System for detecting, tracking, and reconstructing signals in spectrally competitive environments

An apparatus for determining selected information from fluctuations of a physical wave field, the properties of the physical wave field being detectable over three spatial dimensions and a temporal dimension, the apparatus comprising:

• at least one antenna that generates output signals representative of the physical wave field;
• said output signals being sufficient to define a physical wave field modeling vector characterizing the physical wave field;
• at least one converter that converts said output signals into at least one physical wave field modeling vector;
• at least one differentiator that differentiates said physical wave field modeling vector to obtain a differentiated modeling vector representing a derivative of said physical wave field;
• and
• at least one processor that obtains selected information from said physical wave field modeling vector and said differentiated modeling vector.

A method for determining selected information about at least one resolvable source contributing to a physical wave field, the properties of the physical wave field being detectable over three spatial dimensions and a temporal dimension, the method comprising:

• using at least one processor to characterize said physical wave field by a signal vector representative of a mathematical model of said physical wave field;
• using at least one processor to provide a library of signal vectors having library elements specifying mathematical models of physical wave fields with known properties;
• using said library elements and said signal vector to obtain a resolved signal vector representing the contribution to the physical wave field of said at least one resolvable source;
• and
• using said resolved signal vector to reconstruct the time series representing said contribution to the physical wave field;
• and
• using time series to determine selected information about said at least one resolvable source.

A method for determining the signal vectors to be associated with contributions to a physical wave field generated by a source, the properties of the physical wave field being detectable over three spatial dimensions and a temporal dimension, the method comprising;

• using at least one processor to characterize said physical wave field by a signal vector representative of a mathematical model of said physical wave field;
• providing criteria for determining which said contributions to the physical wave field can be considered resolvable contributions;
• using said criteria to determine the directions which can be associated with said resolvable contributions;
• using at least one processor to provide a signal vector library having elements corresponding to possible physical wave fields;
• and
• determining said signal vectors from said library elements generally consistent with said criteria.

A method for determining the presence of a source of a signal contributing to a physical wave field, the properties of the physical wave field being detectable over three spatial dimensions and a temporal dimension, the method comprising:

• using at least one processor to characterize the physical wave field by a physical wave field signal vector representing a mathematical model of the physical wave field;
• using at least one processor to provide a library of library signal vectors having library elements representing physical wave fields with known properties;
• and
• using at least one said library vector and said physical wave field signal vector to determine the presence of the source.

A method for classifying the properties of a source of a signal contributing to a physical wave field, the properties of the physical wave field being detectable over three spatial dimensions and a temporal dimension, the method comprising:

• using at least one processor to characterize a physical wave field signal vector representing a mathematical model of the physical wave field;
• using at least one processor to provide a library of library signal vectors having library elements characterizing physical wave fields with known properties;
• and
• using at least one of said library signal vectors and said physical wave field signal vector to classify the properties of the source.

A method of determining the presence of multiple sources generating contributions contributing to a physical wave field, the properties of the physical wave field being detectable over three spatial dimensions and a temporal dimension, the method comprising:

• using at least one processor to characterize the physical wave field by a physical wave field signal vector representing a mathematical model of the physical wave field;
• using at least one processor to provide a library of library signal vectors having library elements representing potential physical wave fields;
• using at least one of said library signal vectors and said physical wave field signal vector to determine probable detections;
• using at least one processor to determine at least one resolved signal vector characterizing the contributions of at least one of said multiple sources to said physical wave field;
• and
• determining the presence of at least one source using said at least one said resolved signal vector.