Performance Analysis of Pseudolite Tropospheric Delay Models Using Meteorological Radiosonde with Flight Test Results

H. So, K. Lee, Y. Park, J. Park, K. Song

Abstract:	Pseudolite is a pseudo-GNSS satellite transmitting GNSS-like signal for navigation. Because it could be installed anywhere, it has been studied for increasing navigation availability and alternatives for GNSS. There have been many studies and most of them were focused on relatively short range applications such as indoor pseudolite, several hundred meters range application in urban canyon and aircraft landing. Recently, however, the coverage is becoming wider, several tens of kilometers for being served as a navigation reference system during the whole aviation procedures and for being used as an alternative navigation system to cope with jamming situation. When the pseudolite is used in short range, tropospheric delay could be negligible, because the lower troposphere causes signal delay about 300~400 mm/km in general. However, as the coverage is broadening, the tropospheric delay is becoming a major error source. Locata Corp. has shown the importance of tropospheric delay estimation in the recent article about USAF's new reference system, Locatalite. Because pseudolite signal passes through the lower troposphere and experiences spatial atmospheric irregularities, the tropospheric delay estimation is very difficult. And the conventional tropospheric models used for GNSS couldn't be applicable. There have been several studies for pseudolite tropospheric delay estimation. From the paper of J.J. Wang in UNSW, the estimation method could be categorized into three schemes, integration method, single difference method and length ratio method. For standalone navigation application, RTCA model, Hopfield model-based schemes and single difference methods of mapping functions are widely known. However, there hasn't been enough studies for test and evaluation of these schemes. We've done performance analysis and comparison of existing pseudolite tropospheric delay models through flight tests and meteorological observation for wide-range aviation application. And then, from the quantitative analysis results, we proposed Kalman filter-based tropospheric delay error compensation method. Contents of this paper are as in the following. First of all, we proposed tropospheric delay estimation method using meteorological data collected from radiosonde. The existing integration method, RTCA and Hopfield model, uses empirical refractivity model as a function of the height. We investigated the error of the empirical model from the real meteorological data. We did linear interpolation between two consecutive weather data sample to get a vertical refractivity profile and then performed numerical integration through the signal path. It is used as a tropospheric truth model. And for 100 days radiosonde meteorological observation data of 1 year, we did quantitative error analysis of existing pseudolite tropospheric delay models. The existing models are function of slant distance, height difference and elevation angle between the user receiver and pseudolite. So, several cases of signal path scenario were adopted to account for each function argument. From this error analysis, error models of each existing delay models were acquired. Second, we proposed Kalman filter-based tropospheric delay model. Because meteorological radiosonde observation couldn't be used for real-time application, we used Kalman filter to compensate the existing models. Establishing the truth model is the most important contribution of this work in order to model uncancelled residual tropospheric delay after applying the existing model and to implement Kalman filter. Finally, we've done flight tests using ground-installed pseudolites. The tests were performed to evaluate the effects of each parameters of the existing models and verify the performance of the Kalman filter model in the range and navigation domain. For the results, we found out that the integration methods are appropriate for relatively short distance application but show the abnormal performance for large height difference situation. And the difference-based method using Saastamoinen model is good for long distance and high altitude application. For the navigation performance analysis, standalone code-based positioning has been done, using about 10 pseudolites that are not symmetric constellation. Navigation results show that the residual tropospheric delay error causes several meters horizontal positioning error when HDOP is below 2. And the Kalman filter approach shows the effect of tropospheric delay error to the horizontal navigation performance can be reduced to below 1 meter.
Published in:	Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013) September 16 - 20, 2013 Nashville Convention Center, Nashville, Tennessee Nashville, TN
Pages:	1802 - 1809
Cite this article:	So, H., Lee, K., Park, Y., Park, J., Song, K., "Performance Analysis of Pseudolite Tropospheric Delay Models Using Meteorological Radiosonde with Flight Test Results," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 1802-1809.
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