USA As Represented by Secretary of the Navy

Bruce J Bates

Francis J O'Brien, Jr

Chung Tien Nguyen

Sherry E Hammel

Steven C Nardone

Susan M Bates

Mark J DiPippo

Mark J Di Pippo

A method and apparatus are provided for automatically characterizing the spatial arrangement among the data points of a three-dimensional time series distribution in a data processing system wherein the classification of said time series distribution is required. The method and apparatus utilize grids in Cartesian coordinates to determine (1) the number of cubes in the grids containing at least one input data point of the time series distribution; (2) the expected number of cubes which would contain at least one data point in a random distribution in said grids; and (3) an upper and lower probability of false alarm above and below said expected value utilizing a discrete binomial probability relationship in order to analyze the randomness characteristic of the input time series distribution. A labeling device also is provided to label the time series distribution as either random or nonrandom, and/or random or nonrandom within what probability, prior to its output from the invention to the remainder of the data processing system for further analysis.

System and apparatus for the detection of randomness in three dimensional time series distributions made up of sparse data sets

Enhanced model identification in signal processing using arbitrary exponential functions

A method and apparatus are provided for automatically characterizing the spatial arrangement among the data points of a time series distribution in a data processing system wherein the classification of said time series distribution is required. The method and apparatus utilize a grid in Cartesian coordinates to determine (1) the number of cells in the grid containing at least-one input data point of the time series distribution; (2) the expected number of cells which would contain at least one data point in a random distribution in said grid; and (3) an upper and lower probability of false alarm above and below said expected value utilizing a discrete binomial probability relationship in order to analyze the randomness characteristic of the input time series distribution. A labeling device also is provided to label the time series distribution as either random or nonrandom, and/or random or nonrandom.

System and apparatus for the detection of randomness in time series distributions made up of sparse data sets

A method and apparatus to determine the f that provides optimal image resolution for a predetermined depth-of-field. An approximate and exact method and apparatus are provided to determine the optimal resolution f . The optimal resolution f is a function of the lens focal length, depth-of-field in front of the object, wavelength of light, and distance of the object to the lens center. Once the optimal resolution f is determined, the camera is adjusted to the closest discrete f available. When the approximate field technique is utilized, the camera must be adjusted to the discrete f closest to, but not exceeding, the computed f .

Optical fstop/resolution apparatus and method for specified depth-of-field

A method for manipulating a three-dimensional sub-volume within a graphical display is disclosed and includes selecting an option from a menu screen to relocate or re-size a three-dimensional sub-volume within the graphical display, and upon selecting the option to relocate or re-size, proceeding with the following. A cursor is placed on either the sub-volume or a selected corner of the sub-volume within the graphical display, a selected one of a left and a right mouse buttons is depressed, and the sub-volume is dragged to a relocation area or resized within an 'x-y' plane and/or a 'z' plane of the graphical display according to depression of the selected mouse button and placement of the cursor. When the selected one of the left and right mouse buttons is released, the x, y, and z-coordinates of the relocation area and/or resizing are locked. The sub-volume is, therefore, manipulated within a three-dimensional frame of reference by controlling the mouse.

Three-dimensional volume selection tool

A method for finding a probability density function (PDF) and its statistical moments for an arbitrary exponential function of the form g(x)=.alpha.x.sup.m e.sup.-.beta.x.spsp.n,0&lt;x&lt;.infin., where .alpha., .beta., n&gt;0, m&gt;-1 are real constants in one-dimensional distributions and g(x.sub.1,x.sub.2, . . . ,x.sub.l) in the hyperplane. Non-linear regression analyses are performed on the data distribution and a root-mean-square (RMS) is calculated and recorded for each solution set until convergence. The basis function is reconstructed from the estimates in the final solution set and a PDF is obtained. The moment generating function (MGF), which characterizes any statistical moment of the distribution, is obtained using a novel function derived by the inventors and the mean and variance are obtained in standard fashion. Simple hypotheses about the behavior of such functional forms may be tested statistically once the empirical least squares methods have identified an applicable model derived from actual measurements.

Model identification and characterization of error structures in signal

A chaotic signal processing system receives an input signal provided by a nsor in a chaotic environment and performs a processing operation in connection therewith to provide an output useful in identifying one of a plurality of chaotic processes in the chaotic environment. The chaotic signal processing system comprises an input section, a processing section and a control section. The input section is responsive to input data selection information for providing a digital data stream selectively representative of the input signal provided by the sensor or a synthetic input representative of a selected chaotic process. The processing section includes a plurality of processing modules each for receiving the digital data stream from the input means and for generating therefrom an output useful in identifying one of a plurality of chaotic processes. The processing section is responsive to processing selection information to select one of the plurality of processing modules to provide the output. The control module generates the input data selection information and the processing selection information in response to inputs provided by an operator.

System and method for chaotic signal identification

A signal processing system and computer-implemented method for processing a igital data sequence representing an input signal to generate a fractal dimension value. The system includes a correlation integral value generation module, correlation plot generation module, a segmentation module, correlation dimension generation module, and a control module. The correlation integral value generation module generates a series of correlation integral values for points w.sub.n (k) in 'N'-dimensional space corresponding to vectors of said digital data sequence, and in particular generates inter-point distance values within each of a plurality of volume elements of said 'N'-dimensional space. The correlation plot generation module generates a correlation integral plot comprising a plot of the correlation integral values as a function of said 'N'-dimensional space volume elements. The segmentation module generates, from the plot, a series of correlation integral plot segments.

System and computer-implemented method for fractal-dimension measurement

The present invention comprises a method for filling in missing data intels in a quantized time-dependent data signal that is generated by, e.g., an underwater acoustic sensing device. In accordance with one embodiment of the invention, this quantized time-dependent data signal is analyzed to determine the number and location of any intervals of missing data, i.e., gaps in the time series data signal caused by noise in the sensing equipment or the local environment. The quantized time-dependent data signal is also modified by a low pass filter to remove any undesirable high frequency noise components within the signal. A plurality of mathematical models are then individually tested to derive an optimum regression curve for that model, relative to a selected portion of the signal data immediately preceding each previously identified data gap. The aforesaid selected portion is empirically determined on the basis of a data base of signal values compiled from actual undersea propagated signals received in cases of known target motion scenarios. An optimum regression curve is that regression curve, linear or nonlinear, for which a mathematical convergence of the model is achieved. Convergence of the model is determined by application of a smallest root-mean-square analysis to each of the plurality of models tested. Once a model possessing the smallest root-mean-square value is derived from among the plurality of models tested, that optimum model is then selected, recorded, and stored for use in filling the data gap. This process is then repeated for each subsequent data gap until all of the identified data gaps are filled.

Method for data gap compensation

An apparatus and method for determining the range and depth to an acoustic ource from a sampling site in a medium. A linear array of pressure transducers monitors the acoustic field produced by the acoustic source. A measurement processor utilizes the measured acoustic field to produce an initial field condition for each member of the array. An environmental model includes environmental data in the form of acoustically pertinent variables that define acoustic energy transfer characteristics through the medium at different ranges and depths. A backpropagation processor utilizes the initial field condition and the acoustically pertinent variables to produce, for each incremental range and depth, an amplitude function. An index processor normalizes the amplitude functions for each incremental range and depth, and an index extreme value processor selects the amplitude function with the maximum amplitude. The range and depth of that extreme value amplitude function is used to determine the range and depth for the acoustic source.

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Portsmouth, RI, United States of America

Bruce J Bates