Optimized Filter Design for Non-Differential GPS/IMU Integrated Navigation

The endeavours in improving the performance of a conventional non-differential GPS/MEMS IMU tightly-coupled navigation system through filter design, involving nonlinear filtering methods, inertial sensors' stochastic error modelling and the carrier phase implementation, are described and introduced in this thesis. The main work is summarised as follows. Firstly, the performance evaluation of a recently developed nonlinear filtering method, the Cubature Kalman filter (CKF), is analysed based on the Taylor expansion. The theoretical analysis indicates that the nonlinear filtering method CKF shows its benefits only when implemented in a nonlinear system. Accordingly, a nonlinear attitude expression with direction cosine matrix (DCM) is introduced to tightly-coupled navigation system in order to describe the misalignment between the true and the estimated navigation frames. The simulation and experiment results show that the CKF performs better than the extended Kalman filter (EKF) in the unobservable, large misalignment and GPS outage cases when attitude errors accumulate quickly, rendering the psi-angle expression invalid and subsequently showing certain nonlinearity. Secondly, the use of shaping filter theory to model the inertial sensors' stochastic errors in a navigation Kalman filter is also introduced. The coefficients of the inertial sensors' noises are determined from the Allan variance plot. The shaping filter transfer function is deduced from the power spectral density (PSD) of the noises for both stationary and non-stationary processes. All the coloured noises are modelled together in the navigation Kalman filter according to equivalence theory. The coasting performance shows that the shaping filter based modelling method has a similar and even smaller maximum position drift than the conventional 1st-order Markovian process modelling method during GPS outages, thus indicating its effectiveness. Thirdly, according to the methods of dealing with carrier phase ambiguities, tightly-coupled navigation systems with time differenced carrier phase (TDCP) and total carrier phase (TCP) as Kalman filter measurements are deduced. The simulation and experiment results show that the TDCP can improve the velocity estimation accuracy and smooth trajectories, but position accuracy can only achieve the single point positioning (SPP) level if the TDCP is augmented with the pseudo-range, while the TCP based method's position accuracy can reach the sub-meter level. In order to further improve the position accuracy of the TDCP based method, a particle filter (PF) with modified TDCP observation is implemented in the TDCP/IMU tightly-coupled navigation system. The modified TDCP is defined as the carrier phase difference between the reference and observation epochs. The absolute position accuracy is determined by the reference position accuracy. If the reference position is taken from DGPS, the absolute position accuracy can reach the sub-meter level. For TCP/IMU tightly-coupled navigation systems, because the implementation of TCP in the navigation Kalman filter introduces additional states to the state vector, a hybrid CKF+EKF filtering method with the CKF estimating nonlinear states and the EKF estimating linear states, is proposed to maintain the CKF's benefits while reducing the computational load. The navigation results indicate the effectiveness of the method. After applying the improvements, the performance of a non-differential GPS/MEMS IMU tightly-coupled navigation system can be greatly improved

Contributions to Positioning Methods on Low-Cost Devices

Global Navigation Satellite System (GNSS) receivers are common in modern consumer devices that make use of position information, e.g., smartphones and personal navigation assistants. With a GNSS receiver, a position solution with an accuracy in the order of five meters is usually available if the reception conditions are benign, but the performance degrades rapidly in less favorable environments and, on the other hand, a better accuracy would be beneficial in some applications. This thesis studies advanced methods for processing the measurements of low-cost devices that can be used for improving the positioning performance. The focus is on GNSS receivers and microelectromechanical (MEMS) inertial sensors which have become common in mobile devices such as smartphones. First, methods to compensate for the additive bias of a MEMS gyroscope are investigated. Both physical slewing of the sensor and mathematical modeling of the bias instability process are considered. The use of MEMS inertial sensors for pedestrian navigation indoors is studied in the context of map matching using a particle filter. A high-sensitivity GNSS receiver is used to produce coarse initialization information for the filter to decrease the computational burden without the need to exploit local building infrastructure. Finally, a cycle slip detection scheme for stand-alone single-frequency GNSS receivers is proposed. Experimental results show that even a MEMS gyroscope can reach an accuracy suitable for North seeking if the measurement errors are carefully modeled and eliminated. Furthermore, it is seen that even a relatively coarse initialization can be adequate for long-term indoor navigation without an excessive computational burden if a detailed map is available. The cycle slip detection results suggest that even small cycle slips can be detected with mass-market GNSS receivers, but the detection rate needs to be improved

Ordinal Outcome State-Space Models for Intensive Longitudinal Data

Intensive longitudinal (IL) data are increasingly prevalent in psychological science, coinciding with technological advancements that make it simple to deploy study designs such as daily diary and ecological momentary assessments. IL data are characterized by a rapid rate of data collection (1+ collections per day), over a period of time, allowing for the capture of the dynamics that underlie psychological and behavioral processes. One powerful framework for analyzing IL data is state-space modeling, where observed variables are considered measurements for underlying states (i.e., latent variables) that change together over time. However, state-space modeling has typically relied on continuous measurements, whereas psychological data often comes in the form of ordinal measurements such as Likert scale items. In this manuscript, we develop a general estimating approach for state-space models with ordinal measurements, specifically focusing on a graded response model for Likert scale items. We evaluate the performance of our model and estimator against that of the commonly used ``linear approximation'' model, which treats ordinal measurements as though they are continuous. We find that our model resulted in unbiased estimates of the state dynamics, while the linear approximation resulted in strongly biased estimates of the state dynamicsComment: 28 pages, 6 figures, 7 pages supplementary material

Attitude Determination Method by Fusing Single Antenna GPS and Low Cost MEMS Sensors Using Intelligent Kalman Filter Algorithm

For meeting the demands of cost and size for micronavigation system, a combined attitude determination approach with sensor fusion algorithm and intelligent Kalman filter (IKF) on low cost Micro-Electro-Mechanical System (MEMS) gyroscope, accelerometer, and magnetometer and single antenna Global Positioning System (GPS) is proposed. The effective calibration method is performed to compensate the effect of errors in low cost MEMS Inertial Measurement Unit (IMU). The different control strategies fusing the MEMS multisensors are designed. The yaw angle fusing gyroscope, accelerometer, and magnetometer algorithm is estimated accurately under GPS failure and unavailable sideslip situations. For resolving robust control and characters of the uncertain noise statistics influence, the high gain scale of IKF is adjusted by fuzzy controller in the transition process and steady state to achieve faster convergence and accurate estimation. The experiments comparing different MEMS sensors and fusion algorithms are implemented to verify the validity of the proposed approach