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This paper presents alternate forms of a signal tracking algorithm for Global Navigation Satellite System (GNSS) receivers that use a maximum likelihood estimation (MLE) technique. The cost function of the MLE for estimating signal parameters such as code delay, carrier phase, and Doppler frequency is used to derive discriminator functions to create error signals from incoming and reference signals. Assuming a code-free signal and an additive white Gaussian noise, we derive an efficient, practical form of general purpose signal tracking algorithms by using a noniterative MLE approach for arbitrary spreading codes and modulation schemes in accordance with computational efficiency. Two versions of an MLE algorithm are derived. The first is a coherent MLE algorithm derived from the gradient of the log-likelihood cost function for signal parameters. The second is a noncoherent MLE algorithm derived on the basis of complex domain signal that is insensitive to carrier phase error and data bits, thereby eliminating the coupling effect between the carrier phase and Doppler frequency. Analytical test results demonstrate the performance of the proposed algorithms in comparison with those from conventional approaches in terms of pull-in-range, coupling effect, and computational efficiency.