This article focuses on the study of time-delay and Doppler estimation under high dynamic non-Gaussian scenarios. We aim at analysing the Mean Squared Error (MSE) performance of a misspecified receiver architecture which deliberately simplifies the signal model by neglecting the acceleration parameter and assumes the noise process as complex normal distributed. Specifically, we derive the pseudo-true parameters by minimazing the Kullback-Leibler (KL) divergence between the true and assumed models and the related Misspecified Cramér-Rae Bound (MCRB) will be provided in closed form. Theoretical derivations are validated via Monte Carlo simulations showing the asymptotic efficiency of the Misspecified Maximum Likelihood Estimator (MMLE). One remarkable outcome of this study is that the lack of knowledge of the true statistical noise model does not lead to asymptotic performance degradation in the estimation of the parameters of interest.

This paper studies a robust algorithm allowing the estimation of the center and the radius of a hypersphere in the presence of outliers. To that extend, the Student-t distribution is assigned to the noise samples to mitigate the impact of the outliers. A von Mises-Fisher prior distribution is also assigned to latent variables in order to exploit the fact that the observed samples are located in a part of the hypersphere. A robust Bayesian algorithm based on a Gibbs sampler is then proposed to solve the hypersphere fitting problem. This algorithm generates samples asymptotically distributed according to the joint distribution of the unknown parameters of the hypersphere (radius and center), as well as the other model parameters such as the noise variance. Simulations conducted on synthetic data with controlled ground truth allow the performance of this algorithm to be appreciated.

This paper studies an auxiliary particle filter with variational inference for jointly estimating the system mode, the state and the measurement noise covariance matrix of jump Markov systems. The joint posterior distribution of the system mode, the state and the noise covariance matrix is marginalized out with respect to the system mode. The marginalized posterior distribution of the mode is then approximated by using an auxiliary particle filter, and the state and noise covariance matrix conditionally on each particle of the mode variable are updated using variational Bayesian inference. A simulation study is conducted to compare the proposed method with state-of-the-art approaches for a target tracking scenario.

Since time-delay estimation is a fundamental task in various engineering fields, several expressions for the CRB and MLE have been developed over the past decades. In all of these previous studies, a common assumption was that the wave transmission process introduced an unknown phase component, which made it impossible to exploit the phase component related to the delay from the carrier signal. However, there are practical scenarios where this unknown phase can be estimated and compensated for, enabling the utilization of the delay phase component from the carrier signal. In this context, we provide a comprehensive treatment of this scenario, including the derivation of the MLE and the associated CRB. This approach allows us to analyze the impact of each signal component (carrier frequency and baseband signal) on the achievable MSE of delay estimation relative to the SNR. It also reveals five distinct regions of operations, in contrast to the well-known three.

Understanding greenhouse gas fluxes at the Earth’s surface is becoming crucial in the context of climate change. The aim of the CNES/UKSA MicroCarb mission is therefore to map, on a planetary scale, the sources and sinks of carbon, the main greenhouse gas in the atmosphere. To do this, a spectrometer will be sent in space to acquire spectra in 4 narrow bands around wavelengths associated with O2 and CO2. However, measurement errors can occur due to the instrument used, and induce errors in the resulting trace gas concentrations. It is therefore crucial to estimate the spectral response of the instrument as accurately as possible. This paper investigates a new estimation method for this spectral response that uses a sparse representation in a dictionary of appropriate basis functions. This sparse representation is performed using the LASSO and Orthogonal Matching Pursuit (OMP) algorithms. Simulations conducted on data mimicking observations resulting from the MicroCarb instrument allow the performance of this method to be appreciated.

State estimation techniques appear in a plethora of engineering fields, in particular for the attitude estimation application of interest in this contribution. A number of filters have been devised for this problem, in particular Kalman-type ones, but in their standard form they are known to be fragile against outliers. In this work, we focus on error-state filters, designed for states living on a manifold, here unit-norm quaternions. We propose extensions based on robust statistics, leading to two robust M-type filters able to tackle outliers either in the measurements, in the system dynamics or in both cases. The performance and robustness of these filters is explored in a numerical experiment. We first assess the outlier ratio that they manage to mitigate, and second the type of dynamics outliers that they can detect, showing that the filter performance depends on the measurements’ properties.

Accurately determining signal time-delay is crucial across various domains, such as localization and communication ystems. Understanding the achievable optimal estimation peformance of such technologies, especially during design phases, is essential for benchmarking purposes. One common approach is to derive bounds like the Cramer-Rao Bound (CRB), which directly reflects the minimum achievable estimation error for unbiased estimators. Different studies vary in their approach to deal with the degree of misalignment in the global phase originating from both the transmitter and the receiver in a single input, single output (SISO) link during time-delay estimation assessment. While some treat this phase term as unknown, others assume ideal calibration and compensation. As an alternative to these two opposing approaches, this study adopts a more balanced approach by considering that such a phase can be estimated with a defined uncertainty, a measure that could be mplemented in many practical applications. The primary contribution provided lies in the derivation of a closed-form CRB expression for this alternative signal model, which, as observed, exhibits an asymptotic behavior transitioning between the results observed in previous studies, influenced by the uncertainty assumed for the mentioned phase term.

In this paper, we propose an unsupervised statistical approach for near real-time monitoring of forest loss, leveraging Bayesian inference. We address the identification of forest loss as a change-point detection problem within non-filtered Sentinel-1 single polarization time series data. Each new observation contributes to the probability of deforestation occurrence, utilizing prior knowledge and a data model. Our method offers the advantage of detecting small-scale deforestation without resorting to spatial filtering techniques, thus preserving the native spatial resolution of the Sentinel-1 measurements. To assess its effectiveness, we conducted comparative evaluations against existing operational deforestation monitoring systems. The validation campaign revealed that our method exhibits enhanced detection performance with low false alarm rates with respect to existing systems across diverse landscapes, including dense forest regions such as the Brazilian Amazon, as well as seasonality-dependent areas like the Cerrado, which is strongly under-monitored by existing technology. This robustness stems from the sequential adaptive process inherent in our approach, which enables effective monitoring even in the presence of backscatter variations.

The Modified Cramér-Rao Bound (MCRB) proves to be of significant importance in non-standard estimation scenarios, when in addition to unknown deterministic parameters to be estimated, observations also depend on random nuisance parameters. Given the interest of applications that involve estimation on Lie Groups (LGs), as well as the relevance of nonstandard estimation problems in many practical scenarios, the main concern in this communication is to derive an intrinsic MCRB on LGs (LG-MCRB). For this purpose, a modified unbiasedness constraint must be defined, yielding a modified Barankin Bound. A closed-form formula of the LG-MCRB is then provided for a LG Gaussian model on $S O(2)$, representing $2 D$ rotation matrices, while considering non-Gaussian random nuisance parameters. The validity of this expression is then assessed through numerical simulations, and compared with the intrinsic CRB on LGs for a simplified illustrative scenario, involving a concentrated Gaussian prior distribution on the random nuisance parameters.