In this paper, a novel Strong Tracking Sigma-Point Predictive Variable Structure Filter (ST-SP-PVSF) is presented as a further development of the Adaptive Predictive Variable Structure Filter (APVSF) for attitude synchronisation during Satellite Formation Flying (SFF). First, the sequence orthogonal principle is adopted to enhance the robustness of the APVSF for any nonlinear system with uncertain model errors. Then, sigma-point sampling strategies (such as unscented transfer, cubature rule and Stirling's polynomial interpolation) are introduced to extend the APVSF with the ability to capture the second central moment's information on the model errors to update the system model with higher precision. The new methodology has advantages in dealing with the various types of uncertainties or model errors compared with the APVSF. In addition, it does not need to choose the limit boundary layer ψlim it for system estimation, which reduces the sensitivity to the initial parameters and improves its adaptive ability over the APVSF. Simulations are performed to demonstrate that the proposed method is more suitable for attitude synchronisation estimation of the SFF system.

Global Navigation Satellite System (GNSS) attitude determination and positioning play an important role in many navigation applications. However, the two GNSS-based problems are usually treated separately. This ignores the constraint information of the GNSS antenna array and the accuracy is limited. To improve the performance of navigation, an integrated attitude and position determination method based on an affine constraint model is presented. In the first part, the GNSS array model and affine constrained attitude determination method are compared with the unconstrained methods. Then the integrated attitude and position determination method is presented. The performance of the proposed method is tested with a series of static data and dynamic experimental GNSS data. The results show that the proposed method can improve the success rate of ambiguity resolution to further improve the accuracy of attitude determination and relative positioning compared to the unconstrained methods.

In this paper, a novel Predictive Variable Structure Filter (PVSF) and its adaptive deformation (APVSF) are presented for attitude synchronisation during Satellite Formation Flying (SFF). The PVSF is proposed based on the variable structure control concept and applied to any nonlinear system with model errors. The model errors in the PVSF need not satisfy the assumption of Gaussian white noise; therefore, it has advantages in dealing with various kinds of uncertainties, parameter variations or noises. Then, the APVSF is also presented to adjust the smoothing boundary layer of PVSF by minimising the Mean-Square Error (MSE). Simulations are performed to demonstrate the accuracy, robustness, and stability of the proposed methodologies for the attitude synchronisation estimation of the SFF system.

To solve the problem of attitude determination using magnetometers independently and uniquely, which is important for underwater vehicles, a type of full attitude determination method based on geomagnetic gradient tensor is proposed in this paper. In this method, a group of non-linear equations concerning geomagnetic gradient tensors is established, where a quaternion is selected to calculate three attitude angles of an underwater vehicle. The optimal quaternion is estimated using Newton Down-hill to optimise the object function. The detailed steps of the full attitude determination based on geomagnetic gradient tensor are given, and the effects of the initial angle error and the sensor noise on the attitude determination are investigated. Simulations show that the algorithm can identify precisely and quickly the attitudes even in the presence of larger initial angle error and sensor noise, which proves the attitude determination algorithm.

A prerequisite for a Global Positioning System (GPS) attitude determination is to calculate baselines between antennae with accuracy at the millimetre level simultaneously. However, in order to have a low cost attitude determination system, a set of Commercial-Off-The-Shelf (COTS) receivers with separate clocks are used. In this case, if the receiver clocks are not precisely synchronized, the baseline vector between antennae will be calculated from the GPS signals received at different times. This can be a significant error source for high-kinematic applications. In this paper, two equivalent and effective approaches are developed to compensate this significant bias for baseline estimation and attitude determination. Test results using real airborne GPS data demonstrate that the receiver time misalignment between the two receivers can result in a 5 cm baseline offset for an aircraft with a 50 m/s velocity; the corresponding attitude errors can reach about 0·50° in yaw and 0·10° in pitch respectively for the attitude determination system with a baseline length of 3·79 m. With the proposed methods, these errors can be effectively eliminated.

This paper presents the results of a new multipath mitigating antenna “V-Ray” for use with terrestrial ranging signals in severe multipath indoor environments. The V-Ray antenna – as used in the Locata positioning system – forms tight beams that provide line-of-sight range measurements as well as azimuth measurements. To take advantage of these two types of measurements a new navigation algorithm – Position and Attitude Modelling System (PAMS) – is proposed for processing carrier phase and azimuth measurements via an unscented Kalman filter. The PAMS can output the complete navigation parameters of position, velocity, acceleration and attitude simultaneously. The indoor test was conducted in a metal warehouse and the results confirmed that the horizontal positioning solutions had an accuracy of better than four centimetres and an orientation accuracy of better than 1°.

This paper describes the verification of a real-time attitude determination algorithm during GPS attitude receiver hardware development. The GPS attitude receiver of 24 channels had been already developed in Surrey University. However 24 channels were not enough for practical usage. For this reason, a 48-channel attitude receiver with 12 channels for each antenna has been developed. To estimate attitude in real time, precise relative positions of the GPS antenna array have to be determined as rapidly as possible. However, the calculation load based on the conventional algorithm is too burdensome to perform using the RISC microprocessor. Therefore, in this paper, the cycle ambiguities of each base vector are resolved using SNUGLAD (Seoul Nat Univ GNSS Lab Attitude Determination), the design focus of which is to allow the receiver to estimate the 10 Hz onboard solutions. To keep precise solutions continuously, after ambiguity removal, cycle slip must be detected or isolated. Otherwise, the receiver would output erroneous solutions after a short signal blockage or fading of the GPS signal. To prevent this, we defined the cycle slip detection and repair scheme using a standard extended Kalman filter, which can detect and repair cycle slip within one cycle. As a result, this paper shows that time synchronized measurement with good quality and a reliable solution can be provided by the hardware developed with inexpensive chipsets and that this may be a possible cost efficient sensor for UAV or microsatellites.

Small Unmanned Aerial Vehicles (UAVs) or inexpensive airplanes, such as a Cessna single engine aircraft, require a navigation system with a cheap, compact and precise sensor. Over the past ten years, GPS receivers have begun to be used as primary or alternative navigation sensors, because their use can significantly reduce the overall system cost. This paper describes a navigation system incorporating a velocity-based attitude estimation system with an attitude determination system using multiple antennae, which was implemented and tested using a UAV. The main objective was to obtain precise attitude information using low cost GPS OEM boards and antennae. Attitude boundaries are derived from the relationship between the body frame and the wind coordinates, which are used to validate the resolved cycle ambiguity in an Euler angle domain. Angular rate based on Doppler measurements was used to exclude the degenerate pseudo-roll angle information during severe uncoordinated flight. Searching for cycle ambiguity at every epoch of the flight showed that the developed system gave reliable cycle integer solutions, although the carrier phase measurement was subject to additional errors, such as multipath, external interference, and phase centre variation. A flight test was performed using a 1/4-scale Piper J3 Cub model, CMC Allstar OEM boards, OEM AT575-70 antennae, and 700 MHz PC104 board.

An adaptive Kalman filtering approach is proposed for attitude determination to replace the fixed (conventional) Kalman filtering approach. The filter is used to adaptively reflect system dynamics changes or rapid changes in vehicle trajectory. The estimation procedure is carried out through the use of a measurement residual sequence. The sequence is used as a piece-wise stationary process inside an estimation window. The measurement noise covariance matrix and the system noise matrix are adaptively estimated. An extended Kalman filter approach with iteration of the states within-an-epoch was performed to overcome the non-linearity of the observation equations. A test was performed to evaluate the proposed technique. Different trajectory scenarios are presented to show the difference in performance between the adaptive Kalman filter and the conventional one. Results show that the proposed adoptive filtering approach has a better performance than the conventional filter.

The Global Positioning System (GPS) can be employed as a free attitude determination interferometer when carrier phase measurements are utilized. Conventional approaches for the baseline vectors are essentially based on the least-squares or Kalman filtering methods. The raw attitude solutions are inherently noisy if the solutions of baseline vectors are obtained based on the least-squares method. The Kalman filter attempts to minimize the error variance of the estimation errors and will provide the optimal result while it is required that the complete a priori knowledge of both the process noise and measurement noise covariance matrices are available. In this article, a neural network state estimator, which replaces the Kalman filter, will be incorporated into the attitude determination mechanism for estimating the attitude angles from the noisy raw attitude solutions. Employing the neural network estimator improves robustness compared to the Kalman filtering method when uncertainty in noise statistical knowledge exists. Simulation is conducted and a comparative evaluation based on the neural network estimator and Kalman filter is provided.

The use of low-cost GPS receivers and antennas for attitude determination can significantly reduce the overall hardware system cost. Compared to the use of high performance GPS receivers, the carrier phase measurements from low-cost equipment are subject to additional carrier phase measurement errors, such as multipath, antenna phase centre variation and noise. These error sources, together with more frequent cycle slip occurrences, severely deteriorate attitude determination availability, reliability and accuracy performance. This paper presents the investigation of a low-cost GPS/gyro integration system for attitude determination. By employing the dead reckoning sensor type, the ambiguity search region can be specifically defined as a small cube to enhance the ambiguity resolution process. A Kalman filter is implemented to fuse the rate gyro data with GPS carrier phase measurements. The quality control system based on innovation sequences is used to identify cycle slip occurrences and incorrect inter-antenna vector solutions. The availability of the integrated system also improves with respect to the GPS standalone system since the attitude parameters can be estimated using the angular rate measurements from rate gyros during GPS outages. The low-cost hardware used to design and test the integrated system consists of CMC Allstar receivers with the OEM AT575-70 antennas and Murata ENV-05D-52 piezoelectric vibrating rate gyroscopes. Tests in the urban area demonstrated that the introduction of rate gyros in a GPS-based attitude determination system not only effectively decreased the noise level in the estimated attitude parameters but coasted the attitude output during GPS outages and also significantly improved the system reliability.