Bias estimation for moving optical sensor measurements with targets of opportunity

Integration of space based sensors into a Ballistic Missile Defense System (BMDS) allows for detection and tracking of threats over a larger area than ground based sensors [1]. This paper examines the effect of sensor bias error on the tracking quality of a Space Tracking and Surveillance System (STSS) for the highly non-linear problem of tracking a ballistic missile. The STSS constellation consists of two or more satellites (on known trajectories) for tracking ballistic targets. Each satellite is equipped with an IR sensor that provides azimuth and elevation to the target. The tracking problem is made more difficult due to a constant or slowly varying bias error present in each sensor's line of sight measurements. It is important to correct for these bias errors so that the multiple sensor measurements and/or tracks can be referenced as accurately as possible to a common tracking coordinate system. The measurements provided by these sensors are assumed time-coincident (synchronous) and perfectly associated. The line of sight (LOS) measurements from the sensors can be fused into measurements which are the Cartesian target position, i.e., linear in the target state. We evaluate the Cramér-Rao Lower Bound (CRLB) on the covariance of the bias estimates, which serves as a quantification of the available information about the biases. Statistical tests on the results of simulations show that this method is statistically efficient, even for small sample sizes (as few as two sensors and six points on the (unknown) trajectory of a single target of opportunity). We also show that the RMS position error is significantly improved with bias estimation compared with the target position estimation using the original biased measurements.