There is an unavoidable time offset between the camera stream and the inertial measurement unit (IMU) data due to the sensor triggering and transmission delays, which will seriously affect the accuracy of visual-inertial odometry (VIO). A novel online time calibration framework via double-stage EKF for VIO is proposed in this paper. First, the first-stage complementary Kalman filter is constructed by adapting the complementary characteristics between the accelerometer and the gyroscope in the IMU, where the rotation result predicted by the gyroscope is corrected through the measurement of the accelerometer so that the IMU can output a more accurate initial pose. Second, the unknown time offset is added to the state vector of the VIO system. The estimated pose of IMU is used as the prediction information, and the reprojection error of multiple cameras on the same feature point is used as the constraint information. During the operation of the VIO system, the time offset is continuously calculated and superimposed on the IMU timestamp to obtain the data synchronized by the IMU and the camera. The Schur complement model is used to marginalize the camera state that carries less information in the system state, avoiding the loss of prior information between images, and improving the accuracy of camera pose estimation. Finally, the effectiveness of proposed algorithm is verified using the EuRoC dataset and the real experimental data.

Wind turbine towers are subjected to highly varying internal loads, characterized by large uncertainty. The uncertainty stems from many factors, including what the actual wind fields experienced over time will be, modeling uncertainties given the various operational states of the turbine with and without controller interaction, the influence of aerodynamic damping, and so forth. To monitor the true experienced loading and assess the fatigue, strain sensors can be installed at fatigue-critical locations on the turbine structure. A more cost-effective and practical solution is to predict the strain response of the structure based only on a number of acceleration measurements. In this contribution, an approach is followed where the dynamic strains in an existing onshore wind turbine tower are predicted using a Gaussian process latent force model. By employing this model, both the applied dynamic loading and strain response are estimated based on the acceleration data. The predicted dynamic strains are validated using strain gauges installed near the bottom of the tower. Fatigue is subsequently assessed by comparing the damage equivalent loads calculated with the predicted as opposed to the measured strains. The results confirm the usefulness of the method for continuous tracking of fatigue life consumption in onshore wind turbine towers.

This paper, in allusion to the limitations of traditional transfer alignment methods based on the external measurement equipment or the empirical model of angular deformation, proposes a rapid and accurate transfer alignment method without relying on the empirical angular deformation model. Firstly, the relationship between the actual angular deformation and the angular velocities measured by the gyroscopes in the master and slave inertial navigation systems (INSs) is derived to roughly estimate the angular deformation. Secondly, according to the error characteristics of gyroscopes, the error model of angular deformation is established. Thirdly, expanding the angular deformation error instead of the installation error angle, flexure angle and flexure angle rate into the state vector, a low-order transfer alignment filtering model independent of the empirical angular deformation model is established. The proposed method not only gets rid of the dependence on an empirical angular deformation model, but also realises the rapid and accurate initial alignment of the slave INS without adding any external measurement equipment. The simulations and experiments evidence the validity of the proposed transfer alignment method.

Robotics and computer vision problems commonly require handling rigid-body motions comprising translation and rotation – together referred to as pose. In some situations, a vectorial parameterization of pose can be useful, where elements of a vector space are surjectively mapped to a matrix Lie group. For example, these vectorial representations can be employed for optimization as well as uncertainty representation on groups. The most common mapping is the matrix exponential, which maps elements of a Lie algebra onto the associated Lie group. However, this choice is not unique. It has been previously shown how to characterize all such vectorial parameterizations for SO(3), the group of rotations. Some results are also known for the group of poses, where it is possible to build a family of vectorial mappings that includes the matrix exponential as well as the Cayley transformation. We extend what is known for these pose mappings to the $4 \times 4$ representation common in robotics and also demonstrate three different examples of the proposed pose mappings: (i) pose interpolation, (ii) pose servoing control, and (iii) pose estimation in a pointcloud alignment problem. In the pointcloud alignment problem, our results lead to a new algorithm based on the Cayley transformation, which we call CayPer.

A multi-agent engagement scenario is considered in which a high-value aircraft launches two defenders to intercept two homing missiles aimed at the aircraft. Under the assumption that all aircrafts have first-order linear dynamic characteristics, a combined multiple-mode adaptive estimation (MMAE) and a two-way cooperative optimal guidance law are proposed for the target–defenders team. Considering the full cooperation of the target and both the two defenders, the two-way cooperative strategies provide the analytical expressions for their optimal control input, enabling the target–defenders team to intercept the missiles with minimal control effort. To successfully intercept the missiles, MMAE is used to identify the guidance laws adopted by the missiles and estimate their states. The simulation results show that the target cooperating with the defenders to perform lure manoeuvres for the missiles can improve the guidance performance of the defenders as well as reduce the control effort of the defenders for intercepting the missiles.

In this paper, a fault-tolerant velocity estimation method is proposed for quadrotors in a GPS denied environment. A novel filter is developed in light of the quadrotor model and measurements from optical flow and inertial sensors. The proposed filter is capable of detecting and isolating the optical flow sensor faults, by which the velocity estimation accuracy and stability will be improved. It is also demonstrated that the wind velocity is observable in the proposed filter. Therefore, the new filter can also be implemented in a windy environment, which is a significant improvement to the previous model-aided inertial sensor estimator. At the end, some simulations are carried out to verify the advantages of our method.

This paper introduces an observer strategy, namely a Sliding Mode Observer (SMO), to realise the fault detection and estimation of general uncertain non-linear systems. The use of a non-linear observer is considered for monitoring the states of a high incidence research model (HIRM) aircraft system. For a special class of Lipschitz non-linear system, a fault reconstruction scheme is presented where the reconstructed signal can approximate the fault signal to any accuracy. The proposed method is based only on the available plant input-output information and can be calculated online. Moreover, the globally asymptotic stability of the closed-loop system is mathematically proved. Finally, an HIRM aircraft system example is given to illustrate the efficiency of the proposed approach.

A nonholonomic system subjected to external noise from the environment, or internal noise in its own actuators, will evolve in a stochastic manner described by an ensemble of trajectories. This ensemble of trajectories is equivalent to the solution of a Fokker–Planck equation that typically evolves on a Lie group. If the most likely state of such a system is to be estimated, and plans for subsequent motions from the current state are to be made so as to move the system to a desired state with high probability, then modeling how the probability density of the system evolves is critical. Methods for solving Fokker-Planck equations that evolve on Lie groups then become important. Such equations can be solved using the operational properties of group Fourier transforms in which irreducible unitary representation (IUR) matrices play a critical role. Therefore, we develop a simple approach for the numerical approximation of all the IUR matrices for two of the groups of most interest in robotics: the rotation group in three-dimensional space, SO(3), and the Euclidean motion group of the plane, SE(2). This approach uses the exponential mapping from the Lie algebras of these groups, and takes advantage of the sparse nature of the Lie algebra representation matrices. Other techniques for density estimation on groups are also explored. The computed densities are applied in the context of probabilistic path planning for kinematic cart in the plane and flexible needle steering in three-dimensional space. In these examples the injection of artificial noise into the computational models (rather than noise in the actual physical systems) serves as a tool to search the configuration spaces and plan paths. Finally, we illustrate how density estimation problems arise in the characterization of physical noise in orientational sensors such as gyroscopes.

Given a d-dimensional random field and a Poisson process independent of it, suppose that it is possible to observe only the location of each point of the Poisson process and the value of the random field at that (randomly located) point. Non-parametric estimators of the mean and covariance function of the random field—based on observation over compact sets of single realizations of the Poisson samples—are constructed. Under fairly mild conditions these estimators are consistent (in various senses) as the set of observation becomes unbounded in a suitable manner. The state estimation problem of minimum mean-squared error reconstruction of unobserved values of the random field is also examined.

For a continuous time Markov chain the time points of transitions, belonging to a subset of the set of all transitions, are observed. Special cases include the point process generated by all transitions and doubly stochastic Poisson processes with a Markovian intensity. Equations are derived for the conditional distribution of the state of the Markov chain, given observations of the point process. This distribution may be used for prediction. For the forward recurrence time of the point process, distributions corresponding to synchronous and asynchronous sampling are also derived. The Palm distribution for the point process is specified in terms of the corresponding initial distribution for the Markov chain. In examples the point processes of arrivals and departures in a queueing system are studied. Two biological applications deal with estimation of population size and detection of epidemics.

Consider a Poisson point process with an intensity parameter forming a Markov chain with continuous time and finite state space. A system of ordinary differential equations is derived for the conditional distribution of the Markov chain given observations of the point process. An estimate of the current intensity, optimal in the least-squares sense, is computed from this distribution. Applications to reliability and replacement theory are given. A special case with two states, corresponding to a process in control and out of control, is discussed at length. Adjustment rules, based on the conditional probability of the out of control state, are studied. Regarded as a function of time, this probability forms a Markov process with the unit interval as state space. For the distribution of this process, integro-differential equations are derived. They are used to compute the average long run cost of adjustment rules.