Analogous to astrogeodetic methods, the geoid undulation may be determined along profiles by integrating the horizontal components of the gravity vector estimated by airborne GPS inertial navigation system. This has the advantage of obviating large regional surveys of the vertical gravity component that are required in the usual boundary value problem approach. Two data sets were tested, one over the Canadian Rocky Mountains and one over the North Atlantic Ocean. Comparisons with the Canadian geoid model and an Arctic geoid model, respectively, showed better than 10 cm (SD) agreement in the relative geoid, with resolution judged to be between 10 and 20 km. The geoid estimation was found to be sensitive to the curvature of the geopotential field in the mountainous region, and, in the ocean area, the estimates clearly revealed the difference between the geoid and the mean sea surface at this resolution and accuracy.

Measurements of specific force using inertial measurement units (IMU) combined with Global Positioning System (GPS) accelerometry can be used on an airborne platform to determine the total gravitational vector. Traditional methods, originating with inertial surveying systems and based on Kalman filtering, rely on choosing an appropriate stochastic model for the gravity disturbance components included in the set of system error states. An alternative procedure that uses no a priori stochastic model has proven to be as effective, or moreso, in extracting the gravity vector from airborne IMU/GPS data. This method is based on inspecting acceleration residuals from a Kalman filter that estimates only sensor biases. Using actual data collected over the Canadian Rocky Mountains, this method was compared to the traditional approach adapted for different types of stochastic models for the gravity disturbance vector. In all test cases, the estimation filter without a gravitational model yielded better results—up to 50%. This implies that accurate gravity vector determination from airborne IMU/GPS need not rely on an a priori stochastic model of the field, even though the theory of optimal estimation requests it. However, no filter was able to remove all systematic errors from the data; these remaining errors could only be reduced by elementary methods such as endpoint matching and correlative processing of adjacent passes of the system over the gravity field. The final, best gravity estimates had standard deviations with respect to control data of 6 mGal in the horizontal components and 3–4 mGal in the vertical component.

A new method for airborne vector gravimetry using GPS/INS has been developed and the results are presented. The new algorithm uses kinematic accelerations as updates instead of positions or velocities, and all calculations are performed in the inertial frame. Therefore, it is conceptually simpler, easier, more straightforward and computationally less expensive compared to the traditional approach in which the complex navigation equations should be integrated. Moreover, it is a unified approach for determining all three vector components, and no stochastic gravity modeling is required. This approach is based on analyzing the residuals from the Kalman filter of sensor errors, and further processing with wavenumber coefficient filterings is applied in case closely parallel tracks of data are available. An application to actual test-flight data is performed to test the validity of the new algorithm. The results yield an accuracy in the down component of about 3–4 mGal. Also, comparable results are obtained for the horizontal components with accuracies of about 6 mGal. The gravity modeling issue is discussed and alternative methods are presented, none of which improves on the original approach.

An algorithm for very accurate absolute positioning through Global Positioning System (GPS) satellite clock estimation has been developed. Using International GPS Service (IGS) precise orbits and measurements, GPS clock errors were estimated at 30-s intervals. Compared to values determined by the Jet Propulsion Laboratory, the agreement was at the level of about 0.1 ns (3 cm). The clock error estimates were then applied to an absolute positioning algorithm in both static and kinematic modes. For the static case, an IGS station was selected and the coordinates were estimated every 30 s. The estimated absolute position coordinates and the known values had a mean difference of up to 18 cm with standard deviation less than 2 cm. For the kinematic case, data obtained every second from a GPS buoy were tested and the result from the absolute positioning was compared to a differential GPS (DGPS) solution. The mean differences between the coordinates estimated by the two methods are less than 40 cm and the standard deviations are less than 25 cm. It was Verified that this poorer standard deviation on 1-s position results is due to the clock error interpolation from 30-s estimates with Selective Availability (SA). After SA was turned off, higher-rate clock error estimates (such as 1 s) could be obtained by a simple interpolation with negligible corruption. Therefore. the proposed absolute positioning technique can be used to within a few centimeters' precision at any rate by estimating 30-s satellite clock errors and interpolating them.

Gravity field modeling using airborne vertical component gravimetry has made significant strides over the last decade. We demonstrate the feasibility of extending this to three‐dimensions using data from inertial navigation systems (INS) and the Global Positioning System (GPS). A significant advantage of measuring the horizontal gravity components is that the geoid can be determined in profiles by direct along‐track integration, thus not only adding strength to conventional methods, but reducing the required area of survey support, especially along model boundaries. As such, the ultimate limitation of the method is in the quality of the INS and GPS sensors. In our test case, all three components of the gravity vector were determined over a profile in the Canadian Rocky Mountains. Differences between available truth data and the computed gravity components have standard deviations of 7–8 mGal (horizontal) and 3 mGal (vertical). These standard deviations include uncertainties in the truth data (<5 mGal, for horizontal; 1.3 mGal, for vertical). The resolution in the computed values is about 10 km. These analyses have demonstrated for the first time that the total gravity vector can be determined from airborne INS and GPS to reasonable accuracy and resolution, without any external orientation information, nor prior statistical hypothesis on the gravity signature, using medium‐accuracy INS and geodetic quality GPS receivers.