Generative state estimators based on probabilistic filters and smoothers are one of the most popular classes of state estimators for robots and autonomous vehicles. However, generative models have limited capacity to handle rich sensory observations, such as camera images, since they must model the entire distribution over sensor readings. Discriminative models do not suffer from this limitation, but are typically more complex to train as latent variable models for state estimation. We present an alternative approach where the parameters of the latent state distribution are directly optimized as a deterministic computation graph, resulting in a simple and effective gradient descent algorithm for training discriminative state estimators. We show that this procedure can be used to train state estimators that use complex input, such as raw camera images, which must be processed using expressive nonlinear function approximators such as convolutional neural networks. Our model can be viewed as a type of recurrent neural network, and the connection to probabilistic filtering allows us to design a network architecture that is particularly well suited for state estimation. We evaluate our approach on synthetic tracking task with raw image inputs and on the visual odometry task in the KITTI dataset. The results show significant improvement over both standard generative approaches and regular recurrent neural networks.

Estimating patient's clinical state from multiple concurrent physiological streams plays an important role in determining if a therapeutic intervention is necessary and for triaging patients in the hospital. In this paper we construct a non-parametric learning algorithm to estimate the clinical state of a patient. The algorithm addresses several known challenges with clinical state estimation such as eliminating bias introduced by therapeutic intervention censoring, increasing the timeliness of state estimation while ensuring a sufficient accuracy, and the ability to detect anomalous clinical states. These benefits are obtained by combining the tools of non-parametric Bayesian inference, permutation testing, and generalizations of the empirical Bernstein inequality. The algorithm is validated using real-world data from a cancer ward in a large academic hospital.

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.