We consider the problem of selecting an optimal set of sensor precisions to estimate the states of a non-linear dynamical system using an Ensemble Kalman filter and an Unscented Kalman filter, which uses random and deterministic ensembles respectively. Specifically, the goal is to choose at run-time, a sparse set of sensor precisions for active-sensing that satisfies certain constraints on the estimated state covariance. In this paper, we show that this sensor precision selection problem is a semidefinite programming problem when we use l1 norm over precision vector as the surrogate measure to induce sparsity. We formulate a sensor selection scheme over multiple time steps, for certain constraints on the terminal estimated state covariance.
Internet of Things (IoT) applications have opened up numerous possibilities to improve our lives. Most of the remote devices, part of the IoT network, such as smartphones, data loggers and wireless sensors are battery powered. It is vital to collect battery measurement data (Voltage or State-of-Charge (SOC)) from these remote devices. Presence of noise in these measurements restricts effective utilization of this dataset. This paper presents the application of Unscented Kalman Filter (UKF) to mitigate measurement noise in smartphone dataset. The simplicity of this technique makes it a construc…
In counter-adversarial systems, to infer the strategy of an intelligent adversarial agent, the defender agent needs to cognitively sense the information that the adversary has gathered about the latter. Prior works on the problem employ linear Gaussian state-space models and solve this inverse cognition problem by designing inverse stochastic filters. However, in practice, counter-adversarial systems are generally highly nonlinear. In this paper, we address this scenario by formulating inverse cognition as a nonlinear Gaussian state-space model, wherein the adversary employs an unscented Kalma…
Millimeter wave (mmWave) communication links for 5G cellular technology require high beamforming gain to overcome channel impairments and achieve high throughput. While much work has focused on estimating mmWave channels and designing beamforming schemes, the time dynamic nature of mmWave channels quickly renders estimates stale and increases sounding overhead. We model the underlying time dynamic state space of mmWave channels and design sounding beamformers suitable for tracking in a Kalman filtering framework. Given an initial channel estimate, filtering efficiently leads to refined estimat…
The Covid-19 pandemic has resulted in a variety of approaches for managing infection outbreaks in international populations. One example is mobile phone applications, which attempt to alert infected individuals and their contacts by automatically inferring two key components of infection risk: the proximity to an individual who may be infected, and the duration of proximity. The former component, proximity, relies on Bluetooth Low Energy (BLE) Received Signal Strength Indicator(RSSI) as a distance sensor, and this has been shown to be problematic; not least because of unpredictable variations …
State estimation when only a partial model of a considered system is available remains a major challenge in many engineering fields. This work proposes a joint, square-root unscented Kalman filter to estimate states and model uncertainties simultaneously by linear combinations of physics-motivated library functions. Using a sparsity promoting approach, a selection of those linear combinations is chosen and thus an interpretable model can be extracted. Results indicate a small estimation error compared to a traditional square-root unscented Kalman filter and exhibit the enhancement of physicall…
The problem of multisensor multitarget state estimation in the presence of constant but unknown sensor biases is investigated. The classical approach to this problem is to augment the state vector to include the states of all the targets and the sensor biases, and then implement an augmented state Kalman filter (ASKF). In this paper, we propose a novel decoupled Kalman filtering algorithm. The decoupled Kalman filtering first processes each target in a separate branch, namely the single-target Kalman filtering branch, where the single-target states and the sensor biases are estimated. Then the…
This paper concerns Kalman filtering when the measurements of the process are censored. The censored measurements are addressed by the Tobit model of Type I and are one-dimensional with two censoring limits, while the (hidden) state vectors are multidimensional. For this model, Bayesian estimates for the state vectors are provided through a recursive algorithm of Kalman filtering type. Experiments are presented to illustrate the effectiveness and applicability of the algorithm. The experiments show that the proposed method outperforms other filtering methodologies in minimizing the computation…
Neural Kalman Filtering for Unknown Dynamics: Task-Aware Learning with a Koopman Backbone
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）；Yonsei University（延世大学）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）；Weizmann Institute of Science（魏茨曼科学研究所）；Northeastern University（东北大学）
The real-world applications in signal processing generally involve estimating the system state or parameters in nonlinear, non-Gaussian dynamic systems. The estimation problem may get even more challenging when there are physical constraints on the system state. This tutorial-style paper reviews the Bayesian state estimation for (non)linear state-space systems and introduces the formulation of constrained state estimation in such scenarios. Specifically, we start by providing a review of unconstrained state estimation using Kalman filters (KF) for the linear systems and their extensions for no…
ETH Zürich（苏黎世联邦理工学院）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）；Eindhoven University of Technology（埃因霍温理工大学）；Phillips Research（飞利浦研究院）；Weizmann Institute of Science（魏茨曼科学研究所）
State estimation of dynamical systems in real-time is a fundamental task in signal processing. 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 r…
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 to do Kalman filtering on infinite-dimensional systems using Gaussian processes. This is possible because i) we are obtaining a linear model from numerical Gaussian processes, and ii) the states of this model are by definition Gaussian distributed random variables. Convenient prop…
