Robust Statistics - 2nd Edition
鲁棒统计，现代统计方法， Robust Statistics第二版，学习现代统计方法R○ BUST STAT|STCSSecond editionPeter j, huberProfessor of Statistics, retiredKlosters SwitzerlandEⅣ ezio m. RonchettiProfessor of StatisticsUniversity of Geneva, SwitzerlandWILEYA JOHn WileY SONS INC. PUBliCAtIONCopyrightc 2009 by John Wiley Sons, Inc. All rights reservedPublished by John Wiley sons, Inc, Hoboken, New JerseyPublished simultaneously in CanadaNo part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form orby any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except aspermitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the priorwritten permission of the Publisher, or authorization through payment of the appropriate per-copy fee tothe Copyright Clearance Center, Inc, 222 Rosewood Drive, Danvers, MA 01923, (978)750-8400, fax978)750-4470,oronthewebatwww.copyrigom. requests to the publisher for permission shouldbe addressed to the permissions department John Wiley sons, Inc., 11 1 River Street, Hoboken, NJ07030,(201)748-6011,fax(201)748-6008,oronlineathttp:/www.wileycom/go/permissionLimit of Liability /Disclaimer of Warranty: While the publisher and author have used their best efforts inpreparing this book, they make no representations or warranties with respect to the accuracy orcompleteness of the contents of this book and specifically disclaim any implied warranties ofmerchantability or fitness for a particular purpose. No warranty may be created or extended by salesrepresentatives or written sales materials. The advice and strategies contained herein may not be suitablefor your situation. You should consult with a professional where appropriate. Neither the publisher norauthor shall be liable for any loss of profit or any other commercial damages, including but not limitedto special, incidental, consequential, or other damagesFor general information on our other products and services or for technical support, please contact ourCustomer Care Department within the United States at(800)762-2974, outside the United States at(317)572-3993 or fax(317)572-4002.Wiley also publishes its books in a variety of electronic formats. Some content that appears in print maynot be available in electronic format. For information about wiley products, visit our web site atwww.wileycomLibrary of Congress Cataloging-in-Publication Data:Huber Peter JRobust statistics, second edition/ Peter J. Huber, Elvezio ronchettip. cnIncludes bibliographical references and indeISBN978-0-470-12990-6( cloth)1. Robust statistics. I. Ronchetti. elvezio. II. TitleQA276.H7852009519.5-dc222008033283Printed in the United States of america10987654321To the memory o1John w. tukeyThis Page Intentionally Left BlankCONTENTSPrefacePreface to first editionGeneralities1 Why robust Procedures1. 2 What Should a robust procedure achieve?1.2.1 Robust. Nonparametric and Distribution-Free1.2.2 Adaptive procedures1.2.3 Resistant Procedures1.2. 4 Robustness versus Diagnostics1.2.5 Breakdown point1.3 Qualitative Robustness567888911. 4 Quantitative Robustness1.5 Infinitesimal Aspects141.6 Optimal Robustness171.7 Performance Comparisons18CONTENTS1.8 Computation of robust estimates181.9 Limitations to Robustness Theory202 The Weak Topology and its Metrization23eneral remarks232.2 The Weak Topology232.3 Levy and prohorov metrics272.4 The bounded Lipschitz metric322.5 Frechet and Gateaux derivatives366 Hampels Theorem413 The Basic Types of Estimates453. 1 General Remarks453.2 Maximum Likelihood Type Estimates(M-Estimates)3.2.1 Influence Function of m-estimates73.2.2 Asymptotic Properties of M-Estimates483.2.3 Quantitative and Qualitative Robustness of MEstimates3.3 Linear Combinations of Order Statistics(L-Estimates)3.3.1 Influence Function of -Estimates3.3.2 Quantitative and Qualitative robustness of l-Estimates 593. 4 Estimates Derived from Rank Tests(R-estimates3.4.1 Influence Function of R-Estimates623.4.2 Quantitative and Qualitative robustness of R-Estimates 643.5 Asymptotically Efficient M-, L,and R-Estimates674 Asymptotic Minimax Theory for Estimating Location4.1 General remarks4.2 Minimax bias4.3 Minimax Variance: Preliminaries744. 4 Distributions minimizing fisher Information764.5 Determination of Fo by Variational Methods814.6 Asymptotically Minimax M-Estimates914.7 On the minimax Property for L-and R-estimates954.8 Redescending m-estimates74.9 Questions of Asymmetric Contamination101CONTENTSScale Estimates1055.1 General remarks1055.2 M-Estimates of scale1075.3 L-Estimates of scale5.4 R-Estimates of Scale1125.5 Asymptotically efficient Scale estimates1145.6 Distributions Minimizing fisher Information for Scale5.7 Minimax Properties116 Multiparameter Problemsin Particular Joint Estimationof Location and scale1256. 1 General remarks1256.2 Consistency of M-Estimates1266.3 Asymptotic Normality of M-Estimates1306. 4 Simultaneous m-Estimates of Location and scale1336.5 M-Estimates with Preliminary Estimates of Scale1376.6 Quantitative robustness of Joint Estimates of Location and Scale 1396.7 The Computation of M-Estimates of Scale14368Studentizing1457 Regression1497. 1 General remarks1497. 2 The Classical Linear Least Squares Case1547. 2.1 Residuals and Outliers1587.3 Robustizing the Least Squares Approach1607.4 Asymptotics of robust regression Estimates163741 The Cases hp2→0 and hp→07.5 Conjectures and Empirical Results1687.5.1 Symmetric Error Distributions1687.5.2 The Question of Bias1687.6 Asymptotic Covariances and Their estimation1707. 7 Concomitant Scale estimates1727.8 Computation of Regression M-Estimates1757.8.1 The Scale Step1767.8.2 The Location Step with Modified residuals1787.8.3 The Location Step with Modified Weights179CONTENTS7.9 The Fixed Carrier Case: What Size hi?1867. 10 Analysis of Variance1907. 11 LI-estimates and Median polish1937. 12 Other Approaches to Robust Regression1958 Robust Covariance and Correlation Matrices1998. 1 General remarks8.2 Estimation of Matrix Elements Through robust Variances2038.3 Estimation of Matrix Elements Through robust Correlation2048.4 An Affinely equivariant approach2108.5 Estimates Determined by Implicit Equations2128.6 Existence and Uniqueness of Solutions2148.6. 1 The Scatter estimate v2148.6.2 The Location estimate t2198.6.3 Joint Estimation of t and y2208.7 Influence Functions and Qualitative robustness2208.8 Consistency and asymptotic normality2238.9 Breakdown Point48.10 Least informative distributions2258.1058. 10.2 Covariance2278.11 Some Notes on Computation2339 Robustness of Design2399.1 General remarks2399.2 Minimax Global Fit9.3 Minimax Slope24610 Exact Finite Sample Results24910.1 General Remarks24910.2 Lower and Upper Probabilities and Capacities25010.2.1 2-Monotone and 2-Alternating Capacities25510.2.2 Monotone and Alternating Capacities of Infinite Order 25810.3 Robust Tests25910.3. 1 Particular Cases26510.4 Sequential Tests267
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多摩川编码器说明书.pdf
多摩川编码器说明书 串行信号接收芯片AU5561可 以解码Ts5647、 Ts5648、Ts5667、 Ts5668、 Ts5669等 型号的编码器 ,可以提供40到iiO位串并信号的转换 ,并且可以和1s/32位 CPU或DsP总线接 口。AU5661N1,提 供中断信号与CPU同步 ,它也能在没有CPU的两种方式 (手动模式 )下读取编码器数据 :lD3(单回转数据 ,多回转数据与报警7S508TS5170O/S128serieso/S85 series产品类型增量式产品类型增量式incrementalIncremental电源电压电源电压Supply voltageDC+24V±20%Supply voltageDC+5V±5%外径128Imrn85mm分解能25~5000C/T分解能9600~50,000CResolutionResolution输出方式电压输出 otago Cutput输出方式长线驱动Output for推拉互补输出 Push pul OutputOutput formLine Drive保护构造P=57保护构造P-52Protective constructionProtective construction质量7 kg Max据置型,8 kg max/加载型质量1 kg MaxMassvass用途: Application用途: Application制造钢铁生产线 Iron steel line■交流伺服马达 AC servo motors工程机械 Machine tools造纸生产线 Paper Producing LineT55410S5647755648O/S90 SeriesSA56 Series产品类型增量式产品类型智能绝对式IncrementalSmart Abs电源电压DC+5V±5%电源比压Supply VoltageSupply Voltage外径56mmSizeSize分解能00c0C/T,100,000G丌,12000T,分解能20or16oit多回转计数量16bt器Resolution36000CcT,400,000c7,480,0007Resolution(65,536转)合计6or32bt输出方式长线驱动20 or 16bit/tum and 16bit/65, 536Output formturns(total 36 or 32bit)保护构造输出方式Protective constructionOutput formLine driver质量3kg Max保护构造开放构造Protective constructionNot Enclosed用途: Application0. 6kg Max测量设备 Measuring Equipment工程机械 Machine tools用途: Application■工程机械 Machine tools机器人 Robots机器人 Robots计测机器 Measuring Instruments高精度角度割出装置Hgh- accuracy Angular Indexing Equipment半导体生产设备 Semiconductor manufacturing Equipment7S5667N2537S5667N650SA100 SeriesSA135 Seeres产品类型智能绝对式产品类型智能绝对式Smart AbsSmart Abs电源电压电源电压DC+5V±5%DC45V±5%Supply voltageSupp y voltage外径135mm100mm分解能17b转,16bt转总计3bt分解能17b转,16多转总计33btResolution17cit/um and 1 6bit multitums Total 33 bitResolution7btturm and 16bit multiturn Total 33 bit长线驱动输出方式长线驱动输出方式Output formLinc drivcrLine Driver保护构造保护构造P-40Protective constructionProtective construction质量12 ka Max(不含引线)质量15 kg max(不含引线) Without cable)Mass(Without cable)用途: Application用途: Application大功率马达 Large wattage motors大功率马达 Large wattage motors机器人 Robots机器人 Robots工程机械 Machine Tools工程机械 Machine tools树脂成形机 njection Machines树脂成形机 njection MachinesQAnD艾而特22电梯专用编码器ELEVATOR ENCODER尺寸 mm Dimer sion mmTS5200N500PCD4Do/H48Serieshounding plate details蝙码器安装面Encocer mounting surtace用途特点252M3闪六角丝APPLICATIONFEATURESpicket se: screw在轴上痄荐尺寸(Attachedsions or shaft●有齿、无齿电引机●易安装Gear and gearless tractive motor Easy to attach除非特别说明,否则公券一律为=05 mnUnless otherwise specified tolerance is s+n5m尺寸 mm Dimension mnTS5200N400p35O/H60Series空」用途特点APPLICATIONFEATURES器有齿、无齿曳引机易安装雄明细图内六角手拧紧Gear and gearless tractive motorEasy to attach轴推荐尺寸出除非特别说明,否则公差一律为±0.5 Ium Urless otherwise spccificd tolerance is+0:m755208N1e OlH100 series式样SPECIFICATIONS135●输出方式:长线驱动、推拉互补、集电极开路、正余弦=52留投线表CTION TABLEOutput form: Line Driver, push Pull, open collector, Sincos我色功能「引线频色。●电源电压 Supply voltage:5-15V●分解能 resolution:1024、40965000、6000、8190、10000CT当U儿在轴上批荐只寸抽璃址图、的普属2警出PU安装方式:各种各样Attaching way: VariousOH分解能C丌光电式 Optical外径SizeN。 TSLLLUNLI增量型中48mmResolution中6o512中空轴 Hollow Shalt4100mm1024TS5208编码器 EncoderTs5213翰出相4096TS5216ABZs52176 A, B, Z u, M,wTs52337: A, B, ZFOF1F2, F360008192TS524610000TS5236输出方式C:开放电极 Open Co lecto拉写补 Push pull长线驱动 Line driver⑧对于特殊情况,请联系我们O For special cases, pleasc consult us.23【AnD艾而特连接方面的注意事项NOTICE IN TRANSMITTING1.怎样连接到电源1. HOW TO CONNECT TOA POWER SUPPLY应该通过单独的带屏蔽线的电源线进行连接,任何Connection should be made using a plus and ground不正确的连接方法或不合适的连接线都可能导致传power line which is shielded within a single insulatedcable. Incorrect connection or improper cables will cause输噪音。unwanted noise in transmission编码器应该单独连接到电源,并且独立于编码器一The encoder should be connected to the power supply起作的电子设备,每样设备都应该使用独立的电separate from the electric device that the encoder is缆连接到电源。operating. Each should be connected to the power supplyusing separate cables而不要通过中间电子设备连接到电源。编码器和中Do not connect the encoder thru the electric device to间电子设备的地线之间仔在的阻抗会导致编码器和the power supply. The potential difference between the电源之间产生潜在的差异,这种差异将导致异常ground levels of the encoder and the power supply willbe produced by impedance of zero level bus within theelectric device. This will cause malfunction.编码器输出Encoder Output编码器输出coder Output电源电了装置电源④电子装置PowerElectricSupply编码PowerSupplyElectric device掮码器′Bu图-1好例子图-2不可取例子Fig 1 Favorable SampleFig2. No Recommendable Sampl2.地线应该尽可能的粗2. GROUND LINE SHOULD BEAS THICK AS POSSIBLEIi是电源旳输岀电流,Io是编码器流过地线的输li for power supply current and lo for output signals of an州燃出信号,Re是接地线直流阻抗,Ⅵ为输出信号可encoder will flow thru a ground line. In case of Re for DCresistance of the ground line, VL for the level of the output表达如下signals will be as followsVL=(o+li)·Re(V)=(o+i)·Re(V)ⅥL值不会超出接收器阈值电平Vt,Re要尽可能小The value of vi should not exceed t of threshold level因为当Ⅵ接近Ⅵ时,编码器对于外部噪音米说是脆for a receiver. Re should be as small as possible sincethe encoder will be vulnerable to external noise when Vl弱的。is closer toⅥt.对丁长距离信号传送,除了电源插头上的一条地线In case of long-distance transmission, another ground外,再加·条地线也是必要的。line besides the ground line paired with the plus line maybe necessary.〖()AnD艾而特243.外壳和电路之间短接3. SHORT BETWEEN CASE GROUNDAND CIRCUIT GROUND在喚音比较重的环境中,在编码器外壳地和电路地In case of having noise more than 50V between case之间的噪音信号可能会超过50V,编码器电路可能会ground and circuit ground under noisy circumstances, anelectric circuit for an encoder may not function normally.出现功能异常,在这种情况下,我们建议将外壳和In this case, the short-circuiting of case ground and cir电路地短接。cuit ground is recommendable然而,有时侯由于传送距离过长,短接可能会产生一However, in case that other adverse effects appear些相反的效果,或者说根本不可能将其短接时,我们 because of a long transmitting distance when case andcircuit ground for an encoder are short-circuited and in建议将外壳和电路之间加接个几个微法的有较好的case shorting them is impossible for some reason, it is频率特性的电容,用米做过滤噪音的滤波器。recommendable to provide, between case and circuitground, a few micro farad condensers with better fre-uency characteristics used for a noise filter.4.电源线有噪声的情况4. IN CASE OF HAVING NOISE ONPOWER LINE电源应该通过一根完全被屏蔽好了的传输线提供给Power should be supplied to an encoder thru a transmit-编码器,这样就不会有喚音信号出现在电源线上。ting line completely shielded so that no noise occurrs onpower line将屏蔽线接地以稳定信号Stable potential should be maintained by grounding thehield有必要加长屏蔽线,这样在编码器附近的传输线就It is necessary to distribute lines so that a transmitting不会被暴露在屏蔽线外面。line should not be exposed from the shield near anencoder删5编码带输出信号有尖峰的情况5. IN CASE OF SPIKE WAVESBETWEEN OUTPUT SIGNALSFOR AN ENCODER在尖峰脉冲出现的情况下,将由双绞线传送信号消In case of spike waves as shown in fig 3, Spike waves除尖峰脉冲。shall be deleted by transmitting by twist pair shield line尖峰信号尖峰信号图-3峰形波图-3峰形波Fig 3 spike wavesFig 3 spike waves6.编码器盒的潜在安全措施6. POTENTIAL STABILIZATION FORAN ENCODER CASE编码器盒必须被保持在稳定的电位状态。An encoder case must be maintained in stable potential5[AnD艾而特传送距离TRANSMITTING DISTANCE在开放集电极的情况下!IN CASE OF OPEN COLLECTOR传输距离在大约50m以内(12VDC上拉),20mA集电极Transmission within a distance of about 50m(12V DC pull电流将是允许的!up) and 20mA as collector current shall be allowable在长距离传输的情况下,带光耦的接受电路在图4In case of a long range transmission, receiving circuit with适合消灭在传输线中的噪音!photo couplers in fig. 4 is suitable for eliminating noisein transmission编码器屏酸线编码器屏蔽线EncoderShield CableShield Cable≤RR2Dc输出输出Output图-4Fig.4图-4Fig.4在长线驱动的情况下IN CASE OF LINE DRIVER26Ls3126LS32(编码器 Encoder/※传送距离1km以下编码器 Encoder/※传送距离1m以下Transfer distance 1km MaxTransfer distance 1km max双絞线屏蔽双绞线屏蔽Twisted Pair Shield cableTwisted Pair Shield Cable图-5Fg.5图-5Fig.5在推拉互补的情况下!IN CASE OF COMPLIMENTARY双绞线屏蔽双绞线屏辙Twisted Pair Shield CableTwisted Pair Shield CableA:2Sc3733B: 2SA1电源 Power SupplyA2sC3733电源 Power SupplyB2SA1460A这XGNDXXXX GND厂输出信号线输出信号线itput signal编码器 EncoderL:负载L编码器EL:负载ncodeL: Load怎样使用编码器控制信号H0WT0 USE ENCODER G0 NTROL SIGNALS反向输入REVERSE INPUT通过端了“”或‘L”输入可以改变编4.7kgEncoder direction can be changed by码器方向,CCW和CW之间切换成为可能。输入inputting Hor L to this terminal.如果不需要改变方向,电路输入4.7K欢In case of no necessity of changing相对的电压为正5伏电压,或接地direction wire this terminal to +5v thru4.7K Q2 or ground to the terminal.门集输入GATE INPUT在该端子输入"凵"低电平可以保持编码器的Angle data for an encoder shall be held角度数据(直到输入高电平将数据锁存)by inputting L to this terminal(Data shall be latched until H is输入putted)数据输入门电路后,大约需10μs的时间rptAfter inputting data to gate, about 10us米锁存数据,因此这段时间过去后才能is required to latch data. So data can be刷新数据。renewed after passing this elapsed time.〖)AnD艾而特26用语定义DEFINITIONS在本书中主要术语的定义如下Definitions of principal terminology used in this catalog areas follows①旋转式编码器:一种将轴旋转角度转化为数字信息的检测① Rotary encoder: a detector that converts the rotary dis.placement of the shaft into digital signal.②增量型:根据轴旋转位移输出脉冲序列的类型2)Incremental type The type that outputs a pulse train inaccordance with the rotary displacement of the shaft.③光电型:通过检测旋转轴上改变的光量来接收信号的类型, Optical type. The type that rece, due to is by detecting在轴上附带了光电检测机构和光栅the shaft, coming with an optical detecting mechanismand an optical lattice fixed to the shaft.④磁性型:通过检测轴上旋转而改变的磁场来接收信号4 Magnetic type The type that receives signals by detect-ing the change in the magnetic field due to the rotation ofthe shaft, coming with an magnetic detecting mechanismand a magnetic lattice fixed to the shaft⑤2相输出:一种由A、B相输出信号组成的模式,其相位差为⑤2 phase output: A mode with two outputs called A phase/4周期。⑥6相输出:一种由A、B、Z相和U、V、W相组成的模式。(66-phase output: A mode consisting of A, B Phase andZero reference pulse commutation output of UWw signal⑦参考0位:也叫做Z相,作为转一圈的位置参考(7) Zero reference: Output(also called Z phase)which servesas reference for the position during one rotation.⑧开集输出:输出采川共发射极电路,并且集电极开路。(8)Open collector output An output circuit having the emitter of the transistor of the output circuit as common ancthe collector of open typeNPNNPNK⑨长线驱动输出:输出电路兼容EA(电子工业协会)(9) Line driver output Output circuit in compliance with EIARS-122A(Electric Industries Association)RS-422A(Some products are excepted from the standard.c outo out⑩最大旋转速度:轴的旋转对机械允许的速度最大值(10 Maximum rotation speed: The value indicating the maximum revolving speed mechanically permissible witrespect to the rotation of the shaft.假①最大响应频率:轴的旋转对电气响应的最大频率(有时受① Maximum response frequency: Frequency showing th最大转速限制)。limit of electrical response with respect to the rotationtne shaft(Sometimes limited by the maximum permissiblrotation speed)①2径向负载:轴的径向负载(12 Radial load: A vertical load onto the shaft①3推力负载:轴的轴向负载。(13)Thrust load A longitudinal load onto the shaft⑩轴类型:从旋转式编码器本身连接轴的轴结构。(14) Shaft type A structure with a shaft projecting from throtary encoder body.⑩中空轴类型:轴中空,被测量部分的轴直接被插入来迮接。① Hollow shaft type: A shaft with a hole inside, into whica shaft of the measured side is directly inserted for co⑩UW信号:元刷马达的120度相位差3信号(电气角16 UVW signal: Three signals of 120 phase difference forbrushless motor.240W①绝对编码器的备用电池:多回转绝对值编码器上用来提供 Battery backup absolute encoder: A multiturn absolu给计数ICencoder with counter IC provided within it.⑩3串行传输:传达许多数据信号系统以时差给电路的Serial transmission A system of transmitting many da输出线signals with time differences to an output line of a circuit27【AnD艾而特1.保护构造的种类和各类命名Types and Designations of protective structure表1防止固体物进入的保护结构种类Table 1 Types of Protective Structure against Entry of Solids第1记号保护等级First CodingProtection Degree3(半封闭型)固体的末端直径2.5mm或不能进入甲面。3( Semi totally-enclosed typeEnds of solids 2.5mm or over in diameter do not enter inside4(全封閉型)固体的末端直径1.0mm或不进入里面。4(Totally-enclosed typeEnds of solids 1. 0mm or over in diameter do not enter inside5(防尘型编码器所定的动作及安全性阻止粉尘进入。5(Dustproof typeDust that impairs the designed operation or safety of the rotary encoder do not enter inside6(耐尘型)粉尘不进入里面。6(Dusttight typeDust particles do not enter inside.表2对水侵入的保护结构的种类Table 2 Types of Protective Stucture against Entry of Water第2记号保护等级Second CodingProtection Degree0(开放型)不能防止水不进入。o(Open typeNot protected against entry of water.2(防滴2型)沿垂直15度以内下落水滴没有损害。2(Drip-proof 2 typeSubject to no harmful effects by waterdrops falling at angles 15 or less from vertical.3(防雨型)沿垂直60度以内下落水滴没有损害。3(Rain-proof typeSubject to no harmful effects by waterdrops falling at angles 60%or less from vertical4(防喷雾型)由任意方向喷雾都没有损害。4(Spray-proof type,Subject to no harmful effects by water spray from any direction.5(防喷射型)由任意方向喷射都没有损害。5( Jet-proof typeSubject to no harmful effects by water jets from any direction6(防水型)由任何方向直接喷流的水都没有损害。6(Water-proof type)Impervious to water in strong jets from any direction. ( Note 1)7(防浸型)规定的压力和时间浸没在水之下没有水进入7(Immersion-proof typeNo water entering when immersed under water at specified pressure for specified time注:耐水型意思是产品结构上不会让强水柱由任意方向进入,但Note(1)"Water-proof"means a structure that does not allow the entry of假不代表结构允许在水下使用water against strong water jets from any directions, but it doesnot mean a structure that allows use under water.2.保护构造的命名2. Designations of Protective Structure编码器的防护结构的命名包括防护结构文字IP,第1The designation of protective structure of a rotary记号和第2记号次序。encoder is comprised with IP meaning the protectivestructure. first characteristic numeral and second characteristic numeral in this order如果或第一代码或第二个代码不被指定,它必须由XIn case either the first code or the second code is not代表specified, it must be represented by X.例1|P40|P40Characteristic letters例2|P65第2记号(开放型)Example 1 IP 40 P 40Example 2 IP 652nd characteristic numeral例3|P4X第1记号(全闭型)例4|PX5Example 3 IP 4X1st characteristic numeralExample 4 IPX5(AnD艾而特28换算表CONVERSION TABLE二进制总数°(度)(分(秒Binary Bit Countsdegree(min)(sec)128281251687510125001.406258437550625095120.70312542.1875253125100351562521.093751265632,0480.1757812510.546875632811240960.087890642552734375316.411381920.0439453132.636718751582014163840.0219726561.31835937579101532,7680.0109863280.65917968839551665,5360.0054931640.3295898441978131,0720.0027465820.1647949229.18262,1440.0013732910.0823974614.94192880.0006866460.0411982.201.0485760.003433230.0205993651.242,097,1520.0001716610.0102996830.624,194,3040.0000858310.0051498410.31228388,6080.0000429150.0025749210.152416,777,2160.0000214580.00128746033.5544320.00010290.0006437300.0467,1088640.00000536400003218650.019134,217,7280.0000026820.0001609330010268435,456000001410.000804660.00229536,870,9120.0000006710.000040233301,073,741,8240.0000003350.0000201170.001角度换算表ANGLE CONVERSION TABLE1弧度( radian)=57295780=34377468=206,264801°=0174533弧度( radian)=17.4533mrad1=00290888弧度( radian)=290888mrad1”=.00000484814弧度( radian)=00484814mrad.角度概念角度(视角)(视角d相当于人的标准身高17T10.000秒(28度)35m秒(0.28度350m秒(0.028度3.5km10秒35km(东京←→八王子)(饭田←→伊那2秒180km(东京←·饭田)1秒350km(东京←→京都)0.6秒东京←→八户)0.5秒650km(饭田←→八户0.1秒冲绳←→北海道稚内5.00km(到达静止卫星的距离角度x距离29【△DD艾而特
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