Adaptive filtering algorithms for quaternion-valued signals

Advances in sensor technology have made possible the recoding of three and four-dimensional signals which afford a better representation of our actual three-dimensional world than the ``flat view'' one and two-dimensional approaches. Although it is straightforward to model such signals as real-valued vectors, many applications require unambiguous modeling of orientation and rotation, where the division algebra of quaternions provides crucial advantages over real-valued vector approaches. The focus of this thesis is on the use of recent advances in quaternion-valued signal processing, such as the quaternion augmented statistics, widely-linear modeling, and the HR-calculus, in order to develop practical adaptive signal processing algorithms in the quaternion domain which deal with the notion of phase and frequency in a compact and physically meaningful way. To this end, first a real-time tracker of quaternion impropriety is developed, which allows for choosing between strictly linear and widely-linear quaternion-valued signal processing algorithms in real-time, in order to reduce computational complexity where appropriate. This is followed by the strictly linear and widely-linear quaternion least mean phase algorithms that are developed for phase-only estimation in the quaternion domain, which is accompanied by both quantitative performance assessment and physical interpretation of operations. Next, the practical application of state space modeling of three-phase power signals in smart grid management and control systems is considered, and a robust complex-valued state space model for frequency estimation in three-phase systems is presented. Its advantages over other available estimators are demonstrated both in an analytical sense and through simulations. The concept is then expanded to the quaternion setting in order to make possible the simultaneous estimation of the system frequency and its voltage phasors. Furthermore, a distributed quaternion Kalman filtering algorithm is developed for frequency estimation over power distribution networks and collaborative target tracking. Finally, statistics of stable quaternion-valued random variables, that include quaternion-valued Gaussian random variables as a special case, is investigated in order to develop a framework for the modeling and processing of heavy-tailed quaternion-valued signals.Open Acces

Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing

Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices. Although such matrices have a tremendous amount of structure and their decomposition is a powerful tool in a variety of applications, the non-commutative nature of the quaternion product has been prohibitive to the development of quaternion uncorrelating transforms. To this end, we introduce novel techniques for a simultaneous decomposition of the covariance and complementary covariance matrices in the quaternion domain, whereby the quaternion version of the Takagi factorisation is explored to diagonalise symmetric quaternion-valued matrices. This gives new insights into the quaternion uncorrelating transform (QUT) and forms a basis for the proposed quaternion approximate uncorrelating transform (QAUT) which simultaneously diagonalises all four covariance matrices associated with improper quaternion signals. The effectiveness of the proposed uncorrelating transforms is validated by simulations on both synthetic and real-world quaternion-valued signals.Comment: 41 pages, single column, 10 figure

Beamforming and Direction of Arrival Estimation Based on Vector Sensor Arrays

Array signal processing is a technique linked closely to radar and sonar systems. In communication, the antenna array in these systems is applied to cancel the interference, suppress the background noise and track the target sources based on signals'parameters. Most of existing work ignores the polarisation status of the impinging signals and is mainly focused on their direction parameters. To have a better performance in array processing, polarized signals can be considered in array signal processing and their property can be exploited by employing various electromagnetic vector sensor arrays. In this thesis, firstly, a full quaternion-valued model for polarized array processing is proposed based on the Capon beamformer. This new beamformer uses crossed-dipole array and considers the desired signal as quaternion-valued. Two scenarios are dealt with, where the beamformer works at a normal environment without data model errors or with model errors under the worst-case constraint. After that, an algorithm to solve the joint DOA and polarisation estimation problem is proposed. The algorithm applies the rank reduction method to use two 2-D searches instead of a 4-D search to estimate the joint parameters. Moreover, an analysis is given to introduce the difference using crossed-dipole sensor array and tripole sensor array, which indicates that linear crossed-dipole sensor array has an ambiguity problem in the estimation work and the linear tripole sensor array avoid this problem effectively. At last, we study the problem of DOA estimation for a mixture of single signal transmission (SST) signals and duel signal transmission (DST) signals. Two solutions are proposed: the first is a two-step method to estimate the parameters of SST and DST signals separately; the second one is a unified one-step method to estimate SST and DST signals together, without treating them separately in the estimation process

Results of the attitude reconstruction for the UniSat-6 microsatellite using in-orbit data

UniSat-6 is a civilian microsatellite that was launched in orbit on the 19th of June, 2014. Its main mission consisted in the in-orbit release of a number of on-board carried Cubesats and in the transmission to the UniSat-6 ground station of telemetry data and images from an on-board mounted camera. The spacecraft is equipped with a passive magnetic attitude control system. Gyros and magnetometers provide the information about the attitude of the spacecraft. The importance of reconstructing the attitude motion of UniSat-6 lies in the dual possibility, for future missions, of:controlling the direction of ejection of the on-board carried satelliteshaving an accurate pointing for remote sensing operation.The reconstruction of the attitude motion of UniSat-6 is based on the data of the on-board Commercial Off The Shelf (COTS) gyros and magnetometers, downloaded at the passages over the ground station in Roma, Italy. At ground, these data have been processed with the UnScented QUaternion Estimator (USQUE) algorithm. This estimator is an adaptation of the Unscented Filter to the problem of spacecraft attitude estimation. The USQUE is based on a dual attitude representation, which involves both quaternions and Generalized Rodrigues Parameters. In this work, the propagation phase of the algorithm contains only a kinematic model of the motion of the spacecraft. This paper presents the results of the reconstruction of the UniSat-6 attitude using on-board measurements. The results show that the spacecraft effectively stabilized its attitude motion thanks to the on-board magnetic devices

Multirotor Design Optimization: The Mechatronic Approach

Doktorgradsavhandling ved Fakultet for teknologi og realfag, Universitetet i Agder, 2015Multirotors such as the more famous quadcopter have been a favoured research object the last years. It is widely used as a flying platform for the hobby enthusiasts, but recently also used more and more by the industry. The multirotor has complex dynamics and requires sensors and a control system in order to fly. To get the desired flight characteristics batteries, motor and the propeller have to be chosen wisely as different combinations create different properties. The usual design approach is to test different combinations of motors and propellers, and based on experience select components that will be closest to the desired flight properties. This thesis presents an optimization method that calculates what hardware to use in order to get closest to the demanded properties. The method will only select from a given database, hence not returning a diameter and pitch of a propeller that are not available. A wide range of criteria can be optimized, examples are dynamics of the motor/propeller, flight dynamics, flight time, payload etc. The optimization routine will also calculate if the better choice is a quadcopter with four propellers, a hexacopter with six or an octocopter with eight propellers. The optimization is not trivial due to the non-linear characteristics of the propeller. A lot of experimental work was done to test the response of the propeller, both for acceleration and deceleration. Theory and experimental work show that the thrust response of the propeller can be more or less equal if the electronic speed controller controls the motor in a special mode. This mode also makes the response of the motor faster than normal. The new design is tested with a new approach for attitude estimation, and a controller operating directly with the result of the estimator. Most of the multirotors use a microcontroller with limited resources as the control system, hence the attitude and controller were designed specifically without time consuming trigonometric functions such as the sine and cosine. Overall, the methods and results presented in this thesis will aid the engineer when designing a multirotor system consisting of control system, mechanical frame, battery, actuators and propellers