Sensor Calibration using In-Situ Celestial Observations to Estimate Bias in Space-Based Missile Tracking

The work presented here demonstrates a new methodology of using star observations and advanced nonlinear estimation algorithms to improve the ability of a space-based electro-optical (EO) tracking system to track targets in space. Nominally, the tracking system consists of two satellites flying in a lead-follower formation tracking a ballistic or space target. Each satellite is equipped with a narrow-view EO sensor that provides azimuth and elevation measurements to the target. The tracking problem is made more difficult due to a constant, nonvarying or slowly varying bias error present in each sensor's line of sight (LOS) measurements. The conventional sensor calibration process occurs prior to the start of the tracking process and does not account for subsequent changes in the sensor bias. This study develops a technique to estimate the sensor bias from celestial observations while simultaneously tracking the target. As stars are detected during the target tracking process, the instantaneous sensor pointing error can be calculated as the difference between a measurement of the celestial observation and the known position of the star. The system then utilizes a bias filter to estimate the bias value based on these measurements and correct the target line of sight measurements. After bias correction, we compare the ability of three advanced nonlinear state estimators to update the target state vector: a linearized Kalman filter (LKF); an extended Kalman filter (EKF); and an unscented Kalman filter (UKF). The bias correction-state estimation algorithm is validated with a number of scenarios that were created using The Satellite Toolkit (STK). The target position error resulting from the nonlinear estimation filters are compared to the Cramer-Rao lower bound (CRLB) and a filter consistency check. The results of this research provide a potential solution to sensor calibration while simultaneously tracking a space target with a space-based sensor system.