Various Ways to Compute the Continuous-Discrete Extended Kalman Filter

International audienceThe Extended Kalman Filter (EKF) is a very popular tool dealing with state estimation. Its continuous-discrete version (CD-EKF) estimates the state trajectory of continuous-time nonlinear models, whose internal state is described by a stochastic differential equation and which is observed through a noisy nonlinear form of the sampled state. The prediction step of the CD-EKF leads to solve a differential equation that cannot be generally solved in a closed form. This technical note presents an overview of the numerical methods, including recent works, usually implemented to approximate this filter. Comparisons of theses methods on two different nonlinear models are finally presented. The first one is the Van der Pol oscillator which is widely used as a benchmark. The second one is a neuronal population model. This more original model is used to simulate EEG activity of the cortex. Experiments showed better stability properties of implementations for which the positivity of the prediction matrix is guaranteed

Kinematic motion models based vessel state estimation to support advanced ship predictors

Advanced ship predictors can generally be considered as a vital part of the decision-making process of autonomous ships in the future, where the information on vessel maneuvering behavior can be used as the source of information to estimate current vessel motions and predict future behavior precisely. As a result, the navigation safety of autonomous vessels can be improved. In this paper, vessel maneuvering behavior consists of continuous-time system states of two kinematic motion models—the Curvilinear Motion Model (CMM) and Constant Turn Rate & Acceleration (CTRA) Model. Two state estimation algorithms—the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are implemented on these two models with certain modifications so that they can be compatible with discrete-time measurements. Four scenarios, created by combining different models and algorithms, are implemented using simulated ship maneuvering data from a bridge simulator. These scenarios are then verified through the proposed stability and consistency tests. The simulation results show that the EKF tends to be unstable combined with the CMM. The estimates from the other three scenarios can generally be considered more stable and consistent, unless sudden actions or variations in vessel heading occurred during the simulation. The CTRA is also proven to be more robust compared to the CMM. As a result, a suitable combination of mathematical models and estimation filters can be considered to support advanced ship predictors in future ship navigation

Modelling and control of direct steam generation in solar cavity receivers powered by paraboloidal dish concentrators

The control of steam temperature in direct steam generation plants is challenging due to the complex physical process involved in turning water into steam, and the variable nature of solar radiation. This thesis explores the control of steam temperature at the outlet of a mono-tube cavity receiver powered by a 500m2 dish concentrator, using state feedback control. The dish concentrator, receiver and ancillary equipment constitute the SG4 once-through steam generation system at the Australian National University in Canberra, Australia. The control of temperature in the receiver employs a linear full state feedback control strategy. The controller manipulates the feed-water mass flow entering the receiver, to maintain constant steam temperature at the receiver outlet under variations in solar radiation, inlet flow conditions and ambient temperature. To implement the temperature controller, this thesis develops a dynamic model of the steam generation process in the receiver. The mono-tube cavity receiver consists of a single path of steel tubing coiled to form a cylindrical cavity with a frustum opening. The cavity side of the tube intercepts concentrated radiation from the dish concentrator and heats up. Water passes through the inside of the tube and absorbs heat, turning into superheated steam before leaving the receiver. The dynamic model of the receiver is a switched movingboundary description of the heat exchange process taking place in the absorber tube, including the transition between single and two-phase flow that water undergoes as it turns into superheated steam. The advantage of this modelling approach is that it provides a state-space representation of the receiver that is suitable for the development of state feedback controllers. Computer simulations in this thesis validate the receiver model, as they show good agreement with experimental measurements of the SG4 steam generation system. The practical implementation of the receiver temperature controller in this thesis requires a state observer to estimate the state of the mono-tube cavity receiver during operation. This thesis proposes a modified Extended Kalman Filtering scheme to compute the state of the receiver, built around the switched moving-boundary receiver model. The filtering scheme is implemented in computer simulations and demonstrated experimentally in the SG4 steam generation system as part of this thesis. The linear full state feedback temperature controller proposed in this thesis generates a feed-water mass flow command to control the temperature at the receiver outlet. The mass flow command is generated from three separate regulation mechanisms: a set of full state feedback gains, an integrator and a feedforward law. The feedback and integrator mechanisms are designed from a linear approximation of the receiver model, and the feedforward law corresponds to a steady state energy balix x ance in the receiver. The temperature controller is implemented in simulations and experimentally on the SG4 steam generation system. This thesis presents the first experimental results of the SG4 system running successfully with automatic steam temperature control