Showing papers by "Patrick Henkel published in 2012"

Reliable Integer Ambiguity Resolution: Multi‐Frequency Code Carrier Linear Combinations and Statistical A Priori Knowledge of Attitude

Abstract: This paper provides two methods to improve the reliability of carrier phase integer ambiguity resolution: The first one is a group of multi-frequency linear combinations that include both code and carrier phase measurements, and allow an arbitrary scaling of the geometry, an arbitrary scaling of the ionospheric delay, and any preferred wavelength. The maximization of the ambiguity discrimination results in combinations with a wavelength of several meters and a noise level of a few centimeters. These combinations could be beneficial for both Real-Time Kinematics (RTK) and Precise Point Positioning (PPP). The second method incorporates some statistical a priori knowledge of attitude into the actual fixing. The a priori knowledge includes the length and direction of the baseline between two receivers and is given either as a uniform or Gaussian distribution. It enables a substantial reduction of the search space volume but also ensures a large robustness over errors in the a priori information. Both methods improve the accuracy of the float solution, which motivates a simple rounding for ambiguity fixing. A method is described, which enables an efficient computation of its success rate with a few integral transformations. Copyright © 2012 Institute of Navigation.

Integer Ambiguity Estimation for Satellite Navigation

Abstract: Carrier phase measurements of pseudoranges often allow for millimeter precision. The periodic nature of the carrier phase, however, leads to integer ambiguities. These ambiguities need to be resolved for accurate positioning. Blewitt and Teunissen provide two methods for the associated estimation process. The present paper complements their work with an improved real-valued diagonalization of the ambiguity covariance matrix, and a functional determination of an integer decorrelation transformation. The proposed method achieves a similar performance as Teunissen's LAMBDA method-in terms of the probability of wrong fixing, but with a reduced complexity. Furthermore, it shows a slightly different path towards ambiguity resolution.

Bootstrapping with Multi-frequency Mixed Code Carrier Linear Combinations and Partial Integer Decorrelation in the Presence of Biases

Abstract: Carrier phase measurements are extremely accurate but ambiguous. The reliability of integer ambiguity resolution is improving with Galileo which uses a Binary Offset Carrier (BOC) modulation, large signal bandwidths of up to 50 MHz and additional carrier frequencies.

Best Integer Equivariant estimation for Precise Point Positioning

Abstract: A key prerequisite for Precise Point Positioning (PPP) with Global Navigation Satellite Systems (GNSS) is the precise knowledge of satellite phase and code biases. This paper proposes a method, that is based on a very general measurement model with an individual phase and code bias for each receiver, satellite and frequency. We compute a recursive least-squares float solution with a Kalman filter, and a subsequent ambiguity fixed solution using Teunissen's Best Integer Equivariant (BIE) estimator. The latter one minimizes the mean squared error (MSE) and, thus, outperforms the well-known Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method. Simulation results show the achievable performance of the BIE estimator in comparison to the LAMBDA method.

Method and apparatus for determining the relative position between two receivers of a satellite navigation system

Abstract: A method for determining the relative posision between two recievers includes the method steps: - the position parameters of the relative position are determined by searching integer candidate phase ambiguities, that - for each integer candidate phase ambiguity associated position parameters of the relative position are determined, which are maximizing an a-posteriori-probability for the position parameters under the condition of the phase measurement, and that - the final integer candidate phase ambiguity and the position parameters associated with the final integer candidate phase ambiguity are selected by evaluating a final cost function, which is arranged for evaluating the deviation of the candidate integer phase ambiguity and position parameters from estimates of the integer phase ambiguities and the position parameters

Testing of a statistical approach for local ionospheric disturbances detection

Abstract: Global Navigation Satellite Systems (GNSSs) may become a viable guidance means for safety-critical applications, such as the final approach and landing phases of a flight. To this purpose, Ground-Based Augmentation Systems (GBAS) are designed to enhance the navigation service, in terms of both accuracy and integrity. One of the tasks performed by GBAS stations is the timely and reliable detection of atmospheric disturbances that may compromise safety through biased or erroneous solutions. We address in this work the problem of detecting bi-dimensional ionospheric disturbances via GNSS carrier phase measurements from small-scale networks. Carrier phase measurements enable higher sensitivity for bias detection, but their inherent ambiguous nature has to be properly addressed. The reliable detection of biases is performed through standard Detection, Identification and Adaptation (DIA) techniques, and the impact of both observation noise and local baseline geometry (lengths and mutual orientations) is analyzed.

Multi-Stage Satellite Phase and Code Bias Estimation

Abstract: Precise point positioning with satellite navigation signals requires the determination of satellite phase and code biases. In this paper, a new multi-stage method is proposed for the estimation of these biases using measurements from a geodetic network. The method first subtracts all available a priori knowledge on the orbits, satellite clocks and multipath from the measurements to reduce their dynamics. Secondly, satellite phase biases, ionospheric delays, carrier phase integer ambiguities and the geometry combining all non-dispersive parameters are jointly estimated in a Kalman filter. Finally, the a posteriori geometry estimates are refined in a second Kalman filter for the computation of orbital errors, code biases and tropospheric delays. As the first Kalman filter has introduced some time correlation, a generalized Kalman filter for colored measurement noise is applied. The proposed algorithm is applied to dual frequency GPS measurements from a local geodetic network in Germany. A remarkable bias stability with variations of less than 3 cm over 4 hours is observed.

Cascaded heading estimation with phase coasting

Abstract: In this paper, a cascaded heading estimation is proposed for low cost single-frequency GPS receivers and patch antennas. The method performs a kinematic calibration of double difference carrier phase measurements, and a subsequent phase coasting without the need of ambiguity resolution. The algorithm was successfully tested on a car, where it enabled a heading accuracy of 0.2 degrees, which corresponds to a relative positioning accuracy of 5 mm.

GNSS based Attitude Determination with Statistical and Deterministic Baseline A Priori Information

Abstract: Attitude determination with carrier phase measurements is becoming increasingly popular for maritime and automobile navigation. However, multipath, frequent loss of lock, cycle slips and severe clock drifts prevent reliable integer ambiguity resolution especially for low-cost GNSS receivers. The reliability of carrier phase ambiguity resolution can be improved by a few methods: One option is the use of some baseline a priori information to reduce the integer search space. This a priori information can be given either in a deterministic or stochastic (Jurkowski [1], Jurkowski et al. [2], Henkel et al. [3]) form. Another option is the use of multi-frequency linear combinations, which increase the wavelength to noise ratio and, thereby, reduce the number of grid points within the search space volume. A third option is the use of state space models, which exploit the inertia of the vehicles and can be efficiently implemented by recursive least-squares estimation/ Kalman Filtering. Finally, one can include additional measurements from inertial sensors and/ or further antennas, and perform an on-board calibration of double difference measurements. In this paper, a method is proposed that uses precise carrier phases for attitude determination without the need of ambiguity resolution: First, a synchronization of double difference measurements is performed by computing a range correction based on the satellite movement within the receiver differential clock offset time. Secondly, if the receiver is moving on a straight path, a linear least- squares fitting of a sequence of absolute code-based position solutions gives an estimate of the path direction and, thus, an on-board calibration of double difference measurements can be even performed with the help of the base-line length, pitch and roll angle a priori information and satellite-receiver direction vectors. The calibrated carrier phases can then be coasted without the need of ambiguity resolution. The observed accuracy is 0.5?/ baseline length, i.e. 0.5? for a baseline length of 1 m an 0.005? for a baseline length of 100 m. The proposed algorithm was tested with real measurements from two low-cost, single frequency u-blox LEA 6T receivers mounted on the roof of a car and compared with the high precision INS/GPS coupled navigation system iTraceRT-F400 of iMAR as a reference sensor. The measurement results show that our kinematic calibration of the double difference phases provides a heading accuracy that is sufficient for most applications. Secondly, a Maximum Likelihood (ML) and Maximum A posteriori Probability (MAP) estimation of ambiguities and baselines is proposed. These estimators find the optimum trade-off between an estimator that minimizes only the range residuals (e.g. unconstrained LAMBDA) and one which minimizes only the distance to the a priori information. The Gaussian a priori knowledge of the baseline length, pitch, roll and yaw angles serves as a soft constraint, i.e. it gives a certain preference direction but allows some uncertainties in the a priori knowledge. Consequently, the development of methods for their reliable resolution has received a lot of attraction during the last years. Approaches include the coupling of GNSS and INS measurements, the use of multi-frequency linear combinations to increase the ambiguity discrimination [4, 5, 6], the introduction of a priori knowledge [7, 2], and the use of multi-antenna systems. Ambiguity resolution uses the code and carrier phase measurements as provided by the delay locked loop and phase locked loop. Note that the integer search is not discussed in this paper as it is described in detail in [8, 9, 10].

Accuracy bounds for positioning of geostationary data relays using LEO satellites

Abstract: The use of Low Earth Orbit (LEO) satellites as navigation satellites for geostationary data relays promises positioning with centimetre accuracy. Thereby, the number of visible LEO satellites, the geometry of the LEO constellation, the antenna gains and the signal design have a huge influence on the achievable precision. In addition, LEO satellite position biases propagate into geostationary (GEO) satellite positioning errors. This paper provides a lower bound for the achievable GEO positioning accuracy based on these effects and gives an insight into the correlation between the GEO satellite position and clock estimates.

Verfahren und Vorrichtung zur Bestimmung der Relativposition zwischen zwei Empfängern und Verwendung der Vorrichtung zur Stabilisierung schwebender Lasten

Abstract: Es wir ein Verfahren und eine Vorrichtung zur Bestimmung der Relativpositionen zwischen zwei Empfangern (10, 11) fur die Satellitennavigation vorgeschlagen. Bei dem Verfahren und der Vorrichtung werden von den Empfangern (10, 11) Phasenmessungen an Tragersignalen (3) eines Satellitennavigationssystems (1) durchgefuhrt. Anhand der Code- und Phasenmessungen werden von einer Auswerteeinheit (14) die Relativposition der Empfanger (10, 11) bestimmt, indem die ganzzahligen Phasenmehrdeutigkeiten und der die Relativposition beschreibende Abstandsvektor (15) bestimmt werden. Zu diesem Zweck wird von der Auswerteeinheit (14) eine Bewertungsfunktion optimiert, die neben einem ersten Mas zur Bewertung der ganzzahligen Phasenmehrdeutigkeiten ein zweites Mas beinhaltet, durch das die Abweichung des die Relativposition beschreibenden und den ganzzahligen Phasenmehrdeutigkeiten zugeordneten Abstandsvektors (15) von einem Abstandsvektor vorbestimmter Lange bestimmt wird.

Precise positioning and orbit estimation for geostationary data relays

Abstract: This paper presents a novel concept and algorithms for the precise positioning of geostationary data relays using Low Earth Orbit (LEO) satellites. Simulations show positioning accuracies at centimetre level. A time synchronization between the LEO satellite and the ground station is decisive for achieving such high accuracies. The estimated positions enable orbit predictions for geostationary data relays with accuracies below one meter for more than six hours in advance.

Method and apparatus for determining the relative position between two receivers and use of the apparatus for stabilizing suspended loads

Abstract: The invention proposes a method and an apparatus for determining the relative positions between two receivers (10, 11) for satellite navigation. In the case of the method and the apparatus, phase measurements are carried out on carrier signals (3) of a satellite navigation system (1) by the receivers (10, 11). An evaluation unit (14) determines the relative position of the receivers (10, 11) using the code and phase measurements by determining the integer phase ambiguities and the distance vector (15) which describes the relative position. For this purpose, the evaluation unit (14) optimizes an assessment function which, in addition to a first measure for assessing the integer phase ambiguities, comprises a second measure which is used to determine the difference between the distance vector (15), which describes the relative position and is assigned to the integer phase ambiguities, and a distance vector of a predetermined length.