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Low earth orbit (LEO) satellite navigation signal can be used as an opportunity signal in case of a Global navigation satellite system (GNSS) outage, or as an enhancement means of traditional GNSS positioning algorithms. No matter which service mode is used, signal acquisition is the prerequisite of providing enhanced LEO navigation service. Compared with the medium orbit satellite, the transit time of the LEO satellite is shorter. Thus, it is of great significance to expand the successful acquisition time range of the LEO signal. Previous studies on LEO signal acquisition are based on simulation data. However, signal acquisition research based on real data is very important. In this work, the signal characteristics of LEO satellite: power space density in free space and the Doppler shift of LEO satellite are individually studied. The unified symbol definitions of several integration algorithms based on the parallel search signal acquisition algorithm are given. To verify these algorithms for LEO signal acquisition, a software-defined receiver (SDR) is developed. The performance of those integration algorithms on expanding the successful acquisition time range is verified by the real data collected from the Luojia-1A satellite. The experimental results show that the integration strategy can expand the successful acquisition time range, and it will not expand indefinitely with the integration duration.

The use of Bayesian information criterion (BIC) in the model selection procedure is under the assumption that the observations are independent and identically distributed (i.i.d.). However, in practice, we do not always have i.i.d. samples. For example, clustered observations tend to be more similar within the same group, and longitudinal data is collected by measuring the same subject repeatedly. In these scenarios, the assumption in BIC is not satisfied. The concept of effective sample size is brought up and improved BIC is defined by replacing the sample size in the original BIC expression with the effective sample size, which will give us a better theoretical foundation in the circumstance that mixed-effects models involve. Numerical experiment results are also given by comparing the performance of our new BIC with other widely used BICs.

With the rapid development of China's BeiDou Navigation Satellite System(BDS), the application of real-time precise point positioning (RTPPP) based on BDS has become an active research area in the field of Global Navigation Satellite System (GNSS). BDS has provided the service of broadcasting RTPPP information. It indicates that BDS has become the second satellite system that provides RTPPP services, following Galileo among the GNSS, but work based on this direction has yet to be explored. Therefore, this paper evaluates the performance of precise point positioning (PPP) service using a software-defined receiver (SDR). An experiment was carried out tu verify the feasibility of the SDR. The PPP-B2b signal was processed to obtain PPP service information, including orbit corrections, clock corrections, and differential code bias corrections. The time-varying attributes of these corrections of BDS and GPS are evaluated, and the integrity and stability of the PPP service were analyzed. The results show the PPP-B2b signal can stably provide PPP services for staellites in the Asia-Pacific region, including centimeter to decimeter-level orbit corrections and meter-level clock correction for GPS satellites. Finally, detection tip for bitream availability in SDR is proposed. Some content which is not defined in the official document, such as the PPP-B2b frame arrangement, various correction update cycles and the progress of PPP service are discussed.

In this paper, we investigate the reasons that the Bayesian estimator of the tail probability is always higher than the frequentist estimator. Sufficient conditions for this phenomenon are established both by using Jensen's Inequality and by looking at Taylor series approximations, both of which point to the convexity of the distribution function.