Reliable carrier phase positioning [Elektronische Ressource] / Patrick Henkel

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• Publié par: technische_universitat_munchen
• Publié le: 01 janvier 2010
• Nombre de lectures: 24
• Langue: English
• Poids de l'ouvrage: 4 Mo

Extrait

¨ ¨TECHNISCHE UNIVERSITAT MUNCHEN
Lehrstuhl fu¨r Kommunikation und Navigation
Reliable Carrier Phase Positioning
Patrick Henkel
Vollsta¨ndiger Abdruck der von der Fakulta¨t fu¨r Elektrotechnik und Informationstechnik
der Technischen Universit¨at Mu¨nchen zur Erlangung des akademischen Grades eines
Doktor–Ingenieurs
genehmigten Dissertation.
Vorsitzender: Univ.–Prof. Dr.–techn. J. A. Nossek
Pru¨fer der Dissertation:
1. Univ.–Prof. Dr. sc. nat. Chr.-G. Gu¨nther
2. Prof. P. Enge, Ph.D.,
Stanford University, California/USA
3. Prof. Dr. ir. S. Verhagen,
Delft University of Technology, Niederlande
DieDissertationwurdeam5.07.2010beiderTechnischenUniversit¨atMu¨ncheneingereicht
und durch die Fakulta¨t fu¨r Elektrotechnik und Informationstechnik am 30.08.2010
angenommen.iii
Preface
Currently, theGlobalNavigationSatelliteSystems(GNSS)GPSandGLONASSaremod-
ernized and new GNSS such as Galileo and Compass are developed. The modernization
of GPS includes an additional signal on L5 which lies in an aeronautical band. This
will enable a dual frequency positioning on board an aircraft and an elimination of the
dispersive ionospheric delay, which is one of the largest error sources for current single
frequency receivers. DatalesspilotsignalswillbeintroducedonallGPSfrequencies which
will enable a longer integration time and faster signal acquisition. Moreover, the Multi-
plexed Binary Offset Carrier (MBOC) modulation will be used on L1. Galileo uses larger
signal bandwidths than GPS, which will substantially reduce the code tracking error and
improve the positioning accuracy. For example, the Alternate BOC modulated E5 signal
has a bandwidth of 92.07 MHz, which enables a five times lower code tracking error than
the BPSK(10) modulated GPS L5 signal. The additional frequencies and new signals will
improve the estimation and elimination of ionospheric delays, which is one of the major
error sources for positioning.
The GPS and Galileo satellites transmit spread spectrum signals that enable a position-
ing accuracy of 1 m. A significantly higher positioning accuracy can be achieved with
the carrier phase which can be tracked with millimeter accuracy. However, the carrier
phase is period and requires the resolution of an integer ambiguity for each satellite. The
reliability ofthis integerambiguity resolutionwas so farlimitedby thesmall carrierwave-
length of 19.0 cm, receiver and satellite biases, multipath and a large number of unknown
atmospheric delays, which result in an ill-conditioned equation system and a probabil-
ity of wrong fixing of a few percent. This thesis provides new algorithms and methods
to reduce the failure rate by more than seven orders of magnitude. The key to reliable
integer ambiguity resolution are multi-frequency linear combinations that eliminate the
ionospheric delay, increase the wavelength to more than 3 m and keep the noise at a
centimeter level. There exist two further challenges for carrier phase positioning that are
addressed inthisthesis: oneisa continuous tracking ofthecarrierphases inenvironments
with strong multipath and/ or during ionospheric scintillations, and the second one is a
precise estimation of both receiver and satellite phase biases.
The first chapter gives an intuitive introduction to the suggested methods for reliable
integer ambiguity resolution. Moreover, the benefits of the Galileo system are described,
and a model for the code and carrier phase measurements is given.iv
In the second chapter, different groups of new multi-frequency mixed code carrier linear
combinationsarederived. Thechapterstartswiththederivationofphase-onlylinearcom-
binations and then shows the benefit of including code measurements. The additional de-
grees offreedom areused to minimize the noise, to maximize the wavelength, to constrain
the worst-case bias amplification and/ or to maximize the ratio between the wavelength
and the combined noise. For the latter approach, geometry-preserving, ionosphere-free
linear code carrier combinations with a wavelength of more than 3 m and a noise of a
few centimeters were found. The large wavelength in relation to the geometry-preserving
propertysubstantially improves therobustness ofambiguity resolutionover orbitalerrors,
satellite clock offsets and tropospheric modeling errors. Therefore, this group of multi-
frequencylinearcombinationsareaninteresting candidateforbothWide-AreaReal-Time
KinematicsandPrecisePointPositioningapplications. Fordualfrequencymeasurements,
these combinations show a substantial benefit over phase-only linear combinations, which
can not simultaneously increase the wavelength and eliminate the ionospheric delay. The
use of further frequencies enables an even larger ambiguity discrimination and a lower
probability ofwrong fixing. This chapter also includes the derivation ofa multi-frequency
carrier smoothing where the phase-only combination and the code carrier combination
are jointly optimized. Two further groups of new carrier smoothed multi-frequency code
carrier linear combinations are analyzed: the first one includes geometry-free, ionosphere-
preserving and the second one geometry-free, ionosphere-free linear combinations. The
latter ones provide a direct estimate of the integer ambiguities. Additionally, the ca-
pability of detecting erroneous fixings is maximized by a set of linear combinations that
minimizestheprobabilityofthemostlikelyundetectableuncombinedintegererrorvector.
The chapter ends with code carrier linear combinations including next generation C-band
signals and with linear combinations for estimating second order ionospheric effects.
The third chapter contains several methods to improve the reliability of carrier phase
integer ambiguity resolution, and starts with a description of the currently used integer
ambiguity resolution techniques: rounding, sequential conditional rounding (bootstrap-
ping), integer least-squares estimation (including a search) and integer aperture estima-
tion. It is shown that the optimized multi-frequency code carrier linear combinations
enable a reduction of the probability of wrong fixing by several orders of magnitude, and
thata flatambiguity spectrum andanextremely efficient search can beachieved withtwo
multi-frequency linear combinations even without an integer decorrelation. A sequential
conditional ambiguity fixing is proposed which outperforms the traditional bootstrapping
as it reduces the impact of erroneous fixings by slightly lower weights. A partial integer
decorrelation transformation is used to obtain an optimum trade-off between variance
reduction and worst-case bias amplification, a new cascaded ambiguity resolution scheme
with three carrier smoothed ionosphere-free code carrier combinations is provided, and
a partial ambiguity fixing is given where the optimal fixing order is obtained from a
combined forward-backward search while traditional approaches use only a pure forward
search. The optimal fixing order enables a significant increase in the number of reliably
fixable ambiguities for worst-case biases. Finally, the integrity risk due to an erroneous
fixing is evaluated for aircraft landings. The most stringent landing category CAT IIIc
with a vertical alarm limit of 5.3 m and a time to alert of only 2 s has been chosen. Thev
integrity risk is substantially lower than the probability of wrong fixing as a large number
of erroneous fixings does not necessarily result in an integrity threat. It is shown that
the risk of an integrity threat is two orders of magnitude lower than the probability of
wrong fixing forthe optimized dual frequency E1-E5a linear combinations. Moreover, the
large wavelength of the optimized dual frequency E1-E5a code carrier linear combination
ensures that the set of erroneous fixing vectors remains sufficiently small, and that the
probability of wrong fixing is significantly lower than for uncombined measurements.
Thefourthchapterfocusesonanewmethodforimproving thereliabilityofcarrierphase
tracking. AvectorphaselockedloopforjointtrackingofcarrierphasesandDopplershifts
is presented. Additionally, a method for correcting the signal distortion due to wideband
ionospheric effects is suggested. It is required for precise point positioning with Galileo
as the bandwidth of the E5 signal is so large that the ionospheric dispersion within the
E5 band can no longer be neglected.
In chapter 5, a method for estimating the receiver and satellite phase and code biases as
well asforestimating thevertical ionosphericgridbasedonmeasurements fromanetwork
of reference stations is suggested. The method includes several parameter mappings and
a Kalmanfilter, andis validatedwithdual frequency GPSmeasurements fromCORSand
SAPOS reference stations.
Chapter 6 includes a validation of the analyzed differential carrier phase positioning
algorithms with real data. GPS measurements from a stationary baseline on top of the
university’s building as well as kinematic measurements from a flight campaign of the
institute were used. Range residuals of less than 10 % of the wavelength were observed
whichindicateaquitereliableintegerambiguityresolution. Finally,chapter7summarizes
this work.vi
List of publications
Journals:
[1] Patrick Henkel and Christoph Gu¨nther, Partial integer decorrelation for optimum
trade-offbetween variancereduction andbias ampli