In the past years, algorithms for 3D shape tracking using radial functions in spherical coordinates represented with different methods have been proposed. However, we have seen that mainly measurements from the lateral surface of the target can be expected in a lot of dynamic scenarios and only few measurements from the top and bottom parts leading to an error-prone shape estimate in the top and bottom regions when using a representation in spherical coordinates. We, therefore, propose to represent the shape of the target using a radial function in cylindrical coordinates, as these only represent regions of the lateral surface, and no information from the top or bottom parts is needed. In this paper, we use a Fourier-Chebyshev double series for 3D shape representation since a mixture of Fourier and Chebyshev series is a suitable basis for expanding a radial function in cylindrical coordinates. We investigate the method in a simulated and real-world maritime scenario with a CAD model of the target boat as a reference. We have found that shape representation in cylindrical coordinates has decisive advantages compared to a shape representation in spherical coordinates and should preferably be used if no prior knowledge of the measurement distribution on the surface of the target is available.
In this paper, a novel measurement model based on spherical double Fourier series (DFS) for estimating the 3D shape of a target concurrently with its kinematic state is introduced. Here, the shape is represented as a star-convex radial function, decomposed as spherical DFS. In comparison to ordinary DFS, spherical DFS do not suffer from ambiguities at the poles. Details will be given in the paper. The shape representation is integrated into a Bayesian state estimator framework via a measurement equation. As range sensors only generate measurements from the target side facing the sensor, the shape representation is modified to enable application of shape symmetries during the estimation process. The model is analyzed in simulations and compared to a shape estimation procedure using spherical harmonics. Finally, shape estimation using spherical and ordinary DFS is compared to analyze the effect of the pole problem in extended object tracking (EOT) scenarios.
Probabilistic data association for tracking extended targets under clutter using random matrices
(2015)
The use of random matrices for tracking extended objects has received high attention in recent years. It is an efficient approach for tracking objects that give rise to more than one measurement per time step. In this paper, the concept of random matrices is used to track surface vessels using highresolution automotive radar sensors. Since the radar also receives a large number of clutter measurements from the water, for the data association problem, a generalized probabilistic data association filter is applied. Additionally, a modification of the filter update step is proposed to incorporate the Doppler velocity measurements. The presented tracking algorithm is validated using Monte Carlo Simulation, and some performance results with real radar data are shown as well.
The improvement of collision avoidance for vessels in close range encounter situations is an important topic for maritime traffic safety. Typical approaches generate evasive trajectories or optimise the trajectories of all involved vessels. Such a collision avoidance system has to produce evasive manoeuvres that do not confuse other navigators. To achieve this behaviour, a probabilistic obstacle handling based on information from a radar sensor with target tracking, that considers measurement and tracking uncertainties is proposed. A grid based path search algorithm, that takes the information from the probabilistic obstacle handling into account, is then used to generate evasive trajectories. The proposed algorithms have been tested and verified in a simulated environment for inland waters.
The method of signal injection is investigated for position estimation of proportional solenoid valves. A simple observer is proposed to estimate a position-dependent parameter, i.e. the eddy current resistance, from which the position is calculated analytically. Therefore, the relationship of position and impedance in the case of sinusoidal excitation is accurately described by consideration of classical electrodynamics. The observer approach is compared with a standard identification method, and evaluated by practical experiments on an off-the-shelf proportional solenoid valve.
A lot of procedures for estimating the spool position in linear electromagnetic actuators using voltage and current measurements only, can be found in the literature. Subject to the accuracy of the estimated spool position some achieve better, some worse results. However, in almost every approach hysteresis has a huge impact on the estimation accuracy that can be achieved. Regardless whether these effects are caused by magnetic or mechanical hysteresis, they will limit the accuracy of the position estimate, if not taken into account. In this paper, a model is introduced which covers the hysteresis effects as well as other nonlinear ities occurring in estimated position-dependent parameters. A classical Preisach model is deployed first, which is then adjusted by using novel elementary preceding Relay-Operators. The resulting model for the estimated position-dependent parameters including the adjusted Preisach model can be easily applied to position estimation tasks. It is shown that the considered model distinctly improves the accuracy for the spool position estimate, while it is kept as simple as possible for real-time implementation reasons.
In 3D extended object tracking (EOT), well-established models exist for tracking the object extent using various shape priors. A single update, however, has to be performed for every measurement using these models leading to a high computational runtime for high-resolution sensors. In this paper, we address this problem by using various model-independent downsampling schemes based on distance heuristics and random sampling as pre-processing before the update. We investigate the methods in a simulated and real-world tracking scenario using two different measurement models with measurements gathered from a LiDAR sensor. We found that there is a huge potential for speeding up 3D EOT by dropping up to 95\% of the measurements in our investigated scenarios when using random sampling. Since random sampling, however, can also result in a subset that does not represent the total set very well, leading to a poor tracking performance, there is still a high demand for further research.
Analysing observability is an important step in the
process of designing state feedback controllers. While for linear
systems observability has been widely studied and easy-to-check
necessary and sufficient conditions are available, for nonlinear
systems, such a general recipe does not exist and different classes
of systems require different techniques. In this paper, we analyse
observability for an industrial heating process where a stripe-
shaped plastic workpiece is moving through a heating zone where
it is heated up to a specific temperature by applying hot air to its
surface through a nozzle. A modeling approach for this process
is briefly presented, yielding a nonlinear Ordinary Differential
Equation model. Sensitivity-based observability analysis is used
to identify unobservable states and make suggestions for addi-
tional sensor locations. In practice, however, it is not possible
to place additional sensors, so the available measurements are
used to implement a simple open-loop state estimator with
offset compensation and numerical and experimental results are
presented.
In this paper, a gain-scheduled nonlinear control structure is proposed for a surface vessel, which takes advantage of extended linearisation techniques. Thereby, an accurate tracking of desired trajectories can be guaranteed that contributes to a safe and reliable water transport. The PI state feedback control is extended by a feedforward control based on an inverse system model. To achieve an accurate trajectory tracking, however, an observer-based disturbance compensation is necessary: external disturbances by cross currents or wind forces in lateral direction and wave-induced measurement disturbances are estimated by a nonlinear observer and used for a compensation. The efficiency and the achieved tracking performance are shown by simulation results using a validated model of the ship Korona at the HTWG Konstanz, Germany. Here, both tracking behaviour and rejection of disturbance forces in lateral direction are considered.