Renato Zanetti

Andrey A. Popov, Renato Zanetti

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.

Ondrej Straka, Felipe Giraldo-Grueso, Renato Zanetti

Algorithms for Bayesian state estimation of nonlinear systems inevitably introduce approximation errors. These algorithms depend on parameters that influence the accuracy of the numerical approximations used. 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.

Felipe Giraldo-Grueso, Andrey A. Popov, Renato Zanetti

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.

Dalton Durant, Renato Zanetti

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.

Andrey A. Popov, Renato Zanetti

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.