Apparatus and methods for calculating the behavior of linear structures

An apparatus comprising:

• an optical fiber sensor in which an optical fiber is arranged along a linear structure and configured to detect strain of the optical fiber;
• and
• a processor configured to:
• express at least one parameter in a plurality of discrete values for each predetermined length of the linear structure, and forecast behavior of the linear structure by using each of the discrete values;
• acquire behavior of the linear structure detected using the optical fiber;
• calculate a likelihood between the forecasted behavior of the linear structure and the acquired behavior of the linear structure;
• update at least one of the plurality of discrete values on the basis of the likelihood;
• and
• calculate behavior of the linear structure by using the updated plurality of discrete values,
• wherein the likelihood is calculated based on an infinite product of a probability density function defined by an average value of a displacement in a rotation direction of the linear structure derived for each predetermined length, and a standard deviation of an observation error of the behavior of the linear structure detected by using the optical fiber,
• wherein the behavior of the linear structure is acquired by calculating a deflection angle with respect to each unit length of the linear structure, on the basis of the strain detected by the optical fiber sensor.