Cyber-secure UAV communications using heuristically inferred stochastic grammars and hard real-time adaptive waveform synthesis and evolution

This paper initially describes how an inferred context-free (stochastic) grammar can be used to verify command transmissions and serve as a hedge against a successful cyber-attack. The remainder of the paper addresses a computational problem not amenable to closed-form solution; namely, the hard real-time (~57 usec) synthesis of a desired waveform through the adaptive modification of a carrier wave. This effectively increases the signal to noise ratio - ensuring better UAV communications. Here, the modulation of the primary waveform is under user control and is of strictly positive amplitude. The primary waveform induces a secondary waveform having delayed leading and trailing edges and expanded rise and fall times. There is, in general, a direct relation between the period of the primary waveform and the amplitude of the secondary waveform. The relation between the primary and secondary waveforms may be characterized by trigonometric functions or even interpolating polynomials. However, response time will be minimized where the primary waveforms are discretized and stored in the form of array-based cases. The tertiary (target) wave may be any periodic trigonometric function, but is taken to be a simple sine wave without loss of generality. The task of the adaptive program is to minimize ||s(t) - g(t)||2, where f(t) Æ g(t) and f(t) is the primary waveform at time t, g(t) is the secondary waveform at time t, and s(t) is the tertiary waveform at time t. A computationally efficient algorithm is provided for solving this task in real time. Moreover, an evolutionary program (EP) is provided for automatic case acquisition. Primary waveforms are mutated in accordance with a normal distribution.