Terrain following/terrain avoidance path optimization using the method of steepest descent

A path-optimization algorithm for terrain following/terrain avoidance and threat avoidance is presented. The algorithm uses the gradient method for generating the optimal ground track that minimizes a quadratic cost function of the aircraft´s altitude above sea level to maximize terrain masking while penalizing large deviations from a prescribed initial ground track. The vertical flight path for each ground track is obtained by using parabolic flight segments that satisfy vertical path constraints. Confining the optimization process to the horizontal plane improves the convergence properties of the algorithm, reduces the storage requirements, and allows the algorithm to be used on fine-grain terrain data. Simulation results are presented which validate the algorithm