In early 1985, Del Norte Technology, Inc (DNTI) deployed a new ranging system in the Gulf of Mexico with the objective of testing the system's performance. The first question was "How can we compare the new non-line-of-sight (non-LOS) system to anything but a known static calibration checkpoint?" This proved to be an interesting challenge since February in the Gulf of Mexico is not conductive parking a vessel exactly at a known position for any length of time without roll, pitch, yaw, and heave becoming completely uncontrollable. The answer was to use standard X-band equipment to track the non-LOS system's gyrations at the calibration points. By clustering X-brand within LOS of strategic calibration point and placing non-LOS equipment elsewhere so that it would not be in line-of-sight to the sane point, the systems could be compared within the same reference grid. Standard summing techniques show the accuracy of the non-LOS system (for brevity, let us call the non-LOS system UHFB) in comparison with the X-brand system.
Such a simple answer instigated the second question : "Can we track the UHFB performance dynamically with X-brand in an similar fashion?" Certainly! An Apple IIth computer was set up with three serial ports so that measurements from the UHFB system would enter the computer regularly at a three-second update, after which a trigger would be sent to the X-brand system so that a second set of ranges could be acquired. Upon reception of the second data stream the entire data block would be saved on a digital cassette recorder. Calculations showed that at 9600 Baud, the data sets would be separated by about 50 ms, which was an acceptable time differential in the error budget (see Appendix A). it was thought that positions and residuals from each type were static. This proved to be untrue.
After data were collected in the Gulf, laboratory tests showed that the UHFB and X-band data were approximately 800 ms apart rather than 50 ms apart due to the Apple II's I/O handling. Obviously, at 6kn the time offset error was significant. Conventional centroid-fix analysis proved to be useless for comparison purposes since UHFB and X-band fixes occurred at different times. Therefore a second approach was necessary.
Matrix reduction of the data seemed t be the proper approach, particularly as presented by Cross (1981). Linear algebra solutions of positional fixes are common, particularly since many small computers have matrix manipulation embedded into their operational repertoire. Essentially, the equation is solved recursively for a best x fix based upon range measurements. One must have a priori information (a guess) estimating a proposed position of the ranging system under scrutiny in order to ascertain the difference between range as measured and ranges as calculated from the guess. The b term in (1) is that difference of opinion
The A term in (1) is a transition term which relates ranges calculated from the guess to grid positions calculated from that same guess.