Standard state estimation techniques, ranging from the linear Kalman filter to nonlinear sigma-point or particle filters, assume a perfectly known system model, that is, process and measurement functions and system noise statistics (both the distribution and its parameters). This is a strong assumption which may not hold in practice, reason why several approaches have been proposed for robust filtering. In the context of linear filtering, a solution to cope with a possible system matrices mismatch is to use linear constraints. In this contribution we further explore the extension and use of recent results on linearly constrained Kalman filtering (LCKF) for robust tracking/localization under measurement model mismatch. We first derive the natural extension of the LCKF to nonlinear systems, and its use to mitigate parametric modelling errors in the nonlinear measurement function. A tracking problem where a set of sensors at possibly mismatched (unknown to a certain extent) positions track a moving object from time of arrival measurements is used to support the discussion.

The derivation of tight estimation lower bounds is a key player to design and assess the performance of new estimators. In this contribution, we 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, such CRB is particularized to the delay, Doppler, phase and amplitude estimation with band-limited (narrowband) signals, where transmitter and receiver are in relative uniform radial movement. The latter expression is especially easy to use because it only depends on the signal samples. We provide illustrative results for a representative Global Navigation Satellite System positioning example.

In standard two-step Global Navigation Satellite Systems (GNSS) receiver architectures the precision on the position, velocity and time estimates is driven by the precision on the intermediate parameters, i.e., delays and Dopplers. The estimation of the time-delay is in turn driven by the baseband signal resolution, that is, by the type of broadcasted signals. Among the different GNSS signals available the socalled AltBOC modulated signal, appearing in the Galileo E5 band and the new GNSS meta-signal concept, is the one which may provide the better time-delay precision. In order to meet the constraints of safety-critical applications such as Intelligent Transportation Systems or automated aircraft landing, it is fundamental to known the ultimate code-based precision achievable by standalone GNSS receivers. The main goal of this contribution is to assess the time-delay precision of AltBOC type signals. The analysis is performed by resorting to a new compact closed-form Cramér-Rao bound expression for time-delay estimation which only depends on the signal samples. In addition, the corresponding time-delay maximum likelihood estimate is also provided to assess the minimum signal-to-noise ratio that allows to be in optimal receiver operation.

In previous works, new families of Pseudo-Random Noise (PRN) codes of length 1023 chips were proposed in order to ease the acquisition engine. These studies analyzed several metrics for code design in order to improve the acquisition but no analysis was conducted on the estimation performance, which in turn drives the final position, velocity and timing estimates. The main goal of this contribution is to assess if these new PRN codes designed to improve the acquisition engine lose in achievable time-delay estimation performance with respect to the standard GPS L1 C/A Gold codes. The analysis is performed by resorting to a new compact closed-form Cramér-Rao bound expression for time-delay estimation which only depends on the signal samples. In addition, the corresponding time-delay maximum likelihood estimate is also provided to assess the minimum signal-to-noise ratio that allows to be in optimal receiver operation.

Error correcting schemes are fundamental in the new generation of data navigation signals. Thanks to those, the system has the capability to correct possible data navigation errors, which potentially induces delays in first fix of the receiver. In the GNSS receivers, those error correcting schemes use the Log Likelihood Ratio (LLR) as the input of the decoding algorithm. Until now, the LLR was always computed under the Gaussian assumption and considering perfect Complete State Information (CSI), which does not hold in most of the real scenarios. Then, in this paper we proposed several methods to compute the LLR, considering a set of realitic scenarios and considering that perfect CSI is not available at the receiver. We test the proposed LLRs for several new generation GNSS signals.

New generation of GNSS systems seeks to provide new features in order to create or to improve their currents services. Between those possible features; the increase of the data rate is necessary in order to to provide services such as authentication, precise positioning or reduce the Time-To-First-Fix (TTFF). On the other hand, the data availability in harsh environment suggest the need of error correcting technologies. Then, based on previous works over the Code-Shift Keying (CSK) modulation and in Root Protograph LDPC code to reduce the TTFF, in this paper, it is presented the optimization of Root Protograph LDPC codes for the CSK modulation in a Bit-Interleaved Coded Modulation context and the optimization of Root Protograph LDPC codes for the CSK modulation in Bit-Interleaved Coded Modulation Iterative Decoding context. Both optimization where base on the Protograph EXIT chat algorithm, providing promising results.

In this article, we provide the method to construct two error correcting structures for GNSS systems, which are capable to provide Maximum Distance Separable (MDS), full diversity and rate-compatible properties. Thanks to those properties, the GNSS receiver is capable to reduce the Time-To-First-Fix (TTFF) and to enhance the robustness of the data demodulation under low Carrier to Noise ratio environments, urban environments and pulsed jamming environments. The proposed error correcting structures are then simulated and compared with the GPS L1C subframe 2 error correcting scheme under the precedent transmission environments. Simulations show an outstanding improvement of the error correction capabilities (which reduce the TTFF in harsh environments) mainly caused by the rate-compatible and the full diversity properties. Moreover, thanks to the MDS property a high reduction of the TTFF under good environments is appreciated.

Reducing the Time To First Fix (TTFF) and improving the resilience of future Galileo signals are two important characteristics, especially when considering urban environments. To reach these goals, we studied two new advanced techniques based on the co-design of the message structure and the channel coding scheme. The first technique proposes a reduction of time needed to retrieve the data by reinforcing the parity check matrix structure constraints. The second technique provides an enhancement of the retrieved data error rate in parallel to a reduction of the time needed to retrieve the data thanks to a new co-design requirement based on a family of codes inspired from the rate-compatible root LDPC codes. The results obtained are promising, since the time to retrieve the data (and thus the TTFF) is significantly reduced, while keeping a good level of demodulation performance.

In the recent times, the interest of reducing the time to retrieve the Clock and Ephemerides Data (CED) has provided an open subject of study to design the structure of the message along with the channel coding scheme of the GNSS signals. As a direct consequence, a new methodology to co-design the navigation message and the channel coding scheme structure is proposed in this paper. This new co-design enables both to reduce the time to retrieve the CED and enhanced error correction capabilities under degraded channel conditions. In order to accomplish such as requirements, codes, which provide both maximum distance separable and full diversity properties under the non-ergodic channel assumption, are designed.