本文選題：慣性導(dǎo)航 + 重力梯度　； 參考：《武漢大學(xué)》2014年博士論文

【摘要】：慣性導(dǎo)航在軍用和民用領(lǐng)域都有著廣泛的應(yīng)用,是載體實現(xiàn)高精度導(dǎo)航定位的重要技術(shù)手段。以慣性導(dǎo)航定位系統(tǒng)為基礎(chǔ),結(jié)合GPS、重力觀測、磁場、星象等其它觀測手段,可以實現(xiàn)多種多樣、不同精度和應(yīng)用目的的組合導(dǎo)航模式。重力梯度輔助慣性導(dǎo)航技術(shù)就是一項能夠?qū)崿F(xiàn)高精度自主導(dǎo)航定位的新型組合導(dǎo)航模式,在軍事上有著重要作用。隨著慣性元件的精度不斷地提高,對于高精度慣性導(dǎo)航來說,由重力引起的誤差已經(jīng)到了不可忽略的地步,是進(jìn)一步提高導(dǎo)航精度必須考慮的一項因素。重力梯度對地球重力場的高頻信號比較敏感,可以很好地反映地球表面的重力變化,是描述擾動重力場的理想物理量。利用實時觀測的重力梯度值來消除慣性導(dǎo)航中的擾動重力誤差,得到更高精度的實時重力矢量,而后實現(xiàn)慣性導(dǎo)航中重力矢量和慣性力的分離,進(jìn)而獲得高精度的載體速度和位置信息是重力梯度輔助慣性導(dǎo)航的發(fā)展趨勢。 早在上個世紀(jì)六七十年代,美國軍方就開始了這項技術(shù)的研究,但是限于當(dāng)時的技術(shù)水平,這些研究主要停留在理論探討階段。相關(guān)資料顯示,在上世紀(jì)末,有些機(jī)構(gòu)對這項技術(shù)進(jìn)行了一些初步的實驗。進(jìn)入本世紀(jì)以來,隨著慣性導(dǎo)航精度的不斷提高和重力梯度移動測量平臺技術(shù)的逐漸成熟,這項技術(shù)又得到了人們的重視,開始重新活躍起來。目前來說,國內(nèi)的高精度慣性導(dǎo)航產(chǎn)品的精度已經(jīng)與國外相差不多,只是實用上的穩(wěn)定性稍遜,而國內(nèi)的重力梯度測量技術(shù)由于起步較晚,與國外還有一定的差距。就目前的相關(guān)文獻(xiàn)來看,國內(nèi)對這項技術(shù)的研究主要還停留在理論探討階段。由于這項技術(shù)的重要性,國內(nèi)的許多科研機(jī)構(gòu)已經(jīng)開始了重力梯度儀的研發(fā),取得了一些初步成果。 本文的主要工作和研究成果如下： 1.總結(jié)和介紹了慣性導(dǎo)航和重力梯度測量的國內(nèi)外現(xiàn)狀,討論了當(dāng)前重力梯度儀的性能指標(biāo)。根據(jù)重力梯度儀的設(shè)計原理的不同,分別討論了幾種重力梯度儀的測量原理,并分析了各自的優(yōu)缺點,探討了未來的梯度儀發(fā)展趨勢,討論了原子/量子干涉重力梯度儀的發(fā)展前景。 2.分析和研究了重力梯度的特性。定量計算和分析了質(zhì)量與距離對重力梯度值的影響,并模擬了一個簡單的均勻密度山峰,計算了固定高度的一條直線軌跡上的重力矢量和重力梯度各分量的值。結(jié)果表明垂直重力梯度分量E：要大于其它分量,對于一個高度為2000m的高斯形山峰,其最大值約為400E。 3.分析了地球重力場以及地形對重力梯度值的貢獻(xiàn)。利用EGM96模型,計算了1°×1°格網(wǎng)的重力梯度值。根據(jù)Jekeli給出的地形計算重力梯度值的公式,使用SRTM地形數(shù)據(jù),計算了一個1°×1°格網(wǎng)內(nèi)某條直線上的重力梯度值,并驗證了地形與計算得到的重力梯度值的相關(guān)性。計算結(jié)果顯示,在經(jīng)度范圍為東經(jīng)108°～109°,緯度范圍為33°～34°的格網(wǎng)內(nèi)的地表附近,EGM96對擾動重力的貢獻(xiàn)約為-20～20E,而地形的影響大約為-100～100E。 4.從基本的導(dǎo)航方程開始,系統(tǒng)總結(jié)了慣性導(dǎo)航的基本原理、慣性導(dǎo)航中的坐標(biāo)轉(zhuǎn)換、誤差方程、觀測單元以及慣性導(dǎo)航中常用的數(shù)值方法。 5.介紹了旋轉(zhuǎn)平臺式重力梯度儀的測量原理,利用模擬的12-軸重力梯度儀模型,分別推導(dǎo)了其在捷聯(lián)式和平臺式移動平臺下的誤差方程。 6.分析了高精度慣性導(dǎo)航對重力場模型的要求。采用由距離倒數(shù)模型描述的擾動重力位模型,計算了各向同性的空間頻率和時間頻率上的重力梯度功率譜密度,并由得到的功率譜密度值計算了對慣性導(dǎo)航速度誤差和位置誤差的影響。由給定的高精度慣性導(dǎo)航位置誤差要求,分析了其對重力場模型的階數(shù)和分辨率的要求。結(jié)果表明,在載體速度分別為50km/h,400km/h,1000km/h時受到重力擾動影響的重力誤差的功率譜密度的最大值分別為10.4mGal2,1.3mGal2,0.52mGal2.如果要滿足一小時內(nèi)5m精度的下一代高精度慣性導(dǎo)航目標(biāo),則重力場階數(shù)至少要達(dá)到3600階。 7.建立了一個多傳感器的重力梯度輔助慣性導(dǎo)航測量平臺,進(jìn)行了重力和重力測量移動平臺誤差分析。根據(jù)移動平臺上的加速度計、陀螺儀、重力梯度儀、GPS等傳感器,分別給出了各自適用的誤差模型。根據(jù)給出的傳感器精度指標(biāo),計算了各自本身的空間和時間分辨率上的功率譜密度。根據(jù)給出的不同誤差之間耦合誤差計算公式,分析了不同傳感器之間的耦合誤差。 8.根據(jù)模擬的重力擾動位模型,計算并分析了對地表附近擾動重力梯度值進(jìn)行觀測所需的重力梯度儀靈敏度。結(jié)果表明,一個靈敏度為30E/(?)的重力梯度儀可以感應(yīng)到波長約為7km到17km的梯度信號。但是,由于信號的衰減,實際上我們需要靈敏度更高的重力梯度儀。如果其靈敏度為1E/(?),則可以感應(yīng)到波長約為1.4km到2.3km的梯度信號。 9.針對短航時、高精度重力梯度補償?shù)膽T性導(dǎo)航系統(tǒng),設(shè)計并實現(xiàn)了慣性儀器精度指標(biāo)與擾動重力梯度誤差指標(biāo)的組合分析模型,對利用重力梯度測量輔助慣性導(dǎo)航平臺的誤差進(jìn)行了數(shù)值分析。給出了測量平臺的卡爾曼濾波狀態(tài)方程和觀測方程,并根據(jù)高精度慣性導(dǎo)航要求的慣導(dǎo)元件精度指標(biāo),以及由距離倒數(shù)擾動重力位模型計算的擾動重力梯度值,計算了不同精度指標(biāo)組合的最終位置誤差影響。結(jié)果表明,采用10E精度的重力梯度觀測,則慣導(dǎo)精度可控制在5km左右,而1E精度的重力梯度觀測則最高可達(dá)到4～6m的導(dǎo)航精度。
[Abstract]:Inertial navigation is widely used in military and civil fields. It is an important technical means to realize high precision navigation and positioning. Based on inertial navigation and positioning system, combined with other observation means such as GPS, gravity observation, magnetic field and star image, a variety of integrated navigation modes, different precision and application purpose, can be realized. The degree aided inertial navigation technology is a new integrated navigation mode which can realize high precision autonomous navigation and positioning. It plays an important role in the military. With the continuous improvement of the precision of the inertial components, the error caused by gravity has reached the point which can not be ignored for the high precision inertial navigation system, and it is to further improve the navigation precision. The gravity gradient is more sensitive to the high frequency signal of the earth's gravity field. It can well reflect the gravity variation on the earth's surface, and it is an ideal physical quantity to describe the disturbed gravity field. Then, the separation of the gravity vector and the inertia force in the inertial navigation system, and then obtain the high precision information of the carrier velocity and position is the trend of the gravity gradient auxiliary inertial navigation.
As early as the 60s and 70s of the last century, the US military began the study of the technology, but limited to the level of technology at that time. These studies were mainly at the stage of theoretical discussion. At present, the precision of the high precision inertial navigation products in China is a little different from that of the foreign countries, but the practical stability is a little worse than the domestic gravity gradient measurement technology. In the current relevant literature, the domestic research on this technology is still at the stage of theoretical discussion. Because of the importance of this technology, many research institutions in China have begun the research and development of gravity gradiometer, and some preliminary results have been obtained.
The main work and research results of this paper are as follows:
1. summarize and introduce the current situation at home and abroad of inertial navigation and gravity gradient measurement, discuss the performance indexes of gravity gradiometer. According to the different design principles of gravity gradiometer, the measuring principles of several gravity gradients are discussed respectively, their advantages and disadvantages are analyzed, the development trend of the gradiometer in the future is discussed, and the original method is discussed. The development prospect of sub / quantum interference gravity gradiometer.
2. the characteristics of gravity gradient are analyzed and studied. The effects of mass and distance on the gravity gradient are calculated and analyzed. A simple uniform density mountain is simulated and the values of the gravity vector and the gravity gradient components on a straight line track are calculated. The results show that the vertical gravity gradient component E is greater than that of it. Its component, for a Gauss shaped mountain with a height of 2000m, is about 400E..
3. analysis the contribution of earth gravity field and terrain to gravity gradient. Using the EGM96 model, the gravity gradient value of the 1 * 1 degree grid is calculated. According to the formula of gravity gradient calculated by the topographic calculation given by the Jekeli, the gravity gradient value of a straight line in a 1 * 1 degree grid is calculated by using the topographic data of SRTM, and the terrain and the meter are verified. The calculated results show that the contribution of EGM96 to the disturbed gravity is about -20 to 20E, and the effect of the terrain is about -100 to 100E. in the range of 108 degrees to 109 degrees and the latitude range from 33 to 34 degrees.
4. starting from the basic navigation equation, the system summarizes the basic principle of inertial navigation, the coordinate transformation in inertial navigation, the error equation, the observation unit and the common numerical methods in the inertial navigation.
5. the measuring principle of the rotating platform gravity gradiometer is introduced, and the error equations of the 12- axis gravity gradiometer model are derived respectively in the strapdown peace platform mobile platform.
6. the requirement of the gravity field model with high precision inertial navigation is analyzed. The gravity gradient model is used to calculate the gravity gradient power spectral density of the isotropic space frequency and time frequency. The influence of the velocity error and position error on the inertial navigation velocity error and the position error is calculated by the obtained power spectral density value. The requirements for the order and resolution of the gravity field model are analyzed by the requirement of the position error of a given high precision inertial navigation system. The results show that the maximum power spectral density of gravity error affected by gravity disturbance at the velocity of 50km/h, 400km/h and 1000km/h, respectively, is 10.4mGal2,1.3mGal2,0.52mGal2. if the maximum value of the gravity error is satisfied. For the next generation of high-precision inertial navigation targets with 5m accuracy within one hour, the order of gravity field should be at least 3600 orders.
7. a multi-sensor gravity gradient auxiliary inertial navigation measurement platform is set up, and the error analysis of the moving platform for gravity and gravity measurement is carried out. According to the accelerometers, gyroscopes, gravity gradiometer, GPS and other sensors on the mobile platform, the applicable error models are given respectively. According to the precision index of the proposed sensor, the calculation is calculated. The power spectral density of the space and time resolution in each of its own space and time resolution. The coupling error between different sensors is analyzed based on the calculation formula of the coupling error between different errors.
8. according to the simulated gravity disturbance position model, the sensitivity of gravity gradiometer required to observe the disturbed gravity gradient near the surface is calculated and analyzed. The results show that a gradient instrument with a sensitivity of 30E/ (?) can induce a gradient signal with a wavelength of about 7km to 17km. However, the attenuation of the signal is actually necessary. If the sensitivity is 1E/ (?), the gradient signal with a wavelength of about 1.4km to 2.3km can be induced.
9. for the inertial navigation system with high precision gravity gradient compensation in short navigation, the combined analysis model of the inertial instrument precision index and the disturbance gravity gradient error index is designed and realized. The numerical analysis of the error of the auxiliary inertial navigation platform by gravity gradient measurement is carried out. The Calman filtering state equation of the measuring platform is given out. According to the precision index of inertial navigation elements required by high precision inertial navigation and the value of gravity gradient calculated by the gravity position model of the distance reciprocal disturbance gravity model, the influence of the final position error of the combination of different precision indexes is calculated. The result shows that the inertial navigation precision can be controlled in the left 5km by the gravity gradient observation of 10E precision. Right, and the 1E accuracy of gravity gradient observation can reach up to 4 ~ 6m navigation accuracy.
【學(xué)位授予單位】：武漢大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：P223;TN96

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