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Abstract Images are an important source of information for spacecraft navigation. Based on an image and a known attitude, triangulation techniques (intersection or resection) are often used for positioning and navigation. In the resection problem, an observer estimate its unknown location by using angle measurements to points at known locations (i.e., landmarks), the localization performance depending on the accuracy of the angle measurements. As a contribution to resection for spacecraft navigation, we considers the dynamic image estimation problem based on radio interferometry, i.e., image of radio source power, where the measurements are sample covariance matrices (SCMs). Considering the case where several measurements are available as well as a known dynamic linear model of image evolution, a.k.a a linear state model, the minimum mean-squared error image estimator (MMSE) is given by the Kalman filter (KF) or one of its variants. However standard Kalman-like filters are not a priori suitable for the problem at hand since the measurements (i.e., SCMs) cannot be formulated analytically as a function of state parameters to be estimated (i.e., radio source power). In fact, this lack of analytical formulation can be circumvented by a statistical linear fitting allowing the SCMs to be expressed in terms of the state. This linear fitting introduces an additive residual noise, equivalent to a measurement noise, whose covariance matrix depends on the current state, a non-standard case for a measurement model. The covariance matrix of the residual noise is derived whatever the distributions of the radio sources and of the additive noise at the samples level, unveiling the contribution of their multivariate kurtosis. The proposed method is evaluated on simulated data representative of a dynamic radio interferometry framework. The results show that the proposed method is capable of effectively tracking moving radio sources in complex scenes with theoretical guaranties when the signal multivariate kurtosis is known.

L0 sparse methods are not widespread in Direction-Of-Arrival (DOA) estimation yet, despite their potential superiority over classical methods in difficult scenarios. This comes from the difficulties encountered for global optimization on hill-climbing error surfaces. In this paper, we explore the loss landscapes of L0 and Continuous Exact L0 (CEL0) regularized problems in order to design a new optimization scheme. As expected, we observe that the recently introduced CEL0 penalty leads to an error surface with less local minima than the L0 one. This property explains the good behavior of the CEL0-regularized sparse DOA estimation problem for well-separated sources. Unfortunately, CEL0-regularized landscape enlarges L0-basins in the middle of close sources, and CEL0 methods are thus unable to resolve two close sources. Consequently, we propose to alternate between both error surfaces to increase the probability of reaching the global solution. Experiments show that the proposed approach offers better performance than existing ones, and particularly an enhanced resolution limit.

High-resolution methods for estimating signal processing parameters such as bearing angles in array processing or frequencies in spectral analysis may be hampered by the model order if poorly selected. As classical model order selection methods fail when the number of snapshots available is small, this paper proposes a method for noncoherent sources, which continues to work under such conditions, while maintaining low computational complexity. For white Gaussian noise and short data we show that the profile of the ordered noise eigenvalues is seen to approximately fit an exponential law. This fact is used to provide a recursive algorithm which detects a mismatch between the observed eigenvalue profile and the theoretical noise-only eigenvalue profile, as such a mismatch indicates the presence of a source. Moreover this proposed method allows the probability of false alarm to be controlled and predefined, which is a crucial point for systems such as RADARs. Results of simulations are provided in order to show the capabilities of the algorithm.