In a data-ferrying unmanned aircraft system, ferrying performance requires knowledge of the communication environment through which the aircraft moves. This work integrates ferry planning with opportunistically learning the radio environment through the use of a Gaussian process. The unmanned aircraft's trajectory is initially optimized with an a priori model. After flying one circuit of the closed trajectory, radio-frequency variations observed by the ferry are used to train a Gaussian process and improve the model of the environment. This iterative ferry-andlearn system is analyzed through a simulation study, showing ferry performance improves rapidly. The ferry achieves 80% of optimal within four iterations and 93% after nine iterations, as the Gaussian process is able to converge quickly to the true radio-frequency environment. This work further compares the Gaussian process to common parameter-based estimation methods through two extremes of radio-frequency environments. The nonparametric nature of a Gaussian process allows for a higher-resolution model, resulting in the ferry's performance converging to a significantly higher upper bound than parameter-based methods.
Nomenclature= set of all buffers over all points b 1 ; : :node buffers at time t i b f i = state of ferry buffer at time t i C N = covariance matrix for Gaussian process training samples c = Shannon-Hartley channel capacity e= radio-frequency variation, i.e., a priori model residual f m , f t , f c = functionals for vehicle, time, and buffer dynamics GP j;n = Gaussian process predictor for node j after n iterations J = objective function for the ferrying problem, i.e., the system's effective throughput J c = objective function for bandwidth control policy K = kernel matrix k = vector of correlations L = length scale matrix l s = Gaussian process hyperparameter representing spatial length scale M j;n = radio-frequency environment model learned for node j after n iterations N = number of segments in the discretized ferry path n = iteration of the ferry-and-learn process p = ferry's path; the set of ferry poses p 1 ; : : : ; p N p i = ferrying vehicle pose at time t i s = mean received signal strength t i = time corresponding to when the ferry is at location instance i u c = control variables for the ferry's communication u m = control variables for the ferry's motion v i = location-dependent noise X = set of input variables in Gaussian process training set Y = set of response or output variables in Gaussian process training set z = measured wireless signal strength β = bandwidth of the wireless channel δ = Kronecker delta θ = set of Gaussian process hyperparameters l s ; σ 2 f ; σ 2 n μ e;j = mean radio-frequency variation prediction from the Gaussian process of node j ν = additive white Gaussian noise Ξ j = a priori model for node j π = optimal bandwidth control policy