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.

The exponential increase in the number of satellites along with the hazards of the space environment they encounter endangers the sustainability of low earth orbit (LEO). The consequences of events such as collisions, fragmentations and fatal failures are then becoming more than ever a threat to any kind of space activity. Therefore, the space situational awareness is of utter importance in all its aspects, i.e., assessing and predicting the risks from space weather and SST (Space Surveillance and Tracking), in addition to implementing mitigation measures. In this context, this paper covers the benefits of in-orbit inspection combined with the aggregation and processing of existing space data, proposed by the French company SpaceAble for low earth orbit sustainability. Collision risk awareness for a LEO constellation is raised in this paper through the analysis of the conjunction risks of the Starlink constellation. An inspection plan is also derived in terms of the number of inspections for different scenarios, and with respect to different LEO altitudes.

Global Navigation Satellite Systems (GNSS) are a key player in a plethora of applications, ranging from navigation and timing, to Earth observation or space weather characterization. For navigation purposes, interference scenarios are among the most challenging operation conditions, which clearly impact the maximum likelihood estimates (MLE) of the signal synchronization parameters. While several interference mitigation techniques exist, a theoretical analysis on the GNSS MLE performance degradation under interference, being fundamental for system/receiver design, is a missing tool. The main goal of this contribution is to provide such analysis, by deriving closed-form expressions of the estimation bias, for a generic GNSS signal corrupted by an interference. The proposed bias are validated for a tone interference and a linear frequency modulation chirp interference.

We consider the transmission of a continuous phase modulated (CPM) signal through a Gaussian channel affected by Doppler shifts. We propose a receiver robust to the Doppler shifts derived from a non-coherent detection criterion. We compare its performance to another non-coherent receiver based on a linear approximation of the CPM signal (Laurent decomposition) to which we add a Doppler compensation. Simulation results show that the first algorithm is robust to low-moderate Doppler shifts, while the second is robust to any one. We finally compare these two algorithms to delay-optimized differential detectors which do not require any Doppler shift estimation. We also provide complexity estimations to guide the possible complexity-performance trade-offs.