GPS kinematic positioning for the airborne laser altimetry at Long Valley, California

Abstract

The object of this thesis is to develop a reliable algorithm and software for em-level kinematic GPS (Global Positioning System) data analysis. To assess the accuracy of the software, we use it to determine the trajectory of the aircraft during the surveys at Long Valley, California, in 1993 and 1995. This thesis covers the algorithm development, the modeling, and the software design. We implement a robust Kalman filter to perform the kinematic data processing for GPS measurements. In the kinematic data processing with the Kalman filter, the estimates of the aircraft's position, the GPS receiver clock, and atmospheric corrections are modeled with appropriate stochastic processes. To achieve em-level accuracy for an aircraft trajectory, the GPS phase observables must be used and the integer-cycles of phase ambiguity must be resolved. In this thesis, we investigate the ambiguity problem in different situations and develop different ambiguity strategies depending on the situation. Firstly, we develop a position-independent (position-free) ambiguity search method for the initial ambiguity search for GPS kinematic surveying. Our ambiguity search method focuses on providing the flexibility and uniqueness to determine the correct ambiguities in most experimental conditions including long baselines (up to 100 km), high noise level in low elevation observations, and "bad" observations during the search. Secondly, we develop a method to utilize position-free wide lane and extra wide lane observables to detect cycle slips that occur when the signal from a GPS satellite is interrupted during the flight, for example, when the satellite is blocked by the aircraft's wing during a turn. Our ambiguity algorithms use dual frequency GPS observables so that the effects of the ionospheric delay can be accounted for. Several tests performed indicate that our ambiguity strategy works well for a separation between the moving and fixed GPS receivers of up to 100 lan. We developed a killematic software developed to automatically detect various errors during the data processing, including detecting and correcting of cycle slips, detecting and removal of bad data, and performing ambiguity searches. The user interface to the software is command driven with default values for most processing. This interface provides flexibility and should make the software usable with little training. To evaluate our software, we processed GPS data taken in the 1993 and 1995 Long Valley airborne laser altimetry surveys. We performed four types of tests: (a) Static tests which the evaluate the root-mean-square (RMS) scatter of the aircraft position while it is stationary on the run-way; (b) runway tests which compare the height estimates of the aircraft at approximately the same position along the runway during taxiing, takeoffs and landings; (c) lake tests in which we compare profiles of Lake Crowley"s surface and crossings on the lake surface; and (d) Benton crossing tests in which we compare surface height estimates at location within 2 m of each other at a grassy region of Benton Crossing. The latter two tests use of combination of the laser altimeter and GPS trajectory data. The processing of the laser data with our GPS trajectory was performed by our colleagues at the Scripps Institute of Oceanography. The static tests show that during the times the aircraft was stationary at the beginning and ends of flights, the R..MS scatter of relative height difference between the aircraft and the reference GPS station at Bishop airport, approximately 500 meters from the aircraft, varied between 4 and 2 mm for both campaigns. The One Way tests show that the average height differences between trajectories repeat to within 4 em for six tracks on the taxiway, during the takeoffs and landings. The lake surface tests show height variations within 3 em for the lake surface after removing the cubic polynomial to approximately fit for the geoid-ellipsoidal height differences and flow within the lake for each of the five flight sections over the lake. The Lake Crowley crossover analysis shows a mean difference of 0.2 em and RMS scatter of 4.5 cm for relative height from laser footprint pairs within 2 m distance. The Benton Crossing crossover results show a mean value of 0.2 cm and RMS scatters of 15.5 cm in a similar cross analysis after outliers are deleted. Based on our analyses, we conclude that laser altimetry over the flat surface (i.e. Lake Crowley) can denning surface heights with -3 cm precision. The contribution from the error in GPS trajectory appears to be 1-2 cm.