Tajul Ariffin Musa Dept. of Geomatics Eng, FKSG, Universiti Teknologi Malaysia, 81310 Skudai, Johor, MALAYSIA. Phone : +6075530830;+6075530883; Mobile : +60177294601 Fax : +6075566163 E-mail : tajul@fksg.utm.my Webpage:http://www.fksg.utm.my/geomatic/academicstaff.php Skype : Tajul.Musa 1
Measurement Errors 2
The Nature of GPS Observable The basic GPS observables are pseudo-range and carrier phase which are essentially biased ranges. These biases arise from a number of sources: clock errors in both the receiver clock (dt j ) and satellite clock (dt i ), the atmospheric refraction delay (I and T), and cycle ambiguities (N ji ) in the case of carrier phase observations. Others? 3
MEASUREMENT BIASES & ERRORS All GPS pseudo-range and carrier phase measurements are affected by a variety of biases and errors. Biases may be defined as being those effects on the measurements that cause the true range to be different from the measured range by a systematic amount, and which must be accounted for in the measurement model. Hence under the heading of "errors" are assembled all unaccounted for measurement effects, as well as any unmodelled or residual biases. Different GPS applications require different levels of GPS accuracy. There is therefore a different partitioning of "biases" and "errors. 4
Accounting for Biases Several options are available: They can be estimated as explicit (additional) parameters. Those biases linearly correlated across different datasets can be eliminated by differencing. Those biases which are a function of frequency can be eliminated by constructing linear combinations of dual-frequency data. The biases can be directly measured, for example using Water Vapour Radiometer (WVR) observations in the case of the tropospheric delay. The biases can be simply ignored. 5
Satellite Dependent Errors/Biases BIASES & ERRORS Satellite dependent: Satellite clock uncertainties Ephemeris uncertainties Hardware Errors Receiver-Satellite Satellite- dependent: Receiver Atmospheric Delay Dependent Carrier phase ambiguity Errors/Biases Receiver dependent: Multipath (imaging & scattering) Receiver clock uncertainties Receiver Ref. coordinate uncertainties Dependent Hardware & Meas. noise Errors/Biases 6
Satellite Dependent Errors/Biases 7
Satellite Clock Uncertainties The GPS Satellite Clock Uncertainties are modelled thro satellite clock bias, drift and drift-rate. The behaviour of each GPS satellite clock is monitored with respect to GPS Time. The offset, drift and drift-rate of the satellite clocks are available to all GPS users as clock error coefficients broadcast in the Navigation Message. Clock error & corresponding range error: 1 nanosecond 0.3m 1 microsecond 300m 8
Satellite Ephemeris Biases The satellite ephemeris bias is the discrepancy between the true position (and velocity) of a satellite and its known value. This discrepancy can be parameterized in three orbit components: along track, cross track and Radial. Along track component is the one with the largest error. 9
Approximate relationship between baseline length, accuracy and GPS satellite orbit error. Baseline error = (d/20000)*orbit error 10
Satellite Hardware Errors These errors have several sources: 1. the electronic-specific effects that cause signal travel time delay between the satellite signal generator and the satellite transmitter; 2. satellite antenna phase offsets and orientation (the difference between the GPS satellites centre of mass and phase centre of its transmitter); 3. the effect of phase wind-up (a rotation of satellite antenna around its vertical axis). Blewitt (1998) points out that in the past the phase wind-up effect occurred when the satellite began to spin due to some malfunction. 11
Satellite-Receiver Dependent Errors/Biases 12
Atmospheric Delay As GPS signals propagate through Earth s atmosphere, they are refracted. Major influence originates from ionosphere and neutral atmosphere layer (mostly due to troposphere). 13
The atmosphere consists of charged particles, neutral atom, molecules, gases, water vapour, etc., and changes the velocity (speed and direction) of the GPS signals. A change in signal speed changes the signal transit time. Consequently, the measured range between the satellite and the receiver is different from its line-of-sight geometric range. This effect is often addressed as atmospheric refraction or atmospheric delay. 14
Ionospheric Delay The ionosphere is that band of atmosphere extending from about 50 to 1000 kilometers or so above the earth's surface. In this layer the sun's ultraviolet radiation ionizes gas molecules which produce an electron. These free electrons in ionosphere layer influence the propagation of microwave signals (speed, direction and polarization) as they pass through the layer. 15
Ionosphere is divided into several layers; D, E, F1 and F2, based on level of ionisation. In F2 layer the electron concentrations reach their highest values, maximum usually at a height of 350-400km. The electron density is less in the E layer and rapidly decreases below the D layer and above the F2 layer. Ionospheric layers and electron density for a site in the mid-latitude regions. The electron density is higher during the daytime compare to the nighttime in mid-latitude site (HAARP, 2003). Height (km) 16
TEC Variability The effect of ionospheric delay heavily dependent on TEC. The TEC is highly variable, in both a temporal and spatial sense. The following comments can be made on the variability of TEC: Seasonal variation (mid-latitude region)- Typically, the electron density levels are higher in winter than in summer. Since the Sun s radiation is higher in the summer, this is somewhat an unexpected result. Time of day In mid-latitude areas TEC is largest during daytime (typically after local noon) and at its minimum at nighttime until dawn. In equatorial region however, the situation is reversed. Solar Activity Solar activity is usually characterised by sunspot number. Detailed observations of sunspots have been carried out by the Royal Greenwich Observatory since 1874, and can be represented in so-called butterfly diagram. Note that the maximum sunspot number occurs in an 11 year cycle. The last solar maximum occurred during the years 2000/03. 17
The 11 year solar cycle of sunspot numbers (NASA, 2006). Top: the positions of the spots shows that these bands first form at mid-latitudes, widen, and then move toward the equator as each cycle progresses. Bottom: information on the sizes of sunspots show the year 1960 recorded the highest. 18
Two-hourly estimated (red line) and predicted (blue line) mean VTEC values from January 1995 to September 2006 (CODE, 2006). The highest recorded value was about 60TECU in year 2002. 19
AURORAL REGION Geomagnetic location The Earth s magnetic field influences particle motion in the Earth s orbit and traps charged particles such as free electrons. The geomagnetic field is strongest at low latitudes. EQUATORIAL REGION AURORAL REGION Regions of the world with high ionospheric activity (Seeber, 1993). 20
Ionospheric Delay to GPS Signal Extreme at horizon, ~3 times zenith value. It makes cycle slip editing and ambiguity resolution more difficult, and also introduces scale errors, though only significant for long baselines (relative positioning). Figure show the effect to GPS baseline in PPM (Tajul, 2006). Magnitude of the 1 st order ionospheric phase effect for L1, L2 and future L5 as a function of satellite zenith angle (Odijk, 2002). Part Per Million (PPM) 14 12 10 8 6 4 2 50TECU L1 100TECU L1 50TECU L2 100TECU L2 50TECU L5 100TECU L5 0 10 20 30 40 50 60 70 Zenith Angle (deg) 21
OPTIONS Use IONOSPHERE PREDICTION MODELS -- broadcast model generally <50% accuracy, may be useful for point positioning users (eg. Broadcast model, IRI model, etc). Use DUAL-FREQUENCY receivers measure the effect dion = L1 f f 2 L2 2 L1 dion & form ionosphere-free" L1/L2 data combination. DIFFERENCE data between sites -- effect of error is minimized due to its high correlation over short to medium baselines, typically 1-2ppm residual effect. L2 22
Tropospheric Delay The Neutral Atmosphere The neutral atmosphere reaches almost 80km in altitude and consists of stratosphere, troposphere, and part of mesosphere. The most dense and lowest layer of Earth's neutral atmosphere is troposphere. Extending from surface to stratosphere at an approximately 13km altitude, it is within troposphere where almost all weather occurs. The troposphere is composed of a mixture of several neutral dry gases, primarily nitrogen and oxygen, and traces of others including pollutants. The dry gases are dominant in the troposphere with slow variations and are easy to model using the ideal gas law and a hydrostatic model. Source http://www.windows.ucar. edu/citizen_scie$nce/bud burst/climatechange_cont rols.html 23
The troposphere also contains a variable amount of water vapour, which varies depending on the temperature and pressure of the air. Figure shows the water vapour mixing ratio and relationship with temperature, pressure, and height above the surface. As can be seen, water vapour content is significant between 12km altitude and surface. The water vapour content increases with increasing temperature and pressure, but decreases as the elevation increases. The tropospheric and stratospheric layers, and the tropopause. The relations of these layers to temperature, height, and pressure and atmosphere water vapour are clear evidence (Mockler, 1995). 24
For radio frequencies up to about 30GHz, troposphere is nondispersive medium (unlike the ionosphere); i.e., the refraction is independent of the frequency of the signals passing through it. The effect of neutral atmosphere is denoted as tropospheric refraction, tropospheric path delay or simply tropospheric delay (as troposphere is the densest layer). Equatorial region contains the thickest tropsophere layer & high amount of water vapour. Thus, a very significant effect of troposphere delay can be expected in this region. 25
Magnitude: Zenith value of dry delay at sea level 2.3m-2.5m, near horizon at sea level 20m - 40m. 90% due to dry delay can be modelled very well. 10% due to wet delay (due to water vapour in atmosphere) is quite difficult to account for. ZPD and the Region (IGS report) 26
OPTIONS: Avoid tracking low elevation satellites. CORRECT data using a STANDARD TROPOSPHERIC REFRACTION MODEL (Saastamoinen, Hopfield, etc.) -- with or without surface meteorological readings. DIFFERENCE data between sites -- effect of error is minimised due to high correlation over short to medium baselines. Advance modelling of (residual) tropospheric delay requires estimation of troposphere parameters. 27
Effect on baseline length Error in baseline length (ppm). Error in station height (cm). Effect on station height 28
Carrier Phase Ambiguity What is carrier phase ambiguity? f S f ϕ = p + f(dt dt R ) + N + E c c The ambiguity is an integer number (a multiple of carrier wavelength). The ambiguity is different for L1 and L2 phase observations. The ambiguity is different for each satellite-receiver pair. The determination of cycle integer ambiguity integer is generally not an easy task (especially in real-time) because of the presence of other biases and errors in carrier phase measurement. *Note: The ambiguity itself is not an error! However, the unknown integer ambiguity bias the carrier phase measurement. 29
1. "PHASE MEASUREMENT" : (SAY NOW=1/4) FRACTION OF WHOLE WAVELENGTH x SIGNAL WAVELENGTH = 1/4 x 0.190m = 0.0475m 2. "INITIAL AMBIGUITY AT 1 ST OBS" : NUMBER OF FULL WAVELENGTHS x SIGNAL WAVELENTH = 106,000,000 x 0.190m= = 20,140,000m 3. "NUMBER OF FULL CYCLES COUNTED BY RECEIVER" : NUMBER OF COUNTED WAVELENGTHS x SIGNAL WAVELENGTH = 1,000 x 0.190m = 190m TOTAL DISTANCE TO SV: 1 + 2 + 3 = 0.0475 +20,140,000 +190 = 20,140,190.0475m 30
IMPORTANT NOTES: The unknown ambiguity parameter can be estimated along with other parameters of interest via least square estimation. However, the estimation provides only the real value (float) of ambiguity. The solution refer to ambiguity-free solution or float solution. Ambiguity resolution is the process that takes estimated float (real-valued) ambiguity parameters and converts them to the likeliest integer values. If the process is successful this process will strengthen the carrier phase mathematical model (in the float solution), as well as transforming carrier phase observations into high accuracy range measurements. The ambiguity in this case is often called fixed ambiguity, and parameters estimated are referred to as fixed (or ambiguityfixed) solution. 31
OPTIONS: Leave the solution as float solution. For long hours (static GPS), estimate ambiguity parameters to their nearest integer values, and iterate solution, in a so-called ambiguity-fixed solution. Employs special algorithm (searching method) such as AFM, FARA, OMEGA, etc. Currently, Least Square Ambiguity Decorrelation Adjustment (LAMBDA) is the most popular algorithm. These algorithms often use for fast ambiguity resolution in real-time. Difference data between consecutive epochs (socalled triple difference) to ELIMINATE the phase ambiguity bias. However, measurement noise is too large & not suitable for precise positioning. 32
Receiver Dependent Errors/Biases 33
Multipath (Imaging & Scattering) GPS signals may travel along a straight path to receiver antenna (apart from small bending effects due to atmospheric refraction). Because of reflections from nearby objects such as buildings, metallic structures, ground or water surfaces, etc., the signals may travel along more than one path (referred to as multipath) to reach the receiver antenna. 34
The multipath effect is in many respects systematic in nature, but it may also be considered a largely random effect as, affecting both code and phase measurements. Other that are often categorised as multipath are imaging and scattering. Imaging is caused by reflecting object producing an image to confuse GPS signal from original one. Scattering is due to signal scattering around surface of the installed antenna, causing interference with direct signal. This has a number of effects: it may cause signal interference between direct and reflected signal leading to noisier measurement, or it may confuse the tracking electronics of the hardware resulting in a biased measurement that is the sum of the satellite-to-reflector distance and the reflector-to-antenna distance. 35
OPTIONS: Reducing the effect of multipath : Make a careful selection of antenna site in order to avoid reflective environments. Use a good quality antenna that is multipath-resistant. Use an antenna ground plane or choke-ring assembly. Use a receiver that can internally digitally filter out the effect of multipath signal disturbance. Do not observe low elevation satellites (signals are more susceptible to multipath). 36
Receiver Clock Uncertainties The inexpensive receiver clock (usually a low-cost crystal quartz oscillator) has to be synchronised with GPS time if accurate range is to be derived from the signal travel time based on the difference between time of transmission (as measured by the satellite clock) and time of reception (measured by the receiver clock). The synchronisation offset with respect to GPS time for the receiver clock is referred to as receiver clock error. Generally, time origin of a GPS receiver is set automatically as soon as sufficient satellites are tracked to carry out a single point pseudo-range navigation solution. 37
There are also clock uncertainties due to clock drift and driftrate. They are modelled thro receiver clock bias, drift and drift-rate (as in the case of satellite clock). The "clock drift and reset" 38
Image Credits to http://www.ngs.noaa.gov Antenna Phase Centre Offset (and Variations) GPS measurements are referred to the antenna phase centre, which should coincide with the electrical centre. However, there may be a constant offset, and this offset may vary with different signal frequency, strength and direction. Tests have shown that this effect is comparatively insignificant for good antenna, mm level (such as microstrip antennas). Microstrip Antennas Image Credits to http://www.freepatentsonline. com 39
OPTIONS: IGNORE -- generally mm level. BETTER antennas -- use stable micro-strip or dipole antennas. Keep antenna and receiver unit together during survey, and always orient antenna in the same direction -- effect on baseline is constant. Antenna MODELLING, during processing for very high precision surveying, e.g., visit www.ngs.noaa.gov/antcal to obtain the parameters. 40
Reference Station Bias Differential GPS positioning requires that the coordinates of one of the stations upon which a GPS receiver is located be held fixed during data processing. This station is the base or reference receiver. Hence, in effect, only the relative position (or baseline components) relating the second receiver to the first (base or reference) receiver are estimated. Any error in these fixed reference station coordinates therefore will cause a bias in the solution. 41
How well must the fixed base station's coordinates be known? The impact of the bias on relative positioning can be considered in a similar manner as the satellite orbit bias. The more accurate the relative position is required, the more precisely the base station's coordinates must be known in the coordinate reference of the satellite ephemerides. Hence, the accuracy of the base station coordinates must be commensurate with the accuracy of the GPS satellite orbits. 42
Measurement Noise The measurement process in the receiver can be made to a certain level of precision. The receiver itself is not a perfect device, hence small effects due to thermal noise, tracking loop noise and other electronic-specific effects will remain. Even in the absence of any signal, the receiver and antenna will detect a certain noise power. The noise level in the carrier phase measurements can be expected to be much less due to its smaller wavelength (compare to code). Measurement noise is typically at the millimeter level. 43
Residual Biases RESIDUAL, UNMODELLED BIASES: Residual effect could be distance-dependent & station dependent. It can complicate the process of ambiguity resolution. Usually small (mm-cm level) after applying basic a-priori modelling. 44
Carrier Phase Cycle Slips Following a loss-of-lock, on resumption of tracking to the satellite, the accurate fractional part of the carrier phase can be measured again, however, the integer part ( nji + CR(Tj) ) will no longer provide the correction to the fractional phase measurement that yields the true satellitereceiver range. With current receiver technology & data processing algorithm stitch the slips. Problem with small slips. 45
The Complete Observation Equations P C/A = p+c(dt S -dt R )+dion C/A +dtrop+(dh S +dh R ) C/A +dmp C/A +e C/A P L1 = p+c(dts -dt R )+dion P1 +dtrop+(dhs +dh R ) P1 +dmp P1 +e P1 P L2 = p+c(dts -dt R )+dion P2 +dtrop+(dhs +dh R ) P2 +dmp P2 +e P2 L L1 = p+c(dts -dt R )-dion L1 +dtrop+(dhs +dh R ) L1 +dmp L1 +λ L1 N L1 + E L1 L L2 = p+c(dts -dt R )-dion L2 +dtrop+(dhs +dh R ) L2 +dmp L2 +λ L2 N L2 + E L2 where the terms ē and Ē in previous equations have been expanded to include the ionospheric delay (dion ), tropospheric delay (dtrop), satellite hardware delay (dh S ), receiver hardware delay (dh R ), multipath effect (dmp ), pseudorange measurement noise (e ), carrier phase measurement noise (E ), and other terms which have been previously included. The symbol ( ) denotes the terms that are frequency-dependent, which is indicated by the given subscripts in the above equations. 46
THANK YOU 47