Square-root divided difference Rauch-Tung-Striebel smoother

A square-root version of the divided difference Rauch-Tung-Striebel (RTS) smoother is proposed in this paper. The square-root variant essentially propagates the square roots of the covariance matrices and can consistently improve the numerical stability because all the resulting covariance matrices are guaranteed to stay positive semi-definite. Furthermore, the square-root form ensures reliable implementation in an embedded system with fixed or limited precision although it is algebraically equivalent to the standard form. The new smoothing algorithm is tested in a challenging two-dimensional maneuvering target tracking problem with unknown and time-varying turn rate, and its performance is compared with that of other de-facto standard filters and smoothers. The simulation results indicate that the proposed RTS smoother markedly outperforms the associated filters and gives slightly smaller error than an unscented-based RTS smoother.

Intent Inference Based Trajectory Prediction and Smooth for UAS in Low-Altitude Airspace with Geofence

In order to meet the higher accuracy requirement of trajectory prediction for Unmanned Aircraft System(UAS)in Unmanned Aircraft System Traffic Management(UTM),an Intent Based Trajectory Prediction and Smooth Based on Constrained State-dependent-transition Hybrid Estimation(CSDTHE-IBTPS)algorithm is proposed.Firstly,an intent inference method of UAS is constructed based on the information of ADS-B and geofence system.Moreover,a geofence layering algorithm is proposed.Secondly,the Flight Mode Change Points(FMCP)are used to define the relevant mode transition parameters and design the guard conditions,so as to generate the mode transition probability matrix and establish the continuous state-dependent-transition model.After that,the constrained Kalman filter(CKF)is applied to improve State-dependent-transition Hybrid Estimation(SDTHE)algorithm by applying equality constraint to the velocity of UAS in the straight phase and turning phase,respectively,and thus the constrained state-dependent-transition hybrid estimation(CSDTHE)algorithm is constructed.Finally,the results of intent inference and hybrid estimation are used to make trajectory prediction.Furthermore,each flight segment of trajectory is smoothed respectively by Rauch-Tung-Striebel(RTS)backward smooth method using the proposed CSDTHE-RTS algorithm,so as to obtain more accurate trajectory prediction results.The simulation shows that the proposed algorithm can reduce the errors of trajectory prediction and the time delay of intent inference.

Non-Linear Approximation of Functions with Mixed Smoothness by Sets of Finite Pseudo-Dimension

In this paper, the non-linear approximation on the class of multivariate functions with bounded mixed derivatives is investigated, and the asymptotic degree of the non-linear width on this class is determined.