Abstract: Embodiments described herein describe the construction of frequency domain estimates of generalized power density and the filters that can be constructed from those estimates. Using the concept of the Stokes vector representation of the spectral matrix in an M-dimensional vector space, a generalization of the process in which the spectral matrix may be represented by a set of trace-orthogonal matrices that are based upon a particular signal state can be produced. One aspect of the process is as follows: given a particular signal, represented as by a state vector in the space, a complete, orthonormal set of vectors can be produced that includes the signal of interest. Then, a generalized set of matrices is constructed, based upon the developed vectors, that are trace-orthogonal and which serve as a basis set for the expansion of the spectral matrix. The coefficients of this expansion form a generalized Stokes vector that represents the power in the spectral matrix associated with the various state vectors.

Abstract: Methods and systems are provided herein for signal source tracking. A signal emitted over time from a moving source is a collection of small sub-signals that were emitted by the source at different positions along its path. If the source is traveling at a slower speed than the signal, the sub-signals will arrive at a given sensor in the same order that they were released. By identifying the locations and times of the releases of several of these sub-signals, the path and velocity of the moving source can be estimated.

Abstract: Methods and systems are provided herein for signal source tracking. A signal emitted over time from a moving source is a collection of small sub-signals that were emitted by the source at different positions along its path. If the source is traveling at a slower speed than the signal, the sub-signals will arrive at a given sensor in the same order that they were released. By identifying the locations and times of the releases of several of these sub-signals, the path and velocity of the moving source can be estimated.

Abstract: Embodiments described herein describe the construction of frequency domain estimates of generalized power density and the filters that can be constructed from those estimates. Using the concept of the Stokes vector representation of the spectral matrix in an M-dimensional vector space, a generalization of the process in which the spectral matrix may be represented by a set of trace-orthogonal matrices that are based upon a particular signal state can be produced. One aspect of the process is as follows: given a particular signal, represented as by a state vector in the space, a complete, orthonormal set of vectors can be produced that includes the signal of interest. Then, a generalized set of matrices is constructed, based upon the developed vectors, that are trace-orthogonal and which serve as a basis set for the expansion of the spectral matrix. The coefficients of this expansion form a generalized Stokes vector that represents the power in the spectral matrix associated with the various state vectors.

Abstract: Disclosed herein is a fast method that locates nearby sources based solely on the time-of-flight of a signal across an array of sensors. The time delay for signal passage between all pairs of sensors is determined using cross-correlation estimates and a vector of time delays, ?, is constructed from the results. In the noise free case, each point in the plane is associated with a unique value of the ? vector. The plane is searched for a source location by minimizing the difference between the value of ? associated with the candidate location on the plane and the value estimated from cross-correlations. The search takes place over the three dimensional space that includes two coordinates in the plane and the propagation speed. The starting point for the search is constructed from an analytic fit of circular wave fronts to groups of sensors within the array.

Abstract: Methods and systems are provided herein for signal source tracking. A signal emitted over time from a moving source is a collection of small sub-signals that were emitted by the source at different positions along its path. If the source is traveling at a slower speed than the signal, the sub-signals will arrive at a given sensor in the same order that they were released. By identifying the locations and times of the releases of several of these sub-signals, the path and velocity of the moving source can be estimated.