This paper examines learning the optimal filtering policy, known as the Kalman gain, for a linear system with unknown noise covariance matrices using noisy output data. The learning problem is formulated as a stochastic policy optimization problem, aiming to minimize the output prediction error. This formulation provides a direct bridge between data-driven optimal control and, its dual, optimal filtering.

Many practical settings call for the reconstruction of temporal signals from corrupted or missing data. Classic examples include decoding, tracking, signal enhancement and denoising.

Inference and simulation in the context of high-dimensional dynamical systems remain computationally challenging problems.Some form of dimensionality reduction is required to make the problem tractable in general.In this paper, we propose a novel approximate Gaussian filtering and smoothing methodwhich propagates low-rank approximations of the covariance matrices.This is accomplished by projecting the Lyapunov equations associated with the prediction step to a manifold of low-rank matrices,which are then solved by a recently developed, numerically stable, dynamical low-rank integrator.Meanwhile, the update steps are made tractable by noting that the covariance update only transforms the column space of the covariance matrix, which is low-rank by construction.The algorithm differentiates itself from existing ensemble-based approaches in thatthe low-rank approximations of the covariance matrices are deterministic, rather than stochastic.Crucially, this enables the method to reproduce the exact Kalman filter as the low-rank dimension approaches the true dimensionality of the problem.Our method reduces computational complexity from cubic (for the Kalman filter) to quadratic in the state-space size in the worst-case, and can achieve linear complexity if the state-space model satisfies certain criteria.Through a set of experiments in classical data-assimilation and spatio-temporal regression, we show that the proposed method consistently outperforms the ensemble-based methods in terms of error in the mean and covariance with respect to the exact Kalman filter. This comes at no additional cost in terms of asymptotic computational complexity.

We present an efficient and practical (polynomial time) algorithm for online prediction in unknown and partially observed linear dynamical systems (LDS) under stochastic noise. When the system parameters are known, the optimal linear predictor is the Kalman filter. However, in unknown systems, the performance of existing predictive models is poor in important classes of LDS that are only marginally stable and exhibit long-term forecast memory. We tackle this problem by bounding the generalized Kolmogorov width of the Kalman filter coefficient set. This motivates the design of an algorithm, which we call spectral LDS improper predictor (SLIP), based on conducting a tight convex relaxation of the Kalman predictive model via spectral methods. We provide a finite-sample analysis, showing that our algorithm competes with the Kalman filter in hindsight with only logarithmic regret. Our regret analysis relies on Mendelson's small-ball method, providing sharp error bounds without concentration, boundedness, or exponential forgetting assumptions. Empirical evaluations demonstrate that SLIP outperforms state-of-the-art methods in LDS prediction. Our theoretical and experimental results shed light on the conditions required for efficient probably approximately correct (PAC) learning of the Kalman filter from partially observed data.

Accurate real-time waypoints estimation for the UAV-based online Terrain Following during wildfire patrol missions is critical to ensuring flight safety and enabling wildfire detection. However, existing real-time filtering algorithms struggle to maintain accurate waypoints under measurement noise in nonlinear and time-varying systems, posing risks of flight instability and missed wildfire detections during UAV-based terrain following. To address this issue, a Residual Variance Matching Recursive Least Squares (RVM-RLS) filter, guided by a Residual Variance Matching Estimation (RVME) criterion, is proposed to adaptively estimate the real-time waypoints of nonlinear, time-varying UAV-based terrain following systems. The proposed method is validated using a UAV-based online terrain following system within a simulated terrain environment. Experimental results show that the RVM-RLS filter improves waypoints estimation accuracy by approximately 88$\%$ compared with benchmark algorithms across multiple evaluation metrics. These findings demonstrate both the methodological advances in real-time filtering and the practical potential of the RVM-RLS filter for UAV-based online wildfire patrol.

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.

We present a novel recurrent neural network architecture designed explicitly for day-ahead electricity price forecasting, aimed at improving short-term decision-making and operational management in energy systems. Our combined forecasting model embeds linear structures, such as expert models and Kalman filters, into recurrent networks, enabling efficient computation and enhanced interpretability. The design leverages the strengths of both linear and non-linear model structures, allowing it to capture all relevant stylised price characteristics in power markets, including calendar and autoregressive effects, as well as influences from load, renewable energy, and related fuel and carbon markets. For empirical testing, we use hourly data from the largest European electricity market spanning 2018 to 2025 in a comprehensive forecasting study, comparing our model against state-of-the-art approaches, particularly high-dimensional linear and neural network models. The proposed model achieves approximately 12% higher accuracy than leading benchmarks. We evaluate the contributions of the interpretable model components and conclude on the impact of combining linear and non-linear structures.

Real-time sea state estimation is vital for applications like shipbuilding and maritime safety. Traditional methods rely on accurate wave-vessel transfer functions to estimate wave spectra from onboard sensors. In contrast, our approach jointly estimates sea state and vessel parameters without needing prior transfer function knowledge, which may be unavailable or variable. We model the wave-vessel system using pseudo mass-spring-dampers and develop a dynamic model for the system. This method allows for recursive modeling of wave excitation as a time-varying input, relaxing prior works' assumption of a constant input. We derive statistically consistent process noise covariance and implement a square root cubature Kalman filter for sensor data fusion. Further, we derive the Posterior Cramer-Rao lower bound to evaluate estimator performance. Extensive Monte Carlo simulations and data from a high-fidelity validated simulator confirm that the estimated wave spectrum matches methods assuming complete transfer function knowledge.

Multi-object tracking (MOT) is one of the most challenging tasks in computer vision, where it is important to correctly detect objects and associate these detections across frames. Current approaches mainly focus on tracking objects in each frame of a video stream, making it almost impossible to run the model under conditions of limited computing resources. T o address this issue, we propose Stable-Track, a novel approach that stabilizes the quality of tracking on low-frequency detections. Our method introduces a new two-stage matching strategy to improve the cross-frame association between low-frequency detections. W e propose a novel Bbox-Based Distance instead of the conventional Mahalanobis distance, which allows us to effectively match objects using the Re-ID model. Furthermore, we integrate visual tracking into the Kalman Filter and the overall tracking pipeline. Our method outperforms current state-of-the-art trackers in the case of low-frequency detections, achieving 11.6% HOTA improvement at 1 Hz on MOT17-val, while keeping up with the best approaches on the standard MOT17, MOT20, and DanceTrack benchmarks with full-frequency detections.