This project was focused on the development of tools for the automatic configuration of signal processing systems. The goal is to develop tools that will be useful in a variety of Government and commercial areas and useable by people who are not signal processing experts. In order to get the most benefit from signal processing techniques, deep technical expertise is often required in order to select appropriate algorithms, combine them into a processing chain, and tune algorithm parameters for best performance on a specific problem. Therefore a significant benefit would result from the assembly of a toolbox of processing algorithms that has been selected for their effectiveness in a group of related problem areas, along with the means to allow people who are not signal processing experts to reliably select, combine, and tune these algorithms to solve specific problems. Defining a vocabulary for problem domain experts that is sufficiently expressive to drive the configuration of signal processing functions will allow the expertise of signal processing experts to be captured in rules for automated configuration. In order to test the feasibility of this approach, we addressed a lightning classification problem, which was proposed by DOE as a surrogate for problems encountered in nuclear nonproliferation data processing. We coded a toolbox of low-level signal processing algorithms for extracting features of RF waveforms, and demonstrated a prototype tool for screening data. We showed examples of using the tool for expediting the generation of ground-truth metadata, for training a signal recognizer, and for searching for signals with particular characteristics. The public benefits of this approach, if successful, will accrue to Government and commercial activities that face the same general problem - the development of sensor systems for complex environments. It will enable problem domain experts (e.g. analysts) to construct signal and image processing chains without the aid of signal processing experts. Thus enabled, problem domain experts will be able to work more quickly and produce better quality work.

Abstract : This paper introduces the use of dynamic features for robust target recognition of ground vehicles. Most current approaches rely on instantaneous spectral features such as those derived from harmonically related spectral lines. Significant drawback of these approaches are that the use of low amplitude (10-20dB below dominant line) spectral lines severely limit classification range. The strongest line is often detectable well before secondary lines. Dynamic features extracted directly from the strongest spectral line if successfully characterizing the target will extend the range of operation to several times. In this report a complete experimental evaluation of the effectiveness of dynamic features is conducted. The analysis is performed using a database consisting of approximately two hundred acoustic signatures collected from six unique vehicles. A number of features captured from the dynamic characteristic of the spectral line are evaluated. Classification performance is measured and presented in terms of confusion matrices. As an additional test of the classifier development tools developed for this task we selected added instantaneous spectral measurements to the dynamic feature and re-tested. We found that the performance of the classifiers using the mixed spectral and dynamic features was excellent but "blind" testing of the classifiers that were developed (testing against vehicle runs that were not used during classifier development) showed disappointing results.

Adding remote deployment capability to unattended surveillance systems provides the capability to unobtrusively monitor activities in hostile or neutral areas where in-situ placement is not practical. Targeted surveillance activities include tracking force movements, monitoring keep-out areas, and detecting the presence of assets hidden underground or in buildings. Key technologies to achieve this capability include localization of deployed nodes, field optimization and control techniques, multi- sensor fusion, and low cost miniaturized sensors.

Techniques that estimate frequency and chirp rate as weighted sums of phase differences have received attention because they can be simple to implement. The novel contributions in this paper include the efficient implementation of these estimates through recursive structuring of the computation and trapezoidal approximation of the weighting functions. A multirate cascade structure for the trapezoidal weighting is given that allows frequency and chirp rate estimates to be formed for multiple analysis window lengths with little extra computation. The techniques described are particularly well suited to hardware implementation because they virtually eliminate multiplications while having little impact on performance.

Along with the introduction of full waveform sonic logging tools has come a variety of associated digital signal processing techniques designed to estimate the formation compressional and shear slownesses (DELTA-t, inverse velocity, travel time). In this paper, we have described these techniques and applied them, for the most part, to the same set of field waveforms. We have divided our treatment into those techniques associated with traditional two-received tools, and those associated with the recent multi-receiver array tools.The processing associated with two-receiver tools generally consists of methods which make use of time windows and coherence measures. Specifically, time windows are positioned on each trace, and the coherence of the windowed signals is computed. The window positions which result in the highest coherence can be used to derive an estimate of the wave slowness. Issues associated with two-receiver processing seem to be focused on methods for locating the arrival time of the waves at the receivers. The semblance coherence measure seems to be more popular in the literature than either cross-correlation methods or cross-spectral techniques. In implementing these methods, we have found the resulting estimates to be somewhat sensitive to issues such as the shape and duration of the time window. The estimation of the shear slowness from two-receiver data is more difficult than the estimation of compressional slowness, due to interference from other arrivals including mode conversions from bed boundaries and fractures, and due to dispersion. Some techniques address the difficulties associated with shear estimation more than others.With the recent commercial introduction of multi-receiver sonic array tools, a number of processing techniques have appeared in the literature. Analogous to windowed coherence methods developed for two-receiver tools, multi-receiver windowed coherence methods have developed for array tools. Again, semblance processing seems to be particularly useful. Because longer array apertures can lead to a reduced ability to resolve thin beds in the formation, a new technique has been developed which extracts sub-arrays from the full arrays associated with successive firings of the source transducer. The shorter arrays result in higher resolution, and the multiplicity of sub-arrays provide added stability. Frequency domain techniques have also been developed which are able to handle dispersive wave propagation and can aid in situations where waves are overlapped in space and time due to close slownesses. These two situations can cause coherence based methods to perform poorly. An assumption common to all processing techniques is that the formation is homogeneous across the aperture of the (sub-)array. This causes the performance of these techniques to degrade when there is a bed boundary or fracture within the aperture. An area of future research is likely to be in the area of processing for arrays in inhomogeneous media.

In recent publication, S. Kay (1988) described a method of estimating the frequency of a complex exponential from noisy samples of the time waveform. The method is attractive because of its computational simplicity, because it is based on phase differences (which may already be available at no cost in some systems), and because its performance attains the Cramer-Rao bound at high SNR. The authors present a novel derivation of Kay's method, extend it to the estimation of the parameters of linear FM chirps and of multiple signals, provide an adaptive version of the algorithm, and provide an explanation for the threshold behavior of phase difference methods

Compressional (P) and shear (S) waves can be separated in vector vertical-seismic profile recordings through the use of multichannel multidimensional filters. These filters have impulse responses that are spatially and temporally infinite, and their application to recordings of finite spatial extent, such as those made in thin beds, results in a truncation error. The use of constrained shift-varying filters helps to minimize this error. The constrained filters are derived under the assumption that most of the energy in the recording is concentrated around a few apparent (vertical) velocities. Implementation of these shift-varying filters requires little additional computation beyond that required by simpler shift-invariant filters. The reduction of truncation error accomplished by this processing scheme is demonstrated with several synthetic data sets

Acoustic wave propagation in a fluid‐filled borehole is affected by the type of rock which surrounds the hole. More specifically, the slowness dispersion of the various body‐wave and borehole modes depends to some extent on the properties of the rock. We have developed a technique for estimating the dispersion relations from data acquired by full‐waveform digital sonic array well‐logging tools. The technique is an extension of earlier work and is based on a variation of the well‐known Prony method of exponential modeling to estimate the spatial wavenumbers at each temporal frequency. This variation, known as the forward‐backward method of linear prediction, models the spatial propagation by purely real‐valued wavenumbers. The Prony exponential model is derived from the physics of borehole acoustics under the assumption that the formation does not vary in the axial or azimuthal dimensions across the aperture of the receiver array, but can vary arbitrarily in the radial dimension. The exponential model fits the arrivals of body waves (i.e., head waves) well, because the body waves are dominated by a pole rather than a branch point. Examples of this processing applied to synthetic waveforms, laboratory scale‐model data, and field data illustrate the power of the technique and verify its ability to recover dispersion relations from sonic array data. The interpretation of the estimated dispersion in terms of rock properties is not discussed.

This correspondence concerns a particular method for the design and implementation of shift-varying filters for the purpose of approximating, from a finite segment of a data sequence, the response of a shift-invariant filter to the infinite length data sequence.

Image interpolation involves the operations of zero-padding and lowpass filtering. The lowpass filtering operation can never be implemented exactly due to the finite extent of the imagery and approximate implementation results in truncation error which can be quite objectionable when the original image has very limited extent. We present a methology, useful for interpolating imagery containing lines, edges or other directed features, which implements a shift-varying lowpass filter. This filter is designed to minimize (in a constrained L2sense) the objectionable truncation error. A simple example is presented which illustrates the methodology.

A procedure has been proposed for recovering a radially varying electrical resistivity profile from a particular series of dc electrical measurements. Such a procedure has potential applications to the study of the invasion of porous materials by electrically conductive fluids. This paper concerns the sensitivity of such a procedure to inaccuracies in the measurements. It is shown that, for a layered conductivity profile, the sensitivity of the conductivity estimates to measurement inaccuracy grow exponentially with the number of layers. This result indicates that resolution will be severely limited by measurement inaccuracy in the reconstruction of a conductivity profile from this particular series of dc electrical measurements.

An estimation problem in which a finite number of linear measurements of an unknown function is available, and in which the only prior information available concerning the unknown function consists of inequality constraints on its magnitude, is ill-posed in that insufficient information is available from which point estimates of the unknown function can be made with any reliability, even with exact measurements. An alternative to point estimation involves the computation of bounds on linear functionals of the unknown function in terms of the measurements. A generalization is described of the bounding technique to problems in which the measurements are inexact. The bounds are defined in terms of a primal optimization problem. A deterministic interpretation of the bounds is given, as well as a probabilistic one for the case of additive Gaussian measurement noise. An unconstrained dual optimization problem is derived that has an interesting data-adaptive filtering interpretation and provides an attractive basis for computation. Several aspects of the primal and dual optimization problems are investigated that have important implications for the reliable computation of the bounds.

In many applications the solution of a non-linear least squares problem is desired. The solution of such problems can present difficulties: exhaustive search can be very time consuming while descent algorithms can converge to local minima rather than global minima. Branch-and-bound techniques have been proposed for the solution of such problems; they have the potential for being both efficient and reliable. The application of branch-and-bound techniques to a particular class of nonlinear least squares problems is discussed in this paper.

The determination of a power density spectrum from a finite set of correlation samples is an ill-posed problem. Furthermore. it is not possible even to bound the values that consistent power density spectra can take on at a particular point. A more reasonable problem is to try to determine the total spectral power in some frequency interval. Although this power cannot be determined exactly, upper and lower bounds on its possible values can be determined. This observation leads to a unified treatment of certain classical and modern spectral estimation techniques and to new interpretations for two data adaptive spectral estimators. maximum likelihood method (MLM) and data adaptive spectral estimator (DASE). According to these new interpretations. MLM and DASE provide upper bounds on spectral power in a specified frequency region subject to the assumption that the spectral density is constant in that region. These methods make no use of an extendibility constraint that can be used to obtain tight upper bounds, as well as nontrivial lower bounds on power. Cybenko has studied a related problem of bounding windowed power, for an arbitrary window, with no assumptions about the form of the spectral density. A new type of classical resolution limit for these bounds is derived and a numerical example is presented.

It has been noted that not all positive-semidefinite matrices are extendible in the multidimensional case. However, no example of such a matrix has been presented for a simple multidimensional analog of the one-dimensional time-series case. It is shown how such a matrix can be derived.

Existing variance calculations for spectral estimates are unsatisfactory in that they depend upon information that is usually unavailable in practice. Some recent work in spectral estimation has involved the computation of bounds on the average spectral density in some region from a true correlation matrix. The computation of these bounds involves optimization over a set of spectra that are consistent with the correlation matrix. The specific new work to be reported on involves the construction of confidence regions for the true correlation matrix, based on a Wishart distributed sample correlation matrix. Bounds computed over spectra that are consistent with the true correlation matrix being in this set are valid with a certain minimum a priori probability which does not depend upon unavailable information about the spectrum. The result is a performance characterization for the bounding method which is different and, in some ways, more satisfactory than the existing variance analyses for other spectral estimation methods.

The solution to the general multidimensional MEM spectral estimation problem is described. A detailed derivation of the dual optimisation problem, in which entropy is minimised, is given. A necessary and sufficient condition for the existence of a solution to the general problem is presented. The theory is also extended to a 'correlation-approximating' MEM spectral estimate. Algorithms applicable to the dual problem are discussed.