Adaptive KalmanNet: Data-Driven Kalman Filter with Fast Adaptation

Combining the classical Kalman filter (KF) with a deep neural network (DNN) enables tracking in partially known state space (SS) models. A major limitation of current DNN-aided designs stems from the need to train them to filter data originating from a specific distribution and underlying SS model. Consequently, changes in the model parameters may require lengthy retraining. While the KF adapts through parameter tuning, the black-box nature of DNNs makes identifying tunable components difficult. Hence, we propose Adaptive KalmanNet (AKNet), a DNN-aided KF that can adapt to changes in the SS model without retraining. Inspired by recent advances in large language model fine-tuning paradigms, AKNet uses a compact hypernetwork to generate context-dependent modulation weights. Numerical evaluation shows that AKNet provides consistent state estimation performance across a continuous range of noise distributions, even when trained using data from limited noise settings

Uncertainty Quantification in Deep Learning Based Kalman Filters

Various algorithms combine deep neural networks (DNNs) and Kalman filters (KFs) to learn from data to track in complex dynamics. Unlike classic KFs, DNN-based systems do not naturally provide the error covariance alongside their estimate, which is of great importance in some applications, e.g., navigation. To bridge this gap, in this work we study error covariance extraction in DNN-aided KFs. We examine three main approaches that are distinguished by the ability to associate internal features with meaningful KF quantities such as the Kalman gain (KG) and prior covariance. We identify the differences between these approaches in their requirements and their effect on the training of the system. Our numerical study demonstrates that the above approaches allow DNN-aided KFs to extract error covariance, with most accurate error prediction provided by model-based/data-driven designs

Latent-KalmanNet:Learned Kalman Filtering for Tracking From High-Dimensional Signals

The Kalman filter (KF) is a widely used algorithm for tracking dynamic systems that are captured by state space (SS) models. The need to fully describe an SS model limits its applicability under complex settings, e.g., when tracking based on visual data, and the processing of high-dimensional signals often induces notable latency. These challenges can be treated by mapping the measurements into latent features obeying some postulated closed-form SS model, and applying the KF in the latent space. However, the validity of this approximated SS model may constitute a limiting factor. In this work, we study tracking from high-dimensional measurements under complex settings using a hybrid model-based/data-driven approach. By gradually tackling the challenges in handling the measurement model and the task, we develop Latent-KalmanNet, which implements tracking from high-dimensional measurements by leveraging data to jointly learn the KF along with the latent space mapping. Latent-KalmanNet combines a learned encoder with data-driven tracking in the latent space using the recently proposed-KalmanNet, while identifying the ability of each of these trainable modules to assist its counterpart via providing a suitable prior (by KalmanNet) and by learning a latent representation that facilitates data-aided tracking (by the encoder). Our empirical results demonstrate that the proposed Latent-KalmanNet achieves improved accuracy and run-time performance over both model-based and data-driven techniques by learning a surrogate latent representation that most facilitates tracking, while operating with limited complexity and latency.</p

Nonlinear Kalman Filtering based on Self-Attention Mechanism and Lattice Trajectory Piecewise Linear Approximation

The traditional Kalman filter (KF) is widely applied in control systems, but it relies heavily on the accuracy of the system model and noise parameters, leading to potential performance degradation when facing inaccuracies. To address this issue, introducing neural networks into the KF framework offers a data-driven solution to compensate for these inaccuracies, improving the filter's performance while maintaining interpretability. Nevertheless, existing studies mostly employ recurrent neural network (RNN), which fails to fully capture the dependencies among state sequences and lead to an unstable training process. In this paper, we propose a novel Kalman filtering algorithm named the attention Kalman filter (AtKF), which incorporates a self-attention network to capture the dependencies among state sequences. To address the instability in the recursive training process, a parallel pre-training strategy is devised. Specifically, this strategy involves piecewise linearizing the system via lattice trajectory piecewise linear (LTPWL) expression, and generating pre-training data through a batch estimation algorithm, which exploits the self-attention mechanism's parallel processing ability. Experimental results on a two-dimensional nonlinear system demonstrate that AtKF outperforms other filters under noise disturbances and model mismatches.Comment: 7 pages, 4 figure

DANSE: Data-driven Non-linear State Estimation of Model-free Process in Unsupervised Learning Setup

We address the tasks of Bayesian state estimation and forecasting for a model-free process in an unsupervised learning setup. In the article, we propose DANSE -- a Data-driven Nonlinear State Estimation method. DANSE provides a closed-form posterior of the state of the model-free process, given linear measurements of the state. In addition, it provides a closed-form posterior for forecasting. A data-driven recurrent neural network (RNN) is used in DANSE to provide the parameters of a prior of the state. The prior depends on the past measurements as input, and then we find the closed-form posterior of the state using the current measurement as input. The data-driven RNN captures the underlying non-linear dynamics of the model-free process. The training of DANSE, mainly learning the parameters of the RNN, is executed using an unsupervised learning approach. In unsupervised learning, we have access to a training dataset comprising only a set of measurement data trajectories, but we do not have any access to the state trajectories. Therefore, DANSE does not have access to state information in the training data and can not use supervised learning. Using simulated linear and non-linear process models (Lorenz attractor and Chen attractor), we evaluate the unsupervised learning-based DANSE. We show that the proposed DANSE, without knowledge of the process model and without supervised learning, provides a competitive performance against model-driven methods, such as the Kalman filter (KF), extended KF (EKF), unscented KF (UKF), and a recently proposed hybrid method called KalmanNet.Comment: 12 pages, The paper is under revie

KalmanNet:Neural Network Aided Kalman Filtering for Partially Known Dynamics

Real-time state estimation of dynamical systems is a fundamental task in signal processing and control. For systems that are well-represented by a fully known linear Gaussian state space (SS) model, the celebrated Kalman filter (KF) is a low complexity optimal solution. However, both linearity of the underlying SS model and accurate knowledge of it are often not encountered in practice. Here, we present KalmanNet, a real-time state estimator that learns from data to carry out Kalman filtering under non-linear dynamics with partial information. By incorporating the structural SS model with a dedicated recurrent neural network module in the flow of the KF, we retain data efficiency and interpretability of the classic algorithm while implicitly learning complex dynamics from data. We numerically demonstrate that KalmanNet overcomes nonlinearities and model mismatch, outperforming classic filtering methods operating with both mismatched and accurate domain knowledge.</p

Robust LSTM-based Vehicle Velocity Observer for Regular and Near-limits Applications

Accurate velocity estimation is key to vehicle control. While the literature describes how model-based and learning-based observers are able to estimate a vehicle's velocity in normal driving conditions, the challenge remains to estimate the velocity in near-limits maneuvers while using only conventional in-car sensors. In this paper, we introduce a novel neural network architecture based on Long Short-Term Memory (LSTM) networks to accurately estimate the vehicle's velocity in different driving conditions, including maneuvers at the limits of handling. The approach has been tested on real vehicle data and it provides more accurate estimations than state-of-the-art model-based and learning-based methods, for both regular and near-limits driving scenarios. Our approach is robust since the performance of the state-of-the-art observers deteriorates with higher dynamics, while our method adapts to different maneuvers, providing accurate estimations even at the vehicle's limits of handling

GSP-KalmanNet: Tracking Graph Signals via Neural-Aided Kalman Filtering

Dynamic systems of graph signals are encountered in various applications, including social networks, power grids, and transportation. While such systems can often be described as state space (SS) models, tracking graph signals via conventional tools based on the Kalman filter (KF) and its variants is typically challenging. This is due to the nonlinearity, high dimensionality, irregularity of the domain, and complex modeling associated with real-world dynamic systems of graph signals. In this work, we study the tracking of graph signals using a hybrid model-based/data-driven approach. We develop the GSP-KalmanNet, which tracks the hidden graphical states from the graphical measurements by jointly leveraging graph signal processing (GSP) tools and deep learning (DL) techniques. The derivations of the GSP-KalmanNet are based on extending the KF to exploit the inherent graph structure via graph frequency domain filtering, which considerably simplifies the computational complexity entailed in processing high-dimensional signals and increases the robustness to small topology changes. Then, we use data to learn the Kalman gain following the recently proposed KalmanNet framework, which copes with partial and approximated modeling, without forcing a specific model over the noise statistics. Our empirical results demonstrate that the proposed GSP-KalmanNet achieves enhanced accuracy and run time performance as well as improved robustness to model misspecifications compared with both model-based and data-driven benchmarks.Comment: Submitted for possible publication in the IEE

KALMANBOT: KalmanNet-Aided Bollinger Bands for Pairs Trading

Pairs trading is a family of trading policies based on monitoring the relationships between pairs of assets. A common pairs trading approach relies on state space (SS) modeling, from which financial indicators can be obtained with low complexity and latency using a Kalman filter (KF), and processed using classic policies such as Bollinger bands (BB). However, such SS models are inherently approximated and mismatched, often degrading the revenue. In this work we propose KalmanBOT, a data-aided policy that preserves the advantages of KF-aided BB policies while leveraging data to overcome the approximated nature of the SS model. We adopt the recent KalmanNet architecture, and approximate the BB policy with a differentiable mapping, converting the policy into a trainable model. We empirically demonstrate that KalmanBOT yields improved rewards compared with model-based and data-driven benchmarks

RobustStateNet: Robust ego vehicle state estimation for Autonomous Driving

Control of an ego vehicle for Autonomous Driving (AD) requires an accurate definition of its state. Implementation of various model-based Kalman Filtering (KF) techniques for state estimation is prevalent in the literature. These algorithms use measurements from IMU and input signals from steering and wheel encoders for motion prediction with physics-based models, and a Global Navigation Satellite System(GNSS) for global localization. Such methods are widely investigated and majorly focus on increasing the accuracy of the estimation. Ego motion prediction in these approaches does not model the sensor failure modes and assumes completely known dynamics with motion and measurement model noises. In this work, we propose a novel Recurrent Neural Network (RNN) based motion predictor that parallelly models the sensor measurement dynamics and selectively fuses the features to increase the robustness of prediction, in particular in scenarios where we witness sensor failures. This motion predictor is integrated into a KF-like framework, RobustStateNet that takes a global position from the GNSS sensor and updates the predicted state. We demonstrate that the proposed state estimation routine outperforms the Model-Based KF and KalmanNet architecture in terms of estimation accuracy and robustness. The proposed algorithms are validated in the modified NuScenes CAN bus dataset, designed to simulate various types of sensor failures