This work proposes a SLAM (Simultaneous Localization And Mapping) solution based on an Extended Kalman Filter (EKF) in order to enable a robot to navigate along the environment using information from odometry and pre-existing lines on the floor. These lines are recognized by a Hough transform and are mapped into world measurements using a homography matrix. The prediction phase of the EKF is developed using an odometry model of the robot, and the updating makes use of the line parameters in Kalman...

Existence of strong and weak solutions to stochastic inclusions $x_t-x_s\in {\int }_s^t{F}_{\tau }\left(x_{\tau }\right)d\tau +{\int }_s^t{G}_{\tau }\left(x_{\tau }\right)d{w}_{\tau }+{\int }_s^t{\int }_{{ℝ}^n}{H}_{\tau ,z}\left(x_{\tau }\right)q(d\tau ,dz)$ and $x_t-x_s\in {\int }_s^t{F}_{\tau }\left(x_{\tau }\right)d\tau +{\int }_s^t{G}_{\tau }\left(x_{\tau }\right)d{w}_{\tau }+{\int }_s^t{\int }_{\left|z\right|\le 1}{H}_{\tau ,z}\left(x_{\tau }\right)q(d\tau ,dz)+{\int }_s^t{\int }_{\left|z\right|>1}{H}_{\tau ,z}\left(x_{\tau }\right)p(d\tau ,dz)$, where p and q are certain random measures, is considered.

This paper deals with continuous-time Markov decision processes with the unbounded transition rates under the strong average cost criterion. The state and action spaces are Borel spaces, and the costs are allowed to be unbounded from above and from below. Under mild conditions, we first prove that the finite-horizon optimal value function is a solution to the optimality equation for the case of uncountable state spaces and unbounded transition rates, and that there exists an optimal deterministic...

In this paper a new multifractal stochastic process called Limit of the Integrated Superposition of Diffusion processes with Linear differencial Generator (LISDLG) is presented which realistically characterizes the network traffic multifractality. Several properties of the LISDLG model are presented including long range dependence, cumulants, logarithm of the characteristic function, dilative stability, spectrum and bispectrum. The model captures higher-order statistics by the cumulants. The relevance...

In this paper a new multifractal stochastic process called Limit of the Integrated Superposition of Diffusion processes with Linear differencial Generator (LISDLG) is presented which realistically characterizes the network traffic multifractality. Several properties of the LISDLG model are presented including long range dependence, cumulants, logarithm of the characteristic function, dilative stability, spectrum and bispectrum. The model captures higher-order statistics by the cumulants. The relevance...

Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.

Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.

This paper addresses a sweep coverage problem of multi-robot networks with general topologies. To deal with environmental uncertainties, we present discrete time sweep coverage algorithms to guarantee the complete coverage of the given region by sweeping in parallel with workload partition. Moreover, the error between actual coverage time and the optimal time is estimated with the aid of continuous time results. Finally, numerical simulation is conducted to verify the theoretical results.