Bit Synchronization and Doppler Frequency Removal at Very Low Carrier to Noise Ratio Using a Combination of the Viterbi Algorithm with an Extended Kalman Filter

N.I. Ziedan, J.L. Garrison

Abstract:	A Bit synchronization, navigation message detection, and Doppler frequency removal algorithm is developed to work at very low power signals. The core of the algorithm is based on a dynamic programming technique, the Viterbi Algorithm (VA). VA estimates the most likely sequence of data given a set of 1 msec complex correlations. This operation is done through an optimal recursive search process. Each possible bit edge position is represented by a separate state diagram. A weight function, derived from a log-likelihood function of the received signal value, is assigned to each transition in the trellis graph. The path that generates the minimum cumulative weight of its transitions contains the estimated data sequence, and corresponds to the estimated edge position. For the application to GPS tracking, this algorithm must be able to handle signals with unknown initial phase and frequency biases, as well as random walk disturbance from the local oscillator. An Extended Kalman Filter (EKF) is applied to estimate the frequency and phase history of the GPS ranging signal. For large frequency errors, the EKF is initialized using VA with extended states. Simulation results indicate the ability of the algorithm to produce high bit edge detection rate (EDR), and optimal Bit Error rate (BER), even at very low power signals (15 dB-Hz). The BER is reduced further by utilizing the fact that some sub-frames are repeated every 30 seconds, in a method that results in an increase in the signal to noise ratio.
Published in:	Proceedings of the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS/GNSS 2003) September 9 - 12, 2003 Oregon Convention Center Portland, OR
Pages:	616 - 627
Cite this article:	Ziedan, N.I., Garrison, J.L., "Bit Synchronization and Doppler Frequency Removal at Very Low Carrier to Noise Ratio Using a Combination of the Viterbi Algorithm with an Extended Kalman Filter," Proceedings of the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS/GNSS 2003), Portland, OR, September 2003, pp. 616-627.
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