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Units m rad/s sec sec sec rad/s rad rad rad rad rad m rad rad m rad m m rad m m m in Software
493 Units m rad/s sec sec sec rad/s rad rad rad rad rad m rad rad m rad m m rad m m m Denso QR Bar Code Creator In None Using Barcode creator for Software Control to generate, create QRCode image in Software applications. QR Code ISO/IEC18004 Recognizer In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Table C4: Calculated Satellite Position in ECEF Coordinates
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EAN13 Maker In None Using Barcode maker for Software Control to generate, create UPC  13 image in Software applications. UPCA Supplement 2 Creation In None Using Barcode creator for Software Control to generate, create UCC  12 image in Software applications. Section C2 presented the standard equations use to compute the position pi (ti ) of the ith satellite vehicle at the time of transmission ti as represented in the ECEF frame at time ti A subtlety in the equations presented in Table C2 is the fact that the computed position for each satellite is in a distinct frameofreference and are therefore not compatible The ECEF is not an inertial frame Due to the rotation of the frame, the ECEF frame a time t1 is distinct from the ECEF frame at time t2 Let [Pi ]e(t) denote the coordinates of the point Pi with respect to the ECEF frame at time t Even in the case that P1 is xed in inertial space, in general [P1 ]e(t1 ) = [P1 ]e(t2 ) for t1 = t2 Use of timeoftransit to measure range is premised on the fact that the speedoflight through a vacuum is constant relative to inertial reference frames Therefore, if the coordinates of two points were known in an ineri i tial frame [P1 ] and [P2 ] the time for light to transit between the points through a vacuum would be [P1 ] [P2 ] c Bar Code Generation In None Using Barcode creation for Software Control to generate, create barcode image in Software applications. Code128 Printer In None Using Barcode generation for Software Control to generate, create Code128 image in Software applications. When the coordinates of the two points are known in distinct reference a b frames a and b, [P1 ] and [P2 ] , neither of which is an inertial frame, then they could be transformed to an inertial frame: Ri [P1 ] Ri Ra [P2 ] a a b c Making USPS POSTal Numeric Encoding Technique Barcode In None Using Barcode generator for Software Control to generate, create Delivery Point Barcode (DPBC) image in Software applications. Data Matrix ECC200 Reader In None Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications. Because the norm of a vector is invariant under rotational transformation, this is equivalent to a b [P1 ] Ra [P2 ] b = c There are two important points First, to calculate the distance between these two points P1 and P2 , they must rst be represented in the same reference frame Second, there is not a unique best frame The following discussion will use the ECEF frame at an arbitrary time denoted as ta Often the selected time is tr the time at which the receiver measured the pseudoranges e(t ) e(t ) Given [P1 ] 1 and [P2 ] 2 the coordinates of P1 and P2 with respect to the ECEF frame at time ta are [P1 ] [P2 ] GS1  13 Printer In .NET Using Barcode generator for .NET framework Control to generate, create GTIN  13 image in .NET applications. Bar Code Encoder In Java Using Barcode encoder for Android Control to generate, create barcode image in Android applications. e(ta ) e(ta ) Printing GTIN  128 In None Using Barcode drawer for Office Word Control to generate, create UCC128 image in Word applications. Bar Code Decoder In Visual Basic .NET Using Barcode Control SDK for .NET Control to generate, create, read, scan barcode image in .NET framework applications. = Re(ta) [P1 ] 1 = Re(ta) [P2 ] 2 Bar Code Creator In Java Using Barcode printer for Java Control to generate, create bar code image in Java applications. Code 3 Of 9 Scanner In .NET Using Barcode decoder for .NET framework Control to read, scan read, scan image in VS .NET applications. e(t ) e(t ) e(t1 ) e(t2 ) C4 SATELLITE VELOCITY
The coordinate transformation matrix e e cos ( ie (ta ti )) sin ( ie (ta ti )) 0 e(ta ) e e e Re(ti ) = [ ie (ta ti )]3 = sin ( ie (ta ti )) cos ( ie (ta ti )) 0 0 0 1 is a plane rotation that accounts for the the rotation of the Earth over the time span (ta ti ) at angular rate ie around the ECEF zaxis In the case where ta = tr , then for the ith satellite, its position is roe e tated by the angle ( ie ti ) = ie (tr ti ) where ti and ti are the quantities p sv p sv de ned in eqn (C1) referred to the ith satellite Neglecting to transform all satellite positions to the same frameofreference can result in range errors of up to 40m Satellite Velocity
Use of the GPS Doppler measurements requires knowledge of the velocity of the satellite That issue is addressed in this section C41 Equations from Ephemeris
Equations for the satellite position as a function of time are shown in Table C2 The satellite velocity can be computed as the derivative of the satellite position as summarized in Table C5 Ek k uk rk k X Yk
dik dt
= = = = = = = = = = =

