We design a variational state estimation (VSE) method that provides a closed-form Gaussian posterior of an underlying complex dynamical process from (noisy) nonlinear measurements. The complex process is model-free. That is, we do not have a suitable physics-based model characterizing the temporal evolution of the process state. The closed-form Gaussian posterior is provided by a recurrent neural network (RNN). The use of RNN is computationally simple in the inference phase. For learning the RNN, an additional RNN is used in the learning phase. Both RNNs help each other learn better based on variational inference principles. The VSE is demonstrated for a tracking application - state estimation of a stochastic Lorenz system (a benchmark process) using a 2-D camera measurement model. The VSE is shown to be competitive against a particle filter that knows the Lorenz system model and a recently proposed data-driven state estimation method that does not know the Lorenz system model.

Traditional filtering algorithms for state estimation -- such as classical Kalman filtering, unscented Kalman filtering, and particle filters - show performance degradation when applied to nonlinear systems whose uncertainty follows arbitrary non-Gaussian, and potentially multi-modal distributions. This study reviews recent approaches to state estimation via nonlinear filtering based on conditional normalizing flows, where the conditional embedding is generated by standard MLP architectures, transformers or selective state-space models (like Mamba-SSM). In addition, we test the effectiveness of an optimal-transport-inspired kinetic loss term in mitigating overparameterization in flows consisting of a large collection of transformations. We investigate the performance of these approaches on applications relevant to autonomous driving and patient population dynamics, paying special attention to how they handle time inversion and chained predictions. Finally, we assess the performance of various conditioning strategies for an application to real-world COVID-19 joint SIR system forecasting and parameter estimation.

This paper advances temporal reasoning within dynamically changing high-dimensional noisy observations, focusing on a latent space that characterizes the nonlinear dynamics of objects in their environment. We introduce the (GIN), an efficient approximate Bayesian inference algorithm for state space models (SSMs) with nonlinear state transitions and emissions. GIN disentangles two latent representations: one representing the object derived from a nonlinear mapping model, and another representing the latent state describing its dynamics. This disentanglement enables direct state estimation and missing data imputation as the world evolves. To infer the latent state, we utilize a deep extended Kalman filter (EKF) approach that integrates a novel compact RNN structure to compute both the Kalman Gain (KG) and smoothing gain (SG), completing the data flow. This design results in a computational cost per step that is linearly faster than EKF but introduces issues such as the exploding gradient problem. To mitigate the exploding gradients caused by the compact RNN structure in our model, we propose a specialized learning method that ensures stable training and inference. The model is then trained end-to-end on videos depicting a diverse range of simulated and real-world physical systems, and outperforms its ounterparts --RNNs, autoregressive models, and variational approaches-- in state estimation and missing data imputation tasks.

This letter extends the exactly sparse Gaussian variational inference (ESGVI) algorithm for state estimation in two complementary directions. First, ESGVI is generalized to operate on matrix Lie groups, enabling the estimation of states with orientation components while respecting the underlying group structure. Second, factors are introduced to accommodate heavy-tailed and skewed noise distributions, as commonly encountered in ultra-wideband (UWB) localization due to non-line-of-sight (NLOS) and multipath effects. Both extensions are shown to integrate naturally within the ESGVI framework while preserving its sparse and derivative-free structure. The proposed approach is validated in a UWB localization experiment with NLOS-rich measurements, demonstrating improved accuracy and comparable consistency. Finally, a Python implementation within a factor-graph-based estimation framework is made open-source (https://github.com/decargroup/gvi_ws) to support broader research use.

High-speed, head-to-head autonomous racing presents substantial technical and logistical challenges, including precise localization, rapid perception, dynamic planning, and real-time control-compounded by limited track access and costly hardware. This paper introduces the Autonomous Race Stack (ARS), developed by the IU Luddy Autonomous Racing team for the Indy Autonomous Challenge (IAC). We present three iterations of our ARS, each validated on different tracks and achieving speeds up to 260 km/h. Our contributions include: (i) the modular architecture and evolution of the ARS across ARS1, ARS2, and ARS3; (ii) a detailed performance evaluation that contrasts control, perception, and estimation across oval and road-course environments; and (iii) the release of a high-speed, multi-sensor dataset collected from oval and road-course tracks. Our findings highlight the unique challenges and insights from real-world high-speed full-scale autonomous racing.

This paper reports an attempt to model the system dynamics and estimate both the unknown internal control input and the state of a recently developed marine autonomous vehicle, the Jaiabot. Although the Jaiabot has shown promise in many applications, process and sensor noise necessitates state estimation and noise filtering. In this work, we present the first surge and heading linear dynamical model for Jaiabots derived from real data collected during field testing. An adaptive input estimation algorithm is implemented to accurately estimate the control input and hence the state. For validation, this approach is compared to the classical Kalman filter, highlighting its advantages in handling unknown control inputs.

Accurate state estimation is critical for legged and aerial robots operating in dynamic, uncertain environments. A key challenge lies in specifying process and measurement noise covariances, which are typically unknown or manually tuned. In this work, we introduce a bi-level optimization framework that jointly calibrates covariance matrices and kinematic parameters in an estimator-in-the-loop manner. The upper level treats noise covariances and model parameters as optimization variables, while the lower level executes a full-information estimator. Differentiating through the estimator allows direct optimization of trajectory-level objectives, resulting in accurate and consistent state estimates. We validate our approach on quadrupedal and humanoid robots, demonstrating significantly improved estimation accuracy and uncertainty calibration compared to hand-tuned baselines. Our method unifies state estimation, sensor, and kinematics calibration into a principled, data-driven framework applicable across diverse robotic platforms.

Efficient nutrient management is critical for crop growth and sustainable resource consumption (e.g., nitrogen, energy). Current approaches require lengthy analyses, preventing real-time optimization; similarly, imaging facilitates rapid phenotyping but can be computationally intensive, preventing deployment under resource constraints. This study proposes a flexible, tiered pipeline for anomaly detection and status estimation (fresh weight, dry mass, and tissue nutrients), including a comprehensive energy analysis of approaches that span the efficiency-accuracy spectrum. Using a nutrient depletion experiment with three treatments (T1-100%, T2-50%, and T3-25% fertilizer strength) and multispectral imaging (MSI), we developed a hierarchical pipeline using an autoencoder (AE) for early warning. Further, we compared two status estimation modules of different complexity for more detailed analysis: vegetation index (VI) features with machine learning (Random Forest, RF) and raw whole-image deep learning (Vision Transformer, ViT). Results demonstrated high-efficiency anomaly detection (73% net detection of T3 samples 9 days after transplanting) at substantially lower energy than embodied energy in wasted nitrogen. The state estimation modules show trade-offs, with ViT outperforming RF on phosphorus and calcium estimation (R2 0.61 vs. 0.58, 0.48 vs. 0.35) at higher energy cost. With our modular pipeline, this work opens opportunities for edge diagnostics and practical opportunities for agricultural sustainability.

Accurate proprioceptive odometry is fundamental for legged robot navigation in GPS-denied and visually degraded environments where conventional visual odometry systems fail. Current approaches face critical limitations: analytical filtering methods suffer from modeling uncertainties and cumulative drift, hybrid learning-filtering approaches remain constrained by their analytical components, while pure learning-based methods struggle with simulation-to-reality transfer and demand extensive real-world data collection. This paper introduces AutoOdom, a novel autoregressive proprioceptive odometry system that overcomes these challenges through an innovative two-stage training paradigm. Stage 1 employs large-scale simulation data to learn complex nonlinear dynamics and rapidly changing contact states inherent in legged locomotion, while Stage 2 introduces an autoregressive enhancement mechanism using limited real-world data to effectively bridge the sim-to-real gap. The key innovation lies in our autoregressive training approach, where the model learns from its own predictions to develop resilience against sensor noise and improve robustness in highly dynamic environments. Comprehensive experimental validation on the Booster T1 humanoid robot demonstrates that AutoOdom significantly outperforms state-of-the-art methods across all evaluation metrics, achieving 57.2% improvement in absolute trajectory error, 59.2% improvement in Umeyama-aligned error, and 36.2% improvement in relative pose error compared to the Legolas baseline. Extensive ablation studies provide critical insights into sensor modality selection and temporal modeling, revealing counterintuitive findings about IMU acceleration data and validating our systematic design choices for robust proprioceptive odometry in challenging locomotion scenarios.

Abstract-- Filter-based visual inertial navigation system (VINS) has attracted mobile-robot researchers for the good balance between accuracy and efficiency, but its limited mapping quality hampers long-term high-accuracy state estimation. T o this end, we first propose a novel filter-based stereo VINS, differing from traditional simultaneous localization and mapping (SLAM) systems based on 3D map, which performs efficient loop closure constraints with implicit environmental map composed of keyframes and 2D keypoints. Secondly, we proposed a hybrid residual filter framework that combines landmark reprojection and ray constraints to construct a unified Ja-cobian matrix for measurement updates. Finally, considering the degraded environment, we incorporated the camera-IMU extrinsic parameters into visual description to achieve online calibration. Benchmark experiments demonstrate that the proposed SP-VINS achieves high computational efficiency while maintaining long-term high-accuracy localization performance, and is superior to existing state-of-the-art (SOT A) methods.