Pseudo-Linear Mechanics with Pseudo-Translation Symmetry

In this paper, we will consider the simplest pseudo-addition where pseudo-multiplication and pseudo-division are the same as the ordinary ones and distributivity hold. Using this we consider a special type of the non-uniform discrete times with the pseudo-translation symmetry. Besides, we demand that the displacement should be invariant under the pseudo-translation. From these, we obtain the new definition of the instantaneous velocity which is pseudo-translation symmetry in both time and position and formulate the mechanics which are pseudo-linear and pseudo-translation invariant.

Pseudo-linear inertial navigation algorithm

A new method is illustrated for processing the output of a set of triad orthogonal rate gyros and accelerometers to reconstruct vehicle navigation parameters(attitude, velocity, and position). The paper introduces two vectors with dimensions 4×1 as velocity and position quaternions.The navigation equations for strapdown systems are nonlinear but after using these parameters, the navigation equations are converted into a pseudo-linear system. The new set of navigation equations has an analytical solution and the state transition matrix is used to solve the linear timevarying differential equations through time series. The navigation parameters are updated using the new formulation for strapdown navigation equations. Finally, the quaternions of velocity and position are converted into the original position and velocity vectors. The combination of the coning motion and a translational oscillatory trajectory is used to evaluate the accuracy of the proposed algorithm. The simulations show significant improvement in the accuracy of the inertial navigation system, which is achieved through the mentioned algorithm.

Comparison of different pseudo-linear estimators for vision-based target motion estimation

Vision-based target motion estimation based Kalman filtering or least-squares estimators is an important problem in many tasks such as vision-based swarming or vision-based target pursuit.In this paper,we focus on a problem that is very specific yet we believe important.That is,from the vision measurements,we can formulate various measurements.Which and how the measurements should be used?These problems are very fundamental,but we notice that practitioners usually do not pay special attention to them and often make mistakes.Motivated by this,we formulate three pseudo-linear measurements based on the bearing and angle measurements,which are standard vision measurements that can be obtained.Different estimators based on Kalman filtering and least-squares estimation are established and compared based on numerical experiments.It is revealed that correctly analyzing the covariance noises is critical for the Kalman filtering-based estimators.When the variance of the original measurement noise is unknown,the pseudo-linear least-squares estimator that has the smallest magnitude of the transformed noise can be a good choice.

Capturability of Pseudo Differential Games of Pursuit

This paper discusses the capturability with fixed time of a pseudo-linear differential game of pursuit. The pursuit set in which the pursuit will end once the initial state lies in this set is given by the method of integration of multi-valued function. The results obtained here solve an open problem of Pontrjagin’s on the linear differential game of pursuit. Meanwhile, the requirement of the convexity of the control set and other related Pontrjagin’s conditions are removed.