Abstract: A path in three-dimensions for an object in flight is determined according to a radar signal reflected by the object. The radar signal is transmitted at an offset angle from horizontal sufficient to capture the object within the transmitted radar signal. The transmitted radar signal is reflected by the object to form a reflected radar signal containing an indication of a position of the object. The reflected radar signal is received and used to determine two-dimensional position information for the object by detection of the indication of the position of the object in the received radar signal. Position information is derived in three-dimensions from the position information in two-dimensions. The path information representative of the path for the object is obtained from the position information in three-dimensions based on an optimization of a curvature of said path information.

Abstract: An object producing an acoustic wave is located and identified by passive detection of the acoustic wave. The acoustic wave is defined by different sensors in an array having a plurality of passive acoustic detectors. The sensors produce signals in response to the detection of the acoustic wave. A wavelet derived from an acoustic wave of a known form with which each of the at least three signals correlates, is determined. Time difference of arrival measurements between the at least three signals using correlation intensity with the wavelet is used to performed acoustic reciprocity from each of the different detectors. The result of the acoustic reciprocity is a hemisphere centered around each of the different sensors. The hemispheres produced by the acoustic reciprocity are examiner to determine an intersection point of at least three hemispheres. The size of the hemispheres is increased according to the velocity of the acoustic wave and pre-determined intervals until an intersection point is found.

Abstract: A path in three-dimensions for an object in flight is determined according to a radar signal reflected by the object. The radar signal is transmitted at an offset angle from horizontal sufficient to capture the object within the transmitted radar signal. The transmitted radar signal is reflected by the object to form a reflected radar signal containing an indication of a position of the object. The reflected radar signal is received and used to determine two-dimensional position information for the object by detection of the indication of the position of the object in the received radar signal. Position information is derived in three-dimensions from the position information in two-dimensions. The path information representative of the path for the object is obtained from the position information in three-dimensions based on an optimization of a curvature of said path information.