毕业论文（设计）基于RBF 神经网络的GPS 高程转换.doc

基于RBF神经网络的GPS高程转换李大军，程朋根，刘 波（东华理工大学地测学院 江西 抚州 344000）摘要：本文采用二次曲面拟合、BP网络和RBF网络进行了GPS高程转换，并在网络结构改进等方面作了分析。通过RBF网络与二次曲面拟合、BP网络的对比分析，结果表明RBF网络进行GPS高程转换是可行的。因此，RBF网络模型对于GPS高程转换具有一定的实用价值。关键词：GPS高程；高程转换；BP网络；RBF网络测绘信息网Study on RBF network model used for GPS height conversionLi Da-jun, Cheng Peng-gen，Liu Bo(1.Geosciences and Geomatics University of East China Institute of Technology, Fuzhou 344000, China)Abstract: In this paper, the fifing method which stimulates the Geoid using quadric polynomial, BP network and RBF network are provided for the GPS height conversion. At the same time, some problems, such as improving the structure of network model are deeply investigated. Comparing with the fitting method which simulates Geoid using quadric polynomial and BP network for conversion of GPS height, the RBF network is feasible. So, the RBF network has some practical value for the conversion of GPS height.Key words: GPS height；height conversion；BP network；RBF network 1引言测绘信息网随着GPS技术的不断发展，GPS技术的应用也越来越广泛，尤其在测绘方面。但目前国内外应用GPS定位技术建立各种控制时，仅解决了平面坐标的精度，而GPS定位中高程转换精度较差，使得GPS高程还没有得到广泛的应用。由于GPS测量所提供的高程为相对于WGS-84椭球的大地高，而我国使用的是正常高。因此，在实际工程中应将大地高转换为水准高程（正常高）。两者的差值称为高程异常。如果GPS测量的大地高经过某种模型的转换而能够得到高精度的水准高程，则不但能减少外业工作量和提高工作效率，而且也能提高经济效益。目前转换GPS高程的方法有很多种，主要有GPS水准高程，GPS重力高程和GPS三角高程等方法，但应用广泛的还是GPS水准高程。在GPS水准高程中一般采用某种几何曲面去逼近高程异常面，而实际的高程异常面是受到很多因素的影响，很不规则。这样就使得几何方法拟合受到限制，而在某些地区效果并不理想。本方讨论的RBF网络模型实现GPS高程转换是一种较新的方法，它以其自适应映射和在转换GPS高程中没作假设而使得拟合的结果具有较高的精度。2 径向基网络原理测绘信息网到目前为止，神经网络模型已有40多种，根据连接方式的不同可分为前向型网络和反馈型网络两大类，而径向基网络（RBF网络）就是前向型网络中的一种。RBF网络是由输入层、隐含层和输出层构成的三层前向网络，见图2（以单个输出神经元为例），隐含层神经元采用径向基函数作为激励函数，通常采用高斯函数作为径向基函数。神经网络信息的传输为：对于输入层，只负责信息的传输，其输入与输出相同。对于隐层：每个神经元将自己和输入层神经元相连的连接权值矢量（也称为第i个隐层神经元的基函数中心）与输入矢量（表示第q个输入矢量，）之间的距离乘以本身的阈值作为自己的输入，见图2，从中可见：对应输入层第q个输入产生的隐含层第i个神经元的输入为：隐含层第i个神经元的输出为： 图1 径向基网络结构图 图2 RBF网络隐层神经元的输入与输出示意图值得说明一点：径向基函数的阈值可以调节函数的灵敏度，但实际工作中更常用另一参数（称为扩展常数），和的关系在实际应用中有多种确定方法，在MATLAB神经网络函数中和的关系设置为，此时隐含层神经元的输出变为：对于输出层而言：输出为各隐层神经元输出的加权求和，激励函数采用纯线性函数，对应输入层第q个输入产生的输出层神经元输出为：RBF网络的训练分为两步，第一步为非监督式学习训练输入层与隐层间的权值，第二步为监督式学习训练隐含层与输出层间的权值。网络的训练需要提供输入矢量、对应的目标矢量以及径向基函数的扩展常数。训练的目的是求取两层权值、和阈值、（当隐含层单元数等于输入矢量数时，取）。3 实例计算测绘信息网实例一应用RBF网络对表1数据（数据来源于参考文献3）进行计算表1 某GPS控制网的定位成果序号点号x/10 kmy/10 km/m120014.856 220-1.578 8912.172220024.826 826-1.013 1252.366320083.748 925-0.745 2642.509420103.764 185-1.850 4322.839530154.627 002-1.624 0612.206630184.433 584-1.700 7342.306730273.942 168-0.623 2592.463830293.760 029-0.992 1262.554930323.769 341-1.579 3442.7731030364.385 549-0.728 8142.4541130434.580 938-0.893 1182.4891240504.442 349-0.866 9732.4761340753.915 812-1.238 1382.7211440783.655 339-1.300 2142.6791540814.147 118-0.926 1152.581假设GPS点高程异常值与平面坐标（,）有如下关系：= f（,）因此，可将（,）作为输入层向量，则输出为。则此时的输入神经元个数为2，而输出层神经元个数为1。对于RBF网络，在MATLAB中利用函数newrbe创建一个精确的网络时，自动选择隐含层神经元的个数，使得误差为0，故不需要人为确定隐含层神经元数目。由于多种因素的影响，为了加快网络的学习速度和提高计算精度，需要对网络结构进行改进。在此，根据二元泰勒级数对输入层神经元个数进行扩充，由二元泰勒级数有：= f（x,y）=+ 、+ 、+ 、+其中，、， ，、，为待定系数，对应于函数在（,）处的各阶偏导数。这样函数关系式就可以看作是多个变量的函数关系式。因此，可用（,、,）代替原来的（,）。但是对于进行GPS高程转换，并不是展开的次数越高就越好。展开的次数太高，不但增加了计算量，而且还会容易产生龙格现象，从而影响最终精度。对于本例，取n=2即可。所以输入层元个数为5，输出层神经元个数仍为1，而隐含层神经元个数仍利用函数newrbe自动确定。为了加快网络的收敛速度，需要对表1的数据进行归一化处理，即要进行输入层和输出的变换。归一化处理过程如下：=（）/（）=（）/（）=（）/（）式中，分别为系列中的最大值和最小值，可知,均位于0,1之间。测绘信息网经过归一化处理的原始数据加载到神经网络后，即可选取一定的训练参数进行训练和学习。选取前10组作为学习样本，后5组作为测试样本，在MATLAB7中经过反复的训练和学习，得到如表2所示的计算结果。表2 实例一各种模型计算残差 (单位：cm)序号曲面拟合BP网络RBF网络改进后的神经网络BP网络RBF网络学习样本11.96-0.490-0.6802-1.29-0.0200.4703-0.29-0.3800.1304-1.321.6700.8905-1.630.2800.5006-0.27-0.0700.02070.47-0.0600.2708-1.540.4500.27092.77-0.640-0.280101.150.0300.110测试样本117.847.735.597.233.14125.972.162.351.250.701316.63-2.9813.368.169.2714-4.729.534.36-0.68-5.811513.91-7.499.071.089.65内符精度1.550.66cm00.47cm0外符精度12.147.47cm8.90cm5.53cm7.47cm精度计算公式为：测绘信息网m=其中n为相应样本集的总数，v为已知高程异常值和计算所得高程异常值的差值，即残差。图3 RBF网络改进结构前目标输出与实际输出图4 RBF网络改进结构后目标输出与实际输出从图3和图4中可以看出，RBF的内逼近精度相当高，而外推精度相对而言要差些。从图5中可以看出，改进结构后的RBF网络，计算精度有所提高，这对于用RBF网络进行GPS高程转换具有一定的适用价值。测绘信息网从表2中我们可以发现，不论是内符精度，还是外符精度，BP网络和RBF网络的计算精度比二次曲面拟合计算精度都要高，因此，RBF网络可以应用于GPS高程转换。图5 RBF网络改进结构前与改进结构后的残差对比实例二为了进一步说明用RBF网络进行GPS高程转换的可行性及在转换中的优点，对参考文献2中的数据再次用RBF网络进行计算，得到如表3所示的结果。表3 实例二各种模型计算残差 (单位：cm)序号曲面拟合BP网络RBF网络改进后的神经网络模型BP网络RBF网络学习样本10.060.1500.07020.150.0500.02030000.06040.160.0100.12050.070.0200.050600.0500070000.010测试样本82.102.770.330.170.1495.064.130.981.720内符精度0.0970.06800.0640外符精度5.7484.9731.0351.7310.14从表3中发现，RBF网络计算的精度比二次曲面拟合与BP网络计算的精度都要高。从而再次说明RBF网络进行GPS高程转换的可行性。以前的学者在用神经网络模型进行GPS高程转换时，大多用的是BP网络，虽然BP网络有许多优点，但也存在不足。在以上两组数据的计算过程中，就发现了BP网络的一些不足这处。例如：BP网络隐含层神经元个数需要人为确定，是一个比较复杂的问题，确定个数的合理与否，将直接影响到GPS高程转换的精度；网络的学习和记忆具有不稳定性，使得计算结果不稳定，在MATALAB，每次运行的结果都不相同。BP网络存在的这些问题，降低了BP网络在GPS高程转换中的应用。测绘信息网而RBF网络就克服了BP网络的这些不足。它具有结构自适应确定，输出与初始值无关等特点。在MATALAB中计算时，它不需要人为确定隐含层神经元个数，计算结果也很稳定，这些优点使得RBF网络在进行GPS高程转换时具有一定的适应价值。但RBF网络也存在不足，在它的网络设计过程中，需要用不同的SPREAD（径向基函数的分布密度）值进行尝试，以确定一个最优值。 SPREAD的大小不但影响网络的逼近精度，而且还影响着网络的预测精度。在用RBF网络进行GPS高程转换时，是用已知的GPS点的坐标和高程异常值通过对网络的训练和学习，来构造一个理想的RBF网络模型，从而来预测其它GPS点的高程异常值。因此，SPREAD的大小对于用RBF网络来进行GPS高程转换来说是十分重要的。从表2和表3中还可以发现一点，就是经过改进后的神经网络模型，其精度迅速提高。因此，在用神经网络模型进行GPS高程转换时，需要选择合适的网络模型，对模型不断地进行改正，确定合理的网络结构，以便取得理想的效果。4 结束语从以上的计算结果及其分析，我们可以得出如下结论：RBF网络模型转换GPS高程是可行的，且精度比较高。在进行GPS高程转换时，BP网络计算的结果不太稳定，而RBF网络的计算结果比较稳定将GPS点的高程异常值与平面坐标关系式用泰勒级数展开，可以增加输入层神经元个数，从而在一定程度上提高了计算精度。在应用RBF网络模型进行GPS高程转换时，网络结构的设计、网络参数的选取，以及初始值的选取十分重要，它们的合理与否将直接影响到GPS高程转换的精度。二次曲面拟合计算比较简单，由于有理论假设，故存在模型误差。神经网络模型参数的选择以及网络结构的确定等问题，都有待于进一步的研究和实践。测绘信息网参考文献：1鲁铁定，周世健，藏德彦关于BP网络转换GPS高程的若干问题J测绘通报，2003，（8）2成国辉，许曦一种GPS过河水准新方法的试验J测绘通报，2004，（6）3鲁铁定，周世健，张立亭，吕开云GPS高程转换的神经元网络方法分析J全球定位系统，20044吴良才，胡振琪基于神经网络的GPS高程转换方法J工程勘察，20045邢文训，谢金星现代优化计算方法M北京：清华大学出版社，19996飞思科技产品研发中心神经网络理论与MATLAB7实现M北京：电子工业出版社，20057从爽面向MATLAB工具箱的神经网络理论与应用M合肥：中国科学技术大学出版社，19988王末然MATALAB与科学计算M北京：电子工业出版社，20039徐绍铨，张华海，杨志强，王泽民GPS测量原理用应用M武汉：武汉大学出版社，200310刘基余，李征航，王跃虎，桑吉章全球定位系统原理及其应用M北京：测绘出版社，199911徐绍铨，李振洪，吴云孙GPS高程拟合系统的研究J武汉测绘科技大学学报，1999Editor's note: Judson Jones is a meteorologist, journalist and photographer. He has freelanced with CNN for four years, covering severe weather from tornadoes to typhoons. Follow him on Twitter: jnjonesjr (CNN) - I will always wonder what it was like to huddle around a shortwave radio and through the crackling static from space hear the faint beeps of the world's first satellite - Sputnik. I also missed watching Neil Armstrong step foot on the moon and the first space shuttle take off for the stars. Those events were way before my time.As a kid, I was fascinated with what goes on in the sky, and when NASA pulled the plug on the shuttle program I was heartbroken. Yet the privatized space race has renewed my childhood dreams to reach for the stars.As a meteorologist, I've still seen many important weather and space events, but right now, if you were sitting next to me, you'd hear my foot tapping rapidly under my desk. I'm anxious for the next one: a space capsule hanging from a crane in the New Mexico desert.It's like the set for a George Lucas movie floating to the edge of space.You and I will have the chance to watch a man take a leap into an unimaginable free fall from the edge of space - live.The (lack of) air up there Watch man jump from 96,000 feet Tuesday, I sat at work glued to the live stream of the Red Bull Stratos Mission. I watched the balloons positioned at different altitudes in the sky to test the winds, knowing that if they would just line up in a vertical straight line "we" would be go for launch.I feel this mission was created for me because I am also a journalist and a photographer, but above all I live for taking a leap of faith - the feeling of pushing the envelope into uncharted territory.The guy who is going to do this, Felix Baumgartner, must have that same feeling, at a level I will never reach. However, it did not stop me from feeling his pain when a gust of swirling wind kicked up and twisted the partially filled balloon that would take him to the upper end of our atmosphere. As soon as the 40-acre balloon, with skin no thicker than a dry cleaning bag, scraped the ground I knew it was over.How claustrophobia almost grounded supersonic skydiverWith each twist, you could see the wrinkles of disappointment on the face of the current record holder and "capcom" (capsule communications), Col. Joe Kittinger. He hung his head low in mission control as he told Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunday.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause), he can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet (22.7 miles/36.53 kilometers). Here, "Fearless Felix" will unclip. He will roll back the door.Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, he'll be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end.Skydiver preps for the big jumpWhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him completely.If he goes too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes it's not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everything goes as planned, it won't. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).It might not be the moon, but Kittinger free fell from 102,800 feet in 1960 - at the dawn of an infamous space race that captured the hearts of many. Baumgartner will attempt to break that record, a feat that boggles the mind. This is one of those monumental moments I will always remember, because there is no way I'd miss this.