GNSS Attitude Determination Research Articles

Baseline configuration for GNSS attitude determination with an analytical least-squares solution

The GNSS attitude determination using carrier phase measurements with 4 antennas is studied on condition that the integer ambiguities have been resolved. The solution to the nonlinear least-squares is often obtained iteratively, however an analytical solution can exist for specific baseline configurations. The main aim of this work is to design this class of configurations. Both single and double difference measurements are treated which refer to the dedicated and non-dedicated receivers respectively. More realistic error models are employed in which the correlations between different measurements are given full consideration. The desired configurations are worked out. The configurations are rotation and scale equivariant and can be applied to both the dedicated and non-dedicated receivers. For these configurations, the analytical and optimal solution for the attitude is also given together with its error variance–covariance matrix.

Rotation Matrix Method Based on Ambiguity Function for GNSS Attitude Determination.

Global navigation satellite systems (GNSS) are well suited for attitude determination. In this study, we use the rotation matrix method to resolve the attitude angle. This method achieves better performance in reducing computational complexity and selecting satellites. The condition of the baseline length is combined with the ambiguity function method (AFM) to search for integer ambiguity, and it is validated in reducing the span of candidates. The noise error is always the key factor to the success rate. It is closely related to the satellite geometry model. In contrast to the AFM, the LAMBDA (Least-squares AMBiguity Decorrelation Adjustment) method gets better results in solving the relationship of the geometric model and the noise error. Although the AFM is more flexible, it is lack of analysis on this aspect. In this study, the influence of the satellite geometry model on the success rate is analyzed in detail. The computation error and the noise error are effectively treated. Not only is the flexibility of the AFM inherited, but the success rate is also increased. An experiment is conducted in a selected campus, and the performance is proved to be effective. Our results are based on simulated and real-time GNSS data and are applied on single-frequency processing, which is known as one of the challenging case of GNSS attitude determination.

A novel method for low-cost MIMU aiding GNSS attitude determination

Global navigation satellite systems (GNSS) are well suited for attitude determination. In most cases, the success rate of the initialization is always a difficult problem, especially the single-frequency measurement model of the double-difference carrier phase. The main reason for this is excessively large noise error that arises in the measurement of the double-difference carrier phase. When the geometric relations of the equations are not good, the difference between the residual error of the optimal solution and that of the suboptimal solution is not very obvious. In this study, we design a smoothing model based on MEMS. The noise error of the measurement of the double-difference carrier phase is suppressed and smoothed via this model. It is designed to reduce the initialization time and improve the success rate of the solution. In addition, we propose a new method based on the rotation matrix to resolve the attitude angle. This method produces a better performance in reducing computation time and selecting satellites. The condition of the baseline length is combined with the ambiguity function method (AFM) to search for integer ambiguity, and this method is validated in reducing the span of candidates. The experiment is conducted in a selected campus, and the performance is proved to be effective. Our results are based on simulated and real-time GNSS data and are applied on single-frequency processing, which is known as one of the challenging cases of GNSS attitude determination.

GNSS space-time interference mitigation and attitude determination in the presence of interference signals.

The use of Space-Time Processing (STP) in Global Navigation Satellite System (GNSS) applications is gaining significant attention due to its effectiveness for both narrowband and wideband interference suppression. However, the resulting distortion and bias on the cross correlation functions due to space-time filtering is a major limitation of this technique. Employing the steering vector of the GNSS signals in the filter structure can significantly reduce the distortion on cross correlation functions and lead to more accurate pseudorange measurements. This paper proposes a two-stage interference mitigation approach in which the first stage estimates an interference-free subspace before the acquisition and tracking phases and projects all received signals into this subspace. The next stage estimates array attitude parameters based on detecting and employing GNSS signals that are less distorted due to the projection process. Attitude parameters enable the receiver to estimate the steering vector of each satellite signal and use it in the novel distortionless STP filter to significantly reduce distortion and maximize Signal-to-Noise Ratio (SNR). GPS signals were collected using a six-element antenna array under open sky conditions to first calibrate the antenna array. Simulated interfering signals were then added to the digitized samples in software to verify the applicability of the proposed receiver structure and assess its performance for several interference scenarios.

An iterative method for attitude determination based on misaligned GNSS baselines

Multiple Global Navigation Satellite System (GNSS) antennae systems have been among the well-known approaches to attitude determination of moving platforms in recent years. However, the constraints on the onboard GNSS antennae configuration, that is, installing the antennae baselines along the main axes of the platform, can lead to practical difficulties and inevitable uncertainty. In this contribution we present an iterative method to obtain the accurate attitudes by means of the onboard misaligned baselines. In order to remove the effects of the horizontal and vertical misalignments from GNSS observations of the baselines, attitude-induced corrections have been developed through the relative lever-arm coordinates of the onboard antennae. This approach provides us with more freedom from spatial distribution of the onboard antennae. The performance of the proposed method has been analyzed by simulated data and an actual experiment in low- and high-dynamic situations. The simulation has been designed to evaluate the capability and reliability of the iterative method under the presence of small and large misalignments. The field experiment was carried out in the offshore waters of Kish harbor using three dual-frequency GNSS receivers with choke-ring antennae onboard a survey vessel, which was also equipped with an inertial measurement unit (IMU). The maximum allowable misalignments, the convergence of the iteration, and the advantage of the proposed method over the trigonometric approach in spite of applying the traditional calibration are presented. The long-term stability of GNSS attitude determination as well as IMU accuracy degradation, due largely to the increase in the time-varying biases/noises, have demonstrated the potential of the method to estimate the accuracies and biases of the onboard inertial sensor. The overall results affirm that the presented method can effectively provide the platform attitudes using the misaligned GNSS baselines with as much flexibility as possible for the onboard antennae configuration.

저가형 수신기를 이용한 실시간 GNSS 자세결정 시스템 설계 및 성능 평가

In this paper, the real-time attitude determination based Matlab using low-cost receivers was designed and evaluated. The GNSS attitude determination system was implemented to operation in real-time by TimerCallback in MATLAB. The TTM(Transmission Time Misalignment) of U-blox receiver was confirmed through zero baseline tests and this problem was revised. The computed attitude by the high-cost NovAtel receiver was compared to the computed attitude by the low-cost U-blox receiver. As a result of this, the performance of attitude determination systems by low-cost receiver was confirmed. To determine baseline, LAMBDA and BC-LAMBDA for integer ambiguities search methods were used. To confirm suitable integer ambiguity search method in real-time attitude determination algorithm, determined baselines by two methods were compared, and it was confirmed that BC-LAMBDA is more suitable. As a result of this, the operation of real-time attitude determination system was confirmed using 3 low-cost receivers.

Integrated GNSS Attitude Determination and Positioning for Direct Geo-Referencing

Direct geo-referencing is an efficient methodology for the fast acquisition of 3D spatial data. It requires the fusion of spatial data acquisition sensors with navigation sensors, such as Global Navigation Satellite System (GNSS) receivers. In this contribution, we consider an integrated GNSS navigation system to provide estimates of the position and attitude (orientation) of a 3D laser scanner. The proposed multi-sensor system (MSS) consists of multiple GNSS antennas rigidly mounted on the frame of a rotating laser scanner and a reference GNSS station with known coordinates. Precise GNSS navigation requires the resolution of the carrier phase ambiguities. The proposed method uses the multivariate constrained integer least-squares (MC-LAMBDA) method for the estimation of rotating frame ambiguities and attitude angles. MC-LAMBDA makes use of the known antenna geometry to strengthen the underlying attitude model and, hence, to enhance the reliability of rotating frame ambiguity resolution and attitude determination. The reliable estimation of rotating frame ambiguities is consequently utilized to enhance the relative positioning of the rotating frame with respect to the reference station. This integrated (array-aided) method improves ambiguity resolution, as well as positioning accuracy between the rotating frame and the reference station. Numerical analyses of GNSS data from a real-data campaign confirm the improved performance of the proposed method over the existing method. In particular, the integrated method yields reliable ambiguity resolution and reduces position standard deviation by a factor of about 0.8, matching the theoretical gain of for two antennas on the rotating frame and a single antenna at the reference station.

GNSS instantaneous ambiguity resolution and attitude determination exploiting the receiver antenna configuration

A novel instantaneous method for Global Navigation Satellite System (GNSS) attitude determination using a new phase-difference ambiguity resolution approach is presented. A triple-antenna receiver configuration with baseline constraints is exploited for ambiguity resolution. It is shown that the ambiguity resolution and attitude determination problems can be solved using simple closed and semiclosed form solutions, without using GNSS codes. Simulation results demonstrate high success rates (>90%) in most cases, even when the number of visible satellite vehicles is small.

The inertial attitude augmentation for ambiguity resolution in SF/SE-GNSS attitude determination.

The Unaided Single Frequency/Single Epoch Global Navigation Satellite System (SF/SE GNSS) model is the most challenging scenario for ambiguity resolution in the GNSS attitude determination application. To improve the performance of SF/SE-GNSS ambiguity resolution without excessive cost, the Micro-Electro-Mechanical System Inertial Measurement Unit (MEMS-IMU) is a proper choice for the auxiliary sensor that carries out the inertial attitude augmentation. Firstly, based on the SF/SE-GNSS compass model, the Inertial Derived Baseline Vector (IDBV) is defined to connect the MEMS-IMU attitude measurement with the SF/SE-GNSS ambiguity search space, and the mechanism of inertial attitude augmentation is revealed from the perspective of geometry. Then, through the quantitative description of model strength by Ambiguity Dilution of Precision (ADOP), two ADOPs are specified for the unaided SF/SE-GNSS compass model and its inertial attitude augmentation counterparts, respectively, and a sufficient condition is proposed for augmenting the SF/SE-GNSS model strength with inertial attitude measurement. Finally, in the framework of an integer aperture estimator with fixed failure rate, the performance of SF/SE-GNSS ambiguity resolution with inertial attitude augmentation is analyzed when the model strength is varying from strong to weak. The simulation results show that, in the SF/SE-GNSS attitude determination application, MEMS-IMU can satisfy the requirements of ambiguity resolution with inertial attitude augmentation.

Instantaneous GPS–Galileo Attitude Determination: Single-Frequency Performance in Satellite-Deprived Environments

New and modernized global navigation satellite systems (GNSSs) are paving the way for an increasing number of applications in positioning, navigation, and timing (PNT). A combined GNSS constellation will significantly increase the number of visible satellites and, thus, will improve the geometry of observed satellites, enabling improvements in navigation solution availability, reliability, and accuracy. In this paper, a global positioning system (GPS) +Galileo robustness analysis is carried out for instantaneous single-frequency GNSS attitude determination. Precise attitude determination using multiple GNSS antennas mounted on a platform relies on successful resolution of the integer carrier-phase ambiguities. The multivariate-constrained least squares ambiguity decorrelation adjustment (MC-LAMBDA) method has been developed to resolve the integer ambiguities of the nonlinearly constrained GNSS attitude model that incorporates the known antenna geometry. In this paper, the method is used to analyze the attitude determination performance of a combined GPS +Galileo system. Special attention is thereby given to the GPS and Galileo intersystem biases (ISBs). The attitude determination performance is evaluated using GPS/Galileo data sets from a hardware-in-the-loop experiment and two real-data campaigns. In the hardware-in-the-loop experiment, a full GPS/Galileo constellation is simulated, and performance analyses are carried out under various satellite-deprived environments, such as urban canyons, open pits, and other satellite outages. In the first real-data experiment, single-frequency GPS data, combined with the data of Galileo in-orbit validation element (GIOVE) satellites GIOVE-A/GIOVE-B (the two experimental Galileo satellites), are used to analyze the two constellation attitude solutions. In the second real-data experiment, we present the results based on single-frequency data from one of the Galileo IOV satellites, combined with the data of GIOVE-A and GPS. We demonstrate and quantify the improved availability, reliability, and accuracy of attitude determination using the combined constellation.

Rate-Gyro-Integral Constraint for Ambiguity Resolution in GNSS Attitude Determination Applications

In the field of Global Navigation Satellite System (GNSS) attitude determination, the constraints usually play a critical role in resolving the unknown ambiguities quickly and correctly. Many constraints such as the baseline length, the geometry of multi-baselines and the horizontal attitude angles have been used extensively to improve the performance of ambiguity resolution. In the GNSS/Inertial Navigation System (INS) integrated attitude determination systems using low grade Inertial Measurement Unit (IMU), the initial heading parameters of the vehicle are usually worked out by the GNSS subsystem instead of by the IMU sensors independently. However, when a rotation occurs, the angle at which vehicle has turned within a short time span can be measured accurately by the IMU. This measurement will be treated as a constraint, namely the rate-gyro-integral constraint, which can aid the GNSS ambiguity resolution. We will use this constraint to filter the candidates in the ambiguity search stage. The ambiguity search space shrinks significantly with this constraint imposed during the rotation, thus it is helpful to speeding up the initialization of attitude parameters under dynamic circumstances. This paper will only study the applications of this new constraint to land vehicles. The impacts of measurement errors on the effect of this new constraint will be assessed for different grades of IMU and current average precision level of GNSS receivers. Simulations and experiments in urban areas have demonstrated the validity and efficacy of the new constraint in aiding GNSS attitude determinations.

LOW-COST NAVIGATION AND GUIDANCE SYSTEMS FOR UNMANNED AERIAL VEHICLES — PART 2: ATTITUDE DETERMINATION AND CONTROL

ABSTRACT This paper presents the second part of the research activity performed by Cranfield University to assess the potential of low-cost navigation sensors for Unmanned Aerial Vehicles (UAVs). This part focuses on carrier-phase Global Navigation Satellite Systems (GNSS) for attitude determination and control of small to medium size UAVs. Recursive optimal estimation algorithms were developed for combining multiple attitude measurements obtained from different observation points (i.e., antenna locations), and their efficiencies were tested in various dynamic conditions. The proposed algorithms converged rapidly and produced the required output even during high dynamics manoeuvres. Results of theoretical performance analysis and simulation activities are presented in this paper, with emphasis on the advantages of the GNSS interferometric approach in UAV applications (i.e., low cost, high data-rate, low volume/weight, low signal processing requirements, etc.). The simulation activities focussed on the AEROSONDE UAV platform and considered the possible augmentation provided by interferometric GNSS techniques to a low-cost and low-weight/volume integrated navigation system (presented in the first part of this series) which employed a Vision-Based Navigation (VBN) system, a Micro-Electro-Mechanical Sensor (MEMS) based Inertial Measurement Unit (IMU) and code-range GNSS (i.e., GPS and GALILEO) for position and velocity computations. The integrated VBN-IMU-GNSS (VIG) system was augmented using the inteferometric GNSS Attitude Determination (GAD) sensor data and a comparison of the performance achieved with the VIG and VIG/GAD integrated Navigation and Guidance Systems (NGS) is presented in this paper. Finally, the data provided by these NGS are used to optimise the design of a hybrid controller employing Fuzzy Logic and Proportional-Integral-Derivative (PID) techniques for the AEROSONDE UAV.

Carrier-phase GNSS Attitude Determination and Control for Small Unmanned Aerial Vehicle Applications

As part of our recent research to assess the potential of low-cost navigation sensors for Unmanned Aerial Vehicle (UAV) applications, we investigated the potential of carrier-phase Global Navigation Satellite System (GNSS) for attitude determination and control of small size UAVs. Recursive optimal estimation algorithms were developed for combining multiple attitude measurements obtained from different observation points (i.e., antenna locations), and their efficiencies were tested in various dynamic conditions. The proposed algorithms converged rapidly and produced the required output even during high dynamics manoeuvres. Results of theoretical performance analysis and simulation activities are presented in this paper, with emphasis on the advantages of the GNSS interferometric approach in UAV applications (i.e., low cost, high data-rate, low volume/weight, low signal processing requirements, etc.). The simulation activities focussed on the AEROSONDE UAV platform and considered the possible augmentation provided by interferometric GNSS techniques to a low-cost and low-weight/volume integrated navigation system (presented in the first part of this series) which employed a Vision-Based Navigation (VBN) system, a Micro- Electro-Mechanical Sensor (MEMS) based Inertial Measurement Unit (IMU) and code-range GNSS (i.e., GPS and GALILEO) for position and velocity computations. The integrated VBN-IMU-GNSS (VIG) system was augmented using the inteferometric GNSS Attitude Determination (GAD)sensor data and a comparison of the performance achieved with the VIG and VIG/GAD integrated Navigation and Guidance Systems (NGS) is presented in this paper. Finally, the data provided by these NGS are used to optimise the design of a hybrid controller employing Fuzzy Logic and Proportional-Integral-Derivative (PID) techniques for the AEROSONDE UAV.

Development of an instantaneous GNSS/MEMS attitude determination system

Global navigation satellite systems (GNSS) are well suited for attitude determination. The key to high-precision GNSS-attitude determination is the ambiguity resolution. In case of kinematic applications, the rapidity of this process is of particular importance. We present a new instantaneous attitude determination system for GNSS-challenged environments. The single-epoch ambiguity resolution is performed by the ambiguity function method aided by a micro-electro-mechanical system (MEMS), leading to success rates above 99 %. The GNSS/MEMS fusion is realized by the use of an extended Kalman filter. When the system is stationary, a state vector augmentation with a shaping filter reduces systematic effects in the GNSS-attitudes. By means of two field experiments, the system was tested successfully. Despite poor GNSS measurement conditions, it provided reliable and accurate results, with empirical standard deviations in the range of 0.03---0.1 deg for the yaw angle.

Integer least-squares theory for the GNSS compass

Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is the key to highprecision positioning and attitude determination. In this contribution, we develop new integer least-squares (ILS) theory for the GNSS compass model, together with efficient integer search strategies. It extends current unconstrained ILS theory to the nonlinearly constrained case, an extension that is particularly suited for precise attitude determination. As opposed to current practice, our method does proper justice to the a priori given information. The nonlinear baseline constraint is fully integrated into the ambiguity objective function, thereby receiving a proper weighting in its minimization and providing guidance for the integer search. Different search strategies are developed to compute exact and approximate solutions of the nonlinear constrained ILS problem. Their applicability depends on the strength of the GNSS model and on the length of the baseline. Two of the presented search strategies, a global and a local one, are based on the use of an ellipsoidal search space. This has the advantage that standard methods can be applied. The global ellipsoidal search strategy is applicable to GNSS models of sufficient strength, while the local ellipsoidal search strategy is applicable tomodels for which the baseline lengths are not too small. We also develop search strategies for the most challenging case, namely when the curvature of the non-ellipsoidal ambiguity search space needs to be taken into account. Two such strategies are presented, an approximate one and a rigorous, somewhat more complex, one. The approximate one is applicable when the fixed baseline variance matrix is close to diagonal. Both methods make use of a search and shrink strategy. The rigorous solution is efficiently obtained by means of a search and shrink strategy that uses nonquadratic, but easy-to-evaluate, bounding functions of the ambiguity objective function. The theory presented is generally valid and it is not restricted to any particular GNSS or combination of GNSSs. Its general applicability also applies to the measurement scenarios (e.g. single-epoch vs. multiepoch, or single-frequency vs. multi-frequency). In particular it is applicable to the most challenging case of unaided, single frequency, single epoch GNSS attitude determination. The success rate performance of the different methods is also illustrated.

Testing of a new single-frequency GNSS carrier phase attitude determination method: land, ship and aircraft experiments

Global navigation satellite system (GNSS) ambiguity resolution is the process of resolving the unknown cycle ambiguities of the carrier phase data as integers. The sole purpose of ambiguity resolution is to use the integer ambiguity constraints as a means of improving significantly on the precision of the remaining GNSS model parameters. In this contribution, we consider the problem of ambiguity resolution for GNSS attitude determination. We analyse the performance of a new ambiguity resolution method for GNSS attitude determination. As it will be shown, this method provides a numerically efficient, highly reliable and robust solution of the nonlinearly constrained integer least-squares GNSS compass estimators. The analyses have been done by means of a unique set of extensive experimental tests, using simulated as well as actual GNSS data and using receivers of different manufacturers and type as well as different platforms. The executed field tests cover two static land experiments, one in the Netherlands and one in Australia, and two dynamic experiments, a low-dynamics vessel experiment and high-dynamics aircraft experiment. In our analyses, we focus on stand-alone, unaided, single-frequency, single-epoch attitude determination, as this is the most challenging case of GNSS compass processing.

Integer least squares with quadratic equality constraints and its application to GNSS attitude determination systems

In this paper we introduce the quadratically constrained integer least-squares problem and show how the LAMBDA method can be used to solve it for the purpose of GNSS attitude determination. The integer least-squares principle with quadratic equality constraints (ILSQE) is used to formulate our cost function. The solution of the ILSQE problem is derived and it is shown how the solution can be computed efficiently and rigorously with a novel LAMBDA based method. Experimental results with various single frequency GPS receivers are given to show the effectiveness of the proposed method. The method is also compared with some current methods of GNSS attitude determination. Apart from its efficiency, the proposed method is shown to dramatically improve the success rates of integer ambiguity GNSS attitude resolution.

GNSS 자세결정시스템의 미지정수 결정을 위한 기저선 제약을 갖는 LAMBDA 기법

In this paper, an efficient integer ambiguity resolution method for GNSS attitude determination system is described. The proposed method solves the integer least-squares with quadratic equality constraints(ILSQE) problem and shows an expansion of the LAMBDA method can be used to solve it. The solution of ILSQE is shown and an efficient implementation with a LAMBDA based method is given. The method is compared with some other methods. The results of static and dynamic tests show the dramatic improvement of the success rates of integer ambiguity resolution.

A General Multivariate Formulation of the Multi-Antenna GNSS Attitude Determination Problem

Global Navigation Satellite System (GNSS) carrier phase ambiguity resolution is the key to high precision positioning, navigation and attitude determination. In this contribution we present a general formulation for the multi-antenna GNSS attitude determination problem. This multivariate formulation provides a general framework for solving various GNSS attitude determination problems. With the use of this formulation we show how the constrained integer least-squares carrier phase ambiguities and corresponding attitude matrix can be solved.

GNSS 자세결정시스템의 오차해석

In this paper an error analysis of 3-dimensional GNSS attitude determination system is given. The attitude error covariance matrix is derived and analyzed. It implies that attitude errors are affected by the baseline length and configuration, the satellites numbers and geometry, receiver measurement noises and the nominal attitude of the vehicle. By defining Euler Angle Dilution Of Precision (EADOP) which is analogous to GDOP, roll, pitch and yaw errors can be efficiently analyzed. However the expression of the attitude error is too complex to get some intuitions. Therefore with a commonly adopted assumption, new expressions for attitude error are derived. The formulas are easy to compute and represent the attitude error as a function of the nominal attitude of a vehicle, the baseline configuration and the receiver noise. Using the formula, the accuracy of the attitude can be analytically predicted without the computer simulations. Applications to some widely used configurations reveal the effectiveness of the proposed method.