Jong-Hoon Won

Characteristics of Kalman Filters for GNSS Signal Tracking Loop

Characteristics of signal tracking Kalman filter (KF) approaches for a Global Navigation Satellite System (GNSS) receiver are presented. In particular the direct-state KF is designed by using a state vector for signal parameters not for signal parameter errors, so as to directly utilize the discriminator output as a measurement residual. This enables the reuse of the existing signal tracking loop structure by simply adjusting the filter coefficients based on a time-varying optimal Kalman gain. The characteristics of the direct-state KF together with the error-state KF are analyzed by comparing their noise bandwidth and open- and closed-loop transfer functions with those of a traditional method. These KF approaches are mathematically equivalent to the traditional method except for the use of time-varying gains. This fact provides an insight how to tune the designed KFs based on their expected performances.

A Tuning Method Based on Signal-to-Noise Power Ratio for Adaptive PLL and its Relationship with Equivalent Noise Bandwidth

This paper presents a tuning method for an adaptive Kalman filter approach to efficiently track faded global navigation satellite system signals based on empirical knowledge of the signal-to-noise ratio with a special emphasis on equivalent noise bandwidths.

Iterative Maximum Likelihood Estimators for High-Dynamic GNSS Signal Tracking

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.

A Novel Adaptive Digital Phase-Lock-Loop for Modern Digital GNSS Receivers

This paper presents a novel adaptive digital phase-lock-loop for modern digital global navigation satellite system receivers. A Kalman filtering method with an adaptive scheme to adjust the noise statics is employed to change the equivalent noise bandwidth by using empirical knowledge of the signal-to-noise ratio and the signal dynamics in response to the faded signals and the user dynamics.

Effectiveness analysis of vector-tracking-loop in signal fading environment

This paper presents a preliminary result of the effectiveness study on vector-tracking-loop for different signal fading effects for different satellite signals in analytical way. In order for this, we use a simple model with a constant pseudorange measurement covariance for all satellites available in channels. After then, we expand the result to the general case of signal fading where only several satellites are impaired by fading effect. Moreover, we define Geometry-related Range Accuracy Coefficient (GRAC) based on the covariance matrix of pseudorange residuals in vector-tracking. This coefficient can be used in calculating the available signal-to-noise ratio gained by the vector-tracking. The off-diagonal elements of the covariance matrix of pseudorange residuals are interpreted as effective interaction between channels to share the contained information with others. A preliminary numerical simulation was performed to analyze the impact of each element of the covariance matrix to the overall system.

Noniterative Filter-Based Maximum Likelihood Estimators for GNSS Signal Tracking

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.