Research On The Airborne Vector Gravimetry Based On Data From SINS And GNSS

Airborne gravimetry is an efficient way for gravity measurement in the air.After decades of development,it has been the main way to measure medium-high frequency information of the earth gravity field.Compared to airborne scalar gravimetry,airborne vector gravimetry can obtain not only the vertical component of the gravity disturbance vector,but also the horizontal ones,i.e.,deflection of the vertical.Thus,airborne vector gravimetry is being one of the research hotspots in geodesy.So far,there has no technical independent airborne vector gravimetry system in China and the data processing of airborne vector gravimetry is still in the start stage.On the basis of all the related research results in this field,the principles and methods of airborne vector gravimetry based on SINS and GNSS are studied thoroughly in this dissertation.And the corresponding data processing software are developed.The ultimate purpose is not only to establish the foundation of the airborne vector gravimetry practical data processing and related application research,but also to accumulate experiences for the development of our country's airborne vector gravimetry system in the future.The main word and contributions in this dissertation are as following:1)The mathematical model of airborne vector gravimetry is derived base on Newton's second law and mechanics of rigid bodies.On the basis of error model of airborne vector gravimetry,the accuracy requirements of GNSS position,velocity,acceleration and SINS specific force,attitude are analyzed.2)The stochastic errors of SINS are analyzed and processed systematically.Several methods for analyzing and processing the stochastic errors of SINS are introduced in detail,including Allan Variance,ARMA model,ARIMA model and kalman filter.The principles and applications are given.Seven noise terms in SINS,i.e.,quantization noise,angle random walk,bias instability,rate random walk,drift rate ramp,exponentially correlated(Markov)noise and sinusoidal noise are analyzed in detail with Allan Variance,and their different characteristics and forms in Allan Variance are compared.3)The application of Time Series Model in SINS stochastic error modeling is studied intensively.Base on the truncation and trailing property of autocorrelation and partial correlation coefficients,the ARIMA model of SINS stochastic error is established and kalman filter is adopted to implement online compensationin real time.4)The attitude update algorithm of SINS is studied intensively.The advantages and disadvantages of Euler angle algorithm,direction cosine algorithm,quaternion algorithm,rotation vector algorithm and optimized rotation vector algorithm under conic motion are analyzed.Base on the analysis,the conclusion that rotation vector algorithm is the best-fit algorithm for high accuracy attitude update of SINS is drawn.The coning error in attitude update is studied in detail,which shows that coning frequency f affects accuracy the most,sampling interval h less and coning angle a the least.5)The velocity update algorithm of SINS under sculling motion is studied intensively.The result shows that the vibrational frequency f affects accuracy the most,sampling interval h less,angular vibration amplitude A? and linear vibration amplitude Ap the least.Then,the position update algorithm of SINS under scrolling motion is studied intensively.The result shows that,compared to coning error and sculling error,the scrolling error affects accuracy the least while the computation of it is the most complicated and hugest.In this regard,a simplified position update algorithm is recommended,which not only satisfies the accuracy requirement but also reduces the computation burden.6)With the intensive research of the mechanism and compensation algorithm of coning error,sculling error and curlingerror,a complete updating algorithm for SINS is presented in this paper.The impact of coning error is eliminated in the updating algorithm for attitude,as well as the impact of sculling error in the updating algorithm for velocity.Based on the methods above,a practical and high-precision software package for SINS is easy to achieve.7)In order to validate the correctness and effectiveness of the update algorithm of SINS,a set oftrajectory simulation programs are designed,which can implement free combination of various maneuvers and output the measurements of SINS and the real flight data.Through comparison of the calculated result and the real ones,the correctness of SINS update algorithm is checked.8)The error characteristics and their propagation pattern of SINS are researched in this paper.The experiments show that there mainly are three oscillation errors of different periods,which are Schuler oscillation with the period of 84.4 minutes,Earth oscillation with the period of 24 hours and Foucault oscillation whose angular frequency varies with the latitude.Generally,Schuler oscillation appears along with Foucault oscillation.The results are also shown that gyro drift is the dominant error in SINS applications.The cumulative error of position would be induced by north and azimuth gyro drift.East gyro drift could result in constant bias for latitude and azimuth.Offsets of accelerometer always influence the horizontal attitude,while oscillation errors usually originate from initial condition errors.9)The initial alignment of SINS is studied in detail.Through theoretical analysis and numerical computation of two coarse alignments,the modified one outperforms the traditional one in horizontal accuracy.As to the system observability analysis of initial alignment,a method combining observability matrix and SVD is proposed,which can determine the system observability,the least observable state and the observable degrees efficiently.The observability analysis shows that the estimates of three attitude errors after initial alignment are linear combinations of the real ones and the unobservable states.Moreover,the horizontal angle estimation accuracies are determined by the accelerometer biases and the azimuth angle estimation accuracy is determined by the east gyroscope drift.Therefore,estimation and compensation of SINS error are the most effective measure to improve the accuracy of initial alignment.10)Two different acceleration determination methods with GNSS,i.e.position differentiation method and carrier phase direct method,are compared and analyzed from theoretical and experimental aspects.In the static case,the acceleration accuracy are both better than 1mGral after 120s Low-Pass filtering while the carrier phase direct method performs slightly better.In the dynamic case,the internal agreement of these two methodsis adopted to assess the accuracy because the real value is unknown.After 120s Low-Pass filtering,the horizontal acceleration accuracy is better than 1mGal while the vertical one is better than 2mGal.11)The impact of filter parameters on acceleration accuracy is discussed from two aspects,i.e.the type of window function and the length of filter.The results show that,in both static and dynamic case,four kinds of filter,which adopt Hamming Window,Hanning Window,Blackman Window and Kaiser Window,can all meet the 1-2 mGal accuracy requirement of acceleration.Considering both the amplitude-frequency response and the boundary effect of filter,the length of filter can be 201-451 when the data length is long and be 101-251 when the data length is short.12)The computing methods of airborne vector gravimetry based on SINS and GNSS are studied in detail.According to whether the gravity disturbance vector is included in the state vector of SINS/GNSS kalman filter,the methods are divided into two methods:direct difference methods and state model method.The mathematical model and characteristic of these two methods are studied in detail.The results show that,although the state model method is optimal in theory,its practical accuracy is far below the one of direct difference method.The reason is that,the state model method is limited by the stochastically accuracy of a prior gravity field which is very difficult to obtain in practice.Therefore,the direct difference method is adopted to compute the gravity disturbance vector in this dissertation.13)The system observability of the direct difference method is studied based on observability matrix and SVD.The result shows that,although the 15-order kalman filter model of SINS/GNSS integration is not completely observable,the state combinations-fU?N+baE,fU?E and baU for specific force correction are observable,which indicates that the direct difference method in airborne vector gravimetry based on SINS/GNSS is observable.Then,the correctness and rationality of the algorithm are demonstrated with simulated data.14)The impact of SINS errors on gravity disturbance vector is studied intensively.The result shows that,with the same accuracy level of accelerometers,the vertical component of gravity disturbance vector is not influenced by the gyroscope accuracy;low accuracy SINS will introduce systematic errors in the estimates of gravity disturbance vector;SINS errors are the key factor on the low frequency part of gravity disturbance vector.15)The impact of GNSS position,velocity accuracy and sampling rate on gravity disturbance vector is studied intensively.Gravity disturbance vector results with different GNSS position,velocity accuracy are compared,which shows that,with the GNSS sampling rate being 1 Hz,the GNSS velocity accuracy should equal or less than 3 cm/s in order to achieve 1mGal accuracy gravity disturbance vector.Besides,with the same GNSS position,velocity accuracy,the gravity disturbance vector results with the GNSS sampling rate being 10 Hz has a great improvement compared to that with the GNSS sampling rate being 1 Hz,which indicates that improvement in GNSS data sampling rate is a new way for obtain high accuracy gravity disturbance vector.Moreover,the GNSS position,velocity accuracy is found to be the key factor on the high frequency part of the gravity disturbance vector.