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A scene segmentation approach is presented which is based on generating autoregressive field models for each scene component (class) from its a priori spatial statistics. A methodology is also described for using these models in achieving optimal segmentation of a scene. The derivations are presented for the case of single band imagery, however, the method is believed to be extendable to multispectral data.
Over the last decade there has been a dramatic increase in the number and volume of data sets useful for oceanographic studies. Many of these data sets consist of long temporal or spatial series derived from satellites and large-scale oceanographic experiments. These data sets are, however, often 'gappy' in space, irregular in time, and always of finite length. The conventional Fourier transform (FT) approach to the spectral analysis is thus often inapplicable, or where applicable, it provides questionable results. Here, through comparative analysis with the FT for different oceanographic data sets, the possibilities offered by autoregressive (AR) modeling to perform spectral analysis of gappy, finite-length series, are discussed. The applications demonstrate that as the length of the time series becomes shorter, the resolving power of the AR approach as compared with that of the FT improves. For the longest data sets examined here, 98 points, the AR method performed only slightly better than the FT, but for the very short ones, 17 points, the AR method showed a dramatic improvement over the FT. The application of the AR method to a gappy time series, although a secondary concern of this manuscript, further underlines the value of this approach.
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Several random process models in the time domain are defined and discussed. Attention is given to the moving average model, the autoregressive model, and relationships between and combinations of these models. Consideration is then given to methods for investigating pulse structure, procedures of model construction, computational methods, and numerical experiments. A FORTRAN algorithm of time series analysis has been developed which is relatively stable numerically. Results of test cases are given to study the effect of adding noise and of different distributions for the pulse amplitudes. A preliminary analysis of the light curve of the quasar 3C 272 is considered as an example.
A quantile-based approach to statistical analysis and probability modeling of data is presented which formulates statistical inference problems as functional inference problems in which the parameters to be estimated are density functions. Density estimators can be non-parametric (computed independently of model identified) or parametric-select (approximated by finite parametric models that can provide standard models whose fit can be tested). Exponential models and autoregressive models are approximating densities which can be justified as maximum entropy for respectively the entropy of a probability density and the entropy of a quantile density. Applications of these ideas are outlined to the problems of modeling: (1) univariate data; (2) bivariate data and tests for independence; and (3) two samples and likelihood ratios. It is proposed that bi-information estimation of a density function can be developed by analogy to the problem of identification of regression models.
This paper derives algorithms for identifying autoregressive models, with external input, of multi-input multi-output systems from data using a fast transversal filter or a least-squares lattice filter. The autoregressive models including external inputs are used to identify state-space models and the corresponding observer/Kalman filter gains of the system. The derivation is an extension of scalar autoregressive model approaches, modified to cope with multivariables, external inputs and an extra direct-influence term. Comparisons between the fast transversal filter, the least-squares lattice filter and the classical least-squares method are made in terms of complexity, computational cost and practical applications issues. A numerical example is included to illustrate the approach.
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.
This article describes an investigation of a statistical hypothesis testing method for detecting changes in the characteristics of an observed time series. The work is motivated by the need for practical automated methods for on-line monitoring of Deep Space Network (DSN) equipment to detect failures and changes in behavior. In particular, on-line monitoring of the motor current in a DSN 34-m beam waveguide (BWG) antenna is used as an example. The algorithm is based on a measure of the information theoretic distance between two autoregressive models: one estimated with data from a dynamic reference window and one estimated with data from a sliding reference window. The Hinkley cumulative sum stopping rule is utilized to detect a change in the mean of this distance measure, corresponding to the detection of a change in the underlying process. The basic theory behind this two-model test is presented, and the problem of practical implementation is addressed, examining windowing methods, model estimation, and detection parameter assignment. Results from the five fault-transition simulations are presented to show the possible limitations of the detection method, and suggestions for future implementation are given.
The Global Reference Atmospheric Model (GRAM) program includes the capability for simulating pseudo-random perturbations in density, temperature, pressure, or wind components along a simulated reentry trajectory or other path through the atmosphere. Some concerns were expressed by GRAM users, however, that the mean-square perturbation gradients may be too large for small values of the vertical separation Delta z. The present GRAM perturbation simulations, based on a one-step autoregressive model, yield a power spectrum versus wavenumber k which is proportional to k sup -2 at high wavenumbers. This feature also produces mean-square perturbation differences which are directly proportional to Delta z, and mean-square perturbation gradients which are inversely proportional to Delta z. Thus, root-mean-square gradients, (Delta f/Delta z) sub rms, increase with decreasing Delta a as Delta z sup -1/2. A simple modification to GRAM is suggested which overcomes this problem, i.e., which produce root-mean-square gradient that remain bound as Delta z approaches zero. Possible applications of more sophisticated simulation approaches, e.g., second order autoregressive models, or fractal model techniques, were also explored briefly but found to yield improvements which appear too small to justify their considerable added complexity for use in the GRAM programs.
Advances in the use of autoregressive models, pattern recognition methods, and hidden Markov models for on-line health monitoring of dynamic systems (such as DSN antennas) have recently been reported. However, the algorithms described in previous work have the significant drawback that data acquired under fault conditions are assumed to be available in order to train the model used for monitoring the system under observation. This article reports that this assumption can be relaxed and that hidden Markov monitoring models can be constructed using only data acquired under normal conditions and prior knowledge of the system characteristics being measured. The method is described and evaluated on data from the DSS 13 34-m beam wave guide antenna. The primary conclusion from the experimental results is that the method is indeed practical and holds considerable promise for application at the 70-m antenna sites where acquisition of fault data under controlled conditions is not realistic.
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.
A novel approach of integrated system identification and modal state estimation is proposed for control of linear dynamical systems including flexible space structures. There are four steps involved in this approach. First, the relation between a stochastic state space model of a dynamical system and the coefficients of its autoregressive model with exogenous input is derived. Second, an adaptive least-squares transversal predictor is used to estimate the coefficients of the model. Third, a state space model and a steady state Kalman filter gain of the dynamical system are then identified from the coefficients of the model by using the eigensystem realization algorithm. Fourth, a modal state estimator is constructed using the modal parameters of the identified model. On-line implementation of this algorithm can continually improve the modal parameters and the filter gain. It can also gradually update the system model when the system characteristics are slowly changing. A numerical example is used to illustrate the feasibility of the new approach.
A method, suggested by Leith (1975), which employed stochastic-dynamic forecasts obtained from a general circulation model in such a way as to satisfy the definition of climatic noise, was used to validate assumptions accounting for the effects of external influences in estimating the climatic noise. Two assumptions were investigated: (1) that the weather fluctuations can be represented as a Markov process, and (2) that changing external conditions do not influence the atmosphere's statistical properties on short time scales. The general circulation model's simulation of the daily weather fluctuations was generated by performing integrations with prescribed climatological boundary conditions for random initial atmospheric states, with resulting dynamical forecasts providing an ensemble of simulated data for the autoregressive modeling of weather fluctuations. To estimate the climatic noise from the observational data (consisting of hourly values of sea level pressure and surface temperature at 54 U.S. stations for the month of January for the years 1949-1975) use of the short time-scale assumption is made. The simulated and observed data were found not to be consistent with either white noise or a Markov process of weather fluctuations. Good agreement was found between the results of the hypothetical testing of the simulated and the observed surface temperatures; and only partial support was found for the short time-scale assumption, i.e., for sea level pressure.
The first part of this paper presents the description of the GARP (Global Atmospheric Research Program) Atlantic Tropical Experiment (GATE) 1 rain-rate data and its two-dimensional spectral and correlation characteristics, which has made it possible to accomplish the following: to show the concentration of a significant power along the frequency axis in the spatiotemporal spectra; to detect a diurnal cycle (which has a range of variation of about 3.4-5.4 mm/n) as one of the sources of bias in the rain statistics of satellite data; to study the distinction between the north-south and east-west transport of spatial rain-rate field and character of its anisotropy; to evaluate the scales of the distinction between second-moment estimates associated with ground and satellite samples; and to determine the appropriate spatial and temporal scales of simple linear stochastic models fitted to averaged rain-rate fields. The second part of this paper is devoted to an analysis of the diffusion of the rain rate by establishing a relationship between the parameters of the multivariate autoregressive model and the coefficients of a diffusion equation. This analysis led to the use of rain data to estimate the rain advection velocity as well as other coefficients of the diffusion equation of the corresponding field. The results obtained can be used for comparison with corresponding estimates of other sources of data (satellite, Tropical Oceans Global Atmosphere Coupled Ocean - Atmosphere Response Experiment (TOGA, COARE) or simulated by physical models), for generating multiple samples of any size, for solving the inverse problems of some of the hydrodynamic equations, and in some other areas of rain data analysis and modeling.
Several important problems in the fields of signal processing and model identification, such as system structure identification, frequency response determination, high order model reduction, high resolution frequency analysis, deconvolution filtering, and etc. Each of these topics involves a wide range of applications and has received considerable attention. Using the Fourier based sinusoidal modulating signals, it is shown that a discrete autoregressive model can be constructed for the least squares identification of continuous systems. Some identification algorithms are presented for both SISO and MIMO systems frequency response determination using only transient data. Also, several new schemes for model reduction were developed. Based upon the complex sinusoidal modulating signals, a parametric least squares algorithm for high resolution frequency estimation is proposed. Numerical examples show that the proposed algorithm gives better performance than the usual. Also, the problem was studied of deconvolution and parameter identification of a general noncausal nonminimum phase ARMA system driven by non-Gaussian stationary random processes. Algorithms are introduced for inverse cumulant estimation, both in the frequency domain via the FFT algorithms and in the domain via the least squares algorithm.
The estimation of the power spectrum of a time series by fitting a finite autoregressive model to the data has recently found widespread application in the physical sciences. The extension of this method to the analysis of vector time series is presented here through its application to ULF waves observed in the magnetosphere by the ATS 6 synchronous satellite. Autoregressive spectral estimates of the power and cross-power spectra of these waves are computed with computer programs developed by the author and are compared with the corresponding Blackman-Tukey spectral estimates. The resulting spectral density matrices are then analyzed to determine the direction of propagation and polarization of the observed waves.
The objective is to investigate the application of Doppler radar systems for global wind measurement. A model of the satellite-based radar wind sounder (RAWS) is discussed, and many critical problems in the designing process, such as the antenna scan pattern, tracking the Doppler shift caused by satellite motion, and backscattering of radar signals from different types of clouds, are discussed along with their computer simulations. In addition, algorithms for measuring mean frequency of radar echoes, such as the Fast Fourier Transform (FFT) estimator, the covariance estimator, and the estimators based on autoregressive models, are discussed. Monte Carlo computer simulations were used to compare the performance of these algorithms. Anti-alias methods are discussed for the FFT and the autoregressive methods. Several algorithms for reducing radar ambiguity were studied, such as random phase coding methods and staggered pulse repitition frequncy (PRF) methods. Computer simulations showed that these methods are not applicable to the RAWS because of the broad spectral widths of the radar echoes from clouds. A waveform modulation method using the concept of spread spectrum and correlation detection was developed to solve the radar ambiguity. Radar ambiguity functions were used to analyze the effective signal-to-noise ratios for the waveform modulation method. The results showed that, with suitable bandwidth product and modulation of the waveform, this method can achieve the desired maximum range and maximum frequency of the radar system.