IS-GPS-200H (797934), страница 16
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The related algorithm is given inparagraph 20.3.3.4.4.101IS-GPS-200H24 Sep 2013Table 20-II. Ephemeris Data DefinitionsM0Mean Anomaly at Reference Time∆nMean Motion Difference From Computed ValueeEccentricityASquare Root of the Semi-Major AxisΩ0Longitude of Ascending Node of Orbit Plane at Weekly Epochi0Inclination Angle at Reference TimeωArgument of Perigee•ΩRate of Right AscensionIDOTRate of Inclination AngleCucAmplitude of the Cosine Harmonic Correction Term to the Argument of LatitudeCusAmplitude of the Sine Harmonic Correction Term to the Argument of LatitudeCrcAmplitude of the Cosine Harmonic Correction Term to the Orbit RadiusCrsAmplitude of the Sine Harmonic Correction Term to the Orbit RadiusCicAmplitude of the Cosine Harmonic Correction Term to the Angle of InclinationCisAmplitude of the Sine Harmonic Correction Term to the Angle of InclinationtoeReference Time Ephemeris (reference paragraph 20.3.4.5)IODEIssue of Data (Ephemeris)20.3.3.4.2 Subframe 2 and 3 Parameter Characteristics.For each ephemeris parameter contained in subframes 2 and 3, the number of bits, the scalefactor of the LSB (which shall be the last bit received), the range, and the units shall be asspecified in Table 20-III.The AODO word (which is not an ephemeris parameter) is a five-bit unsigned term with an LSBscale factor of 900, a range from 0 to 31, and units of seconds.20.3.3.4.3 User Algorithm for Ephemeris Determination.The user shall compute the ECEF coordinates of position for the phase center of the SVs’antennas utilizing a variation of the equations shown in Table 20-IV.
Subframes 2 and 3parameters are Keplerian in appearance; the values of these parameters, however, are producedby the CS (Block II/Block IIA/IIR/IIR-M/IIF) and SS (GPS III) via a least squares curve fit ofthe predicted ephemeris of the phase center of the SVs’ antennas (time-position quadruples; t, x,y, z expressed in ECEF coordinates). Particulars concerning the periods of the curve fit, theresultant accuracy, and the applicable coordinate system are given in the followingsubparagraphs.102IS-GPS-200H24 Sep 201320.3.3.4.3.1 Curve Fit Intervals.Bit 17 in word 10 of subframe 2 is a "fit interval" flag which indicates the curve-fit interval usedby the CS (Block II/Block IIA/IIR/IIR-M/IIF) and SS (GPS III) in determining the ephemerisparameters, as follows:0 = 4 hours,1 = greater than 4 hours.The relationship of the curve-fit interval to transmission time and the timing of the curve-fitintervals is covered in section 20.3.4.Table 20-III.ParameterNo.
of Bits**IODE8Ephemeris ParametersScale Factor (LSB)Effective Range***Units(see text)-5Crs16*2∆n16*2-43M032*2-31Cuc16*2-29meterssemi-circles/secsemi-circlesradians-33e322Cus16*2-290.03radians-19A322toe1624dimensionlessmeters604,784-29secondsCic16*2Ω032*2-31Cis16*2-29i032*2-31Crc16*2-5ω32*2-3124*2-43semi-circles/sec2-43semi-circles/sec•ΩIDOT****14*radianssemi-circlesradianssemi-circlesmeterssemi-circlesParameters so indicated shall be two's complement, with the sign bit (+ or -) occupying the MSB;**See Figure 20-1 for complete bit allocation in subframe;Unless otherwise indicated in this column, effective range is the maximum range attainable withindicated bit allocation and scale factor.103IS-GPS-200H24 Sep 2013Table 20-IV.µ = 3.986005 x 1014 meters3/sec2Elements of Coordinate Systems (sheet 1 of 2)WGS 84 value of the earth's gravitational constant forGPS user•Ω e = 7.2921151467 x 10-5 rad/secA=n0 =(A)2µA3WGS 84 value of the earth's rotation rateSemi-major axisComputed mean motion (rad/sec)tk = t - toe*Time from ephemeris reference epochn = n0 + ∆nCorrected mean motionMk = M0 + ntkMean anomalyMk = Ek - e sin Ek sin ν k ν k = tan −1 cos ν k Kepler's Equation for Eccentric Anomaly (may be solved byiteration) (radians)True Anomaly 1 − e 2 sin E / (1 − e cos E ) kk= tan −1 ()(cosEe/1ecosE−−kk) *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 time difference between the time t and the epoch time toe, and mustaccount for beginning or end of week crossovers.
That is, if tk is greater than 302,400 seconds, subtract604,800 seconds from tk. If tk is less than -302,400 seconds, add 604,800 seconds to tk.104IS-GPS-200H24 Sep 2013Table 20-IV. Elements of Coordinate Systems (sheet 2 of 2) e + cos ν k E k = cos −1 1 + e cos ν k Eccentric AnomalyΦk = νk + ωArgument of Latitude}δuk = cussin2Φk + cuccos2Φkδrk = crssin2Φk + crccos2Φkδik = cissin2Φk + ciccos2ΦkArgument of Latitude CorrectionRadius CorrectionInclination CorrectionSecond Harmonic Perturbationsuk = Φk + δukCorrected Argument of Latituderk = A(1 - e cosEk) + δrkCorrected Radiusik = i0 + δik + (IDOT) tkCorrected Inclinationxk′ = rkcosukyk′ = rksinuk}•Positions in orbital plane.••Ωk = Ω0 + ( Ω - Ω e ) tk - Ω e toeCorrected longitude of ascending node.xk = xk′cosΩk - yk′cosiksinΩkyk = xk′sinΩk + yk′cosikcosΩkEarth-fixed coordinates.zk = yk′sinik}20.3.3.4.3.2 Parameter Sensitivity.The sensitivity of the SV's antenna phase center position to small perturbations in mostephemeris parameters is extreme.
The sensitivity of position to the parameters A , Crc and Crs isabout one meter/meter. The sensitivity of position to the angular parameters is on the order of108 meters/semicircle, and to the angular rate parameters is on the order of 1012meters/semicircle/second. Because of this extreme sensitivity to angular perturbations, the valueof π used in the curve fit is given here. π is a mathematical constant, the ratio of a circle'scircumference to its diameter. Here π is taken as π = 3.1415926535898.20.3.3.4.3.3 Coordinate Systems.20.3.3.4.3.3.1 ECEF Coordinate System.The equations given in Table 20-IV provide the SV's antenna phase center position in the WGS84 ECEF coordinate system defined as follows:105IS-GPS-200H24 Sep 2013Origin*=Earth's center of massZ-Axis**=The direction of the IERS (International Earth Rotation andReference Systems Service) Reference Pole (IRP)X-Axis =Intersection of the IERS Reference Meridian (IRM) and the plane passingthrough the origin and normal to the Z-axisY-Axis =coordinate systemCompletes a right-handed, Earth-Centered, Earth-Fixed orthogonal* Geometric center of the WGS 84 Ellipsoid** Rotational axis of the WGS 84 Ellipsoid20.3.3.4.3.3.2 Earth-Centered, Inertial (ECI) Coordinate System.In an ECI coordinate system, GPS signals propagate in straight lines at the constant speed c*(reference paragraph 20.3.4.3).
A stable ECI coordinate system of convenience may be definedas being coincident with the ECEF coordinate system at a given time t0. The x, y, z coordinatesin the ECEF coordinate system at some other time t can be transformed to the x′, y′, z′coordinates in the selected ECI coordinate system of convenience by the simple** rotation:x′ = x cos(θ) - y sin(θ)y′ = x sin(θ) + y cos(θ)z′ = zwhere•θ = Ω e (t - t0)* The propagation speed c is constant only in a vacuum.
The gravitational potentialalso has a small effect on the propagation speed, but may be neglected by most users.** Neglecting effects due to polar motion, nutation, and precession which may beneglected by most users for small values of (t - t0).20.3.3.4.3.4 Geometric Range.The user shall account for the geometric range (D) from satellite to receiver in an ECI coordinatesystem. D may be expressed as,D=|→r→(tR) - R (tT)|106IS-GPS-200H24 Sep 2013wheretT and tR are the GPS system times of transmission and reception, respectively,and where,→R(tT) = position vector of the GPS satellite in the selected ECI coordinate system at time tT,→r (tR) = position vector of the receiver in the selected ECI coordinate system at time tR.20.3.3.4.4 NMCT Validity Time.Users desiring to take advantage of the NMCT data provided in page 13 of subframe 4 shall firstexamine the AODO term currently provided in subframe 2 of the NAV data from thetransmitting SV.
If the AODO term is 27900 seconds (i.e., binary 11111), then the NMCTcurrently available from the transmitting SV is invalid and shall not be used. If the AODO termis less than 27900 seconds, then the user shall compute the validity time for that NMCT (tnmct)using the ephemeris toe parameter and the AODO term from the current subframe 2 as follows:OFFSET = toe [modulo 7200]if OFFSET = 0,then tnmct = toe - AODOif OFFSET > 0,then tnmct = toe - OFFSET + 7200 - AODONote that the foregoing computation of tnmct must account for any beginning or end of weekcrossovers; for example,if t* - tnmct > 302,400 then tnmct = tnmct + 604,800if t* - tnmct < -302,400 then tnmct = tnmct - 604,800*t is GPS system time at time of transmission.Users are advised that different SVs will transmit NMCTs with different tnmct and that the bestperformance will generally be obtained by applying data from the NMCT with the latest (largest)tnmct.
As a result, users should compute and examine the tnmct values for all visible and available107IS-GPS-200H24 Sep 2013SVs in order to find and use the NMCT with the latest tnmct. If the same latest (largest) tnmct isprovided by two or more visible and available SVs, then the NMCT from any SV with the latesttnmct may be selected and used; however, the estimated range deviation (ERD) value provided bythe selected NMCT for the other SVs with the same tnmct shall be set to zero if those SVs are usedin the positioning solution.
It should be noted that the intended positioning solution accuracyimprovement will not be obtained if the data from two different NMCTs are appliedsimultaneously or if the data from a given NMCT is applied to just a subset of the SVs used inthe positioning solution (i.e., mixed mode operation results in potentially degraded solutionaccuracy).It should be noted that the NMCT information shall be supported by the Block IIR SV only whenoperating in the IIA like mode of operation including the Autonav Test mode.20.3.3.5 Subframes 4 and 5.Both subframe 4 and 5 are subcommutated 25 times each; the 25 versions of these subframes arereferred to as pages 1 through 25 of each subframe.
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