Research On Inertial Navigation With Real Time Gravity Gradient Compensation

The inertial navigation system has vast applications in both military and civil fields, and is an important technical method for high precise vehicle navigation and position-ing purpose. Based on inertial navigation system, with other measurement sources like GPS, gravity, geomagnetic and astronomic measuring, it can accomplish lots of different precise and different application purpose integrated navigation modules. Gravity gra-dient associated inertial navigation technology is one of these modules that can achieve high precise self-navigation object, it is crucial especially in military application. With the appearances of high precise INS units, the errors introduced by gravity already can not be ignored anymore and is a crucial factor for the precise raising of INS. Gravity gradient is sensitive to the high frequency signal of gravity field, it affected the gravity field changing of the earth and is a ideal physical quantity to describe the disturbing gravity field. The main thought of gravity gradient associated INS is using the real time gravity gradient measurements to compensate the disturbing gravity errors in INS firstly, then separate the obtained high precise gravity vector to get pure inertial force, by integrate the obtained inertial force we can get the velocity and position information of the vehicle finally.In60s to70s of last century, the US military force has started the researches of this technology but mainly on theoretical level because the low technic practical level then. Relative materials show that in1990s there were some tests have been accomplished by some organizations. After this century, with the gradually maturation of high precise INS and gravity gradient moving base surveying technology, it drew people's attentions and got active again. Currently, the precise of native INS products are more or less the same with abroad products, only with less stabilities in practice. For gravity gradient surveying technology, it still has a long way to catch up abroad colleagues. The native research of this technology is still mainly theoretical discussions mentioned by public materials. Because of the importance of this technology, a lot of native organizations have started the designing and manufacture of gravity gradiometer, and got some preliminary fruits by now.The main works and results of this paper includes,1. By reading lots of materials, the current situation of INS and gravity grdiometry are introduced and concluded, meanwhile the specifications of current gradiometers are listed too. With different design theory of gradiometers, the measurement methods of these gradiometers are introduced, the advantages and disadvantages of them are analyzed, and the future development possibilities of gradiometers are concluded.2. The characters of gravity gradient are analyzed. The effects of mass and distance to gravity gradient values are calculated and analyzed, be a simple modeled even density nountain, it calculates the gravity vector and gravity gradient values along a straight trajectory with constant height.3. The contribution of earth's potential model and terrain to gravity gradient values are analyzed. Using the potential model EGM96, the1°×1°grid gravity gradient values are calculated. By the formula used to calculate the terrain influenced gravity gradient values given by Jekeli, with the SRTM terrain data, the gradient component values along a straight line inside a1°×1°grid is calculated, and the correlation relationship of the obtained values and terrain is verified.4. Based on the basic navigation equation, it concluded the principle of INS, the transformation between different coordinate systems, the error equations in INS, the INS units and the numerical methods used in INS.5. The measurement principle of rotating platform gravity gradiometer is introduced, by a modeled12-axis gravity gradiometer model, it derives the error equations in strapdown platform and stabilized platform separately.6. The requirements of high precise INS to gravity potential model are analyzed. For a reciprocal distance gravity disturbing potential model, the spectral densities of gravity gradient in isotropic spatial frequency and temporal frequency are calcu-lated. From the obtained power spectral density, the error influences to INS ve-locity errors and position errors are calculated. Finally, by the given requirements of position errors of high precise INS, the requirements of order and resolution of gravity potential model are analyzed. 7. The gravimetry and gravity gradiometry platform measurement errors are ana-lyzed. For different sensors in the moving base platform like accelerometer, gyro-scope, gradiometer and GPS, it gives suitable error models separately. The power spectral density for each sensor in spatial frequency and temporal frequency are cal-culated by given specifications. The coupling errors between different measurement quantities are also analyzed.8. With the given gravity disturbing potential model, it calculated the required sensi-tivity of gradiometers for disturbing gravity gradients observing. The results show that a gradiometer sensitivity of30E/Hz can sense gravity gradient signals with wavelength of7km to17km, and a gradiometer sensitivity of1E/Hz can sense gravity gradient signals with wavelength of1.4km to2.3km.9. It makes numerical analysis of gravity gradiometry associated INS platform errors by Kalman Filter methods. The statement equation and observation equation of Kalman Filter process are given, and with given high precise IMU specifications and reciprocal distance gravity disturbing potential model parameters, the influences to final position errors of different combination methods are calculated.