Consumer electronics mobile devices, such as smartphones or tablets, are rapidly growing in computing power and are equipped with an increasing number of sensors. This enables to use a present-day mobile device as a viable platform for computation-intensive, real-time applications in navigation and guidance. In this paper, we present a study on the performance of the orientation estimation based on the data acquired by the accelerometer, magnetometer, and gyroscope in a mobile device. Reliable orientation estimation based on the readouts from inertial sensors may be used in more complex systems, e.g., to correct the orientation error of a visual odometry system. We present a rigorous derivation of the mathematical estimation model, and we thoroughly evaluate the performance of the orientation estimation mechanism available in the Android OS, and the proposed alternative solutions on an unique dataset gathered using an actual smartphone. From the experimental results, we draw the conclusions as to the best performing algorithm, and then we evaluate its execution time on Android-based devices to demonstrate the possibility of real-time usage. The Android code for the proposed orientation estimation system is made publicly available for scientific and commercial applications.

In this paper, an easily implementable coaxial quadrotor model and its validation on data from a real unmanned aerial vehicle (UAV), are presented. The proposed mathematical model consists of two parts: description of orientation and position of the UAV in the three-dimensional space. It takes into consideration the gyroscopic effect, influence of the Coriolis force, viscous friction and a several drag-like effects (blade flapping, rotor drag, translational drag and profile drag). In contrast to multirotor models available in the literature, this one is characterized by complementarity in relation to the available control techniques. Depending on selection of these techniques, the model can be narrowed (simplified) to meet the needs without the loss of behaviour adequacy to a real UAV.

Autonomous estimation of the state is of key importance in UAVs, as the measurement systems may experience faults and failures. Thus estimation techniques must provide estimates of the most important variables used in the control algorithms for safe, autonomous, unmanned flights. In this paper, a filter with low computational complexity for attitude estimation of a quadrotor UAV is introduced, with a model suitable for Fault-Tolerant Observation. The new filtration method, called the Square Root Unscented Complementary Kalman Filter (SRUCKF), is based on the commonly-known Kalman Filter (KF) in its nonlinear version, namely the Square Root Unscented Kalman Filter (SRUKF). The fundamental equation of the KF is modified so that the complementary feature of the filter is exalted. The new filter introduces characteristics that are analyzed on the basis of its application in quadrotor state estimation. Finally, the results are compared to an ordinary filter of the same type (using the Unscented Transformation). The presented studies indicate that the newly derived filter (SRUCKF) handles strong nonlinearities and gives results similar to those obtained from the SRUKF. Furthermore, it introduces lower computational burden, as the undergoing process uses diagonal matrices in its crucial places. In the paper, the estimation algorithms are tailored to a quadrotor UAV (Crazyflie 2.0), for which a quaternion-based model is proposed. The contribution of the paper lies in a Kalman-based novel state observer and its application in Fault-Tolerant Observation (FTO).

The parametrized model of the Unmanned Aerial Vehicle (UAV) is a crucial part of control algorithms, estimation processes and fault diagnostic systems. Among plenty of available methods for model structure or model parameters estimation, there are a few, which are suitable for nonlinear UAV models. In this work authors propose an estimation method of parameters of the coaxial quadrotor’s orientation model, based on the Square Root Unscented Kalman Filter (SRUKF). The model structure with different aerodynamic aspects is presented. The model is enhanced with various friction types, so it reflects the real quadrotor characteristics more precisely. In order to validate the estimation method, the experiments are conducted in a special hall and essential data is gathered. The research shows that the SRUKF, can provide fast and reliable estimation of the model parameters, however the classic method may lead to serious instabilities. Necessary modifications of the estimation algorithm are included, so the approach is more robust in terms of numerical stability. The resultant method allows for dynamics of selected parameters to be changed and is proved to be adequate for on-line estimation. The studies reveals tracking properties of the algorithm, which makes the method more viable.

Osteoarthritis of the knee (OAK) is characterized by pain, limitation of joint mobility, and significant deterioration of proprioception resulting in functional decline. This study assessed proprioception in OAK patients following two ten-day rehabilitation programs using the Orthyo^® system. Fifty-four study participants with clinical symptoms and radiological signs of OAK were randomly divided into an exercise group (n = 27) or a manual therapy group (n = 27). The control group consisted of 27 volunteers with radiological signs of OAK, but with no clinical symptoms or prior history of rehabilitation. The following parameters were assessed: knee proprioception using inertial sensors and a mobile application, patients’ function using Western Ontario and McMaster Universities osteoarthritis index (WOMAC), and pain intensity using the visual analog scale (VAS). Following rehabilitation, knee proprioception tests did not improve in either study group. Both study groups showed significant improvement of the WOMAC-assessed function (exercise group: p < 0.01, manual therapy group: p = 0.01) and a significant decrease (p < 0.01) of VAS-assessed pain following rehabilitation, but the post-therapy results did not differ significantly between the aforementioned groups. The Orthyo^® system provided a quick and accurate assessment of the knee joint position sense. There was no direct relationship between functionality, pain, and proprioception threshold in the knee joint.