Real-time curvature estimation for autonomous directional drilling

A system for estimating a wellbore curvature comprising:

• a rotary steerable system (RSS) comprising:
• a drill bit;
• a bottom hole assembly (BHA) connected to the drill bit;
• a first sensor disposed proximal the drill bit and configured to take a first attitude measurement;
• a second sensor disposed on the BHA and configured to take a second attitude measurement;
• and
• an information handling system disposed on the RSS and configured to:
• store a real-time curvature estimation for a borehole;
• apply a filter to at least the first attitude measurement and the second attitude measurement to form a filtered measurement set using a first noise covariance, wherein the first noise covariance is a time-varying function;
• perform a curvature estimation with the filtered measurement set to form an estimated curvature signal, wherein the curve estimation is a difference between a first filtered attitude measurement and a second attitude measurement that is divided by a length between the first sensor and the second sensor;
• compare the estimating curvature signal to a curvature set point to find a difference, wherein the curvature set point is from a stationary survey measurement;
• and
• adjust at least one operating parameter of the RSS based on the difference.