Configuring the fan of spline gradients when approximating the navigational isoline with a linear piecewise functional

Abstract

It is proposed to interpret the linear spline as an analog of the line of the position. In this case, the linear spline approximation is understood in two ways: the spline is associated with the line of the position and as the fragment of the restored navigational isoline at the same time. The author considered the construction of a gradient vector instead of a line of the position relative to its spline analogy, replacing the original isoline with a multi-link one. The new concept of a spline-gradient is introduced as an extended understanding of the classical gradient vector with the difference in the construction of the normal to the spline fragment approximating the isoline in a given neighborhood, and not to the conditional tangent or chord. The architecture fan of spline-gradients is estimated as a factor that determines the actual accuracy of the location of a marine mobile object. The author predicted that the proposed approach could be used as a mathematical support for the future automated navigation system with artificial intelligence within the framework of the concept of unmanned navigation in strategic accordance with the e-Navigation project.