Joint waveform and guidance control optimisation for target rendezvous

The algorithm developed in this paper jointly selects the optimal transmitted waveform and the control input so that a radar sensor on a moving platform with linear dynamics can reach a target by minimising a predefined cost. The cost proposed in this paper accounts for the energy of the transmitted radar signal, the energy of the platform control input and the relative position error between the platform and the target, which is a function of the waveform design and control input. Similarly to the Linear Quadratic Gaussian (LQG) control problem, we demonstrate that the optimal solution satisfies the separation principle between filtering and optimisation and, therefore, the optimum can be found analytically. The performance of the proposed solution is assessed with a set of simulations for a pulsed Doppler radar transmitting linearly frequency modulated chirps. Results show the effectiveness of the proposed approach for optimal waveform design and optimal guidance control.