IS-GPS-200F (811524), страница 25
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Because of this extreme sensitivity to angular perturbations, the value of π used in thecurve fit is given here. π is a mathematical constant, the ratio of a circle’s circumference to its diameter. Here π istaken as 3.1415926535898.158IS-GPS-200F21 Sep 2011Table 30-I.Message Types 10 and 11 Parameters (1 of 2)ParameterNo.
ofBits**ScaleFactor(LSB)1WNWeek No.13URAED IndexED Accuracy Index5*Signal health(L1/L2/L5)EffectiveRange***Unitsweeks(see text)31(see text)topData predict time of week11300∆A ****Semi-major axis difference atreference time26*2-9metersAChange rate in semi-majoraxis25*2-21meters/sec∆n0Mean Motion difference fromcomputed value at referencetime17*2-44semi-circles/sec∆n0Rate of mean motiondifference from computedvalue23*2-57semi-circles/sec2M0-nMean anomaly at referencetime33*2-32semi-circlesenEccentricity332-34ωnArgument of perigee33*2-32••****604,5000.03secondsdimensionlesssemi-circlesParameters so indicated are two’s complement, with the sign bit (+ or -) occupying the MSB;**See Figure 30-1 for complete bit allocation in Message Type 10;Unless otherwise indicated in this column, effective range is the maximum range attainable withindicated bit allocation and scale factor.****Relative to AREF = 26,559,710 meters.159IS-GPS-200F21 Sep 2011Table 30-I.Message Types 10 and 11 Parameters (2 of 2)ParameterNo.
ofBits**ScaleFactor(LSB)EffectiveRange***Units604,500secondstoeEphemeris data reference time of week11300Ω0-n****Reference right ascension angle33*2-32semi-circles∆Ω*****Rate of right ascension difference17*2-44semi-circles/seci0-nInclination angle at reference time33*2-32semi-circlesi0-n –DOTRate of inclination angle15*2-44semi-circles/secCis-nAmplitude of the sine harmonic correctionterm to the angle of inclination16*2-30radiansCic-nAmplitude of the cosine harmoniccorrection term to the angle of inclination16*2-30radiansCrs-nAmplitude of the sine correction term tothe orbit radius24*2-8metersCrc-nAmplitude of the cosine correction term tothe orbit radius24*2-8metersCus-nAmplitude of the sine harmonic correctionterm to the argument of latitude21*2-30radiansCuc-nAmplitude of the cosine harmoniccorrection term to the argument of latitude21*2-30radians•*Parameters so indicated are two’s complement, with the sign bit (+ or -) occupying the MSB;**See Figure 30-1 and Figure 30-2 for complete bit allocation in Message Types 10 and 11;***Unless otherwise indicated in this column, effective range is the maximum range attainable withindicated bit allocation and scale factor.****Ω0-n is the right ascension angle at the weekly epoch (Ω0-w) propagated to the reference time at the rate•of right ascension {ΩREF Table 30-II }.*****•Relative to ΩREF = -2.6 x 10-9 semi-circles/second.160IS-GPS-200F21 Sep 2011Table 30-II.Elements of Coordinate System (part 1 of 2)Element/Equationµ = 3.986005 x 1014 meters3/sec2•DescriptionWGS 84 value of the earth’s gravitational constant for GPS userΩe = 7.2921151467 x 10-5 rad/secWGS 84 value of the earth’s rotation rateA0 = AREF + ∆A *Semi-Major Axis at reference time•Semi-Major AxisAk = A0 + (A) tkn0 =µComputed Mean Motion (rad/sec)A03tk = t – toe **Time from ephemeris reference time•∆nA = ∆n0 +½ ∆n0 tkMean motion difference from computed valuenA = n0 + ∆nACorrected Mean MotionMk = M0 + nA tkMean AnomalyMk = Ek – en sin EkKepler’s equation for Eccentric Anomaly (radians)(may be solved by iteration) sin ν k νk = tan-1 cos ν k 1 − e 2 sin E / (1 − e cos E ) nknk = tan-1 −−(cosEe)/(1ecosEknnk) e + cos ν k Ek = cos-1 n1 + e n cos ν k *True AnomalyEccentric AnomalyAREF = 26,559,710 meters** t is GPS system time at time of transmission, i.e., GPS time corrected for transit time (range/speed of light).Furthermore, tk shall be the actual total difference between the time t and the epoch time toe, and must accountfor beginning or end of week crossovers.
That is if tk is greater than 302,400 seconds, subtract 604,800seconds from tk. If tk is less than -302,400 seconds, add 604,800 seconds to tk.161IS-GPS-200F21 Sep 2011Table 30-II.Elements of Coordinate System (part 2 of 2)Element/Equation *Φk = νk + ωnDescriptionArgument of Latitudeδuk = Cus-nsin2Φk + Cuc-ncos2ΦkArgument of Latitude Correctionδrk = Crs-nsin2Φk + Crc-ncos2ΦkRadial Correctionδik = Cis-nsin2Φk + Cic-ncos2ΦkInclination Correctionuk = Φk + δukCorrected Argument of Latituderk= Ak(1 – en cos Ek) + δrkCorrected Radiusik= io-n + (io-n-DOT)tk + δikCorrected Inclinationxk' = rk cos ukPositions in orbital planeyk' = rk sin uk•••Ω = ΩREF + ∆Ω ***••Rate of Right Ascension•Ωk = Ω0-n + ( Ω − Ωe ) tk – Ωe toeCorrected Longitude of Ascending Nodexk = xk' cos Ωk − yk' cos ik sin Ωkyk = xk' sin Ωk + yk' cos ik cos ΩkEarth-fixed coordinates of SV antenna phase centerzk = yk' sin ik•*** ΩREF = −2.6 x 10-9 semi-circles/second.30.3.3.2 Message Types 30 Through 37 SV Clock Correction Parameters.30.3.3.2.1 Message Type 30 Through 37 SV Clock Correction Parameter Content.
The clock parameters in any oneof message types 30 through 37 describe the SV time scale during the period of validity. The parameters areapplicable during the time in which they are transmitted. Beyond that time, they are still applicable, however, themost recent data set should be used since the accuracy degrades over time.The general format of message types 30 through 37 includes data fields for SV clock correction coefficients.
Anyone of message types 30 through 37 in conjunction with message types 10 and 11 provides users with the requisitedata to correct SV time and to calculate SV position precisely. In general, any message type 30’s (i.e. 30-39) willprovide SV clock correction parameters as described in this section.162IS-GPS-200F21 Sep 201130.3.3.2.1.1 SV Clock Correction. Any one of message types 30 through 37, Figure 30-3 through Figure 30-10,contains the parameters needed by the users for apparent SV clock correction.
Bits 61 to 71 contain toc , clock datareference time of week. Bits 72 to 127 contain SV clock correction coefficients. The related algorithm is given inparagraph 20.3.3.3.3.1.30.3.3.2.1.2 Data Predict Time of Week. Bits 39 through 49 of message types 30 through 37 shall contain the datapredict time of week (top). The top term provides the epoch time of week of the state estimate utilized for theprediction of SV clock correction coefficients.30.3.3.2.2 Clock Parameter Characteristics. The number of bits, the scale factor of the LSB (which is the last bitreceived), the range, and the units of clock correction parameters shall be as specified in Table 30-III.30.3.3.2.3 User Algorithms for SV Clock Correction Data. The algorithms defined in paragraph 20.3.3.3.3.1 allowall users to correct the code phase time received from the SV with respect to both SV code phase offset andrelativistic effects.
However, since the SV clock corrections of equations in paragraph 20.3.3.3.3.1 are estimated bythe CS using dual frequency L1 and L2 P(Y) code measurements, the single-frequency L1 or L2 user and the dualfrequency L1 C/A - L2 C users must apply additional terms to the SV clock correction equations. These terms aredescribed in paragraph 30.3.3.3.1.163IS-GPS-200F21 Sep 2011Table 30-III.Clock Correction and Accuracy ParametersParameterNo. ofBits**ScaleFactor(LSB)EffectiveRange***300604,500tocClock Data Reference Time of Week11URANEDIndexNED Accuracy Index5*URANED2Indexaf2-naf1-naf0-nNED Accuracy Change Index3NED Accuracy Change Rate Index10*2-6020*2-4826*2-35SV Clock Drift Rate CorrectionCoefficientSV Clock Drift CorrectionCoefficientseconds(seetext)3URANED1IndexUnits(seetext)(seetext)sec/sec2sec/secSV Clock Bias Correction Coefficientseconds****Parameters so indicated are two’s complement, with the sign bit (+ or -) occupying the MSB;**See Figure 30-3 through 30-10 for complete bit allocation in Message types 30 to 37;Unless otherwise indicated in this column, effective range is the maximum range attainable withindicated bit allocation and scale factor.30.3.3.2.4 Non-Elevation-Dependent (NED) Accuracy Estimates.
Bits 50 through 54, and 55 through 57, and 58through 60 of message types 30 through 37 shall contain the non-elevation-dependent (NED) component URANED0Index,URANED1 Index, and URANED2 Index, respectively, of the SV (reference paragraph 6.2.1) for the standardpositioning service user. The following equations together with the broadcast URANED0 Index, URANED1 Index, andURANED2 Index shall give the non-elevation dependent user range accuracy of IAURANED over the currentclock/ephemeris fit interval. While the actual NED related URA may vary over the satellite footprint, the IAURANEDcalculated using the parameters in message type 10 at each instant during the current clock/ephemeris fit intervalshall bound the maximum IAURANED expected for the worst-case location within the satellite footprint at thatinstant.The user shall calculate the NED-related URA with the equation (in meters);164IS-GPS-200F21 Sep 2011IAURANED = URANED0 + URANED1 (t - top + 604,800*(WN - WNop))for t - top + 604,800*(WN - WNop) ≤ 93,600 secondsIAURANED = URANED0 + URANED1*(t - top + 604,800*(WN - WNop)) + URANED2*(t - top + 604,800*(WN - WNop)- 93,600)2for t - top + 604,800*(WN - WNop) > 93,600 secondswheret is the GPS system timeWNop -- Data Predict Week Number, identifying the GPS week to which the top term refers.
See Section30.2.2.2.1.2 (Data Predict Time of Week).The CS shall derive URANED0, URANED1, and URANED2 indexes which, when used together in the above equations,results in the minimum IAURANED that is greater than the predicted IAURANED during the clock/ephemeris fitinterval.Non-elevation dependent URA (URANED) accounts for signal-in-space contributions to user range error that include,but are not limited to, the following: the net effect of clock parameter and code phase error in the transmitted signalfor single-frequency L1C/A or single-frequency L2C users who correct the code phase as described in Section30.3.3.3.1.1.1, as well as the net effect of clock parameter, code phase, and intersignal correction error for dualfrequency L1/L2 and L1/L5 users who correct for group delay and ionospheric effects as described in Section30.3.3.3.1.1.2.The user shall use the broadcast URANED0 index to derive the URANED0 value.
The URANED0 index is a signed,two’s complement integer in the range of +15 to -16 and has the following relationship to the URANED0 value:URANED0 IndexURANED0 (meters)(or no accuracy prediction is available)156144.00< URANED0143072.00< URANED0≤6144.00131536.00< URANED0≤3072.0012768.00< URANED0≤1536.0011384.00< URANED0≤768.0010192.00< URANED0≤384.00165IS-GPS-200F21 Sep 2011996.00< URANED0≤192.00848.00< URANED0≤96.00724.00< URANED0≤48.00613.65< URANED0≤24.0059.65< URANED0≤13.6546.85< URANED0≤9.6534.85< URANED0≤6.8523.40< URANED0≤4.8512.40< URANED0≤3.4001.70< URANED0≤2.40-11.20< URANED0≤1.70-20.85< URANED0≤1.20-30.60< URANED0≤0.85-40.43< URANED0≤0.60-50.30< URANED0≤0.43-60.21< URANED0≤0.30-70.15< URANED0≤0.21-80.11< URANED0≤0.15-90.08< URANED0≤0.11-100.06< URANED0≤0.08-110.04< URANED0≤0.06-120.03< URANED0≤0.04-130.02< URANED0≤0.03166IS-GPS-200F21 Sep 2011-140.01-15-16< URANED0URANED00.02≤0.01≤No accuracy prediction available-use at own riskFor each URANED0 index (N), users may compute a nominal URANED0 value (X) as given by:• If the value of N is 6 or less, but more than -16, X = 2(1 + N/2),• If the value of N is 6 or more, but less than 15, X = 2(N - 2),• N = -16 or N = 15 shall indicate the absence of an accuracy prediction and shall advise the standardpositioning service user to use that SV at his own risk.For N = 1, 3, and 5, X should be rounded to 2.8, 5.7, and 11.3 meters, respectively.The nominal URANED0 value (X) shall be suitable for use as a conservative prediction of the RMS NED range errorsfor accuracy-related purposes in the pseudorange domain (e.g., measurement de-weighting RAIM, FOMcomputations).
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