Iterative Maximum Likelihood Estimators for High-Dynamic GNSS Signal Tracking

Abstract

This paper presents novel signal-tracking algorithms for global navigation satellite system (GNSS) receivers using a maximum likelihood estimation (MLE) technique to carry out robust signal tracking under severe signal environments, such as high dynamics for maneuvering users. The cost function of the MLE of signal parameters such as code delay, carrier phase, and Doppler frequency is used to derive a discriminator function and thus generate error signals based on incoming and reference signals. Two distinct forms of algorithms are derived by means of mathematical programming using an iterative approach, which is based on the log-likelihood MLE cost function that assumes various signal parameters as unknown constants over an observation interval. First, the Levenberg-Marquardt method is employed using gradient and Hessian matrices. Second, a conventional nonlinear least-square estimation method is applied to determine the MLE cost function, assuming additive white Gaussian noise. An efficient and practical approach to Doppler frequency tracking is also derived based on the assumption of a code-free signal (i.e., a signal from which the code has been wipe off). The use of MLE for carrier tracking makes it possible to generalize the MLE equation for arbitrary codes and modulation schemes. This is ideally suited to various GNSS signals that have the same tracking module structure. Finally, performance of the receivers, in terms of robustness under dynamic stress, computational efficiency, accuracy, computational burden, and response speed, is assessed using analytical and/or numerical techniques.