Comparison of simple computer algorithms for global positioning system users

The Global Positioning System (GPS) is a navigation system which relies on range and range-rate information between satellites and users. This information must be processed by the user to determine his position and velocity. The following computer algorithms for GPS users are compared: 1) a deterministic solution to the nonlinear range and range-rate equations, 2) two deterministic solution using the linearized equations, and 3) a eight-state Kalman filter solution. These conparisons are based on computer operations required, navigation accuracy neglecting noise and navigation accuracy with realistic noise inputs. A simulated flight of a C5A aircraft is used in these comparisons. The deterministic algorithms all give the same accuracies with noisey input data. The simplest algorithm is a linearized deterministic version that sequencially solves for position and velocity with a resulting mean position error of 324 feet and a mean velocity error of .23 ft/ sec. Use of a kalman filter reduces the mean Position errors to 117 feet with small improvement in the velocity estimate, but a 12-fold increase in required computer operations.