OPERATIONAL RULES AND ACCURACY MODELS FOR GPS-AEROTRIANGULATION

Airborne kinematic camera positioning by GPS has reached a mature state of development. The paper reviews some remaining practical problems, like signal discontinuities, cycle slips, drift errors, datum transformation and derives recommendations which make GPS application to aerial triangulation operationally secure. In the second part the theoretical accuracy of GPS blocks is analyzed for various cases of overlap and control, resulting in simple accuracy models which can be used for planning GPS supported aerial triangulation. 1 Present status of kinematic camera positioning 1.1 State of development Airborne kinematic camera positioning, for aerial triangulation purposes, by differential GPS carrier wave phase observations has recently been thoroughly studied and also experimentally tested. The modern GPS receivers and appropriate software have been developed to a point that successful practical application is imminent. In fact, it has started already, and GPS-supported blockadjustment is expected to become the standard case of aerial triangulation soon. 1.2 Accuracy performance In this paper we refer only to high precision relative kinematic camera positioning for aerial triangulation by differential carrier wave phase observations. Relative positioning eliminates almost all systematic positioning errors directly and also reduces greatly the effects of signal degradation by 'selective availability' (SA). For operational reasons there are always and only two GPS receivers involved, one stationary on a known point in or near the photo-mission area, the other in the aircraft. Both receivers record simultaneously carrier wave (L1 and preferably also L2) phase measurements to at least 4 identical GPS satellites, as well as C/ A-code (or P691 code) pseudo ranges, at measuring rates of ~ 1 sec. The internal r.m.s. precision of ranging by phase observations has been established empirically to be in the order of 1 mm 2 mm. This gives a positioning precision in the stationary mode of 1 cm 2 cm, depending on the satellite constellation (PDOP < 10, preferably < 6). Controlled test flights have shown that relative kinematic camera positioning in-flight comes rather close to that accuracy. R.m.s. coordinate accuracies of < 5 cm « 3 cm) have been empirically confirmed, except for some systematic errors wich will be discussed below. Thus, kinematic GPS camera positioning is of greatest interest to aerial triangulation practically for all conventional photo scales. The computation of the sequence of GPS antenna positions, which represent the flight trajectory, is a standard, straight forward adjustment procedure which does not present particular problems. There are, however, some practical problems which have to be given attention in order to receive high precision camera postions by GPS. They are reviewed next. 2 Some practical problems 2.1 Time off-set and spatial off-set The kinematic GPS positioning gives directly the positions of the GPS antenna on the aircraft, the time sequence being given by the GPS measuring rate. The positions have to be interpolated onto the times of camera exposure and reduced for the spatial off-set between GPS antenna and the perspective centre of the camera (outer node of the lens). The time interpolation is usually based on a signal from the camera with which the mid-time of exposure is recorded on the GPS time scale. All mDdern cameras are equipped for emitting such a pulse. Old cameras can be equipped with a light-detector serving the same purpose. The time accuracy of the pulse must be about 1 msec as it corresponds to a forward movement of the aircraft of 6 cm at a ground speed of 200 km/h. The interpolation of the GPS position is usually linear between the 2 neighbour positions. In 1 sec the aircraft moves about 55 m, at 200 km/h. Hence the GPS measuring rate should preferably be shorter than 1 sec, in order to keep the deviation between the actual flight path and the linearly interpolated positions small « 10 cm). Also a more sophisticated interpolation procedure is recommended. There is a second approach by which the time interpolation can be avoided. If the signal for camera exposure is given by the GPS system, it can be arranged that the camera exposure coincides nearly with a GPS observation. In that case an interpolation is not required at all or it can be kept simple and safe if it has to bridge only 0.1 sec or less. The second kind of correction reduces the (interpolated) GPS antenna position onto the perspective centre of the camera. For that purpose the off-set coordinate components must be known. They can be measured directly at the airplane, by tacheometric ground survey, for instance. The off-set components should refer to the axis system of the aircraft. The computational reduction of the GPS antenna position to the camera position is wanted with regard to the coordinate system of the kinematic GPS positioning. For that purpose the attitude parameters of the aircraft must be known. They may be measured directly by INS. In connection with aerial triangulation there is another solution, as the attitude parameters of the photographs can be derived from the first iterations of the combined blockadjustment. In that case, however, the zero-settings of the camera have to be considered, especially the crab setting, which is to be kept constant during a flight strip and should be manually or automatically recorded during the flight. The off-set corrections do not require precise attitude data. The reduction is particularly insensitive if the GPS antenna is mounted more or less directly above the camera. In that case the horizontal off-set component is small and may be negligible altogether. The z-correction is then reduced to a constant and the remaining xand y-corrections amount to only 3.5 cm per degree tilt, for a 2 m vertical off-set. Thus tilt corrections can be neglected in most cases, except for the high precision demands of large scale photography. 2.2 Ambiguity solution, signal interruption, drift errors There is a second group of problems, related to the ambiguity solution of phase observations and the risk of . ~ycle slips and signal interruptions. Carrier wave phase observations measure only the phase shift within one cycle. The total integer number of cycles, the signal has travelled through from the satellite to the receiver, remains unknown. Those initial unknown phase ambiguities are to be solved before the kinematic positioning can start. In the case of relative positioning by one stationary receiver on the ground and one receiver in the aircraft the problem can be solved by stationary recordings of both receivers before take-off. There are two cases: Either start from a known base-line (both receivers at known GPS points), or deter692 mine an initial base-line from the known stationary receiver position to the unknown position of the also stationary aircraft receiver. The simultaneous stationary recordings had to continue, until recently, for about one hour, in order to solve safely for all initial phase ambiguities. Recently fast ambiguity solutions have been developed which reduce the stationary recording time to a few minutes. Once the initial phase ambiguities are solved the receivers stay locked on the satellites' carrier waves during the flight, until an interruption would occur. Unfortunately, there are several effects which can cause signal interruptions during the flight. They are known as cycle slips, signal obstruction by body and wings of a turning aircraft, and changes of the number and constellation of recorded satellites. There is no need to go into any details here, as to the causes of such disturbancies. It suffice here to state that signal disruptions do occur during the flight missions and are not likely to be completely avoided. As direct effect of a signal disruption the ambiguity solutions are lost. In other words, the common system reference is lost and the continuity of the trajectory is interrupted. Recently, sophisticated software development has succeeded to bridge such gaps or jumps by applying prediction and filter techniques. In many cases the interruptions do not affect all signals, some satellites continue to be recorded with the help of which the lost signals can be reconnected. Software programs become available which are capable of bridging signal interruptions and of reassessing and updating the phase ambiguity solutions. There are cases of quite serious signal interruptions which may extend over 10 sec or more. In such cases it is possible that the ambiguity solution can be restored only approximately. It is well established that approximate ambiguity solutions result in GPS drift errors which are, however, linear in first approximation. This brings us to the general problem of GPS drift errors. Practically all experimental tests on kinematic GPS positioning have shown some systematic GPS drift errors, the typical magnitudes being in the order of 10 cm to 50 cm per hour. It is a matter of controversy amongst experts what are the causes of systematic GPS drift errors and whether they can be avoided completely. From an operational point of view it has to be accepted as a fact, for the time being, that signal discontinuities may occur during a flight mission, especially during flight turns. It has equally to be accepted that there may be small GPS drift errors, possibly as a result of incomplete phase ambiguity solutions, or for other reasons. Considering on the other hand that linear GPS drift errors can be assessed and corrected subsequently, during combined blockadjustment, it can be concluded that no particular efforts need to be made to avoid drift errors. They can be just accepted and dealt with during the blockadjustment. This is an operational consideration which holds only in connection with aerial triangulation. It has, however, convenient operational consequences. If we cannot rule out signal interruptions during the flig