Optimal Hatch Filter With a Flexible Smoothing Window Width

Byungwoon Park and Changdon Kee

Abstract:	Hatch filter is the code smoothing technique using integrated carrier phase observations. It is based on the simple concept that the change of pseudorange in time has similar pattern to that of carrier range. It is such an easy technique that even a non-expert can use this code smoothing technique for reducing receiver noise on the pseudoranges. For DGPS user the multi-path and noise may be the largest contributions to the error budget, and in this case code smoothing does a great job. Furthermore it is useful to single-frequency receiver, which is far cheaper than dual-frequency receiver. In principle the larger a smoothing window width is used in the filtering process, the more precise the smoothed pseudorange should become. It is, however, the problem that the ionospheric divergence effect between code and carrier increases with smoothing window width. Many experts in North America say that 100-epoch-window is acceptable for the smoothing width of Hatch filter, but it is just an empirical value, not an optimal one. In addition, this value is not always true to the other countries. DGPS users in the region where the ionospheric variation is small can use more epochs in the smoothing process to reduce the noise than others. Moreover, it is not reasonable that the constant is helpful to all the satellites for all day long. Small averaging constant should be applied to the measurement of the low-lying satellite, because its ionospheric divergence may be enlarged by the Hatch filter with a large smoothing window. On the other hand, we feel safe to broaden the window size for the satellite of high elevation angle. This paper suggests a new algorithm on the optimal Hatch filter whose smoothing window width varies flexibly depending on the regional, diurnal, and seasonal ionospheric variation and satellite elevation angle. Using the well-known ionospheric model and receiver noise statistics function of the satellite elevation angle, this algorithm can solve the mathematically optimal averaging constant for each satellite at every epoch. Many researchers on GPS throughout the world have had hard times in solving their own smoothing constants by many experiments and experiences. Now we can find this magic number by a simple equation. Moreover we can apply this algorithm to the each measurement so that we construct DGPS system using the optimal Hatch filter. From the 24 hour data process result and real time experiment, we found that the position accuracy of the optimal Hatch filter is more accurate and robuster than that of traditional Hatch filter. The optimal Hatch filter algorithm and its results are expected to provide a new solution of single frequency DGPS receiver and a thorough understanding of the relationship between the position error and the averaging constant. Besides, any DGPS user who applies this algorithm to the low-cost single-frequency receiver can get more accurate and robuster position result than the classical Hatch filter.
Published in:	Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005) September 13 - 16, 2005 Long Beach Convention Center Long Beach, CA
Pages:	592 - 602
Cite this article:	Park, Byungwoon, Kee, Changdon, "Optimal Hatch Filter With a Flexible Smoothing Window Width," Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005), Long Beach, CA, September 2005, pp. 592-602.
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