Improving Land Vehicle Gravimetry Using a New SINS/GNSS/VEL Method

GNSS plays a key role in land vehicle gravimetry. However, GNSS is unstable due to the influence of the observation environment, which adversely affects the gravimetry accuracy. The velometer can get rid of the restrictions on the use of GNSS by land vehicle gravimetry. In this paper, a SINS/GNSS/VEL method is proposed. This method uses both centralized filtering and federated filtering methods to process the gravity data. Based on the SGA-WZ02 strapdown gravimeter developed by the National University of Defense Technology (NUDT), the vehicle gravimetry test was carried out on a road of approximately 37 kilometers in east Changsha. The test consists of 4 lines in the south-north direction with an average speed of 40 km/h. Compared with traditional SINS/GNSS method, the accuracy of repeated lines using the centralized filtering method improves from 1.58mGal to 1.37mGal, and the external accuracy improves from 2.31mGal to 2.19mGal with a resolution of 2 km. Using federal filtering method, the internal accuracy is 1.36mGal and the external accuracy is 2.22mGal. It indicates that these two methods proposed could both improve the accuracy of gravimetry compared with the traditional SINS/GNSS method. Meanwhile, with adding the external sensor observation, these methods can improve the stability of gravimetry especially for practical survey operations that will save cost and improve efficiency. Finally, several discussions are proposed on the applicability and further improvement of the method.


Introduction
Kinematic gravimetry has caused much concern these years. It has been widely studied and rapidly applied in many geophysical applications during the last few decades [1][2] . Several different principles dynamic gravimeters have been developed and used for commercial geophysical surveys, such as LCR Gravimeter that is two-axis stable platform type [3] , GT series gravimeters and AIRGrav gravimeters which are gimbaled inertial navigation systems [4][5] , and SGA-WZ series strapdown gravimeter which are based on strapdown inertial navigation system (SINS) like [6] .
Kinematic gravimetry can be implemented by multiple carriers such as aircraft, ships, satellites and cars. Different applications have different requirements because of different carriers. Especially in certain particular geophysics and geology applications, where the knowledge of a local gravity field with a level of 1-10 km spatial resolution is required. Therefore in the future, the land vehicle gravimetry, which has the properties of slower velocity and closer to the earth surface, is playing and will continue to serve as a critical role in future applications [7][8]  However, land vehicle gravimetry still faces large challenges. In traditional SINS/GNSS gravimetry method, GNSS provides high-precision position and velocity observation for SINS, but there is a problem that the GNSS is unstable due to the large influence of the observation environment, which adversely affects the gravity accuracy results [8] . The SINS/VEL method, as a new vehicle gravimetry method, can perform vehicle gravity measurement tasks with the use of a velometerassisted SINS without being restricted by GNSS usage [9] . In the SINS/VEL vehicle gravimetry method, the velometer can provide stable and smooth speed observation information. However, there is an error accumulated over time inevitably, which leads to an increase in the integrated navigation positioning error and eventually affects the data quality of gravity measurement.
Based on the SINS/GNSS method and SINS/VEL method, a new SINS/GNSS/VEL method which comprehensively utilizing GNSS data and velometer data is proposed in this paper. This multi-source data fusion method helps improve the test efficiency, and meanwhile, ensuring the accuracy of gravity measurement. Section 2 shows the principle of centralized Kalman filtering SINS/GNSS/VEL method and Section 3 shows the principle of federal Kalman filtering SINS/GNSS/VEL method. Practical experiment results of land gravimetry test are shown in Section4 with corresponding discussions. Finally, conclusions and suggestions are made in Section 5.

Principle of Centralized Kalman Filtering SINS/GNSS/VEL Method
There are two main methods for integrated navigation estimation using Kalman Filtering (KF): one is centralized KF method, and the second is federated KF method. Collecting all the state information in the navigation system, centralized Kalman filtering calculates the estimation in one Kalman filter. In theory, the optimal estimation of the error state can be calculated by centralized Kalman filtering. In land vehicle gravimetry, both GNSS and velometer are able to provide the external observations for gravimeter systems. Selecting T  =  ag X(t) δp δv ψ bb as the state variable, the Kalman filter equation of state can be written as following: details of Equation (1) are shown in the reference [10] . In land vehicle gravimetry, the gravimeter is equipped with different sensors such as GNSS and velometer for external observation. Although differential GNSS can provide high-precision position information, it can only provide low speed accuracy and high noise. The velometer, as a professional speed measuring device, can provide high-precision speed information in real time. Therefore, the position difference between GNSS position and SINS calculation position, the speed measured by the velometer and the speed calculated by SINS are selected as the state variables. These two differences are combined as the measuring information, so the measurement equation can be written as Measurement matrix in Equation (2) can be expressed as  In Figure 1, The vehicle gravimetry federated filter uses a two-stage processing structure with a main filter and twosub-filters. SINS is selected as the common reference system, and its output information k X is combined with GNSS and velometer to form a combined navigation sub-filter, in addition to directly entering the main filter. The SINS/GNSS sub-filter system calculates the local filter estimation value 1 X and the covariance matrix 1 P . The SINS/VEL calculates the filtered estimation value 2 X and the covariance matrix 2 P . The data enters the main filter for data fusion. The partial estimation state is comprehensively calculated to obtain a global estimateˆf X and a global covariance matrix Selecting the error equation of SINS/GNSS subsystem,which is Where, T  =  ag X(t) δp δv ψ bb is selected as the state variables.
Selecting the difference between the position and velocity obtained by GNSS and SINS respectively as the measurement information, the SINS/GNSS subsystem measurement equation can be expressed as following.
The measurement information of the SINS/VEL subsystem is selected as the difference between the speed measured by the speedometer and the speed calculated by SINS. The measurement equation is In the processing of federated kalman filtering calculation, the main filter is used to fuse the subfilter estimation values and the covariance matrix of the prediction error to obtain the global error state estimation value, which is It can be seen that the information in the two subsystems is processed by fusion, and this information has an impact on the filtering of the last main function. Especially when one of the subsystems fails, other systems can still provide external observation, which will maintain the reliability of the filtering system.

Experimental Results & Discussions
The test route map is shown in Figure 2.

Results of Centralized Kalman Filtering Method
Using the centralized Kalman filtering method, the gravity disturbances of four repeated measure lines are shown in Figure 3. Generally, we use two methods to evaluate the accuracy of gravity results: internal and external accuracy. To evaluate the accuracy of repeated measuring lines, the internal accuracy represents the gravimeter's repetitiveness property sensed on the similar trajectory for several times. In addition, the external accuracy represents the gravimeter's objectiveness compared with true gravity data by accessing the difference between calculated data and reference data [15] . Statistics Details of the internal and external accuracy results are shown in Table 1. Compared with the traditional SINS/GNSS method, the accuracy of the four repeated lines in the centralized filtering method improves from 1.58mGal to 1.37mGal, and the external accuracy is improved from 2.31mGal to 2.19mGal with a resolution of 2 km.

Results of Federated Kalman Filtering Method
Gravity disturbances of four lines using federated Kalman filtering method are shown in Figure 4. Table 2 shows the statistics details of the internal accuracy and external accuracy results.  From Table II, the result shows that the internal accuracy of the federal filtering method is within 1.36mGal and the external accuracy is 2.22mGal. It indicats that the two methods proposed can both improve the accuracy of gravity measurement compared with the traditional SINS/GNSS method. Meanwhile, with adding the external sensor observation, these methods can improve the stability of gravity measurement especially for practical survey operations that will save cost and improve the efficiency.

Conclusion
An SINS/GNSS/VEL method which uses multi-sensor data is proposed. Both centralized filtering and federated filtering methods were proposed in this paper to obtain the gravity data. Based on the SGA-WZ02 developed by NUDT, the land vehicle gravimetry test was implemented in Changsha. Compared with the traditional SINS/GNSS method, the two methods proposed can both improve the accuracy of gravity measurement. Accuracy of the four repeated lines in the centralized filtering method improved from 1.58mGal to 1.37mGal, and the external accuracy improved from 2.31mGal to 2.19mGal at the resolution of about 2km. Using federated filtering method, the internal accuracy is 1.36mGal and the external accuracy is 2.22mGal. Moreover, these methods can help to save cost and improve the efficiency of practical survey operations by adding the external sensor observation.