In target tracking applications, it is necessary to account for measurement biases present within the sensors. For passive sensors, these biases are commonly represented as unknown rotations of the sensor measurements and must be estimated. As targets may move in un-predictable ways, it is advantageous to decouple target state and sensor bias estimation to simplify the estimation problem. To do this, a bias pseudo-measurement method must be used in which the measurements are converted and differenced to eliminate the presence of the true target state. For passive angle-only sensors, it is important to appropriately convert lines of sight into Cartesian space. By using the closest point of approach method, it is possible to apply the bias pseudo-measurement method to these sensors. The Cramér–Rao lower bound can be obtained for this method, and, furthermore, it can be attained by using a maximum likelihood estimation method.