PPP and RTK 29.02.2016
Content Carrier phase based positioning PPP RTK VRS Slides based on: GNSS Applications and Methods, by S. Gleason and D. Gebre-Egziabher (Eds.), Artech House Inc., 2009 http://www.gnssapplications.org/ and P. Misra, P. Enge, Global Positioning System; Signals, Measurements, and Performance, 2006 And University of New South Wales, Principles and Practice of GPS Surveying http://www.sage.unsw.edu.au/snap/gps/gps_survey/principles_gps.htm 2
Definitions Receiver position is actually the position of the antenna electrical phase center Antennas. (2014, January 28). Navipedia,. Retrieved 08:05, March 9, 2014 from http://www.navipedia.net/index.php?title=a ntennas&oldid=12573. Precision and accuracy Precise but not accurate Accurate but not precise Accurate and precise 3
Precise positioning (1) For many applications the accuracy obtained using code phase measurements (meter level) is not enough, therefore carrier phase measurements have to be used (accuracy on centimeter level) Applications such as Agriculture Intelligent transportation (lane detection, collision warning) Position based paring applications Road maintenance Land surveying Construction 4
Precise positioning (2) GPS was designed to compute the PVT using code phase measurements Code and carrier measurements are corrupted with same error sources Code tracing measurements are coarse but unambiguous Carrier phase measurements are precise but ambiguous Source: P. Misra, P. Enge, Global Positioning System; Signals, Measurements, and Performance, 2006, 569 s. 5
Carrier phase based positioning (1) Precise positioning using carrier phase measurements provides positioning accuracy on the order of millimeters to decimeters, which is a great improvement over the code phase solution The difficulty in performing a carrier phase based pseudorange measurement primarily lies in the challenge of a quic and robust determination of the carrier cycle ambiguity N for each satellite traced This ambiguity is conceptually equal to the exact number of carriers contained in the space between the receiver and the satellite at the initial signal loc Measurement errors mae it very difficult to determine N in real time and therefore sophisticated means has to be used 6
Carrier phase based positioning (2) (x s, y s, z s ) 2 Carrier phase measurement is a measure of the range between a satellite and a receiver expressed in units of cycles of the carrier frequency. Carrier phase observation in unit of length: L = lf = r+ Nl Known satellite locations at time t: (x s, y s, z s ) t Carrier wave length: l User location (x r, y r, z r ) User time difference from GPS time dt r Unnown initial number of phases N 7 1) When a satellite is loced, the GPS receiver starts tracing the incoming phase 2) It counts the (real) number of phases as a function of time = Δϕ(t) 3) The initial number of phases N is unnown 4) However, if no loss of loc, N is constant over an orbit arc (x s, y s, z s ) 0 Df 1 (x s, y s, z s ) 1 Df 2 (x r, y r, z r )
Carrier phase based positioning (3) Carrier phase positioning is performed in a differential mode (relative positioning with respect to a base station) The process of estimating and validating the correct estimate of the integers is a time consuming process E.g. a typical method: the LAMBDA If the receiver maes a sudden move and the carrier phase loc is lost, even for an instant, the count is broen and the ambiguity must be recalculated 8
Carrier phase based positioning (4) Carrier phase based positioning is a differential (and relative) technique to achieve centimetrer level accuracy by using carrier phases of the underlying GNSS carrier wave signals One receiver (or more) is located at a point of nown coordinates (the base stations or reference receiver) and the other receiver is operated by the user If the baseline between the GNSS receivers is more than around 5-20 ilometers, both L1 and L2 frequencies are used to correct for the ionospheric delay For shorter baselines, dual-frequency measurements are still necessary for rapid initialization for cm-level positioning 9
Carrier phase based positioning (5) Current high-accuracy GNSS positioning techniques 10
Mathematical models Pseudorange measurements are used for low accuracy single-point or absolute positioning OR in combination with carrier phase measurements Carrier phase is defined as the difference between the phase of the incoming carrier signal and the phase of the reference signal generated by the receiver 11 u T I t t c r 1 1 1 ] [ u T I t t c r 2 2 2 ] [ on L1 on L2 u u N T I t t c r 1 1 1 0 1 1 1 1 1,, ( ] [ l l u u N T I t t c r 2 2 2 0 2 2 2 2 2,, ( ] [ l l on L1 on L2 Initial fractional phases at the satellite and the receiver
Differencing (1/2) New observables may be obtained via differencing to remove systematic error sources Between-receiver differencing, between-satellite differencing, between-epoch differencing, between frequencies An error of 10 cm in the measurements could correspond to a change of one cycle in the integer ambiguity estimate (L1 wavelength 19 cm) Also errors have to be in centimeter level to be able to get a position accuracy on centimeter level Primary differencing options: Single-differencing mode Double-differencing mode Triple-differencing mode 12
Differencing (2/2) The single-differenced observable (between-receiver) is obtained by differencing two observables to satellite traced simultaneously by two receivers i (reference) and j i, j i j The double-differenced observable is obtained by differencing observables from two receivers i and j observing the same two satellites and l (or differencing two single differences to satellites and l), l l l l i, j ( i j ) ( i j ) i, j i, j Differencing two double-differences separated by a time interval dt generates a triple-differenced observable, l, l, l i, j j j t ( dt) i, ( t2) i, ( 1) 13
Differencing modes and their error characteristics Triple-difference: Assuming no cycle slips, or loss of loc has occurred, this eliminates the integer ambiguity, hence used to detect for cycle slips and loss of loc 14
Single-difference between-receiver Satellite clocs are extremely accurate but still have errors too large to ignore Eliminates satellite bias and drift Single-differencing and DGNSS have a subtle difference: differential corrections vary slowly, but in single-differencing actual measurements at reference station are used and has to be extrapolated 15
The double-difference From two single differences Basic GNSS observable Ambiguity still to be estimated Highest satellite usually the reference because it has smallest propagation and multipath errors 16
The triple-difference From two double differences Eliminates the ambiguity term Very noisy Useful for approximating baseline solutions 17
Ambiguity resolution techniques (1) Carrier-phase integer ambiguity resolution (N) and validation can be solved via Ambiguity resolution in the measurement domain: Code measurements are used for integer ambiguity resolution Dual-frequency double-difference Requires long periods of clean data 18 l l 2 2 1 1 2 1 2 1 0 1 0 0 1 0 1 0 0 1 L L L L L L L L N N r
Ambiguity resolution techniques (2) Search technique in the coordinate domain Uses only fractional part of the carrier-phase measurement Poor computational efficiency => not really used Search techniques in the ambiguity domain Most used and accurate The process will be explained in more detail later related to baseline determination 19
Between-receiver double-differencing l ij,1 r l ij l N 1 l ij,1 l ij,1 l ij,2 r l ij l N 2 l ij,2 l ij,2 Widelane observable l l ij, 1 ij, 2 Narrowlane observable l l ij, 1 ij, 2 20
Combination of L1 and L2 phases (1) Uncertainty in integer estimation depends on the carrier wavelength GPS L1: 0.190 m, L2: 0.244m => not much better Wide-lane measurement has the wavelength of f f f L12 L1 L2 Integer ambiguity easier to be resolved Measurements noisier than L1 or L2 Narrow-lane measurement f Ln f f L1 L2 has the wavelength of Less noisier than wide-lane ll c /( f f 2) 0. 862 12 L1 L lln 0. 107m m 21
Combination of L1 and L2 phases (2) 22
Combination of L1 and L2 phases (3) The ionospheric free wavelength can be useful on longer baselines where atmospheric errors cannot be neglected The widelane wavelength is about four times the magnitude of the GPS L1 signal: therefore, the number of double difference integer ambiguity candidate points in the search space decreases quicer to fix The widelane observable noise is about six times larger in magnitude than L1 noise, whereas narrow-lane noise is actually reduced to approximately 0.7 times the L1 noise To obtain best position estimates, the widelane solution should only be used as intermediate step to fix either the L1-only or narrow-lane integer ambiguities 23
Dealing with ionospheric delay Ionosphere-free phase Linear Combination LC can be defined as 2 r f1 f1 f2 LC f1 N 2 2 1 N 2 2 2 c f f f f 1 2 1 2 Note: Ambiguity terms are no longer integers due to the multiplicators ambiguity fixing is not an option with LC Noise is scaled up General approach Adopting LC for baselines >~10m First ambiguities fixed using e.g. wide-lane approach and then final solution using LC 24
Ambiguity resolution A comprehensive review of ambiguity resolution methods can be found at http:\\gauss.gge.unb.ca/papers.pdf/gnss2000.im.pdf One of the most commonly used ambiguity resolution method is the LAMBDA sequential conditional least-squares estimation preceded by a decorrelation of the ambiguities by which the integer least-squares estimates can be computed very fast and efficiently 25
Baseline determination The basic steps in baseline determination in carrier phase processing Define a priori values to ambiguity parameters Use a search algorithm to identify liely integer values for the ambiguities Employ a decision-maing algorithm to select the best set of integer values Apply a validation test to the integer ambiguities Obtain the unambiguous double-differenced range observable R ( N )l Compute the baseline parameters between the receiver and the reference station using the precise range observables user receiver coordinates (x,y,z) 26
Reliability of ambiguity resolution Ambiguity resolution reliability is a function of Baseline length between receiver and reference Number of satellites Satellite geometry (satellites setting or rising during the measurement session) Multipath disturbance Single or dual-frequency in use Length of observation session If a carrier cycle slip occurs, the carrier phase ambiguities have to be reinitialized 27
ADOP The precision of the ambiguity estimate can be approximated by a quantity called ambiguity dilution of precision (ADOP) Analogously to the traditional DOP, the idea is to measure the mutual correlation and precision of the double differences ADOP det(p) where P is the covariance matrix of the double differences ADOP can be used e.g. to determine whether it is worthwhile to even try to resolve the integer ambiguities 28
Remars Inter-receiver distances can be from ilometers to thousands of ilometers If long observation sessions are used (up to 24 hours), the integer ambiguities are not necessary to be fixed All data typically archived in RINEX and post-processed Scientific software pacages available include (e.g.) GAMIT/GLOBK (from MIT) Bernese (from University of Bern) Static mode is most commonly used in carrier phase based processing, unless real-time inematic positioning is concerned A priori satellite orbits are usually obtained from IGS http://www.igs.org/ 29
RTK Real Time Kinematic (RTK) is a technique relying on a single reference station to provide real-time corrections, providing up to centimetre-level accuracy with carrier phase measurements The base station re-broadcasts the phase of the carrier that it measured to the user receiver, and the mobile unit compares its own carrier phase measurements with the ones received from the base station The Virtual Reference Station (VRS) method extends the use of RTK to a whole area of a reference station networ Operational reliability and the accuracies to be achieved depend on the density and capabilities of the reference station networ, using dual-frequency receivers the distance should be maximum of 50 m A Continuously Operating Reference Station (CORS) networ is a networ of RTK base stations that broadcast corrections, usually over an internet connection 30
Multiple reference station RTK Independent reference receivers: Networ not efficient, of reference too many base stations stations and correction modelling 31
The VRS principle (1) Ref. station Virtual ref. station (VRS) 32
The VRS principle (2) Networ-RTK is operated in the same way as traditional RTK, but a mobile reference receiver is replaced by a virtual reference station (VRS) The reference data from the VRS are based on the nearest physical stations Ref. station Virtual ref. station (VRS) GNSS rover 33
PPP overview (1) Precise point positioning (PPP) cm-position accuracy of a single static receiver using long observation series and sub-meter accuracy with a moving receiver using ionospheric-free pseudorange and carrier phase functions single receiver easy to deploy & cost effective focus on carrier phase measurements the most accurate observables precise satellite orbit and cloc products Ionosphere is the dominant source of error dual-frequency users taes advantage of the ionosphere-free (IF) observations (P3,L3) single-frequency-only users some mitigation process is required 34
PPP overview (2) Form the ionosphere-free carrier phase measurement using dual-frequency I r ct r Tz m( el) li NI Four unnowns receiver cloc tr, changes from epoch to epoch troposphere path delay Tz, changes slowly NI (not integer anymore), doesn t change if the loc is not lost User position (x,y,z) The converge time of solution depends on satellites in view and geometry, user dynamics and quality of measurements In static case position estimation is easy, will converge in 15-30 minutes 35
PPP - Observation errors (1) GNSS observables ( = pseudoranges and carrier phases) contain errors The main errors are, in order of significance: Ionosphere (~5 m typical) Satellite Orbit and Cloc (~4 m) Troposphere (~2.5 m) Signal biases (carrier and code) (~1 m) Phase wind up effects (~ 20 cm) Earth tides (~ 10 cm) Polar tides and ocean loading (~ cm) 36
PPP Observation error (2) Correcting for the errors mentioned on the previous slide is the ey What to correct for depends on requirements => what accuracy is needed We need a source to get these corrections from Sources can be: GNSS SBAS Local networs National networs such as FinnRef http://euref-fin.fgi.fi/fgi/en/positioning-service/use-service 37
Double Differences vs. PPP Similar precision possible in 24 h solutions Software Only few software capable of geodetic PPP (GIPSY mainly) GAMIT is using double differencing PPP requires extra care modelling geophysical phenomena (e.g., ocean tide loading displacements) which may be (partially) differenced in relative analysis orbit/cloc errors (some periodic) map 1:1 into positioning Kinematic PPP requires longer periods of data ambiguity fixing is not possible without a double differenced second step Double differencing is more precise when short-baseline relative motion is all that is required (e.g., glacier monitoring), but depends on the base station 38
Accuracy considerations The receiver antenna also has an effect on the carrier phase positioning quality Consumer-grade receivers use simple patch antennas whereas geodetic-grade receivers are equipped with choe ring antennas Choe ring antennas are more resistant to multipath as they can better reject signals coming from below the horizon Naturally the receiver s sensitivity and ability to maintain phase loc affect carrier phase positioning performance Frequent cycle slips are hazardous for carrier phase positioning Only the satellites traced by both the reference and rover receivers can be used in differential positioning, so the receiver should be able to acquire and trac as many satellites as possible 39
Other systems in carrier phase processing GLONASS measurements can be used when computing the float solution to improve the convergence speed but usually they are omitted from the fixed solution and integer ambiguity resolution GALILEO is better suited for carrier phase differential positioning than GLONASS Using other systems beside GPS will bring not only more frequencies but also a more extensive satellite constellation to use, thus speeding up the ambiguity resolution process GPS L5 => extrawide-laning 40