Alexandros C. Charalampidis

Computationally Efficient Kalman Filtering for a Class of Nonlinear Systems

This paper deals with recursive state estimation for the class of discrete time nonlinear systems whose nonlinearity consists of one or more static nonlinear one-variable functions. This class contains several important subclasses. The special structure is exploited to permit accurate computations without an increase in computational cost. The proposed method is compared with standard Extended Kalman Filter, Unscented Kalman Filter and Gauss-Hermite Kalman Filter in three illustrative examples. The results show that it yields good results with small computational cost.

Speed profile optimization for vehicles crossing an intersection under a safety constraint

This paper considers the case of two vehicles crossing an intersection from perpendicular directions. A second-order kinematic model is assumed as well as that initially both vehicles move with their maximum permissible speed. A braking/reaccelerating speed profile is proposed for the vehicle crossing second that enables it to brake without colliding with the first even if the latter unexpectedly and immediately comes to a stop. Under the aforementioned constraint, the time loss incurred by the second vehicle due to braking is used as an optimization criterion. When the profile that leads to this minimum delay is not unique, the maximum deceleration applied is used as a secondary criterion. The problem is solved analytically providing closed-form solutions.

Kalman Filtering for a Generalized Class of Nonlinear Systems and a New Gaussian Quadrature Technique

The class of nonlinear systems treated in this technical note consists of the discrete time nonlinear systems that are formed by the interconnection of linear systems through static nonlinearities with few inputs. This special structure is exploited to reduce the dimension of the integrals involved in the propagation of mean values and covariances, thus permitting accurate calculations. Furthermore, a new quadrature scheme suitable for nonlinear Kalman filtering is introduced. The proposed techniques are applied to a seven-dimensional numerical example. The results show that they can increase the performance significantly.

Improved auxiliary and Unscented Particle Filter variants

This paper proposes some modifications to the Auxiliary Particle Filter and the Unscented Particle Filter. For the APF, based on some error bound considerations it is suggested that the auxiliary weights are taken into account not proportionally but nonlinearly. An improved way to compensate for the auxiliary weights after the resampling is also proposed. For the UPF, a method is introduced to compute the covariance matrices of the particles not using the UKF equations for each particle separately, but so as to optimize the characteristics of the total distribution. The application of the modified filters to an example shows that the proposed changes lead to performance increase.

Calibration of a microdialysis sensor and recursive glucose level estimation in ICU patients using Kalman and particle filtering

Abstract This paper deals with the estimation of glucose levels in ICU patients by the application of statistical filter theory to the data provided by a commercial continuous glucose monitoring system using a microdialysis sensor. Kalman and particle filtering are applied to simple models of the glucose dynamics. The particle filter enables the joint filtering and calibration of the sensor. The results show that the proposed filters lead to significant reduction in the estimation error with computational cost well within the capabilities of modern digital equipment. Additionally, the filters can be used for the automatic recognition of sensor faults. These results show that suitable filters can help in the construction of an artificial pancreas.

Graph topology optimization for fast consensus based on the influence of new links to a quadratic criterion

This paper studies the problem of graph choice in order to maximize consensus convergence speed. Instead of algebraic connectivity, a quadratic criterion is used which is shown to depend on the whole spectrum of the consensus dynamics matrix. The influence of new links to this cost is investigated and a first-order approximation is given. This approximation can be used to compare the effect that different links will have and this is exploited to propose a simple algorithm that starts from a regular lattice and adds links until all nodes have a specific number of neighbours. The resulting graph is compared with random graphs known to have high connectivity because of the small-world effect. Numerical experimentation showed that, for specific parameters, this algorithm provides a graph outperforming a large number of realizations of random graphs both in terms of algebraic connectivity and of the proposed quadratic criterion; for these random graphs it was also shown that this quadratic criterion correlates better with the characteristic path length than algebraic connectivity does.

Pretending in Dynamic Games, Alternative Outcomes and Application to Electricity Markets

This work studies dynamic game situations with incomplete structural information, motivated by problems arising in electricity market modeling. Some adaptive/learning strategies are considered as an expression of the bounded rationality of the participants of the game. The adaptive strategies are typically not in Nash equilibrium. Thus, the possibility of manipulation appears. That is, a player may use the dynamic rule of the opponent in order to manipulate her. We focus on a smaller class of manipulating strategies, called pretending strategies, where each player acts as if she had different, not real, preferences. It turns out that under certain technical conditions, if only one player pretends, she can achieve the same cost as if she were the Stackelberg leader. The situation where all the players are pretending is then considered, and an auxiliary game, called pretenders’ game, is introduced. A class of quadratic games is then studied, and several relations among pretending and Stackelberg leadership are derived. A linear quadratic environmental game is also studied. We then study some competitive electricity market models. Particularly, a supply function model and the market mechanism described in Rasouli and Teneketzis (electricity pooling markets with strategic producers possessing asymmetric information ii: inelastic demand, arXiv: 1404.5539, 2014) are considered. It turns out that pretending may increase competition or cooperation and in some cases pretending may cause behaviors making the system not working at all.

Comparison of standard and modified recursive state estimation techniques for nonlinear systems

This paper deals with recursive state estimation for nonlinear systems. A new set of σ-points for the Unscented Kalman Filter is proposed as well as a way to substitute a nonlinear output with a linear one. The importance of the function of the state which must be estimated is also illustrated and the need for taking it into account when designing the state estimator. All the proposed methods are compared with standard Extended Kalman Filter, Unscented Kalman Filter and Particle Filter with Sampling Importance Resampling using simulations. The results show that the modifications proposed in some cases lead to considerable reduction in estimation error.