IS-GPS-705D (797936), страница 10

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Integrity properties of the IAURAED are specified withrespect to the scaled (multiplied by either 4.42 or 5.73 as appropriate) upper bound values of thebroadcast URAED index (see 20.3.3.1.1).For the nominal URAED value and the IAURAED value, users may compute an adjusted URAEDvalue as a function of SV elevation angle (E), for E ≥ 0, as follows:Adjusted Nominal URAED = Nominal URAED (sin(E+90 degrees))Adjusted IAURAED = IAURAED (sin(E+90 degrees))URAED and IAURAED account for SIS contributions to user range error which include, but arenot limited to, the following: LSB representation/truncation error, alongtrack ephemeris errors,and crosstrack ephemeris errors.

URAED and IAURAED do not account for user range errorcontributions due to the inaccuracy of the broadcast ionospheric data parameters used in thesingle-frequency ionospheric model or for other atmospheric effects.20.3.3.1.2 Message Types 10 and 11 Ephemeris Parameter Characteristics.For each ephemeris parameter contained in message types 10 and 11, the number of bits, thescale factor of the least significant bit (LSB) (which is the last bit received), the range, and theunits are as specified in Table 20-I.

See Figures 20-1 and 20-2 for complete bit allocation inmessage types 10 and 11.20.3.3.1.3 User Algorithm for Determination of SV Position.The user shall compute the ECEF coordinates of position for the SV’s antenna phase center(APC) utilizing a variation of the equations shown in Table 20-II. The ephemeris parameters areKeplerian in appearance; the values of these parameters, however, are produced by the CS(Block IIF) or the SV (GPS III) via a least squares curve fit of the predicted ephemeris of the SVAPC (time-position quadruples; t, x, y, z expressed in ECEF coordinates).

Particularsconcerning the applicable coordinate system are given in Sections 20.3.3.4.3.3 and 20.3.3.4.3.4of IS-GPS-200.60IS-GPS-705D24 Sep 2013The sensitivity of the SV’s position to small perturbations in most ephemeris parameters isextreme. The sensitivity of position to the parameters A, Crc-n, and Crs-n is about onemeter/meter. The sensitivity of position to the angular parameters is on the order of 108meters/semi-circle, and to the angular rate parameters is on the order of 1012 meters/semicircle/second. Because of this extreme sensitivity to angular perturbations, the value of π used inthe curve fit is given here. π is a mathematical constant, the ratio of a circle’s circumference toits diameter.

Here π is taken as 3.1415926535898.Table 20-I. Message Types 10 and 11 Parameters (1 of 2)ParameterSymbolWNParameter DescriptionWeek No.No. ofBits**13URAED INDEXED accuracy5*Signal health(L1/L2/L5)ScaleFactor(LSB)1EffectiveRange***Unitsweeks(see text)31(see text)topData predict time of week11300∆A ****Semi-major axis difference atreference time26*2-9metersA•Change rate in semi-major axis25*2-21meters/sec∆n0Mean Motion difference fromcomputed value at reference time17*2-44semicircles/sec∆n0•Rate of mean motion differencefrom computed value23*2-57semicircles/sec2M0-nMean anomaly at reference time33*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 20-1 for complete bit allocation in message type 10;Unless otherwise indicated in this column, effective range is the maximum range attainable with indicated bitallocation and scale factor.Relative to AREF = 26,559,710 meters.61IS-GPS-705D24 Sep 2013Table 20-I.

Message Types 10 and 11 Parameters (2 of 2)No. ofBits**11ScaleFactor(LSB)300Longitude of Ascending Node of OrbitPlane at Weekly Epoch33*2-32semi-circles•∆ Ω****Rate of right ascension difference17*2-44semi-circles/seci0-nInclination angle at reference time33*2-32semi-circles•i0-nRate 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 sine harmonic correctionterm to the argument of latitude21*2-30radiansParameterSymboltoeΩ0-n***Parameter DescriptionEphemeris data reference time of weekEffectiveRange***604,500UnitssecondsParameters so indicated are two’s complement, with the sign bit (+ or -) occupying the MSB;See Figure 20-1 and Figure 20-2 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.****Relative to ΩREF = -2.6 x 10-9 semi-circles/second.•62IS-GPS-705D24 Sep 2013Table 20-II.

Elements of Coordinate System (part 1 of 2)Element/Equationµ = 3.986005 x 1014 meters3/sec2DescriptionΩe = 7.2921151467 x 10-5 rad/secWGS 84 value of the earth’s gravitational constant for GPSuserWGS 84 value of the earth’s rotation rateA0 = AREF + ∆A *Semi-Major Axis at reference time••Ak = A0 + (A) tkn0 =µA03Semi-Major AxisComputed Mean Motion (rad/sec)tk = t – toe **Time from ephemeris reference time∆nA = ∆n0 +½ ∆n•0 tkMean motion difference from computed valuenA = n0 + ∆nACorrected Mean MotionMk = M0 + n A t kMean 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 True Anomaly 1 − e 2 sin E / (1 − e cos E ) nknk = tan-1 ()(−−cosEe/1ecosEknnk)  e + cos ν k Ek = cos-1  n1 + e n cos ν k *Eccentric 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.63IS-GPS-705D24 Sep 2013Table 20-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 + δukSecond HarmonicPerturbationsCorrected Argument of Latituderk= Ak(1 – en cos Ek) + δrkik= io-n + (io-n )tk + δikCorrected Radius•Corrected Inclinationxk' = rk cos ukPositions in orbital planeyk' = rk sin uk•••Rate of Right AscensionΩ = ΩREF + ∆Ω ***•••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***• = −2.6 x 10-9 semi-circles/second.ΩREF20.3.3.2 Message Types 30 through 37 SV Clock Correction Parameters.20.3.3.2.1 Message Types 30 through 37 SV Clock Correction Parameter Content.The clock parameters in any one of message types 30 through 37 describe the SV time scaleduring the period of validity.

The parameters are applicable during the time in which they aretransmitted. Beyond that time they are still applicable, however, the most recent data set shouldbe used since the accuracy degrades over time.The general format of message types 30 through 37 includes data fields for SV clock correctioncoefficients.

Any one of message types 30 through 37 in conjunction with message types 10 and11 provide users with the requisite data to correct SV time and to calculate SV position precisely.64IS-GPS-705D24 Sep 2013In general, any message of type 30 to 39 will provide SV clock correction parameters asdescribed in this section.20.3.3.2.1.1 SV Clock Correction.Any one of message types 30 through 37, Figure 20-3 through Figure 20-10, contains theparameters needed by the users for apparent SV clock correction. Bits 61 to 71 contain toc, clockdata reference time of week.

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