Entry guidance with real-time planning of reference based on analytical solutions

• High-precision analytical solutions to hypersonic gliding problem are developed.
• A method is proposed for solving a linear system with variable coefficients.
• An entry guidance based on the analytical solutions is designed.
• A three-dimensional scheme is proposed for suppressing trajectory oscillations.
• A guidance scheme is designed by combining PN and a reference tracking law.

In this paper, first, we develop new analytical solutions to hypersonic gliding problem. In the derivation of these solutions, we propose an innovative method based on spectral decomposition for solving a special type of linear system with variable coefficients, where the system matrix can be expressed as the product of a scale function and a constant matrix. Next, we design an entry guidance based on these analytical solutions. In the guidance, the downrange analytical expression is used to plan the longitudinal reference profile satisfying the downrange requirement in real time. Two bank reversals are needed to eliminate the crossrange error. The first is planned by the crossrange analytical expression such that the second is at a specified point near the end of the flight. After the first bank reversal is performed, the second is slightly corrected using the trajectory simulation. Because the longitudinal reference profile and bank reversals are planned onboard, the entry guidance can handle various urgent tasks and deal well with large dispersions in the initial conditions, aerodynamic model and atmospheric model.