Camera Calibration with Unknown Time Offset between the Camera and Drone GPS Systems

This paper considers a camera calibration problem using a discrete-time drone trajectory recorded by an accurate GPS. The challenge is that the GPS receiver and camera are not time synchronized (there is an unknown time offset between the two systems). The problem is formulated as an estimation problem to estimate the parameter vector consisting of the three camera orientation angles and the time offset. The estimation is based on the camera measurements and the discrete time GPS trajectory. The maximum likelihood (ML) estimator using the Iterated Least Squares (ILS) algorithm is developed. It can estimate the parameter vector in continuous space using discrete-time GPS information. Simulation tests are conducted on three drone trajectories. The estimation accuracy achieves the CRLB, and thus it is statistically efficient. The results are further analyzed from the point of view of real impact: the residual bias error (following the calibration) should not be significant compared to the camera measurement error (noise standard deviation). The most suitable drone trajectory is therefore recommended among the three. Its bias error is 24% of the measurement error.