A vehicle guidance system, including: sensors to detect a surface pressure distribution for a respective location of the corresponding sensor on a vehicle, respectively; and a controller to receive an initial value for a Mach number; and calculate a converged value for an angle of attack based on first surface pressure data from a first set of the sensors, and a converged sideslip angle value based on second surface pressure data from a second set of the sensors. The controller calculates a freestream dynamic pressure based on the initial Mach number, the converged angle of attack, and the converged sideslip angle value, and calculates a freestream pressure, and calculates a converged value for Mach number based on the freestream pressure and the freestream dynamic pressure. A flight control processor provides an output for adjusting an orientation of the vehicle based on the converged Mach number and the freestream pressure.