A statistical model of traffic flows designed for modeling the motion of vehicles on long highways is proposed. The model simulates the motion of groups of vehicles on the road using the fundamental flow–density diagram on a selected segment of the road with the purpose of calculating the speed of the group; it is assumed that the group size linearly depends on its speed. The proposed approach combines the advantages of macroscopic and microscopic simulation. That is, it allows one to simulate the motion of vehicles in megalopolises to a high accuracy and with low requirements for computational resources. The principles of simulation are described, algorithms for recalculating the model states are presented, and computational experiments confirming the validity and workability of the simulation results for various configurations of the road network are discussed. In the experiments, the fundamental flow diagram is constructed on the basis of sensors of the traffic control center.

A pedestrian navigation system consisting of two foot-mounted strapdown inertial navigation systems (SINS)s is considered. The zero velocity conditions of the foot in the stance phase of a step and a limited distance between the feet are used for SINS corrections. The aim of the work is to study some consistency properties of the extended Kalman filter. It is shown that this consistency depends on a form of the error equations.

Existing online continuous-time parameter estimation laws provide exact (asymptotic/exponential or finite/fixed time) identification of dynamical linear/nonlinear systems parameters only if the external perturbations are vanishing to zero or independent with the regressor of the system. However, in real systems the disturbances are almost always nonvanishing and dependent with the regressor. In the presence of perturbations with such properties the abovementioned identification approaches ensure only boundedness of a parameter estimation error. The main goal of this study is to close this gap and develop a novel online continuous-time parameter estimator that guarantees the exact asymptotic identification of unknown parameters of linear systems in the presence of unknown but bounded perturbations and has relaxed convergence conditions. To achieve the aforementioned goal, it is proposed to augment the deeply investigated dynamic regressor extension and mixing (DREM) procedure with the novel instrumental variables (IV)-based extension scheme with averaging. Such an approach allows one to obtain a set of scalar regression equations with asymptotically vanishing perturbation if the initial disturbance that affects the plant is bounded and independent not with the system regressor, but with the IV. It is rigorously proved that a gradient estimation law designed on the basis of such scalar regressions ensures online unbiased asymptotic identification of the parameters of the perturbed linear systems if some weak independence and excitation assumptions are met. Theoretical results are illustrated and supported with adequate numerical simulations.

The restricted circular three-body problem is studied. All global families of periodic orbits adjacent to the libration points are found. A scenario for the evolution of orbits in the family is given. Chains of global families are highlighted; the chain begins at the triangular libration point, contains global families for the triangular and all collinear libration points, and ends with a family whose orbits are pressed against the main bodies. The evolution of global families in the chain associated with changes in the energy of the system is described. Planar and spatial orbits are studied.

We consider a class of well-known high-order trinomial linear difference equations and analyze the non-asymptotic behavior of their solutions under non-zero initial conditions from the unit box. It is shown that, for certain subsets of coefficients in the stability domain, there always exist initial conditions leading to \emph{peak}, a large deviation of solutions from the equilibrium position, and that these deviations may take arbitrarily large values. Various special cases are studied, numerical examples are presented.