On Multi-Step Sensor Scheduling via Convex Optimization

Effective sensor scheduling requires the consideration of long-term effects and thus optimization over long time horizons. Determining the optimal sensor schedule, however, is equivalent to solving a binary integer program, which is computationally demanding for long time horizons and many sensors. For linear Gaussian systems, two efficient multi-step sensor scheduling approaches are proposed in this paper. The first approach determines approximate but close to optimal sensor schedules via convex optimization. The second approach combines convex optimization with a \BB search for efficiently determining the optimal sensor schedule.Comment: 6 pages, appeared in the proceedings of the 2nd International Workshop on Cognitive Information Processing (CIP), Elba, Italy, June 201

Enhancing Decision Tree based Interpretation of Deep Neural Networks through L1-Orthogonal Regularization

One obstacle that so far prevents the introduction of machine learning models primarily in critical areas is the lack of explainability. In this work, a practicable approach of gaining explainability of deep artificial neural networks (NN) using an interpretable surrogate model based on decision trees is presented. Simply fitting a decision tree to a trained NN usually leads to unsatisfactory results in terms of accuracy and fidelity. Using L1-orthogonal regularization during training, however, preserves the accuracy of the NN, while it can be closely approximated by small decision trees. Tests with different data sets confirm that L1-orthogonal regularization yields models of lower complexity and at the same time higher fidelity compared to other regularizers.Comment: 8 pages, 18th IEEE International Conference on Machine Learning and Applications (ICMLA) 201

Kalman-Bucy-Informed Neural Network for System Identification

Identifying parameters in a system of nonlinear, ordinary differential equations is vital for designing a robust controller. However, if the system is stochastic in its nature or if only noisy measurements are available, standard optimization algorithms for system identification usually fail. We present a new approach that combines the recent advances in physics-informed neural networks and the well-known achievements of Kalman filters in order to find parameters in a continuous-time system with noisy measurements. In doing so, our approach allows estimating the parameters together with the mean value and covariance matrix of the system's state vector. We show that the method works for complex systems by identifying the parameters of a double pendulum.Comment: 6 pages, 5 figures, Conference on Decision and Control 202

Gaussian Mixture Reduction via Clustering

Recursive processing of Gaussian mixture functions inevitably leads to a large number of mixture components. In order to keep the computational complexity at a feasible level, the number of their components has to be reduced periodically. There already exists a variety of algorithms for this purpose, bottom-up and top-down approaches, methods that take the global structure of the mixture into account or that work locally and consider few mixture components at the same time. The mixture reduction algorithm presented in this paper can be categorized as global top-down approach. It takes a clustering algorithm originating from the field of theoretical computer science and adapts it for the problem of Gaussian mixture reduction. The achieved results are on the same scale as the results of the current “state-of-the-art” algorithm PGMR, but, depending on the input size, the whole procedure performs significantly faster

Gaussian Filter based on Deterministic Sampling for High Quality Nonlinear Estimation

In this paper, a Gaussian filter for nonlinear Bayesian estimation is introduced that is based on a deterministic sample selection scheme. For an effective sample selection, a parametric density function representation of the sample points is employed, which allows approximating the cumulative distribution function of the prior Gaussian density. The computationally demanding parts of the optimization problem formulated for approximation are carried out off-line for obtaining an efficient filter, whose estimation quality can be altered by adjusting the number of used sample points. The improved performance of the proposed Gaussian filter compared to the well-known unscented Kalman fiter is demonstrated by means of two examples

Gaussian Filtering using State Decomposition Methods

State estimation for nonlinear systems generally requires approximations of the system or the probability densities, as the occurring prediction and filtering equations cannot be solved in closed form. For instance, Linear Regression Kalman Filters like the Unscented Kalman Filter or the considered Gaussian Filter propagate a small set of sample points through the system to approximate the posterior mean and covariance matrix. To reduce the number of sample points, special structures of the system and measurement equation can be taken into account. In this paper, two principles of system decomposition are considered and applied to the Gaussian Filter. One principle exploits that only a part of the state vector is directly observed by the measurement. The second principle separates the system equations into linear and nonlinear parts in order to merely approximate the nonlinear part of the state. The benefits of both decompositions are demonstrated on a real-world example

On Sensor Scheduling in Case of Unreliable Communication

This paper deals with the linear discrete-time sensor scheduling problem in unreliable communication networks. In case of the common assumption of an error-free communication, the sensor scheduling problem, where one sensor from a sensor network is selected for measuring at a specific time instant so that the estimation errors are minimized, can be solved off-line by extensive tree search. For the more realistic scenario, where communication is unreliable, a scheduling approach using a prioritization list for the sensors is proposed that leads to a minimization of the estimation error by selecting the most beneficial sensor on-line. To lower the computational demand for the priority list calculation, a novel optimal pruning approach is introduced