arXiv subjects

Renato Zanetti

Publications and source records attributed to Renato Zanetti.

13 recordsLinked to original sources

arXiv2026

Intrinsic Stochastic Successive Convexification on SE(3) for Chance Constrained 6-DOF Rendezvous

This work presents an intrinsic stochastic successive convexification method formulated on the Special Euclidean group SE(3) for six degrees of freedom spacecraft rendezvous trajectory optimization. The proposed approach extends stochastic successive convexification, originally developed for Euclidean state spaces, to the nonlinear manifold of SE(3), thereby enabling a consistent covariance steering and chance constrained optimization of rigid body pose trajectories. While conventional trajectory optimization methods often treat position and attitude separately, or account for stochastic dispersion only after a deterministic reference trajectory has been generated, the proposed SE(3)-based formulation captures the intrinsic coupling between translational and rotational motion uncertainty. This coupling is especially important for rendezvous problems with safety constraints that depend on the full relative pose, including collision avoidance, docking corridor, camera field of view, and probabilistic force and torque bounds. Numerical simulations show that jointly optimizing the nominal trajectory, covariance, and feedback law shapes the closed loop dispersion and improves probabilistic constraint satisfaction relative to tracking a deterministic reference with a feedback linearization controller.

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arXiv2026

Polynomial-Based Solutions to Targeting Problems for Onboard Applications

This paper solves the targeting problem focusing on accuracy, computational efficiency, and reliability. The trajectory optimization problem is first recast as a polynomial optimization problem (POP) by leveraging differential algebra to compute high-order Taylor expansions of the nonlinear dynamics and constraints. Moment-sum-of-squares (SOS) optimization is then utilized to solve this POP. A convex formulation based on a second-order expansion of the dynamics is also proposed. For impulsive targeting, the moment-SOS and convex approaches are compared against traditional nonlinear programming (NLP) solvers and map inversion techniques. Results indicate that the moment-SOS approach provides solutions as accurate as traditional NLP, but with the critical advantage of guaranteeing convergence to the global optimum under mild assumptions. Furthermore, the method excels at handling large maneuvers and long propagation times, conditions in which standard linear approximations rapidly degrade. To demonstrate its versatility, the methodology is extended to a continuous low-thrust station keeping (SK) scenario in the Earth-Moon Circular Restricted Three-Body Problem. The algorithm's performance is then evaluated in the presence of significant state errors. The ability to directly handle non-convex constraints and recast complex, nonlinear dynamics into formulations with reliable convergence properties makes the moment-SOS approach suitable for autonomous onboard applications.

math.OC↗

arXiv2026

Learning Adaptive Parameter Policies for Nonlinear Bayesian Filtering

For many nonlinear Bayesian state estimation problems, the posterior recursion is not analytically tractable, leading to algorithms that are influenced by numerical approximation errors. These algorithms depend on parameters that affect the approximation's accuracy and computational cost. The parameters include, for example, the number of particles, scaling parameters, and the number of iterations in iterative computations. Typically, these parameters are fixed or adjusted heuristically, although the approximation accuracy can change over time with the local degree of nonlinearity and uncertainty. The approximation errors introduced at a time step propagate through subsequent updates, affecting the accuracy, consistency, and robustness of future estimates. This paper presents adaptive parameter selection in nonlinear Bayesian filtering as a sequential decision-making problem, where parameters influence not only the immediate estimation outcome but also the future estimates. The decision-making problem is addressed using reinforcement learning to learn adaptive parameter policies for nonlinear Bayesian filters. Experiments with the unscented Kalman filter and stochastic integration filter demonstrate that the learned policies improve both estimate quality and consistency.

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arXiv2025

Kernel-Based Ensemble Gaussian Mixture Probability Hypothesis Density Filter

In this work, a kernel-based Ensemble Gaussian Mixture Probability Hypothesis Density (EnGM-PHD) filter is presented for multi-target filtering applications. The EnGM-PHD filter combines the Gaussian-mixture-based techniques of the Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter with the particle-based techniques of the Sequential Monte Carlo Probability Hypothesis Density (SMC-PHD) filter. It achieves this by obtaining particles from the posterior intensity function, propagating them through the system dynamics, and then using Kernel Density Estimation (KDE) techniques to approximate the Gaussian mixture of the prior intensity function. This approach guarantees convergence to the true intensity function in the limit of the number of components. Moreover, in the special case of a single target with no births, deaths, clutter, and perfect detection probability, the EnGM-PHD filter reduces to the standard Ensemble Gaussian Mixture Filter (EnGMF). In the presented experiment, the results indicate that the EnGM-PHD filter achieves better multi-target filtering performance than both the GM-PHD and SMC-PHD filters while using the same number of components or particles.

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arXiv2025

Deterministic Optimal Transport-based Gaussian Mixture Particle Filtering for Verifiable Applications

Mixture-model particle filters such as the ensemble Gaussian mixture filter require a resampling procedure in order to converge to exact Bayesian inference. Canonically, stochastic resampling is performed, which provides useful samples with no guarantee of usefulness for a finite ensemble. We propose a new resampling procedure based on optimal transport that deterministically selects optimal resampling points. We show on a toy 3-variable problem that it significantly reduces the amount of particles required for useful state estimation. Finally, we show that this filter improves the state estimation of a seldomly-observed space object in an NRHO around the moon.

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arXiv2024

The Ensemble Epanechnikov Mixture Filter

In the high-dimensional setting, Gaussian mixture kernel density estimates become increasingly suboptimal. In this work we aim to show that it is practical to instead use the optimal multivariate Epanechnikov kernel. We make use of this optimal Epanechnikov mixture kernel density estimate for the sequential filtering scenario through what we term the ensemble Epanechnikov mixture filter (EnEMF). We provide a practical implementation of the EnEMF that is as cost efficient as the comparable ensemble Gaussian mixture filter. We show on a static example that the EnEMF is robust to growth in dimension, and also that the EnEMF has a significant reduction in error per particle on the 40-variable Lorenz '96 system.

stat.ML↗

arXiv2024

Ensemble-localized Kernel Density Estimation with Applications to the Ensemble Gaussian Mixture Filter

The ensemble Gaussian mixture filter (EnGMF) is a non-linear filter suited to data assimilation of highly non-Gaussian and non-linear models that has practical utility in the case of a small number of samples, and theoretical convergence to full Bayesian inference in the ensemble limit. We aim to increase the utility of the EnGMF by introducing an ensemble-local notion of covariance into the kernel density estimation (KDE) step for the prior distribution. We prove that in the Gaussian case, our new ensemble-localized KDE technique is exactly the same as more traditional KDE techniques. We also show an example of a non-Gaussian distribution that can fail to be approximated by canonical KDE methods, but can be approximated well by our new KDE technique. We showcase our new KDE technique on a simple bivariate problem, showing that it has nice qualitative and quantitative properties, and significantly improves the estimate of the prior and posterior distributions for all ensemble sizes tested. We additionally show the utility of the proposed methodology for sequential filtering for the Lorenz '63 equations, achieving a significant reduction in error, and less conservative behavior in the uncertainty estimate with respect to traditional techniques.

math.OC↗

arXiv2024

Precision Mars Entry Navigation with Atmospheric Density Adaptation via Neural Networks

Spacecraft entering Mars require precise navigation algorithms capable of accurately estimating the vehicle's position and velocity in dynamic and uncertain atmospheric environments. Discrepancies between the true Martian atmospheric density and the onboard density model can significantly impair the performance of spacecraft entry navigation filters. This work introduces a new approach to online filtering for Martian entry using a neural network to estimate atmospheric density and employing a consider analysis to account for the uncertainty in the estimate. The network is trained on an exponential atmospheric density model, and its parameters are dynamically adapted in real time to account for any mismatch between the true and estimated densities. The adaptation of the network is formulated as a maximum likelihood problem by leveraging the measurement innovations of the filter to identify optimal network parameters. Within the context of the maximum likelihood approach, incorporating a neural network enables the use of stochastic optimizers known for their efficiency in the machine learning domain. Performance comparisons are conducted against two online adaptive approaches, covariance matching and state augmentation and correction, in various realistic Martian entry navigation scenarios. The results show superior estimation accuracy compared to other approaches, and precise alignment of the estimated density with a broad selection of realistic Martian atmospheres sampled from perturbed Mars-GRAM data.

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arXiv2024

What are You Weighting For? Improved Weights for Gaussian Mixture Filtering With Application to Cislunar Orbit Determination

This work focuses on the critical aspect of accurate weight computation during the measurement incorporation phase of Gaussian mixture filters. The proposed novel approach computes weights by linearizing the measurement model about each component's posterior estimate rather than the the prior, as traditionally done. This work proves equivalence with traditional methods for linear models, provides novel sigma-point extensions to the traditional and proposed methods, and empirically demonstrates improved performance in nonlinear cases. Two illustrative examples, the Avocado and a cislunar single target tracking scenario, serve to highlight the advantages of the new weight computation technique by analyzing filter accuracy and consistency through varying the number of Gaussian mixture components.

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arXiv2023

Bayesian Recursive Update for Ensemble Kalman Filters

Few real-world systems are amenable to truly Bayesian filtering; nonlinearities and non-Gaussian noises can wreak havoc on filters that rely on linearization and Gaussian uncertainty approximations. This article presents the Bayesian Recursive Update Filter (BRUF), a Kalman filter that uses a recursive approach to incorporate information from nonlinear measurements. The BRUF relaxes the measurement linearity assumption of the Extended Kalman Filter (EKF) by dividing the measurement update into a user-defined number of steps. The proposed technique is extended for ensemble filters in the Bayesian Recursive Update Ensemble Kalman Filter (BRUEnKF). The performance of both filters is demonstrated in numerical examples, and new filters are introduced which exploit the theoretical foundation of the BRUF in different ways. A comparison between the BRUEnKF and Gromov flow, a popular particle flow algorithm, is presented in detail. Finally, the BRUEnKF is shown to outperform the EnKF for a very high-dimensional system.

math.NA↗

arXiv2023

Small-data Reduced Order Modeling of Chaotic Dynamics through SyCo-AE: Synthetically Constrained Autoencoders

Data-driven reduced order modeling of chaotic dynamics can result in systems that either dissipate or diverge catastrophically. Leveraging non-linear dimensionality reduction of autoencoders and the freedom of non-linear operator inference with neural-networks, we aim to solve this problem by imposing a synthetic constraint in the reduced order space. The synthetic constraint allows our reduced order model both the freedom to remain fully non-linear and highly unstable while preventing divergence. We illustrate the methodology with the classical 40-variable Lorenz '96 equations, showing that our methodology is capable of producing medium-to-long range forecasts with lower error using less data.

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arXiv2022

An Adaptive Covariance Parameterization Technique for the Ensemble Gaussian Mixture Filter

The ensemble Gaussian mixture filter combines the simplicity and power of Gaussian mixture models with the provable convergence and power of particle filters. The quality of the ensemble Gaussian mixture filter heavily depends on the choice of covariance matrix in each Gaussian mixture. This work extends the ensemble Gaussian mixture filter to an adaptive choice of covariance based on the parameterized estimates of the sample covariance matrix. Through the use of the expectation maximization algorithm, optimal choices of the covariance matrix parameters are computed in an online fashion. Numerical experiments on the Lorenz '63 equations show that the proposed methodology converges to classical results known in particle filtering. Further numerical results with more advances choices of covariance parameterization and the medium-size Lorenz '96 equations show that the proposed approach can perform significantly better than the standard EnGMF, and other classical data assimilation algorithms.

math.OC↗

arXiv2021

Riemannian Trust-Region based Adaptive Kalman filter with unknown noise Covariance matrices

The problem of adaptive Kalman filtering for a discrete observable linear time-varying system with unknown noise covariance matrices is addressed in this paper. The measurement difference autocovariance method is used to formulate a linear least squares cost function containing the measurements and the process and measurement noise covariance matrices. Subsequently, a Riemannian trust-region optimization approach is designed to minimize the least squares cost function and ensure symmetry and positive definiteness for the estimates of the noise covariance matrices. The noise covariance matrix estimates, under sufficient excitation of the system, are shown to converge to their unknown true values. Saliently, the exponential stability and convergence guarantees for the proposed adaptive Kalman filter to the optimal Kalman filter with known noise covariance matrices is shown to be achieved under the relatively mild assumptions of uniform observability and uniform controllability. Numerical simulations on a linear time-varying system demonstrate the effectiveness of the proposed adaptive filtering algorithm.

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