Advanced Algorithms for Underwater Acoustic Navigation
S.E.A. is involved in on-going research and development in acoustic positioning mathematics and algorithm development.  Besides traditional "least-squares" methods, our "HYPERINGS" (described below) is used in our Acoustic Navigation Processor.  Our long baseline program, SeaScape also contains advanced techniques that achieve real-time ray path bending and solution for motion.
ELSINGS - Elliptical Least Sqares Iterative Navigation System
This method inherently solves the positioning problem for moving, short baseline platforms with three or more detectors.  The method is similar to traditional spherical least squares techniques except that the individual detector positions at transmit and receive become the foci of ellipsoids rather than spheres.  When combined with appropriate pitch, roll, gyro and vessel translation sensors, the accuracy of short baseline systems is substantially improved.  The algorithm is just as fast as the traditional method.
HYPERINGS - HYPErbolic Range-difference Iterative NaviGation System
This is a technique that allows the measurement of the arrival times of acoustic signals to be the sole basis of positioning.  System interrogations (or transmissions) are performed independently of the positioning electronics: no start synchronication is required.  This very fast and unambiguous method provides the opportunity to build a truly passive, remotely wired, long or short baseline array.  Five or more hydrophones in a non-conformal array are required and the technique would greatly benefit from digital signal processing of incoming signals.  Precise ray-path bending corrections are necessary for the short baseline case with long slant ranges in a major sound velocity profile.
This unique combination of active/passive, long baseline mathematics uses the fundemental discoveries of HYPERINGS above.  The method allows a passive listener to long baseline signals triggered by an active object to solve for both his own and the active object's position simultaneously.  The potential uses are many but are chiefly centered on multi-vehicle navigation on an eight (or more) transponder array.  Again, DSP receiver electronics would be a key factor in providing outstanding accuracy for this technique.  Double HYPERINGS is quite fast considing the complexity of the mathematics involved.
RINGS - Range-rate Iterative NaviGation
This system uses only Doppler measurements from a long baseline array in order to compute position.  Like HYPERINGS and Double HYPERINGS, this method is truly passive with a number of potential uses.  RINGS computes 3-D position and velocity components based soley on the measurement of Doppler shift from an eight or more hydrophone array.  Precise frequency measurements are required.
3-D WAD (Wave Angle Detector)
Based on very fast mathematics and ready for DSP techniques, the method requires only three hydrophone detectors to determine the direction cosines of an incoming acoustic wavefront.  3-D WAD is usable in both active and passive systems as a primary tool or as a secondary computation.  Suitable for low, medium or high freqency applications, use of low frequency (typically 8-16 KHz) and large array size would allow long range applications for hull-mounted systems and be superior to ultra-short baseline systems.
For a greater detail on the basis of these techniques, refer to S.E.A.'s paper Advanced Techniques for Acoustic Positioning (PDF).
ELSINGS, HYPERINGS, Double HYPERINGS, RINGS. 3-D WAD are trademarks of Software Engineering Associates.