Random Weighting Estimation Method for Dynamic Navigation Positioning

This paper presents a new random weighting estimation method for dynamic navigation positioning. This method adopts the concept of random weighting estimation to estimate the covariance matrices of system state noises and observation noises for controlling the disturbances of singular observations and the kinematic model errors. It satisfies the practical requirements of the residual vector and innovation vector to sufficiently utilize observation information, thus weakening the disturbing effect of the kinematic model error and observation model error on the state parameter estimation. Theories and algorithms of random weighting estimation are established for estimating the covariance matrices of observation residual vectors and innovation vec- tors. This random weighting estimation method provides an effective solution for improving the positioning accuracy in dynamic navigation. Experimental results show that compared with the Kalman filtering, the extended Kalman filtering and the adaptive windowing filtering, the proposed method can adaptively determine the covariance matrices of observation error and state error, effectively resist the disturbances caused by system error and observation error, and significantly improve the positioning accu- racy for dynamic navigation.

On the rate of complete convergence for weighted sums of NSD random variables and an application

In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator.