these approaches, and in common with many classification paradigms, is that augmentation of the feature dimension can degrade classification ability. Thus, we also introduce the Bayesian data reduction algorithm (BDRA), which imposes a Dirichlet prior on training data and is thus able to quantify probability of error in an exact manner, such that features may be discarded or coarsened appropriately.

Wen, Fang↗