Efficient On-Orbit Singularity-Free Geopotential Estimation

For vehicles in orbital cruise, either in orbit around a body or in a transfer orbit, gravity is the primary external force; therefore, the complexity of the geopotential model heavily influences the accuracy of the navigation state. As this type of spacecraft requires a highly accurate geopotential model and performs the computation numerous times a second, this calculation needs to be efficient. This calculation needs to include the first and second derivatives of the geopotential because navigation systems can require both the gravitational acceleration and gradient for inertial integration and state filtering. The most efficient method for calculating the geopotential, the forward column method, is discussed in detail, as well as a method to avoid the singularities that exist when using this method. This is shown to decrease the computation time of the geopotential compared to other popular methods. In addition, methods for first and second order propagation are discussed, which decrease the rate at which the full geopotential model needs to be calculated while maintaining the accuracy required of navigation systems. These estimation methods are shown to decrease the necessary computation of the gravity model by multiple orders of magnitude. This method decreases the computation time of the Exploration Upper Stage navigation system geopotential model by potentially an order of magnitude compared with the previous model without affecting the navigation error. A properly implemented geopotential model can have the accuracy of an 8 by 8 model while approaching the computational requirement as using only the J234 coefficients