The derivation of tight estimation lower bounds is a key tool to design and assess the performance of new estimators. In this contribution, first, the authors derive a new compact Cramér-Rao bound (CRB) for the conditional signal model, where the deterministic parameter's vector includes a real positive amplitude and the signal phase. Then, the resulting CRB is particularised to the delay, Doppler, phase, and amplitude estimation for band-limited narrowband signals, which are found in a plethora of applications, making such CRB a key tool of broad interest. This new CRB expression is particularly easy to evaluate because it only depends on the signal samples, then being straightforward to evaluate independently of the particular baseband signal considered. They exploit this CRB to properly characterise the achievable performance of satellite-based navigation systems and the so-called real-time kinematics (RTK) solution. To the best of the authors' knowledge, this is the first time these techniques are theoretically characterised from the baseband delay/phase estimation processing to position computation, in terms of the CRB and maximum-likelihood estimation.

This letter deals with carrier synchronization in Global Navigation Satellite Systems. The main goals are to design robust methods and to obtain accurate phase estimates under ionospheric scintillation conditions, being of paramount importance in safety critical applications and advanced receivers. Within this framework, the estimation versus mitigation paradigm is discussed together with a new adaptive Kalman filter-based carrier phase synchronization architecture that copes with signals corrupted by ionospheric scintillation. A key point is to model the time-varying correlated scintillation phase as an AR(p) process, which can be embedded into the filter formulation, avoiding possible loss of lock due to scintillation. Simulation results are provided to show the enhanced robustness and improved accuracy with respect to state-of-the-art techniques.

Bayesian filtering is a statistical approach that naturally appears in many signal processing problems. Ranging from Kalman filter to particle filters, there is a plethora of alternatives depending on model assumptions. With the exception of very few tractable cases, one has to resort to suboptimal methods due to the inability to analytically compute the Bayesian recursion in general dynamical systems. This is why it has attracted the attention of many researchers in order to develop efficient algorithms to implement it. We focus our interest into a recently developed algorithm known as the Quadrature Kalman filter (QKF). Under the Gaussian assumption, the QKF can tackle arbitrary nonlinearities by resorting to the Gauss-Hermite quadrature rules. However, its complexity increases exponentially with the state-space dimension. In this paper we study a complexity reduction technique for the QKF based on the partitioning of the state-space, referred to as the Multiple QKF. We prove that partitioning schemes can effectively be used to reduce the curse of dimensionality in the QKF. Simulation results are also provided to show that a nearly-optimal performance can be attained, while drastically reducing the computational complexity with respect to state-of-the-art algorithms that are able to deal with such nonlinear filtering problems.

Carrier synchronization is a fundamental stage in the receiver side of any communication or positioning system. Traditional carrier phase tracking techniques are based on well-known phase-locked loop (PLL) closed-loop architectures, which are still the methods of choice in modern receivers. Those techniques are well understood, easy to tune and perform well under benign propagation conditions, but their applicability is seriously compromised in harsh propagation environments where the signal may be affected by high dynamics, shadowing, strong fadings, multipath effects or ionospheric scintillation.From an optimal filtering standpoint, the Kalman filter (KF) is clearly a powerful alternative, but the synchronization community seems still reluctant to exploit all the potential it has to offer. The purpose of this paper is twofold: i) to review the basics and state-of-the-art on both PLL and KF-based tracking techniques, and ii) to present and justify the reasoning behind the systematic use of KF-based tracking approaches instead of the well-established PLL-based architectures from both theoretical and practical points of view. To support the discussion, two specific scenarios of interest to the aerospace community are numerically evaluated: robust carrier tracking of Global Navigation Satellite Systems' signals and synchronization in a deep space communications system.

Ionospheric scintillation is the name given to the disturbance caused by electron density irregularities along the propagation path of electromagnetic waves through the iono sphere.