A Gaussian Algorithm Using Coordinate Rotation for Area Navigation Operations with the Microwave Landing System

The Microwave Landing System MLS avionics convert the received signals of range, azimuth angle, and elevation angle to yield aircraft position in Cartesian coordinates. This enables area navigation and computed centerline approaches, including multi-leg and curved approaches. When the three MLS ground units are not collocated, this requires iteration. The speed of convergence and the size of the algorithm and its computational burden affect the MLS avionics storage and timing requirements. Gaussian algorithms tend to be relatively compact but diverge at azimuth angles within the coverage of the MLS, while Newton-Raphson algorithms require more storage and impose a greater computational burden. This report presents a Gaussian algorithm which, by rotating the coordinate system, enables fast convergence everywhere within the MLS coverage, and with a computational burden significantly less than an equivalent Newton-raphson algorithm. Keywords Computed centerline approach, Gauss-Seidel, Microwave landing system MLS, Position reconstruction algorithm, Rotated Gauss-Seidel.