GNSS for Landing Systems and Carrier Smoothing Techniques Christoph Günther, Patrick Henkel Institute of Communications and Navigation Page 1
Instrument Landing System workhorse for all CAT-I III approach and landing today Localizer, Oberpfaffenhofen 108-111.975 MHz [Source: Wikipedia] 328.6-335.4 MHz Institute of Communications and Navigation Page 2
Weaknesses of ILS Localizer and glideslope transmitter at the end of the runway. In order to avoid multipath interference all airplanes must have cleared the runway and taxis limits the arrival frequency under bad weather conditions strong restrictions on the location of buildings Long straight flight segment before landing (straight in approach) curved approach often desirable Fixed glide path intercept point (small / large aircrafts) One equipment per runway and direction not all runways are equipped due to costs Does not provide ground guidance runway incursion, 2 per day in Europe City Airports [Ian Billinghurst] Institute of Communications and Navigation Page 3
Feared Clock Events Phase jump 1 single satellite had no feared event in 168 days of processing Frequency jump Frequency drift Bakharev, Frolova, Moudrak, 2008 Institute of Communications and Navigation Page 4
Unobserved Clock Run-Off PRN 23, January 1 st, 2004 [Source: Boeing] Institute of Communications and Navigation Page 5
Satellite Maneuver without Warning PRN 18, April 10 th, 2007 [Source: FAA] Institute of Communications and Navigation Page 6
Ground Based Augmentation System GPS / Galileo Ionospheric Gradient Navigation Signals Interference Jammer / Spoofing GBAS Reference Receivers Corrections and Integrity VHF Data Broadcast Institute of Communications and Navigation Page 7
Experimental GBAS Systems Research Airport Braunschweig DLR receiver station optional sites for Thales CAT I GBAS DLR EVNet Node GLS Institute of Communications and Navigation Page 8
The Concept of Integrity Horizontal Alert Limit (HAL) accuracy (H) Event: Alert: within time to alert Vertical Alert Limit (VAL) accuracy (V) accuracy: integrity: the average error is small detect when the measured position leaves the box (worst case situation) continuity: it does not happen during a specified maneuver of duration true position measured position availability: accuracy, integrity and continuity are provided Institute of Communications and Navigation Page 9
Accident Statistics - The Basis for Requirements per 1 million flights 10-3 for Navigation Sensor [Source IATA] pilot can handle 99 out of 100 error conditions, provided they have alternative means (CAT I) Institute of Communications and Navigation Page 10
GNSS Landing Systems ILS like performance [Source: FAA] Difficult part! Institute of Communications and Navigation Page 11
Three Elements for Achieving Integrity Monitoring eliminate events which are likely and have a large impact, e.g., satellite clock jumps. Note that this adjusts the tails of the probability distribution of errors. Protection levels in the position domain bound the impact of small errors, which are likely to occur and cannot be easily detected in a short time, e.g. noise, diffuse multipath. Bound the probability of events that are not covered by protection levels and are hard to detect in a short time, e.g. simultaneous failure of two reference receivers. Institute of Communications and Navigation Page 12
Protection Levels in Position Domain The user s position and clock offset are determined from the equation which is linear with a very good level of accuracy, otherwise iterate. Solve by least square Thus bounds on the pseudorange must be preserved under linear transformations to be applicable to position domain. Institute of Communications and Navigation Page 13
Symmetric Overbounding DeCleene, 2000 Institute of Communications and Navigation Page 14
Paired Overbounds Rife, Pullen, Pervan, Enge, 2004 Institute of Communications and Navigation Page 15
Gaussian Overbounds Inflation Factor Nominal ionosphere, gaussian core, heavy tail Lee, Pulle, Datta-Barua, Enge, 2006 Institute of Communications and Navigation Page 16
K-factors The gaussian overbound of the noise contributions are projected into position domain, resulting in an aggregate variance: The gaussian cdf must be evaluated at in order to ensure that the allocation for the -error of not fulfilling the bound is not exceeded: The individual variances are thus inflated twice! (CAT-III, 4 receivers) is not very compatible with standards code measurements and a vertical alert limit of 5.3 m Institute of Communications and Navigation Page 17
Hatch Filter Variant Smoothing - + range, clocks, troposphere [Hwang, Mc. Graw, Bader, J. Nav. 1999] Institute of Communications and Navigation Page 18
Known Smoothing Algorithms I Single carrier smoothing Dual frequency ionosphere free smoothing [Hwang, Mc. Graw, Bader, J. Nav. 1999, Mc. Graw, Young, NTM 2005] Institute of Communications and Navigation Page 19
Known Smoothing Algorithms II Dual frequency divergence free smoothing [Hwang, Mc. Graw, Bader, J. Nav. 1999, Mc. Graw, Young, NTM 2005] Hiro Konno [NTM 2006, ION 2007] compute IF and DF as well as associated VAL, then use method with lower VAL areas with insufficient availability are considerably reduced but not eliminated VAL 10 m, desirable 5.3 m, EUROCAE 2.6 m, ASMCS may require much smaller xal Institute of Communications and Navigation Page 20
Galileo Frequencies aeronautical aeronautical [Courtesy: CNES] L1: SoL service, BOC(1,1) modulation 154 10.23 MHz E5b: SoL service, upper part of ALTBOC(15,10) BPSK(10) 118 E5a: OS service, lower part co-located with L5 115 Institute of Communications and Navigation Page 21
Three Carrier Smoothing Three carrier ionosphere free Hatch smoothing minimize the noise term (marginal improvement in the factor) but: Multipath: factor 3 for code, factor 2 for carrier Institute of Communications and Navigation Page 22
Biases Explicit Solution Bias of the solution Institute of Communications and Navigation Page 23
Generalized Carrier Smoothing Smoothing Ambiguity estimation Institute of Communications and Navigation Page 24
Smoothed Code and Conditions geometry restitution (output) geometry removal (input) ionosphere free (output) ionosphere free (input) ambiguity sufficient condition Institute of Communications and Navigation Page 25
Search for Linear Combinations Search for the solution fraction of all integers with a small noise and a small probability of wrong fixing: Institute of Communications and Navigation Page 26
Good Linear Combinations Search and least square Multipath: factor 3 for code, factor 2 for carrier measure for the probability of wrong fixing Institute of Communications and Navigation Page 27
Position Determination and Ambiguity Resolution These are k equations with k+4 unknowns, expand the system using a Hatch smoothed code (less noisy) -> 4 more equations smoothed auxiliary solution round the float least square solution for N to the next integer, compute fixed position Institute of Communications and Navigation Page 28
Probability of Wrong Fixing Equation Least square solution Distribution of is gaussian with covariance Probability of wrong fixing Institute of Communications and Navigation Page 29
Bound on the Probability of Wrong Fixing with only dependent on Institute of Communications and Navigation Page 30
Biases in Differential Mode u 1 u 2 u 3 u 4 u 5 Differential processing, e.g. Institute of Communications and Navigation Page 31
Biases in Precise Point Positioning w 1 1 w 2 1 w 1 2 w 2 1 w 2 2 w 3 2 u 1 u 2 u 3 u 4 u 5 receiver type 1 receiver type 2 Bias on the link between satellite k and receiver i from class n: Assumption: the satellite bias is stable and is provided by an augmentation system SBAS, GBAS, Institute of Communications and Navigation Page 32
Behavior of the Biases [Laurichesse, Mercier, ION GNSS 07] lines mainly horizontal ~ bias constant duration of each line ~ 1 pass Institute of Communications and Navigation Page 33
Positioning with Biases Invariant under the transformation Institute of Communications and Navigation Page 34
Comments on Biases Run a bias filter, which is update at each step Use filtered biases and fixed ambiguities N to determine the fixed solution Using the solution for i=1, j=-1, k=0 and the minimum noise ionosphere free code combination: control code bias in E5a, E5b (absolute) control phase bias in E5a and E5b (differential) RAIM type verification of the fixed ambiguities. Large ambiguity discrimination Institute of Communications and Navigation Page 35
Combination with Controlled Biases and a Low Noise (i,j,k)=(6,-7,1) lambda=2.673965, sigma=0.052126, discr=25.648821 Coefficients -64.126 75.263-11.779-1.167-0.106 2.273-3.625 2.988-0.006 Carrier biases 62.959-75.369 14.052 Code biases -3.625 2.988-0.006 Probability of wrong fixing <1E-100 Institute of Communications and Navigation Page 36
Ionosphere 2 nd Order Correction S. Bassiri, G.A. Hajj (1993) Similar invariance as in the case of biases, impacted by the difference in the case (i=1,j=-1,k=0) Institute of Communications and Navigation Page 37
Conclusions Aim at accuracy and integrity for demanding applications promising method wrto. performance and simplicity Ambiguity fixed during tracking In the case of a loss of lock or cycle slip, the ambiguity must be reacquired, trading ionospheric disturbances against equipment biases ionospheric disturbances are driven by solar activity, which is out of human control equipment biases can be influenced by careful engineering of the transmitter and receiver Biases are important in undifferenced methods Tropospheric corrections must be performed more precisely as accuracy increases. The corrections provided by SBAS converge in an aeronautical scenario The impact of the ionospheric delay of second order can be suppressed. Institute of Communications and Navigation Page 38