Self-Navigating UAVs for Supervising Moving Objects over Large-Scale Wireless Sensor Networks

Table 1

Definition of key symbols.

Symbol	Meaning/explanation
	The scalar field of parameter whose value changes upon object arrival
	The object-affected region, observing abnormal growth in values of parameter
	The low and high levels of parameter that define probabilistic sections of object presence
	The -degree bivariate polynomial to be regressed for estimating the gradient vector
	The number of terms in , being equal to
	The number of measurement samples available right before regression of
	Gradient vector at the current position of the field
	Ground velocity of the UAV and the object, respectively
	The vector whose coefficients (calculated by local regression) define
	The scalar whose elements are sorted in increasing order of monomials . Lemma 1 later shows the relation between and
	The matrix formed by arranging scalar into its rows
	The square matrix whose coefficients are all equal to . This factor weighs the influence of sensor measurements on
	The vector whose coordinates are samples of reported by ground sensors (used for regression)
U, P	The orthogonal projection position of UAV onto the ground, object position at the time interval
	The time intervals, respectively, for updating the gradient vector and for capturing images to confirm the object presence
	The deviation angle to steer the UAV against the gradient vector at the regression/update interval
	The radius of visible range by on-board camera and object localizable range by ground sensor data, respectively. Lemma 2 later mentions sufficient conditions on them to keep track of the mobile object
	The length of sensor messages, data load per regression, and average uplink throughput from ground sensors to the UAV, respectively
	The tracking deviation (being, respectively, max and average)—distance between the projection of the UAV onto the ground and the object center
	The energy consumption power values on moving and on hovering, respectively