Reference Frame Based on Arch Length of non-Linear Function for Smart Navigation System

There are many tasks of object and vehicle positioning or navigation in space. Each of these tasks considers available data which is usually a result of some parameters sensing and solution of navigation equation in particular reference frame. There are different types of reference frames. In common for a particular task is used a reference frame which required a minimum of computation power to perform navigation. Most reference frames have a linear axis scale. In the paper, a reference frame with a scale of axis distributed by the arch length of non-linear function is proposed. We consider two coordinates systems cartesian and non-linear with deformed axes by a non-linear function. Both coordinate systems use the same reference point and metric. A non-linear reference frame is useful in tasks where measured parameters a distributed non-linear. For example, an airplane trajectory has been converted to non-linear reference frame and the range parameter to fix point is studied in comparison to the cartesian reference frame.