Knowledge Bank

Following a brief history of gravity determination, the general principle and the basic requirement for airborne implementation is presented. The difficulty of extracting gravity information from the time-synchronized series of inertial navigation system (INS) and global positioning system (GPS) measurements is due to the small signal-to-noise ratio. A spectral analysis is performed according to the error spectrum of the system using information from the specification of the Litton LN-93 strapdown system and the power spectral density (PSD) parameter model for GPS-derived acceleration error obtained from flight test data. It is shown that, at the constant aircraft speed of 360 km/hr, vector gravimetry can be performed successfully in the frequency range of 2.99 x 10-4 Hz to 2.23 x 10-3 Hz, i.e., the wavelength from 45 km to 334 km for a baseline gravity model. Similarly the spectral analyses for both smooth and rough gravity signature are also performed. The dominating error sources for airborne gravimetry at different frequency ranges are discussed. The most common two approaches, Kalman filtering and wave estimation, are considered and compared here. In Kalman filtering, a stochastic model is used to describe the gravity disturbance, while in wave estimation, a deterministic model, usually a simple function, is anticipated to approximate the gravity disturbance for a short time interval. For the practical application of vector gravimetry, a full state, 27th-order system model is taken in the Kalman filter by modeling the gravity disturbance with a 3rd-order Gauss- Markov process. As to the wave estimation, a separate algorithm for the horizontal channels is designed considering the weak observability in short time and the feature of deterministic description for the gravity disturbance. The most appropriate estimation cycle for the wave estimation is found to be about 80 seconds. Based on the linear principle, it is proposed here to treat the calibration residual at the initial alignment to be of one single error while regarding the others as zero. In this way, one can avoid the difficulty of estimating and distinguishing each individual initial error. Considering only the essential errors of LN93 inertial system and differential GPS phase measurements, and assuming the aircraft flies at a constant speed, the combined system is simulated thoroughly. The gravity disturbance is also simulated using a sum of two 3rd-order Gauss-Markov models. Finally with the simulated data, two methods, Kalman filtering and wave estimation, are applied to recover the gravity information. The performance with different trajectories and under different circumstances is discussed. The results show that an accuracy of 1--3 mgal (RMS) is achievable within one hour with a medium accuracy strapdown airborne gravity system. It is concluded that the Kalman filter is slightly superior to wave estimation when dealing with the rough gravity signature. This is partially because wave estimation cannot properly account for the contradiction of good deterministic description, which requires a short estimation cycle, and state convergence, which holds for a long period. [Some mathematical expressions are not fully represented in the metadata. Full text of abstract available in document.]