Modeling the Environment and Signal Errors

1. Modeling the Environment and Signal Errors

2. Agenda • Atmosphericeffects • Pseudorange ramps and steps • Satellite clock noise and errors • Obscurations from terrain or vehicles • Creating and modeling multipath • Navigation data modification and errors

3. Agenda • Atmosphericeffects • Pseudorange ramps and steps • Satellite clock noise and errors • Obscurations from terrain or vehicles • Creating and modeling multipath • Navigation data modification and errors

4. The Atmosphere • The two layers of the atmosphere that affect GPS the most are theTroposphereand theIonosphere • Troposphere: Stable with little variation, this is a non-dispersive medium, therefore different wavelengths are delayed the same amount • Ionosphere: Extends from about 50km to about 1000km, caused by the suns radiation • Variability from day/night, day to day and year to year • Solar activity e.g. sunspots, 11year cycle (next peak around 2011) • Geomagnetic disturbances • Seasons (axial tilt towards the sun) • Composed of ions and free electrons, defined by the total electron content (TEC) • TEC – the number of electrons in a tube of 1 m² cross section extending from the receiver to the satellite Proprietary & Confidential—Page 4

5. How the Atmosphere Affects GPS • The transmitted signal results in an incorrect pseudorange measurement because it gets refracted when travelling through the ionosphere and troposphere • The amount of refraction is defined by a medium’s refractive index • If the refractive index of a medium depends upon the frequency of the signal, then the medium is dispersive • The ionosphere is a dispersive medium, affecting the modulation codes (C/A, P) and L1 (1575.42 MHz), L2 (1227.60 MHz) and L5 (1176.45 MHz) carriers differently • Thus, this permits the receivers to quantify the ionospheric delays Proprietary & Confidential—Page 5

6. How the Atmosphere Affects GPS (cont.) • The amount of refractive delay pseudorange error is dependent upon the path of the LOS signal through the atmosphere • At the horizon it travels through more of the atmosphere than at zenith (directly above), thus low elevation satellites typically exhibit more error on their pseudoranges Proprietary & Confidential—Page 6

7. What Receivers Do To Compensate • Troposphere • All receivers employ a model to calculate the estimated Tropospheric delays based on the vehicle position and relative satellite azimuth and elevations • Ionosphere • For single frequency users, the Klobuchar model is commonly used for estimating the world wide Ionospheric delay • Corrects RMS error by about 50% (Ref. ICD-GPS-200C) • Uses the 8 Alpha and Beta coefficients transmitted in the Navigation Data • For dual frequency users, the receiver can measure the Ionospheric delays • Since the ionpshere is dispersive, the L1/L2 dual-frequency receiver can measure the group delay/phase advance caused by the ionosphere • These measurements Include the errors from the satellite clock, ephemeris and tropospheric errors • Comes at the price of noisier measurements, potentially up to 3 times (Ref. Enge/Misra) • Augmentation systems can be used to provide additional compensation • SBAS (i.e. WAAS, EGNOS, MSAS) corrections eliminate around 90% of the error Proprietary & Confidential—Page 7

8. Atmospheric Characteristics Compared • The ionosphere and troposphere characteristics and modeling errors are shown below Misra, Pratap. And Per Enge. Global Positioning System: Signals, Measurements and Performance. 2004. Proprietary & Confidential—Page 8

9. Atmosphere Models (Troposphere) • There are several models available within SimGEN to model the Troposphere • STANAG (SimGEN’s Default) • NATO Standard Agreement STANAG 4294 Issue 1 • Surface Refractivity Index – Range 220 to 420 Default 324.8 • Bean and Dutton Model 2 (BD2) • Model 2 by Bean, B.R. and Dutton, E.J., Radio Meteorology, Dover Publications, New York, 1966 • RTCA-96 • Tropospheric correction reference model as defined in document RTCA/DO-229 January 16, 1996. • RTCA-98 • Tropospheric correction reference model as defined in document RTCA/DO-229 June 8, 1998 • Models differ in their assumptions regarding changes in temperature and water vapor with altitude • If the receiver uses a different troposphere model than SimGEN, this represents a more realistic real world condition Proprietary & Confidential—Page 9

10. Klobuchar Model (Ionosphere) • Specified in ICD-GPS-200C and developed using empirical data • Model uses (8) Alpha (α) and Beta (β) parameters transmitted in the navigation data for the entire constellation • (4) α terms (α0, α1, α2, α3) define the coefficients of the cubic equation representing the amplitude of the ionosphere vertical delay • (4) β terms (β0, β1, β2, β3) definethe coefficients of the cubic equation representing the period of the ionosphere delay model • In addition, it uses the users position, azimuth and elevation to each satellite and GPS time for calculating the estimated ionosphere error • The calculated corrections apply to the mean ionosphere height at the signal ionospheric pierce point (IP), thus may not be ideal for certain space applications • Archive of Broadcast Data (shown right) : • http://radio.feld.cvut.cz/satnav/gps.php3 Proprietary & Confidential—Page 10

11. Atmospheric Modeling in SimGEN • SimGEN supports various methods for modeling the effects of the atmosphere on the RF and navigation data • The desired troposphere and ionosphere models and errors for the scenario are specified in the Atmosphere file, *.atm Proprietary & Confidential—Page 11

12. Atmosphere File (General) • Atmosphere file > General • Select desired Tropospheric model to be used • Specify the Surface Refractivity Index (STANAG only) • Define the Ionospheric delay and switching of Ionospheric models Note: Default models shown Proprietary & Confidential—Page 12

13. Atmosphere File (Troposphere Models) • Troposphere models available • Disabled – Delay set to Zero • STANAG (SimGEN’s Default) • BD2 • RTCA-96 • RTCA-98 • STANAG model Surface Refractivity Index (Ns) at mean sea level • Range 220 to 420 (defaults to STANAG value 324.8) • Typical errors shown below • Note: SimGEN’s troposphere model may be different from the model used in the receiver Proprietary & Confidential—Page 13

14. GPS Terrestrial Iono Model • Specifies the delay applied to the RF signal • Specifies the (8) parameters in the Navigation Data Subframe 4, Page 18 at the Start of the simulation • Specifies the (8) parameters in the Navigation Data Subframe 4, Page 18 at the Next Upload defined in the constellation file *.gps • Uses the Klobuchar (8) Alpha (α) and Beta (β) parameters • Default values shown below Proprietary & Confidential—Page 14

15. GPS Spacecraft Iono Model • Constant TEC • Defines a constant total electron content (TEC) value to be used for modeling the ionospheric error • A simple model to use Proprietary & Confidential—Page 15

16. GPS Spacecraft Iono Model (cont.) • Polynomial TEC • Uses a 5th order polynomial to define the TEC value as a function of height • The reference height defines the point at which the polynomial will be used to calculate the TEC value, below this height the TEC value is constant and is the reference value  (unless switched is selected) Proprietary & Confidential—Page 16

17. GPS Spacecraft Iono Model (cont.) • User Defined TEC • Allows the user to define the TEC level with respect to height via a drag and drop graph • Used to create various representative ionosphere models • For example for modeling TEC effects on orbit transfers Proprietary & Confidential—Page 17

18. Switching Terrestrial to Spacecraft Models • Useful for launch vehicles or other applications where the vehicle transitions through the Troposphere and Ionosphere beyond the mean Ionosphere height where the Klobuchar Iono model is not ideal • Default values shown to the right if Switched enabled • Select a rate between 0.001 and 50 m/s and a height for the switch to occur from the Terrestrial Model to the Spacecraft Model • For example, a 50 m/s switch rate would result in the Spacecraft Iono model being the only contributing factor after only 0.2 seconds • 10 m / 50 m/s = 0.2 seconds • Using the default rate 0.1 m/s it would take 100 seconds (a much smoother transition) • 10 m / 0.1 m/s = 100 seconds Delay 10m Delay 10m Reference Height EARTH Proprietary & Confidential—Page 18

19. Positional Variation with Iono Model • Unlike the Klobuchar model, positional variation (Sun and Vehicle) are not implicit • With each spacecraft model it is possible to add an effect of this type by selecting positional variation • The positional TEC model used for the spacecraft applies the following formula: • Where • TEC” is the TEC value at the current height, determined as a constant value or a polynomial function of height, plus any sinusoidal variation • Usun is a unit vector pointing towards the position of the sun • Usv is a unit vector pointing towards the Space Vehicle • The vector dot product gives a result of +1 when the Sun is immediately above the vehicle, increasing the TEC by a factor of 0.143. Conversely when the vehicle is in the opposite direction to the Sun, i.e. in the Earth's shadow, the TEC is reduced by the same amount Proprietary & Confidential—Page 19

20. Sinusoidal Variation with Iono Model • Daily variations in the ionosphere are a result of the 24-hour rotation of the Earth about its axis, which affect the ionosphere layers differently • For example, day and night fluctuations • In the TEC model it is possible to add an effect of 24-hour sinusoidal variation on the TEC • The sinusoidal TEC model used for the spacecraft applies the following formula where the user defines the Amplitude and Start Phase: • Where • TEC’ TEC value at the current height, determined as a constant value or a polynomial function of height • A = Amplitude (range: 0 to 1) • t = The current GPS time in seconds • T = Period of one day in seconds (86,400s) • Φ = Start phase (range: 0 to 2π, units: radians) Proprietary & Confidential—Page 20

21. Double- Click Anywhere on the Skyplot Viewing the Modeled Atmosphere Errors • The user can view the applied atmospheric errors in real-time during the simulation from the “Signals Received” window accessed from the “Skyplot” window • Atmosphere errors are also available via “Quick-look” Proprietary & Confidential—Page 21

22. Agenda • Atmosphericeffects • Pseudorange ramps and steps • Satellite clock noise and errors • Obscurations from terrain or vehicles • Creating and modeling multipath • Navigation data modification and errors

23. Pseudorange Ramps and Steps • Occasionally pseudoranges may be affected by a satellite fault (e.g. erroneous clock) or an atmospheric anomaly (e.g. ionospheric dispersion event) • If observed by the receiver, the receiver may measure a drift of offset in the calculated pseudorange which can cause an undesired position error • Some receivers have logic that can detect and exclude the “faulty” satellite called Receiver Autonomous Integrity Monitoring (RAIM) • This logic permits the receiver to detect the faulty satellite (when tracking at least 5 satellites) and exclude it (when tracking at least 6 satellites) from the positioning solution • This is required for high integrity applications like aviation and marine navigation Proprietary & Confidential—Page 23

24. Pseudorange Ramps and Steps (cont.) • Modeling these pseudorange “errors” in SimGEN are easily performed by “Pseudorange ramp/step” window Proprietary & Confidential—Page 24

25. Pseudorange Ramps and Steps (cont.) • Defining a ramp or step the user specifies the following: • Desired Satellite (Tx ID) • Start state • Hold – superimposed onto the current value of any active ramp as a bias • Reset – clears any current action before the new ramp is applied • Desired pseudorange error (±10,000,000 meters) • Time to ramp up to desired pseudorange error • How long to hold the pseudorange error • Time to ramp down from pseudorange error • Note: Remember to check to make sure the desired satellite is visible in the scenario Proprietary & Confidential—Page 25

26. Agenda • Atmosphericeffects • Pseudorange ramps and steps • Satellite clock noise and errors • Obscurations from terrain or vehicles • Creating and modeling multipath • Navigation data modification and errors

27. Satellite clock noise and errors • Each of the satellite atomic clocks experience some clock drift and noise that affects the ranging accuracy • The navigation message Subframe 1 contains the clock corrections generated by the Control Segment for compensation by the receiver • These corrections are each satellites estimated clock bias (af0), drift (af1) and acceleration (af2) polynomial terms • These are based on periodic observations however and may not indicate the clock's current state • SimGEN permits the user to model various clock noise and error effects • These models may also be used to model atmosphere events, ramps, error budget parameters, and other unique capabilities Proprietary & Confidential—Page 27

28. Satellite clock noise and errors (cont.) • Although noise applied to the pseudorange may be generated from various sources, Selective Availability (SA) from the satellites is the largest contributor for commercial receivers if applied • Currently SA is set to zero • GPSIII will not support SA • SA introduces intentional, slowly changing random errors of up to a 100 meters (328 ft) into the publicly available navigation signals which results in a degraded positioning solution as shown below with and without SA Proprietary & Confidential—Page 28 http://www.ngs.noaa.gov/FGCS/info/sans_SA/compare/ERLA.htm

29. Clock Errors • SimGEN supports the af0, af1 and af2 clock errors • The af0 and af1 terms can be obtained from the almanac • Clock Errors are declared errors (i.e. provided in the navigation message) • af0, af1, af2, are the polynomial coefficients applied on the RF and contained in the navigation message • Clock divergence terms are undeclared errors • af0, af1,  af2 simulate satellite clock drift, acceleration and jerk • Useful pseudorange manipulator for creating other representative errors Proprietary & Confidential—Page 29

30. Intentional Satellite Clock Noise - ISCN • Used to produce a deliberate, slowly-varying error effect on pseudorange, such as Selective Availability (SA) which results in pseudorange errors • Another use may be for modeling error budget requirements • The ISCN causes modeled variation to the satellite clock to cause range errors that are not declared in the navigation data • Accessed through the SimGEN Constellation editor • Refer to the User Manual for more detail • Below is an example of the ISCN effect on pseudorange rate Proprietary & Confidential—Page 30

31. ISCN (cont.) • Models must be enabled and given an update interval & start value • Update Interval - specifies the model update interval in seconds • Spirent strongly recommend an update interval of 100ms for the Gauss-Markov second-order model • Seed value - Initial seed value for the model • From this seed individual seeds are derived for each satellite, so that the noise applied to each satellite is different, but noise sequences are all repeatable • This also has to be enabled for each individual satellite (next slide) Proprietary & Confidential—Page 31

32. ISCN (cont.) • Select and enable for desired satellites • Individual or for all depending upon desired effect • Currently 2nd & 1st Order Gauss-Markov, Digital Filter and Sinusoidal models provided • The default digital filter model emulates what the public domain says the real world SA Effect is like, which is said to be a slowly varying position error of up to 100m Proprietary & Confidential—Page 32

33. Agenda • Atmosphericeffects • Pseudorange ramps and steps • Satellite clock noise and errors • Obscurations from terrain or vehicles • Creating and modeling multipath • Navigation data modification and errors

34. Depending upon the antenna location, vehicle orientation and environment, there may exist obscurations that block the satellites line-of-sight (LOS) signal This may be from the vehicle, environment or surrounding objects Obscurations from Terrain or Vehicles Obscured signal Proprietary & Confidential—Page 34

35. Obscurations from Terrain or Vehicles (cont.) • SimGEN supports various methods of implementing obscurations in the scenario • Turning satellites on/off • Antenna patterns and antenna switching • Terrain obscuration • Vertical plane model • A careful analysis of the intended environment and the fidelity of the test requirements is necessary to choose the best method Proprietary & Confidential—Page 35

36. Turning Satellites On/Off • Obscurations can easily be modeled by denying satellites to be visible • Knowledge of the environment is essential and may be obtained from logged receiver data which will show which satellites where tracked • This can be compared to the known satellites in view for quantifying the obstructed satellites • SimGEN provides a utility for automatically scripting a command file from a NMEA file • Note: This is dependent upon the date, time and location • This requires more effort by the user, but is useful for replicating an environment or configuring unique satellite configurations Proprietary & Confidential—Page 36

37. Turning Satellites On/Off (cont.) • An easy way to turn satellites Off is by scripting “Off Times” for the desired satellites in the Constellation editor • Allows the user to specify satellite on/off periods • List specifies OFF periods • Can be used for specific tests (e.g. code switching in conjunction with PRNs) • Other similar methods include User Action files, Power Adjustment window, User Command files and remote commands Proprietary & Confidential—Page 37

38. Antenna Patterns • Antenna patterns present an easy way to model both environmental and vehicle obscurations • Using antenna patterns constrains the obscuration to the vehicle • In the antenna pattern editor the user can model an obscuration by inputting the maximum attenuation (+46dB) • For high sensitivity receivers, +46dB attenuation may not be adequate, so the user can load a *.csv file with attenuations >46dB if necessary Proprietary & Confidential—Page 38

39. Antenna Patterns (cont.) • Antenna Switching • Used to model loss of signal when entering tunnel, or moving away from a launch pad, hanger or aircraft • An example of entering a tunnel is described below Proprietary & Confidential—Page 39

40. Terrain Obscuration Model • Applies to Land Vehicle and Aircraft models only • Allows variations in terrain to be modeled as the vehicle moves through the obscuration environment while SimGEN automatically obscures the direct satellite signals • Environment is based upon user parameters • Distance between simulated vehicle and obstacle • Max/Min of the height and width of obscurations • Modeling assumes an omni-directional view and creates a randomized, repeatable environment based on user parameters • Obscuration data can be logged, plotted and displayed (from the antenna keyword set) Proprietary & Confidential—Page 40

41. Terrain Obscuration Model (cont.) • If Obstacle height is relative to vehicle’s height is checked then obscurations are modeled relative to the vehicle, regardless of vehicle height • For example if a car drives up and down hills the surrounding buildings should be relative to the vehicle • If unchecked, obstacle heights are absolute • For example if the vehicle climbs, less satellites will be obscured for a given case Proprietary & Confidential—Page 41

42. Terrain Obscuration Model (cont.) • Data set window allows the user to edit each terrain type definition per the parameters shown to the right • 10 Types supplied by default (shown below), but editable to user preference Proprietary & Confidential—Page 42

43. Terrain Obscuration Model (cont.) • The Terrain Obscuration Command File allows the user to specify switching of the predefined models throughout the scenario • Switching of the models is sequentially defined relative to the Distance into the scenario Distance Command List Model Proprietary & Confidential—Page 43

44. Vertical Plane Model • The Vertical Plane Model model can be applied to all vehicles • Obscurations (e.g. buildings, mountains, etc.) are modeled as vertical plane surfaces of a given height and distance from the vehicle • Specified vertical planes are always parallel to the direction of vehicle motion and of infinite length • Different heights and distances may be assigned on either side of the vehicle, and these may be varied during the run permitting both static and dynamic environmental modeling • During the simulation, SimGEN automatically determines when the direct satellite signals are obscured at the vehicle Proprietary & Confidential—Page 44

45. Vertical Plane Model (cont.) • The vertical plane file permits the user to specify obscurations of a given height and distance parallel to the vehicle • These obscurations have an associative Action Time that tells SimGEN when to apply the desired obscuration into the run • Multiple vertical planes are supported for sequentially switching of obscurations Action Time Vertical Planes Command List Proprietary & Confidential—Page 45

46. Agenda • Atmosphericeffects • Pseudorange ramps and steps • Satellite clock noise and errors • Obscurations from terrain or vehicles • Creating and modeling multipath • Navigation data modification and errors

47. What is multipath? • Multipath is when the antenna receives reflections or echoes via multiple paths of the L1 or L2 signals from the GPS satellites • In terms of GPS, the reflected signals come off structures near to the receiver or off the ground • The reflections, by their very nature, have taken a longer path to the receiver so are delayed with respect to the direct LOS, which results in errors in the estimation of the range measurements to each satellite, hence a position errors is commonly the result of multipath • The reflections generally experience some power loss due to the reflectivity of the surface they are reflecting off (a concrete median will attenuate more than a glass median for example) • The receiver has no way of knowing which signal is which so it treats the resultant signals as the real one, which can result in ranging errors from 0 to a few hundred meters Multipath signal Proprietary & Confidential—Page 47

48. SimGEN Multipath Models • Depending upon the reflective surfaces and environment, the received multipath at the antenna may have unique fading and amplitude characteristics • The following types of multipath models are available in SimGEN • Ground reflection • Fixed offset • Doppler offset • Vertical plane • Reflection pattern • Land Mobile Multipath • Legendre • Polynomial • Sinusoidal • Embedded Multipath (8000 only) Multipath Echoes Assigned in SimGEN Proprietary & Confidential—Page 48

49. Ground Reflection Multipath • For antennas above the ground like automobiles, surveyors, aircraft, etc. ground reflection multipath may be present • This model introduces a ground reflected signal based on arrival angle at the WGS-84 Ellipsoid height • The vehicle (antenna) must have some associated height h • A flat plane earth surface below the vehicle is assumed • Takes into account the antenna pattern • The delay is automatically calculated by SimGEN with only amplitude loss (dB) designated by the user to model loss from reversal of polarization for example Proprietary & Confidential—Page 49

50. Fixed Offset Multipath • Creates a multipath signal with constant user-defined range and power offsets with respect to the normal (LOS) signal • This model permits the user to easily generate a multipath signal of fixed delay and amplitude • The Attenuation field specifies the difference in level between the main signal and the reflected. • The Range Offset field specifies the difference in simulated pseudorange between the normal signal and the multipath. A positive number for the multipath range offset will mean that the multipath pseudorange is GREATER than the LOS pseudorange. • Forced Channel: The forced channel field allows the reflected signal to be forced on to a specified channel, if no channel is specified then the next available channel will be used. Proprietary & Confidential—Page 50