惯性导航,捷联惯导 外国论文

III WORKING MODE OF GAINSThe process of the GAINS is displayed in Figure 2. The navigation processor is composed of correlation processor and kalman filter. There are two main inputs, one is the signal processed and compensated from magnetometers, the other is the output collected and calibrated from IMU. After filter estimates, the navigation processor will provide the optimal information about the vehicle. Because motive vehicle in the geomagnetic field induces its own magnetic field, the signalsof the three-axis magnetometers are available only after the degauss regulator processes. Appropriate registration area is chosen by the correlation processor from the stored geomagnetic map using geomagnetic entropy criterion, and then compares real-time sequence based on calibrated magnetic values with chosen registration map to find the closest match resultsof magnetic contours and develops latitude and longitude reference information. Kalman filter, the core of the processor, processes inertial and reference datato continuously update the output of inertial navigation system.Fig.2 Flow diagram of GAINS processA.Geomagnetic Matching Areaa) Geomagnetic Field and modelAs intrinsic resource, the geomagnetic field influences all the orbits with electricity and magnetism on the earth, meanwhile it provides natural coordinate for aviation, aerospace and sailing. The earth’s magnetic field is complicated, viewed as a sum of several contributions including the main field, the anomaly field and external source fields[5]. The geomagnetic model is established to describe the filed. Although International Geomagnetic Reference Field(IGRF[6]) and World Magnetic Model(WMM[7])are popular models to approach the main geomagnetic field in a large-scale range, they are not accurate enough to precise navigation because magnetic fields originating from sources within the earth’s crust, ionosphere and magnetosphere have been removed.b) Selection of Matching AreaThe geomagnetic map stored in the vehicle is in closed relation with the model, but the navigation effect is related with the uniqueness of matching area. Geomagnetic entropy is presented to evaluate the character of magnetic matching region, because it represents information about magnetic field in the registration region. Geomagnetic entropy H is defined in (1).1logNi i iiH P P==−∑,2211,,k li l kk ll l k kMPM===∑∑(1)where,k lM is all the magnetic value in the matching area, k,l are the numbers of matching area grid and i is serial number of matching district.Geomagnetic entropy reflects the size of geomagnetic information in the matching region. The smaller entropy is, the more information is and the better the matching result is. So it’s good criterion to judge the performance of magnetic matching area and measure the uniqueness of magnetic matching area, which provides a basis for the selection of matching area.B. Matching Algorithms in GAINSa) Contour Matching AlgorithmThe contour mapping is the main matching algorithm due to simple theory and batch processing, which is used in a wide range in the terrain and gravity aided systems. The common rule is MSD(mean square deviation) as shown in (2).211(,)()NMSD n j nnR L x yNλ+==−∑（2）Where n jx+is magnetic value in matching region, andny is value measured from magnetometer. N is matching lengthand j is displacement parameter. When (,)MSDR Lλ is minimum, (,)Lλ is determined as reference position.From the definition of contour matching, the defects of algorithm are obvious.1) Precision of matching results is restricted by the accuracy of the map grid.2) When the initial position error is relatively large, the search area must be enlarged to find the matching location. Calculation will increase correspondingly which impact the real-time algorithm seriously.3) The number of optimum match location may not be the only one due to the relevance of the geomagnetic filed in the matching region.b) ICCP AlgorithmIterated Closest Contour Point (ICCP) algorithm is derived from ICP which is widely used in image registration[8].ICP algorithm can be applied to free-form objects without requiring discrete correspondences between the two images. Geomagnetic digital map is represented in contour line. Theposition in the measured magnetic value isoclines is chosen as match model and track computed from INS is used to find the original track. Eulerian distance is regarded as object function in (3). The optimum transformation is calculated when object function reach a minimum value. It is used to rectify INS track. Compared with contour matching algorithm, ICCP method decreases the computational burden and avoids the wrong matching result. Matching location can be more precise because the search area is limited nearby isoclines instead of in the matching area used in contour matching.21(,)(,)NICCP n R K TI d K TI ==∑（3）Where (,)d i i is Eulerian distance between the two track, and K is track in the measured magnetic value isoclines and I is track computed form INS. When (,)ICCP R K TI is minimum, T is determined as optimum transformation. The ICCP flow diagram [9] is displayed in Figure3.Fig 3. ICCP flow diagramc) Information FusionKalman filter is widely used in the integrated navigation system. According to positioning requirements, the system variables are defined as follows:131[]TE N U E N x y z x y z X v v L φφφδδδδλεεε×=∇∇∇ E φ,N φ,U φ- attitude misalignment angles in the directionof east, north and upE v δ,N v δ- velocity error in the east and northL δ,δλ- error of latitude and Longitude x ε,y ε,z ε- drifts of the three gyroscopes x ∇,y ∇,z ∇- drifts of the three accelerometersSystem state equation is followed as:()()()()()X t F t X t G t W t =+i(4)W(t) is white noise in the gyros and accelerometers with expected values ()~(0,)W t Q . Measure equation is shown as12()[]()()T Z t z z HX t V t ==+(5)1z ,2z are the differences of latitude and longitude betweenthe strapdown INS and matching method. H is a zero matrix with dimension 213×, except that (1,6)1H =and (2,7)1H =. V(t) is observation noise matrix, which is whitenoise with expected values ()~(0,)V t R .IV.SIMULATIONBeijing geomagnetic anomaly field is used in the simulation. Geomagnetic map is shown in Fig4.Fig4. Beijing geomagnetic anomaly fieldMatching area B is chosen rather than area A from Fig4 using geomagnetic entropy criterion. The parameters about two regions are listed in Table1.A BTABLE 1COMPARISON BETWEEN TWO MATCHING REGIONSA BLongitude range (deg) 116.46~116.79 116.60~116.93 Latitude range (deg) 40.28~40.62 39.70~40.03 Grid accuracy (deg) 0.002 0.002 Permissible locationerror(m) 200 200Flying length(m) 25000 25000 Geomagnetic entropy 0.0176 0.0166Parameters in vehicle and inertial component are listed in Table 2. Three tracks shown in Fig.5 are true track, INS track and GAINS track based on ICCP algorithm. MSD and ICCP methods are used as matching algorithm respectively to compare matching effect. Longitude and latitude errors using two algorithms are shown in Fig.6 and Fig.7.TABLE 2PARAMETERS IN VEHILE AND INERTIAL COMPONENTSparameter valueInitial north location error (deg) 0.003Initial east location error (deg) 0.003Initial north velocity error (m/s) 0.1 Initial east velocity error (m/s) 0.1 Gyro zero-bias (/h )0.2 Accelerator zero-bias (2/m s )0.001 variance in measured value (nT)2 Flying time(s)125Fig 5. Simualtion trial for GAINSFig 6. Longitude and Latitude Errors using MSD algorithmFig7. Longitude and Latitude Errors using ICCP algorithmFig.5-7 show that longitude and latitude errors fromGAINS system don’t diverge over time unlike pure INS. It’s obvious that better performance and higher accuracy can be obtained by using ICCP algorithm than MSD algorithm from Fig.6 and Fig.7. Simulations illustrate the feasibility and theadaptability of the architecture of simulation platform. V. CONCLUSIONThe paper describes basic theories, composition of GAINS, and then key technologies, such as selection with geomagnetic entropy, matching method using MSD and ICCP are analyzed. The GAINS system is established to validate better performance using ICCP algorithm.A CKNOWLEDGMENTThe author is grateful to the help of Huang xue-gong. Special thanks to National Earth System Science Data Sharing Network for the support of geomagnetic data.REFERENCES[1]Feizhou Zhang, Xiuwan Chen Min Sun et al. "Simulation Design of Underwater Terrain Matching Navigation Based on Information Fusion". Geoscience and Remote Sensing Symposium. IEEE 2004, Vol. 5, pp. 3114-3117.[2] Feizhou Zhang, Xiuwan Chen Min Sun et al. "Simulation Study ofUnderwater Passive Navigation System Based on Gravity Gradient". Geoscience and Remote Sensing Symposium. IEEE 2004, Vol. 5, pp. 3111-3113.[3] Goldenberg F. "Geomagnetic Navigation beyond MagneticCompass". San Diego, California. pp.684-694, 2006.[4] S.K. 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