1、A quick GPS Primer (assumed knowledge on the course!),Observables Error sources Analysis approaches Ambiguities,If only it were this easy,Review of GPS positioning,Dealing with errors Clock errors (review) Ionosphere (review) Troposphere (part review) Earth body deformations (new) Orbit errors (new)
2、,Orbit Error,Clock Error,Epsilon (SA),Dither (SA),Ionospheric,refraction,Tropospheric,refraction,Multipath,Receiver Noise,Clock Error,GPS Undifferenced observable,Station A,Satellite j,Observed range,True range,Receiver and Satellite clock errors (multiplied by speed of light),Carrier phase ambiguit
3、y,Ionospheric Delay,Tropospheric Delay,Includes Multipath,A somewhat simplified view, but all these need to be dealt with (at least) for precise GPS geodesy,Dealing with clock errors,Undifferenced observable Estimate both receiver and satellite clocks Precise Point Positioning Fix prior satellite cl
4、ocks and estimate only receiver clocks Parameter hungry Double-differenced observable Undifferenced observations to two satellites at two stations Form two between-station differences and then double-difference:Common clock terms difference,Station A,Station B,Satellite j,Satellite k,Dealing with or
5、bit errors,These days somewhat easy Use the IGS final orbits (precise to 2-5cm) Use Rapid or Ultra-rapid if quick turnaround needed (precise to 5cm) Probably no reason to use the broadcast orbits (precise to 0.5-2m) In practice Need orbits from adjacent days when processing against the day boundary
6、Orbit errors are rarely an error source when using IGS products (main exception is pre-IGS data earlier than 1994),Dealing with the Tropospheric Delay (I),Total delay 2.3m at zenith, greater at horizon Elevation angle dependency may be relatively well modelled with a mapping function (M) for each of
7、 two tropospheric components Two components Hydrostatic could be well modelled with accurate pressure Wet not well modelled and must be parameterised Over very short (10km) and small elevation difference (100-200m) baselines, effect cancels in double-difference General approach Model hydrostatic wit
8、h standard pressure or (more accurate) use ECMWF or station met data Parameterise zenith wet delay (Twet), which also absorbs any residual Thydro , once per 1-2 h (static) or every epoch (kinematic),Dealing with the Tropospheric Delay (II),Troposphere is not azimuthally uniform Horizontal gradients
9、are common, particularly N-SHighest precision static processing will further estimate horizontal gradient terms 1-2 for each E-W and N-S per day common In kinematic analysis, steps in estimated tropospheric zenith delay suggest likely wrong ambiguity fixed and hence quality control,Dealing with Iono
10、spheric Delay (I),Different frequency signals (in L-band) delayed by different amounts through Ionosphere Dual frequency GPS receivers allow 99.9% for effect to be removed Higher order terms may be important for most precise geodetic workUse a linear combination of L1 and L2 measurements to form new
11、 measurement ionosphere free combination for carrier (LC or alternatively L3)Where are frequency of the L1 and L2 carrier phase signals,Dealing with Ionospheric Delay (II),Differencing and re-arranging cancels I termIonosphere-free phase Linear Combination LC is defined:Note: Ambiguity terms are no
12、longer integers ambiguity fixing is not an option with LC Noise (“other errors”) is scaled upGeneral approach Adopt LC for baselines 10km Fix ambiguities, where possible, using a different linear combination (e.g., wide-lane) then final solution using LC, holding ambiguities fixed,Matrix Form,Static
13、 case solving for parameters x,1-4hrs,A x = b + V,Obs1,Obsn,Multipath,Generally dealt with through Stochastic model by assumption of elevation-dependence and down-weighting lower elevation observations (GAMIT examines the residuals and allows iterative reweighting on a station-by-station basis) Assu
14、ming to “average toward zero” over 24h sessions Possibly a blind spot in GPS geodesy today,Ambiguity Fixing,Ambiguity for each satellite pass and all cycle slips thereafter Dozens of ambiguity terms for a 24 h periodAmbiguity fixing process is essentially a series of statistical tests Can each ambig
15、uity be confidently (given its uncertainty) be fixed to an integer? Iteration required, since uncertainties will change (normally reduce) as ambiguities are fixed and removed from the least squares parameters setEssential for kinematic (or stabilisation of real-valued estimates in, e.g., Kalman Filt
16、er such as in Track) Not always possible to fix all ambiguitiesLess impact for static Largest effect (normally 10mm) in E, then N & U (see Blewitt, 1989) Can change the way systematic errors propagate,Double Difference vs PPP,Similar precision possible in 24 h solutions Software Few software do geod
17、etic PPP (GIPSY mainly) GAMIT/Track are Double DifferencePPP is requires extra care modelling geophysical phenomena (e.g., ocean tide loading displacements) which may be (partially) differenced in relative analysis orbit/clock errors (some periodic) map 1:1 into positioningKinematic PPP requires lon
18、ger periods of data ambiguity fixing is not possible without a double difference second stepDD is more precise when short-baseline relative motion is all that is required (e.g., glacier monitoring), but depends on base station,Further Reading,Reference Texts Hofmann-Wellenhof, B., H. Lichtenegger, a
19、nd J. Collins. 2001. Global Positioning System: theory and practice, Springer, Wien, 382 pp.Leick, A. 2004. GPS Satellite Surveying, John Wiley & Sons, New York, 435 pp. Review Paper Segall, P., and J.L. Davis. 1997. GPS applications for geodynamics and earthquake studies, Annual Review of Earth Planet Science, 25, 301-336,
