Two proofs of Kalman Theorem using flows of vector fields.
problem Classical result of Control Theory (Kalman Theorem).
method Two proofs using flows of vector fields.
result New criteria for local controllability of non-linear systems.
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48 results for “Kalman controllability”
Transformers can approximate Kalman Filtering in linear systems with small error.
problem Approximating Kalman Filtering using Transformers for linear dynamical systems.
method Two-step reduction: 1) Softmax self-attention block approximates Nadaraya-Watson kernel smoothing, 2) This estimator approximates Kalman Filter.
result Constructs a Transformer that implements the Kalman Filter with small additive error, uniformly bounded in time.
New algorithm learns linear dynamical systems from measurements.
problem Learning system dynamics from linear measurements efficiently and accurately.
method Method of moments estimator to directly estimate Markov parameters.
result First polynomial time algorithm for learning linear dynamical systems.
Graph Kalman Filterscs.LG
Graph Kalman filters adapt classical filters to graph data.
problem Adapting classical Kalman filters to graph data.
method Generalizes Kalman filters to attributed graphs, learning state-transition and readout functions end-to-end.
result Adapted Kalman filters can predict graph outputs.
Controlled interacting particle systems such as the ensemble Kalman filter (EnKF) and the feedback particle filter (FPF) are numerical algorithms to approximate the solution of the nonlinear filtering problem in continuous time. The distinguishing feature of these algorithms is that the Bayesian update step is implemen…
Improved Kalman filter for non-linear, non-Gaussian data.
problem Estimating hidden variables with non-linear, non-Gaussian observations.
method Reproduces and extends Burkhart et al.'s discriminative Kalman filter.
result Enhanced filter performance for complex observation models.
Non-bilinear observations make optimal control harder, showing non-convex costs and non-affine optimal controllers.
problem Optimal control from bilinear observations in linear systems is challenging.
method Analytical and numerical methods to study the non-convex cost-to-go and non-affine optimal controllers.
result The Separation Principle does not hold for bilinear observations, leading to non-convex costs and non-affine optimal controllers.
TASC improves synthetic control for time-series data with trends.
problem Inability of existing SC methods to fully utilize temporal structure in time-series data.
method TASC uses a state-space model with a constant trend and Kalman filter for counterfactual inference.
result TASC offers advantages in settings with strong temporal trends and high observation noise.
Nonlinear RNNs' memory capacity varies widely, making it impractical.
problem The usefulness of memory capacity as a metric for linear RNNs is questioned.
method Analysis of random nonlinear RNNs with varying input scales.
result Memory capacity of nonlinear RNNs is arbitrary and impractical.
A new method improves policy evaluation in RL by tracking value uncertainties.
problem Limitations in existing policy evaluation methods for deep RL tasks.
method KOVA (Kalman Optimization for Value Approximation) based on extended Kalman filter.
result KOVA minimizes a regularized objective function that considers parameter and noisy return uncertainties.
The introduction of automated flight control and management systems have made possible aircraft designs that sacrifice arodynamic stability in order to incorporate stealth technology intro their shape, operate more efficiently, and are highly maneuverable. Therefore, modern flight management systems are reliant on mult…
Dynamical models estimate and predict the temporal evolution of physical systems. State Space Models (SSMs) in particular represent the system dynamics with many desirable properties, such as being able to model uncertainty in both the model and measurements, and optimal (in the Bayesian sense) recursive formulations e…
Neural EKF improves structural dynamics prediction.
problem Accurately predicting structural response for health monitoring.
method Neural Extended Kalman Filter (Neural EKF) for learning dynamics.
result Significant predictive capabilities demonstrated on simulated and real-world data.
Dynamic Ensemble Modeling Approach to Nonstationary Neural Decoding in Brain-Computer Interfaceseess.SP
Brain-computer interfaces (BCIs) have enabled prosthetic device control by decoding motor movements from neural activities. Neural signals recorded from cortex exhibit nonstationary property due to abrupt noises and neuroplastic changes in brain activities during motor control. Current state-of-the-art neural signal de…
Improved Kalman filter for Stiefel manifold measurements.
problem Improving accuracy in measurements on Stiefel manifolds.
method Generalization of extended Kalman filter for Stiefel manifold-valued measurements.
result Significant improvement over raw measurements.
Given a stationary state-space model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for inferring the posterior distribution of the current state given all measurements up to the present time. For example, the Apoll…
DiSK improves DP optimizers by simplifying Kalman filtering for better performance.
problem Performance drop of DP optimizers in large-scale training due to noise injection.
method DiSK uses Kalman filtering to denoise privatized gradients and refine gradient estimations.
result DiSK achieves significant performance improvements over standard DP optimizers in large-scale training.
HKF uses neural networks to adapt Kalman filters for dynamic channel tracking.
problem Tracking channels with varying dynamics and Doppler values.
method Combines Kalman filters with hypernetworks for dynamic adaptation.
result HKF achieves up to 2dB gain over Kalman filters at high Doppler values.
The article improves prediction by aggregating Kalman recursions online.
problem Improving expert aggregation in prediction models.
method Using exponential weights and state-space models to aggregate Kalman recursions.
result New algorithms outperform existing methods in Kalman recursion expert aggregation.
We study optimal regret bounds for control in linear dynamical systems under adversarially changing strongly convex cost functions, given the knowledge of transition dynamics. This includes several well studied and fundamental frameworks such as the Kalman filter and the linear quadratic regulator. State of the art met…
Paper analyzes ensemble Kalman updates for effective dimension and localization.
problem Why small ensemble sizes work well in inverse problems and data assimilation.
method Non-asymptotic analysis of ensemble Kalman updates, focusing on effective dimension and localization.
result Rigorously explains why a small ensemble size is sufficient when prior covariance has moderate effective dimension.
In this paper, we revisit the Kalman filter theory. After giving the intuition on a simplified financial markets example, we revisit the maths underlying it. We then show that Kalman filter can be presented in a very different fashion using graphical models. This enables us to establish the connection between Kalman fi…
Illustrates interleaved learning with Kalman Filter for linear least squares.
problem Improving machine learning algorithms through interleaved learning.
method Simple statistical and optimization framework based on Kalman Filter.
result Demonstrates the effectiveness of interleaved learning.
Recursive KalmanNet combines neural networks with Kalman filters for precise state estimation.
problem State estimation in systems with noisy measurements and non-Gaussian noise.
method Recursive KalmanNet uses a recurrent neural network to estimate states with consistent error covariance, optimizing for Gaussian negative log-likelihood.
result Recursive KalmanNet outperforms conventional Kalman filters and deep learning-based estimators in non-Gaussian noise conditions.
Paper introduces EnDKF for more accurate pose tracking.
problem Accurate pose tracking with directional uncertainty.
method EnDKF integrates unit-quaternion attitude representation for better directional uncertainty capture.
result Significant reduction in error compared to traditional methods.
Proposes a new method to enhance neural learning by maximizing information gain.
problem Improving neural learning by selecting key variables to maximize information gain.
method Adaptive Ensemble Kalman Filter to quantify uncertainty and maximize information gain.
result The proposed method enables the neural network to learn more effectively from stochastic systems.
The extended Kalman filter is perhaps the most standard tool to estimate in real time the state of a dynamical system from noisy measurements of some function of the system, with extensive practical applications (such as position tracking via GPS). While the plain Kalman filter for linear systems is well-understood, th…
The discriminative Kalman filter for nonlinear and non-Gaussian sequential Bayesian filteringstat.ML
The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman filter have been proposed that incorporate linear approximations to nonlinear m…
Long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systemsmath.DS
This paper proves long-time accuracy of ensemble Kalman filters for chaotic and machine-learned systems.
problem Ensuring long-term accuracy of ensemble Kalman filters for complex dynamical systems.
method Established conditions for long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems.
result Ensemble Kalman filters maintain small estimation error over long time horizons for chaotic and machine-learned systems.
A Kalman filter reduces valuation risk in business valuation models.
problem Reducing valuation risk in business valuation models.
method Recursive FCFF model with Kalman filtering to adjust WACC.
result Significant reduction in valuation risk by implementing Kalman filter.
The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian Lévy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian Lévy noise may have infinite variance. A modified Kalman filter for linear systems wi…
KalMamba improves RL efficiency with probabilistic SSMs.
problem Efficiency in learning and inference for probabilistic SSMs in RL.
method Combines Mamba's scalability with Kalman filtering for efficient probabilistic SSMs.
result KalMamba outperforms state-of-the-art SSMs in RL, especially on longer sequences.
Study uses Kalman-Filter to assess market efficiency in major stock markets.
problem Assessing market efficiency in major stock markets.
method Utilizes Kalman-Filter in two stages, assuming a trendline representing true market value.
result Significant portfolio returns in emerging and developed markets.
The Kalman filter and Heston model are used to estimate asset prices and trading performance.
problem Estimating asset prices using stochastic models.
method Kalman filter applied to mean-reverting processes and Heston model with method of moments.
result The Kalman filter and Heston model provide effective methods for estimating asset prices and trading performance.
State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms. Such schemes are equivalent to linear algebraic techniques that minimize a conv…
Paper proves convergence of Kalman filter on Stiefel manifolds with measurement errors.
problem Filtering constant particle with measurement errors on Stiefel manifolds.
method Extended Kalman filter applied to Stiefel manifold-valued observations.
result Convergence of the extended Kalman filter proved for constant system process.
We cast Amari's natural gradient in statistical learning as a specific case of Kalman filtering. Namely, applying an extended Kalman filter to estimate a fixed unknown parameter of a probabilistic model from a series of observations, is rigorously equivalent to estimating this parameter via an online stochastic natural…
In this manuscript we introduce numerical Gaussian process Kalman filtering (GPKF). Numerical Gaussian processes have recently been developed to simulate spatiotemporal models. The contribution of this paper is to embed numerical Gaussian processes into the recursive Kalman filter equations. This embedding enables us t…
Optimization viewpoint on Kalman smoothing, with applications to robust and sparse estimationmath.OC
In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least squares problem, highlight special structure, and show that the classic filtering an…
The Ensemble Kalman Inversion Racephysics.data-an
Ensemble Kalman methods improve climate model calibration from noisy observations.
problem Calibrating parameters in complex climate models from noisy data.
method Comparing ensemble Kalman methods for efficiency in climate model calibration.
result Ensemble Kalman methods are more efficient and robust for parameter learning in climate models.
Proposes MM-KTD for efficient RL learning with reduced sample size.
problem High sensitivity to parameter selection and overfitting in DNN-based RL methods.
method Adapts Kalman filter parameters using observed states and rewards, enhances sampling efficiency through active learning.
result Significantly reduced number of samples needed to learn optimal policy.
Improved stock volume prediction using Kalman Filters with various hidden states.
problem Improving accuracy of intraday trading volume prediction.
method Extended Kalman Filter with various hidden states for different stocks, using cross-validation to determine optimal state number.
result Demonstrated improved accuracy through comparison experiments and numerical analysis.
Extended Linear Regression: A Kalman Filter Approach for Minimizing Loss via Area Under the Curvecs.LG
Enhances linear regression with Kalman filter for loss minimization.
problem Minimizing loss in linear regression models.
method Integrates Kalman filter and SGD for optimal weight updates.
result Develops optimal linear regression equation with minimum area under curve.
In order to integrate uncertainty estimates into deep time-series modelling, Kalman Filters (KFs) (Kalman et al., 1960) have been integrated with deep learning models, however, such approaches typically rely on approximate inference techniques such as variational inference which makes learning more complex and often le…
Paper presents a robust Kalman filter for state estimation.
problem Robust state estimation under process and measurement noise.
method Generalized Bayesian approach to a Weighted Observation Likelihood Filter (WoLF) framework.
result Achieved robust state estimation against both process and measurement noise.
Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, this filters only estimate states that are correlated with the observation. Therefore, sequential esti…
EnCF improves data assimilation for implicit, non-smooth observations.
problem Data assimilation challenges with implicit, many-to-one observations.
method EnCF uses a stochastic controlled flow to update forecast distributions.
result EnCF outperforms Kalman filters for non-Gaussian, implicit observations.
High fidelity behavior prediction of intelligent agents is critical in many applications. However, the prediction model trained on the training set may not generalize to the testing set due to domain shift and time variance. The challenge motivates the adoption of online adaptation algorithms to update prediction model…