Bias Estimation and Observability for Optical Sensor Measurements with Targets of Opportunity

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1 December 2014
Djedjiga Belfadel, Richard W. Osborne, III, Yaakov Bar-Shalom

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In order to carry out data fusion, registration error correction is crucial in multisensor systems. This requires estimation of the sensor measurement biases. 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 co-ordinate system. This paper provides a solution for bias estimation of multiple passive sensors using common targets of opportunity. 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 “composite” measurements, which are Cartesian target positions, i.e., linear in the target state. We evaluate the Cramer´-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 three sensors and three points on the trajectory of a single target of opportunity). We also show that the Root Mean Squared (RMS) position error is significantly improved with bias estimation compared with the target position estimation using the original biased measurements. Bias observability issues, which arise in the case of two sensors, are also discussed.