1. SVY 207: Lecture 7 Differential GPS By now you should understand: –How GPS point positioning works from first principles Aim of this lecture: –To understand the basics of DIFFERENTIAL GPS »why it is needed »how it works Outline –Rationale for Differential GPS »Errors involved in point positioning »Accuracy denial –Components of DGPS

2. Errors in Point Positioning 3-D Position Error    PDOP PDOP = geometrical magnification of error if  4 satellites distributed in different directions varies from ~ 1 to infinity ( > 5 considered bad) can be computed from covariance matrix Q = (A T A) -1  =  observation error »Satellite related orbit errors (few metres) satellite clock errors (few metres) satellite health (if ignored, can be disasterous) »Signal propagation ionospheric refraction (few metres for C/A code receivers) (~zero error for dual frequency) tropospheric refraction (few decimetres) »Receiver related multipathing (metre) measurement error (decimetre) »US Goverment - accuracy denial (up to 100 metres!)

3. Accuracy Denial Selective Availability (S/A) –epsilon »error in broadcast orbit (apparently not in use) –dither »satellite clock corrupted (up to 100 metres) »frequency is dithered with an unknown polynomial »position therefore appears to vary smoothly inside a region of approx. 100 metre radius »intention is to corrupt instantaneous position »position error averages down over time (few hours) –Has same effect on positions in local area at any instant »this fact is important for Differential GPS »is likely to be switched off in few years

4. Accuracy Denial Anti Spoofing (A/S) –Under A/S, P1 and P2 unavailable for civilian positioning: »P code on both L1 and L2 encrypted with secret W code »resulting “P code” + “W code” = “Y code” »some military receivers can unscramble the Y code –What can civilians do about this? »C/A code is not encrypted, hence we can still get a pseudorange on L1: “C1” »Y code is the same on L1 and L2, therefore receivers can measure Y1  Y2 by correlating L1 with L2. »Hence we can get “C2” = C1  (Y1  Y2) –“Signal to noise ratio” (SNR) is not as strong for C2 than P2 »less precise measurement »greater multipath effect (can be > 1 metre)

5. Components of DGPS Basic principle –Errors in position are similar for all receivers in local area –Corrections »Position correction »Range correction Reference station –at known coordinates (in WGS 84 reference system) –must have good view of the sky –transmits corrections to users in the region Mobile station –typically single frequency C/A receivers with radio link Data links –Low and high frequency transmitters –“Age of correction”

6. DGPS Errors With no DGPS –Selective availability S/A dominates, < 100 metres (95%) –other errors amount to several metres With DGPS –S/A cancels out –errors reduced in local area (increases with distance) »orbits, clocks, ionosphere, troposphere »can be reduced to a few centimetres –some errors increase (due to differencing measurements) »measurement error, multipath »therefore, this error typically remains at ~ 1 metre –in addition, any error in “known” reference station position will be passed on to mobile