New Algorithms for Converting LORAN Time Differences to Position

New algorithms requiring a digital computer of minimal complexity are presented for computing the position of a LORAN receiver from LORAN time differences. A total of 8 different algorithms starting from the simplest but least accurate to more accurate algorithms requiring a greater number of algebraic operation are described. These 8 algorithms provide an accuracy range from 31 N.M. to 90 feet for a LORAN receiver located an average distance of 1200 N.M. from the three LORAN transmitters. Three of the algorithms are accurate to less than 600 feet, and six of the algorithms are accurate to less than 1.5 N.M. at this distance. As the average distance from the three LORAN transmitters decreases the accuracy of the algorithms increases significantly. For example, at an average distance of 600 N.M., four of the algorithms are accurate to better than 250 feet. 1973 Institute of Navigation