An Improved Fast Estimation of Satellite Phase Fractional Cycle Biases

Satellite phase fractional cycle biases (FCBs) are crucial to precise point positioning with ambiguity resolution (PPP–AR), and they can improve the accuracy and reliability of a solution. Traditional methods need multiple iterations and need to keep the same reference when estimating satellite phase fractional cycle biases. In this paper, we propose an improved fast estimation of FCB, which does not need any iterations and can select any reference when estimating FCB. We compare the suitability and precision of a traditional and a proposed method by BDS-3 experiments. The results of the FCB experiments show that the calculated time of the proposed method is less than the traditional method and that computation efficiency is increased by 34.71%. These two methods have a similar rate of fixed epochs and ambiguities in the static and dynamic models. However, the time to first fix (TTFF) of the proposed method decreased by 19.69% and 28.83% for the static and dynamic models, respectively. The results show that the proposed method has a better convergence time in PPP–AR.

A fast estimation of the frequency property of the microelectromechanical system oscillator

A nonlinear oscillator with zero initial conditions is considered, which makes some effective methods, for example, the variational iteration method and the homotopy perturbation method, invalid. To solve the bottleneck, this paper suggests a simple transform to convert the problem into a traditional case so that He’s frequency formulation can be effectively used to solve its approximate solution. An microelectromechanical system (MEMS) oscillator is used as example to show the solution process, and a good result is obtained.

Flexible and fast estimation of quantile treatment effects: The rqr and rqrplot commands

Using quantile regression models to estimate quantile treatment effects is becoming increasingly popular. This paper introduces the rqr command that can be used to estimate residualized quantile regression (RQR) coefficients and the rqrplot postestimation command that can be used to effortless plot the coefficients. The main advantages of the rqr command compared to other Stata commands that estimate (unconditional) quantile treatment effects are that it can include high-dimensional fixed effects and that it is considerably faster than the other commands.