Configuring a complex of splines when approximating the navigational isoline with linear piecewise functionals

This paper proposes to consider a linear spline as a mathematical criterion for a line of position. In this context, the linear spline approximation is viewed dually: the spline is associated both with an analog of the line of position and simultaneously with a multi-link of the reconstructed navigational isoline. The spline gradient is interpreted as an enhanced concept of the classical gradient vector, differing in its construction along the normal to the spline segment approximating the isoline near the dead reckoning point. This approach ensures the realism of the multifactorial nature of probable directions of maximum increases in the navigation function by operating with a complex of spline gradients, which objectively reflects the situation of extreme observation accuracy as the most likely point of intersection of spline lines of position. It is noted that the concept of a spline gradient is recognized as a fundamental predicate determining the potential for a ship’s movement during isolinear navigation, taking into account the changing geometric characteristics of the navigation parameter field. The estimation of navigation measurement accuracy is specified due to the variable configuration of the gradient complex’s architecture. It seems reasonable to assume the hypothetical possibility of independent control of a ship’s isolinear movement with special onboard equipment capable of continuously determining the values of the navigation isoline’s parameters with synchronous fixation of the gradient fan, since the internal geometry of the ship’s trajectory is fully characterized by navigation parameters in the generally accepted sense of navigation. It is pointed out that an alternative advantage of maintaining a vessel on an isoline navigation route is the technical ability to navigate by control signals derived from measurements of a complex of gradients without using additional information. The practical application of the gradient fan creates a precedent for organizing a parametric system in which the current true course and coordinates of an isolinearly moving vessel are functions of gradiometric measurements. The theoretical possibility of practical application of spline function theory to approximate the latest isolines is allowed, whose introduction into future navigation is associated with innovations in navigation technology. It is predicted that the proposed approach can also serve as mathematical support for an automated navigation system with artificial intelligence within the framework of unmanned navigation.