A Multiple Model Approach to Track Head Orientation With Delta Quaternions

The Interacting Multiple Model Filter and Smoother on Boxplus-Manifolds

Hybrid systems are subject to multiple dynamic models, or so-called modes. To estimate the state, the sequence of modes has to be estimated, which results in an exponential growth of possible sequences. The most prominent solution to handle this is the interacting multiple model filter, which can be extended to smoothing. In this paper, we derive a novel generalization of the interacting multiple filter and smoother to manifold state spaces, e.g., quaternions, based on the boxplus-method. As part thereof, we propose a linear approximation to the mixing of Gaussians and a Rauch-Tung-Striebel smoother for single models on boxplus-manifolds. The derivation of the smoother equations is based on a generalized definition of Gaussians on boxplus-manifolds. The three, novel algorithms are evaluated in a simulation and perform comparable to specialized solutions for quaternions. So far, the benefit of the more principled approach is the generality towards manifold state spaces. The evaluation and generic implementations are published open source.

Multiobjective and Interactive Genetic Algorithms for Weight Tuning of a Model Predictive Control-Based Motion Cueing Algorithm

Driving simulators are effective tools for training, virtual prototyping, and safety assessment which can minimize the cost and maximize road safety. Despite the aim of a realistic motion generation for the impression of real-world driving, motion simulators are bound in a limited workspace. Motion cueing algorithms (MCAs) aim to plan an acceptable motion feeling for drivers, without infringing the simulated boundaries. Recently, model predictive control (MPC) has been widely used in MCAs; however, the tuning process for finding the best weights of the MPC optimization is still a challenge. As there are several objectives for the optimization without any standard weighting for solution evaluations, a nonbiased scalarization of solutions for the purpose of comparison is impossible. In this paper, a clear method for obtaining the best MPC weighting has been proposed. This method searches for the best tune of MPC cost function weights, reduces the user burden for weight tuning while receiving feedback from the user satisfaction. The MPC-based MCA weights are optimized using a multiobjective genetic algorithm (GA) considering objectives, such as minimization of motion inputs (linear acceleration and angular velocity), input rates, output displacements and the sensed motion errors. Any process based on trial-and-error has been omitted. The adjusted weights have to satisfy a set of predefined conditions related to maximum tolerated error and maximum displacement. The obtained Pareto-front is used for decision making via an interactive GA (IGA), aiming for maximization of the decision maker's satisfaction. A Web interface is developed to interact with the IGA and to influence the region of searching. Simulation results show the superiority of the proposed method compared with the previous empirical tuning method. The sensed motion error is minimized using the proposed method and with the same available workspace, a more realistic motion can be rendered to the driver.

Multi-rate cubature Kalman filter based data fusion method with residual compensation to adapt to sampling rate discrepancy in attitude measurement system

This paper investigates the multi-rate inertial and vision data fusion problem in nonlinear attitude measurement systems, where the sampling rate of the inertial sensor is much faster than that of the vision sensor. To fully exploit the high frequency inertial data and obtain favorable fusion results, a multi-rate CKF (Cubature Kalman Filter) algorithm with estimated residual compensation is proposed in order to adapt to the problem of sampling rate discrepancy. During inter-sampling of slow observation data, observation noise can be regarded as infinite. The Kalman gain is unknown and approaches zero. The residual is also unknown. Therefore, the filter estimated state cannot be compensated. To obtain compensation at these moments, state error and residual formulas are modified when compared with the observation data available moments. Self-propagation equation of the state error is established to propagate the quantity from the moments with observation to the moments without observation. Besides, a multiplicative adjustment factor is introduced as Kalman gain, which acts on the residual. Then the filter estimated state can be compensated even when there are no visual observation data. The proposed method is tested and verified in a practical setup. Compared with multi-rate CKF without residual compensation and single-rate CKF, a significant improvement is obtained on attitude measurement by using the proposed multi-rate CKF with inter-sampling residual compensation. The experiment results with superior precision and reliability show the effectiveness of the proposed method.

Sensor Fusion of Gaussian Mixtures for Ballistic Target Tracking in the Re-Entry Phase

A sensor fusion methodology for the Gaussian mixtures model is proposed for ballistic target tracking with unknown ballistic coefficients. To improve the estimation accuracy, a track-to-track fusion architecture is proposed to fuse tracks provided by the local interacting multiple model filters. During the fusion process, the duplicate information is removed by considering the first order redundant information between the local tracks. With extensive simulations, we show that the proposed algorithm improves the tracking accuracy in ballistic target tracking in the re-entry phase applications.

An Improved Interacting Multiple Model Filtering Algorithm Based on the Cubature Kalman Filter for Maneuvering Target Tracking

In order to improve the tracking accuracy, model estimation accuracy and quick response of multiple model maneuvering target tracking, the interacting multiple models five degree cubature Kalman filter (IMM5CKF) is proposed in this paper. In the proposed algorithm, the interacting multiple models (IMM) algorithm processes all the models through a Markov Chain to simultaneously enhance the model tracking accuracy of target tracking. Then a five degree cubature Kalman filter (5CKF) evaluates the surface integral by a higher but deterministic odd ordered spherical cubature rule to improve the tracking accuracy and the model switch sensitivity of the IMM algorithm. Finally, the simulation results demonstrate that the proposed algorithm exhibits quick and smooth switching when disposing different maneuver models, and it also performs better than the interacting multiple models cubature Kalman filter (IMMCKF), interacting multiple models unscented Kalman filter (IMMUKF), 5CKF and the optimal mode transition matrix IMM (OMTM-IMM).

An Inertial and Optical Sensor Fusion Approach for Six Degree-of-Freedom Pose Estimation

Optical tracking provides relatively high accuracy over a large workspace but requires line-of-sight between the camera and the markers, which may be difficult to maintain in actual applications. In contrast, inertial sensing does not require line-of-sight but is subject to drift, which may cause large cumulative errors, especially during the measurement of position. To handle cases where some or all of the markers are occluded, this paper proposes an inertial and optical sensor fusion approach in which the bias of the inertial sensors is estimated when the optical tracker provides full six degree-of-freedom (6-DOF) pose information. As long as the position of at least one marker can be tracked by the optical system, the 3-DOF position can be combined with the orientation estimated from the inertial measurements to recover the full 6-DOF pose information. When all the markers are occluded, the position tracking relies on the inertial sensors that are bias-corrected by the optical tracking system. Experiments are performed with an augmented reality head-mounted display (ARHMD) that integrates an optical tracking system (OTS) and inertial measurement unit (IMU). Experimental results show that under partial occlusion conditions, the root mean square errors (RMSE) of orientation and position are 0.04° and 0.134 mm, and under total occlusion conditions for 1 s, the orientation and position RMSE are 0.022° and 0.22 mm, respectively. Thus, the proposed sensor fusion approach can provide reliable 6-DOF pose under long-term partial occlusion and short-term total occlusion conditions.