Интерфейсный документ GPS, страница 14

Subframes 2and 3 parameters are Keplerian in appearance; the values of these parameters, however, are produced by the CS viaa least squares curve fit of the predicted ephemeris of the phase center of the SVs’ antennas (time-positionquadruples; 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 following subparagraphs.20.3.3.4.3.1 Curve Fit Intervals. Bit 17 in word 10 of subframe 2 is a "fit interval" flag which indicates the curvefit interval used by the CS in determining the ephemeris parameters, 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-fit intervals is covered insection 20.3.4.IS-GPS-200D7 Dec 200495Table 20-III.ParameterNo.

of Bits**IODE8Crs16*2-5∆n16*2-43M032*2-31Cuc16*2-29e322-33Scale Factor (LSB)Effective Range***Units(see text)meterssemi-circles/secsemi-circlesradians0.03-29Cus16*2A322-19dimensionlessradiansmeters4604,784toe162Cic16*2-29Ω032*2-31Cis16*2-29i032*2-31Crc16*2-5ω32*2-31Ω24*2-43semi-circles/sec14*-43semi-circles/sec•IDOT******Ephemeris Parameters2secondsradianssemi-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.IS-GPS-200D7 Dec 200496Table 20-IV.

Elements of Coordinate Systems (sheet 1 of 2)µ = 3.986005 x 1014 meters3/sec2•Ω e = 7.2921151467 x 10-5 rad/secA=n0 =(A)2µA3WGS 84 value of the earth's gravitational constant forGPS userWGS 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 EkKepler's Equation for Eccentric Anomaly (may be solvedby iteration) (radians) sin ν k ν k = tan −1  cos ν k 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.IS-GPS-200D7 Dec 200497Table 20-IV. Elements of Coordinate Systems (sheet 2 of 2) e + cos ν k E k = cos −1 1 + e cos ν k Eccentric AnomalyΦ k = 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 toexk = xk′cosΩk - yk′cosiksinΩkyk = xk′sinΩk + yk′cosikcosΩkzk = yk′sinikCorrected longitude of ascending node.}Earth-fixed coordinates.IS-GPS-200D7 Dec 20049820.3.3.4.3.2Parameter Sensitivity.The sensitivity of the SV's antenna phase center position to smallperturbations in most ephemeris parameters is extreme.

The sensitivity of position to the parametersCrs is about one meter/meter.A , Crc andThe sensitivity of position to the angular parameters is on the order of 108meters/semicircle, and to the angular rate parameters is on the order of 1012 meters/semicircle/second. Because ofthis extreme sensitivity to angular perturbations, the value of π used in the curve fit is given here. π is amathematical constant, the ratio of a circle's circumference to its diameter. Here π is taken asπ = 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 phasecenter position in the WGS 84 ECEF coordinate system defined as follows:Origin*=Z-Axis** =Earth's center of massThe direction of the IERS (International Earth Rotation and Reference Systems Service)Reference Pole (IRP)X-Axis=Intersection of the IERS Reference Meridian (IRM) and the plane passing through theorigin and normal to the Z-axisY-Axis=Completes a right-handed, Earth-Centered, Earth-Fixed orthogonal coordinate system* Geometric center of the WGS 84 Ellipsoid** Rotational axis of the WGS 84 EllipsoidIS-GPS-200D7 Dec 20049920.3.3.4.3.3.2 Earth-Centered, Inertial (ECI) Coordinate System. In an ECI coordinate system, GPS signalspropagate in straight lines at the constant speed c* (reference paragraph 20.3.4.3). A stable ECI coordinate systemof convenience may be defined as being coincident with the ECEF coordinate system at a given time t0.

The x, y, zcoordinates in the ECEF coordinate system at some other time t can be transformed to the x′, y′, z′ coordinates in theselected 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 potential also has a smalleffect on the propagation speed, but may be neglected by most users.** Neglecting effects due to polar motion, nutation, and precession which may be neglected by most usersfor 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 anECI coordinate system. D may be expressed as,→→D = | r (tR) - R (tT)|wheretT 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.IS-GPS-200D7 Dec 200410020.3.3.4.4 NMCT Validity Time. Users desiring to take advantage of the NMCT data provided in page 13 ofsubframe 4 shall first examine 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 NMCT currently availablefrom the transmitting SV is invalid and shall not be used. If the AODO term is less than 27900 seconds, then theuser shall compute the validity time for that NMCT (tnmct) using the ephemeris toe parameter and the AODO termfrom 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 week crossovers; forexample,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 best performance willgenerally be obtained by applying data from the NMCT with the latest (largest) tnmct.

As a result, users shouldcompute and examine the tnmct values for all visible and available SVs in order to find and use the NMCT with thelatest tnmct. If the same latest (largest) tnmct is provided by two or more visible and available SVs, then the NMCTfrom any SV with the latest tnmct may be selected and used; however, the estimated range deviation (ERD) valueprovided by the selected NMCT for the other SVs with the same tnmct shall be set to zero if those SVs are used inthe positioning solution. It should be noted that the intended positioning solution accuracy improvement will not beobtained if the data from two different NMCTs are applied simultaneously or if the data from a given NMCT isapplied to just a subset of the SVs used in the positioning solution (i.e., mixed mode operation results in potentiallydegraded solution accuracy).It should be noted that the NMCT information shall be supported by the Block IIR SV only when operating in theIIA like mode of operation including the Autonav Test mode.IS-GPS-200D7 Dec 200410120.3.3.5 Subframes 4 and 5.

Both subframe 4 and 5 are subcommutated 25 times each; the 25 versions of thesesubframes are referred to as pages 1 through 25 of each subframe. With the possible exception of "reserved forsystem use" pages and explicit repeats, each page contains different specific data in words three through ten. Asshown in Figure 20-1, the pages of subframe 4 utilize seven different formats, while those of subframe 5 use two.The content of words three through ten of each page is described below, followed by algorithms and materialpertinent to the use of the data.20.3.3.5.1 Content of Subframes 4 and 5.