Extracting gravity vectors from the integration of global positioning system and inertial navigation system data

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Abstract
Consulting records of a past flight, 1‐Hz trajectory, and (roll, pitch, yaw) motion profiles were adopted for a simulated 7.5‐hour balloon flight over New Mexico. The assumed pay load of the balloon was an inertial ring laser gyro strap‐down system and a three‐antenna, minimum 12‐channel Global Positioning System (GPS) receiver. The adopted trajectory was assumed to be GPS determined and interferometric in nature reflecting a second, ground‐fixed receiver. Owing to the strap‐down Inertial Navigation System (INS), a corresponding 1‐Hz profile of accelerometer specific force outputs (total (GPS sensitive) inertially referenced accelerations less gravitational accelerations present) was also required to conduct a covariance error analysis. The gravitational accelerations were computed by a spherical harmonic expansion throughn=m= 360. A 36‐state, 40‐noise process, open‐loop Kaiman filter integrating GPS and INS data was constructed. A full constellation of 18 GPS satellites was simulated. Related to the two receivers, external GPS updating observation types used were pseudorange differences, single differenced carrier phases, and single differenced phase rates. A fourth type of updating observation used was the error in the INS's estimation of phase differences between GPS antenna pairs (an equilateral triangle balloon‐borne configuration was assumed with 1‐m baselines). The filter cycle and update frequency were both set at 1 Hz. A postmission covariance analysis based Kaiman filter mechanization was executed, taking into account the major initial INS and GPS error sources. Hybrid alignment errors were reduced to 0.4 arc sec about the north and east axes (leveling errors) and to 0.7 arc sec about the down axis (heading error). Hybrid positioning and velocity errors were held to the 1–2 cm and 1–2 mm\s range, respectively, and were highly correlated to the corresponding position dilution of precision satellite geometry. The benign motions of the balloon allowed for a smooth time behavior of the states. Assuming the accelerometer errors are essentially bias states that can be calibrated in flight based on very accurate GPS observations, the leveling uncertainties are the main error sources in obtaining the three components of the balloon‐ borne gravity vector. The alignment errors mentioned above contribute a 2.5‐mGal error to the computed horizontal components and a 0.05‐mGal error to the vertical. Limiting the misalignment contributions to the deflection error budgets to 1 mGal will require leveling errors of 0.2 arc sec. Gravity components obtained from a hybrid system can be compared to upward continued (from extensive ground gravity data) components to validate continuation models and to establish instrumental proof of concept. A successful balloon experiment would be a strong argument for a “high‐low” satellite tracking mission involving the GPS constellation and a dedicated, polar orbit, low satellite (altitude ε (160 km, 300 km)) possessing the same payload. At such an altitude the leveling concerns are less pronounced. Such a spaceborne mission would allow for a downward continued gravity mapping over all heretofore inaccessible Earth surface regions.

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