Unbiased Electro-optical/Infrared Camera Angular Measurements and their Cross-Correlated Errors

Electro-optical/Infrared (EO/IR) camera systems are commonly used in target detection and tracking applications. Such camera systems typically comprise a suite of sensors such as narrow/wide Field of View (FOV) cameras that provide target-originated angular measurements. To estimate the target position in Cartesian space, existing techniques in literature employ the non-linear measurement mapping from the Focal Plane Array (FPA) to azimuth and elevation space. A common assumption made in using this conversion is that azimuth and elevation measurement errors have the same standard deviation, are uncorrelated and are uniform across the camera’s FOV. This paper presents an approach to derive the azimuth and elevation statistics including the cross-correlation of their errors. This approach converts the raw target measurements and their covariance in the image space (FPA) to the angular space for subsequent use in Cartesian state filtering. This conversion has been validated to be unbiased and consistent, and results show that the Line of Sight (LOS) angle error variances and their correlations are in fact variable, with magnitudes dependent on the target’s location in the FPA. The correct LOS angle covariance matrices should be used in Cartesian state estimation and fusion rather than the assumed constant angle variances and uncorrelated errors between the azimuth and elevation.