Optimum Digital Filters for GNSS Tracking Loops

Pejman L. Kazemi

Abstract:	In a traditional loop filter the product between loop noise bandwidth and integration time (BLT) should remain well below unity in order to ensure the stability of the loop. This constraint, required for having a stable loop, significantly limits the maximum integration time and/or noise bandwidth. The current methodology in designing digital tracking loop filters mostly relies on transforming a continuoustime system into a discrete-time one. This transform, from the S-domain to Z-domain, is done by means of Laplace to Z-domain mappings, such as the bilinear transform. In these cases, the digital loops will be equivalent to its analog counterpart only if BLT is close to zero (Stephens & Thomas 1995, Lindsey & Chie 1981). As the product BLT increases, the effective loop noise bandwidth and closed loop pole locations deviate from the desired ones and eventually the loop becomes unstable. By designing filters with the controlled-root method the deficiencies of the continuous-update approximation in large BLT applications are avoided (Stephens & Thomas 1995). However, by using this method for the conventional NCOs (denoted as rate-only feedback NCOs in Stephens & Thomas 1995) which are mostly used in software receivers, the BLT is still limited to less than 0.4 for third order loops. In this paper, by considering the effect of integration and dump in the linear model of the digital phase-locked loop and considering rate-only feedback NCOs, loop filters are designed totally in the Z-domain by utilizing a method that minimizes the loop phase jitter. It is shown that, by using these new filters, a significant improvement for high BLT can be achieved, allowing one to operate in ranges where previous methods can not operate. As a result, stable loops with higher bandwidths and/or longer integration time can be easily designed. The deficiencies of previous methods are analyzed and the loop instability for large BLT is shown by employing live GPS signals. New loop filters are implemented in a GPS software receiver and their performance for large BLT evaluated by using live GPS signals for static tests and hardware simulated signals for dynamic tests.
Published in:	Proceedings of the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2008) September 16 - 19, 2008 Savannah International Convention Center Savannah, GA
Pages:	2304 - 2313
Cite this article:	Kazemi, Pejman L., "Optimum Digital Filters for GNSS Tracking Loops," Proceedings of the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2008), Savannah, GA, September 2008, pp. 2304-2313.
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