LS-VCE Applied to Stochastic Modeling of GNSS Observation Noise and Process Noise

Stochastic models play a crucial role in global navigation satellite systems (GNSS) data processing. Many studies contribute to the stochastic modeling of GNSS observation noise, whereas few studies focus on the stochastic modeling of process noise. This paper proposes a method that is able to jointly estimate the variances of observation noise and process noise. The method is flexible since it is based on the least-squares variance component estimation (LS-VCE), enabling users to estimate the variance components that they are specifically interested in. We apply the proposed method to estimate the variances for the dual-frequency GNSS observation noise and for the process noise of the receiver code bias (RCB). We also investigate the impact of the stochastic model upon parameter estimation, ambiguity resolution, and positioning. The results show that the precision of GNSS observations differs in systems and frequencies. Among the dual-frequency GPS, Galileo, and BDS code observations, the precision of the BDS B3 observations is highest (better than 0.2 m). The precision of the BDS phase observations is better than two millimeters, which is also higher than that of the GPS and Galileo observations. For all three systems, the RCB process noise ranges from 0.5 millimeters to 1 millimeter, with a data sampling rate of 30 s. An improper stochastic model of the observation noise results in an unreliable ambiguity dilution of precision (ADOP) and position dilution of precision (PDOP), thus adversely affecting the assessment of the ambiguity resolution and positioning performance. An inappropriate stochastic model of RCB process noise disturbs the estimation of the receiver clock and the ionosphere delays and is thus harmful for timing and ionosphere retrieval applications.

Stochastic Modeling in Stock Market Trend Prediction

n Modern centuries a lot of predicting techniques take been proposed and applied for the stock market movement prediction. In this paper, the pattern examinations of the financial exchange forecast are introduced by utilizing Hidden Markov Model with the one day distinction in close incentive for a particular period. The likelihood esteems π gives the pattern level of the stock costs which is determined for all the notice arrangement and stowed away successions. It supports for decision makers to make decisions in case of indecision on the basis of the proportion of probability values found from the steady state probability distribution.

Time Series Analysis of Evaporation Duct Height over South China Sea: A Stochastic Modeling Approach

The evaporation duct could significantly affect the work status of maritime microwave communication systems in the South China Sea. Therefore, the exact forecasting of the evaporation duct is vital for the normal operation of the systems. This study presents a stochastic modeling approach to predict the future trends of the evaporation duct over the South China Sea. The autoregressive integrated moving average (ARIMA) model has been used for modeling the monthly evaporation duct height estimated from the Climate Forecast System Reanalysis dataset released by the National Centers for Environment Prediction. The long-term evaporation duct height data were collected for a period of 10 years from 2008 to 2017. The analysis of correlation function reveals the existence of seasonality in the time series. Therefore, a seasonal ARIMA model with the form as ARIMA (0,0,1) × (0,1,2)12 is proposed by fitting the monthly data optimally. The fitted model is further used to forecast the evaporation duct variation for the year 2018 at 95% level of confidence, and high-accuracy results are obtained. Our study demonstrates the feasibility of the proposed stochastic modeling technique to predict the future variations of the evaporation duct over South China Sea.