An evaluation of the Tight Optical Integration (TOI) algorithm sensitivity to inertial and camera errors

The objective of this paper is to demonstrate the sensitivity of the GPS-camera tight optical integration (TOI) algorithm to errors stemming from two sources; (a) inertial measurement errors and, (b) camera measurement errors. The TOI algorithm has been described by the authors in a recent paper, "An algorithm for GPS tight optical integration (TOI)". In the TOI algorithm, the inertial measurements are primarily used to derive attitude information to transform the camera measurements from the body frame to the navigation frame of reference. Clearly, errors on these inertial measurements contribute directly to the angular information from the camera used for a final position solution. Also, an initial position estimate is required to transform the measurements from the navigation frame of reference to an earth reference frame. As a result, an error in the initial position estimate will introduce some error in the position solution, which is included as an equivalent inertial error in the overall error analysis. The function of the camera is to make angular measurements from a pre-defined "marker". The errors in these measurements are sensitive to the range of the marker from the camera, i.e. marker range. Although the marker range is not a measurement used in the algorithm, it is necessary to investigate the sensitivity of the algorithm to variations in the marker range. It is shown that the sensitivity of the error in the final position estimate increases as this marker range increases. Moreover, the camera needs to identify the marker and hence, an error in the pixel selection in the image or a marker position error will affect the accuracy of the final position estimates. The sensitivity of the algorithm to these errors contributed by the camera is also analyzed. The TOI algorithm performance is shown to be similar to GPS performance levels, in the presence of the error sources discussed above. This makes it a viable solution for navigation capabilities in environments where sufficient satellites for a GPS only solution are not available, e.g. an urban canyon.