动态对动态GPS高精度定位理论及其应用研究
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摘要
众所周知,传统的DGPS是一个固定的基准站,通过无线电台把基站的数据传输到流动站上,这一模式能够满足大多数应用的需求,但在某些应用场合,这种固定基准站发送DGPS数据的有限覆盖范围,又不能够满足动态用户的应用需要:例如,远洋编队航行、舰载飞机着舰(或登陆海上作业平台)、编队飞行、空中加油等。在这些应用中,如果仍旧采用固定基准站,移动站与基准站的距离将会变得很长,由此将会产生两个问题:① 随着基线的增长,求解载波相位测量整周模糊度的时间将会增长,而且精度也会降低;② DGPS数据链将会变得很昂贵,不可靠,甚至不可能。
为了解决两个运动目标之间需要高精度的相对定位问题,我们在采用GPS动态载波相位测量技术时,将基准站也设置在运动载体上,而解求出动态用户相对于基准站的相对位置;并将它称为GPS动态对动态载波相位差分技术。本文针对这一情况,就整周模糊度的解算、周跳的修复、数学处理模型等问题展开研究,论文主要贡献有以下几点:
1.由于GPS是高轨卫星,如果只有几个历元数据(在动态定位中,GPS接收机采样率一般很高,如10Hz)采用最小二乘估计进行计算时,法矩阵的求逆会出现不稳定,又由于观测噪声不可避免,导致模糊度的浮点解与准确值偏差较大,很难正确地确定整周模糊度,所以以往只有通过增加观测时间来改善法矩阵的状态和模糊度的浮点准确性,这样就降低了快速定位的效率。针对此情况,笔者探讨了用岭估计法、谱迭代修正法、附加约束法来消除其病态性;并用实测结果进行了验证,其结果表明用单频静态数据(采样率为1秒)在连续5个历元即可正确解算出模糊度,从而实现快速定位。
2.动态对动态高精度相对定位的核心问题是如何快速准确地确定载波相位测量整周模糊度,本文在分析已有OTF的基础上,提出一种综合求解模糊度的方法,该方法的基本思想采用分步求解的方法,先用LAMBDA方法搜索一个初始模糊度,然后再组合搜索,实践证明该方法能进一步提高搜索速度。
3.在动态对动态GPS相对定位中,有时两个运动载体相距并不太远(小于10km),针对这种情况,我们提出一种适合单频GPS OTF方法,如果采用常规的算法来求解模糊度,则组成法方程阶数巨大,计算负担太大,难以满足实时性要求,而我们使用QR分解方法,再通过矩阵变换,使模糊度参数与位置参数分离,从而使求模糊度的方程阶数大大减少,该方法具有求解速度快,计算简单,适合在航解算等优点。
4.众所周知,尽管我们在解算过程中采用双差模式,可以消除大部分公共误差的影响,但由于受多路径效应及电离层、对流层残余误差的影响,GPS双差之后数据并不是白噪声,而是含有一个干扰量,如果采用常规的数据处理方法可能会有一个模型误差,针对这种情况,引入H_∞滤波理论。讨论其基本原理及其抗干扰性。
5.分析比较三种数据处理模型,即LS、Kalman滤波、H_∞滤波,我们可以发现,当γ→∞时,递推方程简化为Kalman滤波方程,这就说明Kalman滤波是的H_∞滤波的特例。通过实验对比,我们发现:当观测数据为白噪声时,三种模型精度相当,当观测数据含有干扰时,H_∞滤波精度最好,LS次之,Kalman滤波精度最差。
6.周跳是高精度定位中所特有的问题(高精度定位必须采用载波相位测量,实际上是载波相位测量中所特有的问题),所以周跳的探测与修复是GPS高精度定位中另一个核心问题,本文分析已有动态探测与修复周跳的方法,通过算例来说明各种方法的优
It is well known that the pattern of conventional DGPS is that the data of fixed base station transmitted to rover station by radio. Most applications are met by the pattern, But the pattern can not meet the need of some kinematic users in some cases , for example, the voyages are formed into columns to ocean、 the airplanes carried warship are landed in warship、 the airplanes are formed into columns in air et al. For the DGPS data that the fixed base station transmitted cannot cover with largo range. If the pattern of conventional DGPS is still used in the applications, two problems are caused: Firstly, the time that the carrier cycle ambiguity is solved will be increased and the precision of the position will be decreased with the baseline increased; Secondly, the DGPS data will be costly、 incredibility and even impossible. For the range of between the base station and the rover station will become longer and longer.To solve the problem of positioning relatively between the moving objects with high accuracy, we set up the reference station on the moving carrier, to solve the relative position of kinematic user to reference one by GPS carrier phase positioning On-The-Fly (OTF); It's named to On-the-fly GPS Positioning Relative to (?) Moving Reference (KINRTK). the solution of ambiguity 、 the repair of the cycle slip and the mathematical processing model et al are studied ,The main achievement of this paper are as follows:1. If several epoch data are used to solve the ambiguity by LS (Least Square)(the sampling rate of GPS receiver is commonly high, for example 1 OHz, when the receiver is used to kinematic measure), the invert of normal equation of GPS observation equations will be instable, Because the GPS satellites are high orbit, and the float solution of the ambiguity departured from the exact value because of the inevitably observation noise, So the right ambiguity is difficultly fixed. The normal equation of GPS observation equations and the veracity of ambiguity are improved by increased observation time before, So the efficiency of rapid position is decreased. For this situation, the method of Ridge Estimation、 the method of spectrum correction iteration and the method of restricted condition are discussed to eliminate the ill condition of the normal equation; and the experiments results show, for single frequency GPS ,the initialization can be finished in sequence 5 epoches (the sampling rate of GPS receiver is 1s)and the right ambiguity can be achieved.2.The core problem of high accuracy kinematic to kinematic relative position is how to fast confirm the solution of carrier phase ambiguity. An integrate method of solving ambiguity was put forward on analyzed existed OTF methods, step solution is the basic idea of the method, the initial ambiguity was searched by the method with LAMBDA method firstly, and with combined method, experiments results show the method can improve the search speed.3. Sometimes two moving platforms do not apart far (less than 10km) in kinematic to kinematic relative position, For this situation, an new GPS OTF method was put forward for single frequency. If the routine algorithm of solution ambiguity was used, the formation of normal equation rank is large, thus the calculation burdened greatly, the algorithm can not meet the real-time need, but the method of QR decomposition is used, and then the
ambiguity parameter was apart from position parameter by matrix transformation;and the rank of solution ambiguity reduced greatly. So the method have the advantage of solving speed fast> easily calculating and on-the-fly ambiguity.4. It is well known that though Double Difference patter can eliminate most common error;the remains error of troposphere and ionosphere have influence on DD data;so the data is not white noise;but corruption. If the routine algorithm is used to process the data;there is a model error in its results. So the theory of Hm Filter is introduced;and its basic principle and robust were discussed.5. Three model of data processing were analyzed and compared;that is LS;Kalman Filter and Hw Filter,While analysing and comparing the three model of data processing;namely LS;Kalman Filter and Hn Filter;we can find that when y ->■ oo;the recursion equation can simplify the Kalman Filter equation ,this shows that Kalman Filter is one special case of Hn Filter. Through the experiment contrast;we find that when the observation data has the character of white noise;three kinds of models are equivalent in precision. But when the observation data has the corruption;the Ha Filter can get the best precision and the LS takes second place;Kalman Filter can but get the worst precision.6. Cycle-slip is the peculiar problem of high precision positioning (high precision positioning must adopt the carrier phase observation,. and in nature cycle-slip is a peculiar problem of carrier phase measurement);so the detection and repair of cycle-slip is key question of GPS high precision positioning;and all methods of detection and repair of cycle-slip used in kinematic positioning are analyzed and state the advantages and shortcomings of these methods are compared by experiment results. On this basis;a new method of detection and repair of cycle-slip based on tri-difference which has a similar idea and process with the LS ambiguity resolution is introduced. Experiments results show that the new method has a better result in kinematic positioning.7. In GPS kinematic positioning;if the altitude difference of the base station and the rover station is large;then troposphere error would take considerable effect on positioning result;so the correction of troposphere error is necessary in high precision position. In past application;we mostly use Hopfield model and improved Hopfield model which are based on standard meteorological elements to calculate the correction. This paper puts forward a kind of a dynamic troposphere error correction model by utilizing the relation among temperature;atmospheric pressure;height;and the new model can correct the error according to the real-time height. The contrast results of some tests show that the new model can get better result.8. KINRTK is different to conventional DGPS whose precise position is known;so its theory differs from ones. It's discussed that single-point positioning on pseudo-range provides original coordinates;their precision and influence on KINRTK; then author draws the conclusion that it's same to integer ambiguity researching process and cycle slip disposal with each other; The only difference is that the initialed coordinate must be fixed and known in conventional DGPS. And the results of the practical data processing show that KINRTK algorithm's precision to cm level.
为了解决两个运动目标之间需要高精度的相对定位问题,我们在采用GPS动态载波相位测量技术时,将基准站也设置在运动载体上,而解求出动态用户相对于基准站的相对位置;并将它称为GPS动态对动态载波相位差分技术。本文针对这一情况,就整周模糊度的解算、周跳的修复、数学处理模型等问题展开研究,论文主要贡献有以下几点:
1.由于GPS是高轨卫星,如果只有几个历元数据(在动态定位中,GPS接收机采样率一般很高,如10Hz)采用最小二乘估计进行计算时,法矩阵的求逆会出现不稳定,又由于观测噪声不可避免,导致模糊度的浮点解与准确值偏差较大,很难正确地确定整周模糊度,所以以往只有通过增加观测时间来改善法矩阵的状态和模糊度的浮点准确性,这样就降低了快速定位的效率。针对此情况,笔者探讨了用岭估计法、谱迭代修正法、附加约束法来消除其病态性;并用实测结果进行了验证,其结果表明用单频静态数据(采样率为1秒)在连续5个历元即可正确解算出模糊度,从而实现快速定位。
2.动态对动态高精度相对定位的核心问题是如何快速准确地确定载波相位测量整周模糊度,本文在分析已有OTF的基础上,提出一种综合求解模糊度的方法,该方法的基本思想采用分步求解的方法,先用LAMBDA方法搜索一个初始模糊度,然后再组合搜索,实践证明该方法能进一步提高搜索速度。
3.在动态对动态GPS相对定位中,有时两个运动载体相距并不太远(小于10km),针对这种情况,我们提出一种适合单频GPS OTF方法,如果采用常规的算法来求解模糊度,则组成法方程阶数巨大,计算负担太大,难以满足实时性要求,而我们使用QR分解方法,再通过矩阵变换,使模糊度参数与位置参数分离,从而使求模糊度的方程阶数大大减少,该方法具有求解速度快,计算简单,适合在航解算等优点。
4.众所周知,尽管我们在解算过程中采用双差模式,可以消除大部分公共误差的影响,但由于受多路径效应及电离层、对流层残余误差的影响,GPS双差之后数据并不是白噪声,而是含有一个干扰量,如果采用常规的数据处理方法可能会有一个模型误差,针对这种情况,引入H_∞滤波理论。讨论其基本原理及其抗干扰性。
5.分析比较三种数据处理模型,即LS、Kalman滤波、H_∞滤波,我们可以发现,当γ→∞时,递推方程简化为Kalman滤波方程,这就说明Kalman滤波是的H_∞滤波的特例。通过实验对比,我们发现:当观测数据为白噪声时,三种模型精度相当,当观测数据含有干扰时,H_∞滤波精度最好,LS次之,Kalman滤波精度最差。
6.周跳是高精度定位中所特有的问题(高精度定位必须采用载波相位测量,实际上是载波相位测量中所特有的问题),所以周跳的探测与修复是GPS高精度定位中另一个核心问题,本文分析已有动态探测与修复周跳的方法,通过算例来说明各种方法的优
It is well known that the pattern of conventional DGPS is that the data of fixed base station transmitted to rover station by radio. Most applications are met by the pattern, But the pattern can not meet the need of some kinematic users in some cases , for example, the voyages are formed into columns to ocean、 the airplanes carried warship are landed in warship、 the airplanes are formed into columns in air et al. For the DGPS data that the fixed base station transmitted cannot cover with largo range. If the pattern of conventional DGPS is still used in the applications, two problems are caused: Firstly, the time that the carrier cycle ambiguity is solved will be increased and the precision of the position will be decreased with the baseline increased; Secondly, the DGPS data will be costly、 incredibility and even impossible. For the range of between the base station and the rover station will become longer and longer.To solve the problem of positioning relatively between the moving objects with high accuracy, we set up the reference station on the moving carrier, to solve the relative position of kinematic user to reference one by GPS carrier phase positioning On-The-Fly (OTF); It's named to On-the-fly GPS Positioning Relative to (?) Moving Reference (KINRTK). the solution of ambiguity 、 the repair of the cycle slip and the mathematical processing model et al are studied ,The main achievement of this paper are as follows:1. If several epoch data are used to solve the ambiguity by LS (Least Square)(the sampling rate of GPS receiver is commonly high, for example 1 OHz, when the receiver is used to kinematic measure), the invert of normal equation of GPS observation equations will be instable, Because the GPS satellites are high orbit, and the float solution of the ambiguity departured from the exact value because of the inevitably observation noise, So the right ambiguity is difficultly fixed. The normal equation of GPS observation equations and the veracity of ambiguity are improved by increased observation time before, So the efficiency of rapid position is decreased. For this situation, the method of Ridge Estimation、 the method of spectrum correction iteration and the method of restricted condition are discussed to eliminate the ill condition of the normal equation; and the experiments results show, for single frequency GPS ,the initialization can be finished in sequence 5 epoches (the sampling rate of GPS receiver is 1s)and the right ambiguity can be achieved.2.The core problem of high accuracy kinematic to kinematic relative position is how to fast confirm the solution of carrier phase ambiguity. An integrate method of solving ambiguity was put forward on analyzed existed OTF methods, step solution is the basic idea of the method, the initial ambiguity was searched by the method with LAMBDA method firstly, and with combined method, experiments results show the method can improve the search speed.3. Sometimes two moving platforms do not apart far (less than 10km) in kinematic to kinematic relative position, For this situation, an new GPS OTF method was put forward for single frequency. If the routine algorithm of solution ambiguity was used, the formation of normal equation rank is large, thus the calculation burdened greatly, the algorithm can not meet the real-time need, but the method of QR decomposition is used, and then the
ambiguity parameter was apart from position parameter by matrix transformation;and the rank of solution ambiguity reduced greatly. So the method have the advantage of solving speed fast> easily calculating and on-the-fly ambiguity.4. It is well known that though Double Difference patter can eliminate most common error;the remains error of troposphere and ionosphere have influence on DD data;so the data is not white noise;but corruption. If the routine algorithm is used to process the data;there is a model error in its results. So the theory of Hm Filter is introduced;and its basic principle and robust were discussed.5. Three model of data processing were analyzed and compared;that is LS;Kalman Filter and Hw Filter,While analysing and comparing the three model of data processing;namely LS;Kalman Filter and Hn Filter;we can find that when y ->■ oo;the recursion equation can simplify the Kalman Filter equation ,this shows that Kalman Filter is one special case of Hn Filter. Through the experiment contrast;we find that when the observation data has the character of white noise;three kinds of models are equivalent in precision. But when the observation data has the corruption;the Ha Filter can get the best precision and the LS takes second place;Kalman Filter can but get the worst precision.6. Cycle-slip is the peculiar problem of high precision positioning (high precision positioning must adopt the carrier phase observation,. and in nature cycle-slip is a peculiar problem of carrier phase measurement);so the detection and repair of cycle-slip is key question of GPS high precision positioning;and all methods of detection and repair of cycle-slip used in kinematic positioning are analyzed and state the advantages and shortcomings of these methods are compared by experiment results. On this basis;a new method of detection and repair of cycle-slip based on tri-difference which has a similar idea and process with the LS ambiguity resolution is introduced. Experiments results show that the new method has a better result in kinematic positioning.7. In GPS kinematic positioning;if the altitude difference of the base station and the rover station is large;then troposphere error would take considerable effect on positioning result;so the correction of troposphere error is necessary in high precision position. In past application;we mostly use Hopfield model and improved Hopfield model which are based on standard meteorological elements to calculate the correction. This paper puts forward a kind of a dynamic troposphere error correction model by utilizing the relation among temperature;atmospheric pressure;height;and the new model can correct the error according to the real-time height. The contrast results of some tests show that the new model can get better result.8. KINRTK is different to conventional DGPS whose precise position is known;so its theory differs from ones. It's discussed that single-point positioning on pseudo-range provides original coordinates;their precision and influence on KINRTK; then author draws the conclusion that it's same to integer ambiguity researching process and cycle slip disposal with each other; The only difference is that the initialed coordinate must be fixed and known in conventional DGPS. And the results of the practical data processing show that KINRTK algorithm's precision to cm level.
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66. Frank Van Grass & Michael Braasch. GPS Interferometric Attitude and Heading Determination Initial Flight Tests Results. Navigation 1991,38(4):297-316
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68. M.Hernandez-Pajares, J.M.Juan, J.Sanz. Precise Ionospheric Determination and its Application to Real-Time GPS Ambiguity Resolution.ION GPS1999,1409-1417.
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74. Oscar L.Colombo, Manuel Hernandez-Pajares, J.Miguel Juan et al .Rosolving Carrier-Phase Ambiguities On The Fly, At More Than 100 km From Nearest Reference Site,With The Help of Ionospheric Tomography, ION GPS99,1999:1635-1642.
75. Odijk D, Stochastic modeling of the ionosphere for fast GPS ambiguity resolution. Geodesy beyond 2000-the challenges of the first decade, IAG General Assembly, Vol(121),1999,387-392.
76. Odijk.D, Improving ambiguity resolution by applying ionosphere corrections from a permanent GPS array, Earth, Planes and Space, special issue GPS99, 18-22.
77. Odijk.D, Weighting Ionospheric Corrections to Improve Fast GPS Positioning Over Medium Distances ION_GPS2000,
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