This paper introduces a new statistical model for clock phases assuming a multivariate Gaussian distribution for the clock phase deviations from a common time scale. This model allows us to derive a maximum likelihood estimator for the clock phases, which is consistent with the current methods of computing a common time scale for a collection of clocks. Detailing a statistical model of the clock phases, which assumes a Gaussian distribution allows us to find the MLE for each clock’s phase deviation from a common time scale. For verification, the MLE for the clock phases is shown to be consistent with the result of the existing basic time scale equation. The statistical distribution of the frequency states resulting from this statistical model is Gaussian over a window of past time instants. This property can be used to design a new time scale based on the maximum likelihood estimator of frequency and frequency variances that are alternatives to the exponential filters designed for AT1. With the appropriate number of past frequency samples, this MLE has identical performance to the optimal AT1 algorithm in a nominal context. The statistical distribution of the frequency when the clock suffers a phase jump anomaly is then identified as a Student’s t-distribution. The Student’s t-distribution models the statistics of datasets contaminated by outliers, leading to the derivation of a different MLE that is robust to those outliers. The time scale using the robust MLE provides estimates of each clock’s frequency and frequency variance that are unaffected by phase jump anomalies and improves the long-term frequency stability when each clock in the ensemble experiences phase jump anomalies within some window of time.

The conventional non-coherent differential detection of continuous phase modulations (CPM) is quite robust to channel impairments such as phase and Doppler shifts. Its implementation is on top of that simple. It consists in multiplying the received baseband signal by its conjugate version delayed by one symbol period. However it suffers from a signal-to-noise ratio gap compared to the optimum coherent detection. In this paper, we improve the error rate performance of the conventional differential detection by using a delay higher than one symbol period. We derive the trellis description as well as the branch and cumulative metrics that take into account a delay of K symbol periods. We then determine an optimized delay K opt based on the minimum Euclidean distance between two differential signals for some popular CPM formats. The optimized values are confirmed by error rate simulations.

Multipath is one of the most challenging propagation conditions affecting Global Navigation Satellite Systems (GNSS), which must be mitigated in order to obtain reliable navigation information. In any case, the random multipath nature makes it difficult to anticipate and overcome. Therefore, for legacy GNSS signal performance assessment, modern GNSS signal design and future GNSS-based applications, robustness to multipath is a fundamental criterion. Different multipath metrics exist in the literature, such as the multipath error envelope, usually leading to analyses only valid for a dedicated receiver/signal combination and only providing information on the bias. This paper presents a general criterion to characterize the multipath robustness of a generic band-limited signal (e.g., GNSS or radar), considering the joint delay-Doppler and phase estimation. This criterion is based on the Cramr-Rao bound, which makes it universal, regardless the receiver architecture and the signal under analysis, and provides information on the actual achievable performance in terms of estimated time-delay (i.e., pseudo-range) and Doppler frequency variances.

This is a supplementary material associated with the article "Band-limited impulse response estimation performance" that can be found, in the online version, at doi: https://doi.org/10.1016/j.sigpro.2023.108998.

The new generation of satellite instruments enables the acquisition of images with evergrowing spectral and spatial resolutions. The counterpart is that an increasing amount of data must be processed and transmitted to the ground. Onboard image compression becomes thus crucial to preserve transmission channel bandwidth and reduce data transmission time. Recently, convolutional neural networks have shown outstanding results for lossy image compression compared to traditional compression schemes, however, at the cost of a high computational complexity. Autoencoder architectures are trained end-to-end, taking beneĄt from extensive datasets and computing power available on mighty clusters. Consequently, the potential contributions and feasibility of deep learning techniques for onboard compression are arousing great interest. In this context, nevertheless, computational resources are subject to severe limitations: a trade-off between compression performance and complexity must be established. In this thesis, the main objective is to adapt learned compression frameworks to onboard compression, simplifying them and training them with speciĄc images. In a Ąrst step, we propose simplifying these architectures as much as possible while preserving high performance, particularly maintaining the adaptability to handle diverse input images. In a second step, we investigate how such architectures can further be improved by aggregating other functionalities such as denoising. Thus, we intend to incorporate denoising, either considering the above mentioned compression architectures for joint compression and denoising concurrently or as a sequential approach. The sequential approach consists in using, on the ground, a different architecture to denoise the images issued from the preceding learned compression framework. By running experiments on simulated but realistic satellite images, we show that the proposed simpliĄcations to the learned compression framework result in considerably lower complexity while maintaining high performance. Concerning learned compression and denoising, the joint and sequential approaches are beneĄcial and complementary, allowing to surpass the CNES imaging system performance, and thus opening the path towards operational compression and denoising pipelines for satellite images.

The new generation of satellite instruments enables the acquisition of images with evergrowing spectral and spatial resolutions. The counterpart is that an increasing amount of data must be processed and transmitted to the ground. Onboard image compression becomes thus crucial to preserve transmission channel bandwidth and reduce data transmission time. Recently, convolutional neural networks have shown outstanding results for lossy image compression compared to traditional compression schemes, however, at the cost of a high computational complexity. Autoencoder architectures are trained end-to-end, taking beneĄt from extensive datasets and computing power available on mighty clusters. Consequently, the potential contributions and feasibility of deep learning techniques for onboard compression are arousing great interest. In this context, nevertheless, computational resources are subject to severe limitations: a trade-off between compression performance and complexity must be established. In this thesis, the main objective is to adapt learned compression frameworks to onboard compression, simplifying them and training them with speciĄc images. In a Ąrst step, we propose simplifying these architectures as much as possible while preserving high performance, particularly maintaining the adaptability to handle diverse input images. In a second step, we investigate how such architectures can further be improved by aggregating other functionalities such as denoising. Thus, we intend to incorporate denoising, either considering the above mentioned compression architectures for joint compression and denoising concurrently or as a sequential approach. The sequential approach consists in using, on the ground, a different architecture to denoise the images issued from the preceding learned compression framework. By running experiments on simulated but realistic satellite images, we show that the proposed simpliĄcations to the learned compression framework result in considerably lower complexity while maintaining high performance. Concerning learned compression and denoising, the joint and sequential approaches are beneĄcial and complementary, allowing to surpass the CNES imaging system performance, and thus opening the path towards operational compression and denoising pipelines for satellite images.

Multifractal analysis provides a global description for the spatial fluctuations of the strengths of the pointwise regularity of image amplitudes. A global image characterization leads to robust estimation, but is blind to and corrupted by small regions in the image whose multifractality differs from that of the rest of the image. Prior detection of such zones with anomalous multifractality is thus crucial for relevant analysis, and their delineation of central interest in applications, yet has never been achieved so far. The goal of this work is to devise and study such a multifractal anomaly detection scheme. Our approach combines three original key ingredients: i) a recently proposed generic model for the statistics of the multiresolution coefficients used in multifractal estimation (wavelet leaders), ii) an original surrogate data generation procedure for simulating a hypothesized global multifractality and iii) a combination of multiple hypothesis tests to achieve pixel-wise detection. Numerical simulations using synthetic multifractal images show that our procedure is operational and leads to good multifractal anomaly detection results for a range of target sizes and parameter values of practical relevance.