Second-order autoregressive model-based Kalman filter for the estimation of a slow fading channel described by the Clarke model: Optimal tuning and interpretation

State estimation is widely used in various automated systems, including IoT systems, unmanned systems, robots, etc. In traditional state estimation, measurement data are instantaneous and processed in real time. With modern systems’ development, sensors can obtain more and more signals and store them. Therefore, how to use these measurement big data to improve the performance of state estimation has become a hot research issue in this field. This paper reviews the development of state estimation and future development trends. First, we review the model-based state estimation methods, including the Kalman filter, such as the extended Kalman filter (EKF), unscented Kalman filter (UKF), cubature Kalman filter (CKF), etc. Particle filters and Gaussian mixture filters that can handle mixed Gaussian noise are discussed, too. These methods have high requirements for models, while it is not easy to obtain accurate system models in practice. The emergence of robust filters, the interacting multiple model (IMM), and adaptive filters are also mentioned here. Secondly, the current research status of data-driven state estimation methods is introduced based on network learning. Finally, the main research results for hybrid filters obtained in recent years are summarized and discussed, which combine model-based methods and data-driven methods. This paper is based on state estimation research results and provides a more detailed overview of model-driven, data-driven, and hybrid-driven approaches. The main algorithm of each method is provided so that beginners can have a clearer understanding. Additionally, it discusses the future development trends for researchers in state estimation.

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Second order Kalman filtering channel estimation and machine learning methods for spectrum sensing in cognitive radio networks

Wireless Networks ◽

10.1007/s11276-021-02627-w ◽

2021 ◽

Author(s):

Olusegun Peter Awe ◽

Daniel Adebowale Babatunde ◽

Sangarapillai Lambotharan ◽

Basil AsSadhan

Keyword(s):

Machine Learning ◽

Kalman Filter ◽

Cognitive Radio ◽

Spectrum Sensing ◽

Cognitive Radio Networks ◽

Clustering Algorithm ◽

Polynomial Regression ◽

Primary User ◽

Radio Networks ◽

Second Order

AbstractWe address the problem of spectrum sensing in decentralized cognitive radio networks using a parametric machine learning method. In particular, to mitigate sensing performance degradation due to the mobility of the secondary users (SUs) in the presence of scatterers, we propose and investigate a classifier that uses a pilot based second order Kalman filter tracker for estimating the slowly varying channel gain between the primary user (PU) transmitter and the mobile SUs. Using the energy measurements at SU terminals as feature vectors, the algorithm is initialized by a K-means clustering algorithm with two centroids corresponding to the active and inactive status of PU transmitter. Under mobility, the centroid corresponding to the active PU status is adapted according to the estimates of the channels given by the Kalman filter and an adaptive K-means clustering technique is used to make classification decisions on the PU activity. Furthermore, to address the possibility that the SU receiver might experience location dependent co-channel interference, we have proposed a quadratic polynomial regression algorithm for estimating the noise plus interference power in the presence of mobility which can be used for adapting the centroid corresponding to inactive PU status. Simulation results demonstrate the efficacy of the proposed algorithm.

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Soft-sensors: Model-based estimation of inflow in horizontal wells using the extended Kalman filter

Flow Measurement and Instrumentation ◽

10.1016/j.flowmeasinst.2013.09.002 ◽

2013 ◽

Vol 34 ◽

pp. 91-104 ◽

Cited By ~ 11

Author(s):

A. Gryzlov ◽

W. Schiferli ◽

R.F. Mudde

Keyword(s):

Kalman Filter ◽

Extended Kalman Filter ◽

Horizontal Wells ◽

Soft Sensors ◽

Model Based

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Maximum Correntropy Criterion Constrained Kalman Filter

Volume 2: Mechatronics; Estimation and Identification; Uncertain Systems and Robustness; Path Planning and Motion Control; Tracking Control Systems; Multi-Agent and Networked Systems; Manufacturing; Intelligent Transportation and Vehicles; Sensors and Actuators; Diagnostics and Detection; Unmanned, Ground and Surface Robotics; Motion and Vibration Control Applications ◽

10.1115/dscc2017-5326 ◽

2017 ◽

Cited By ~ 1

Author(s):

Seyed Fakoorian ◽

Mahmoud Moosavi ◽

Reza Izanloo ◽

Vahid Azimi ◽

Dan Simon

Keyword(s):

Kalman Filter ◽

Gaussian Noise ◽

State Constraints ◽

Statistical Information ◽

Second Order ◽

System Model ◽

Error Covariance ◽

Inequality State ◽

Maximum Correntropy Criterion ◽

Non Gaussian

Non-Gaussian noise may degrade the performance of the Kalman filter because the Kalman filter uses only second-order statistical information, so it is not optimal in non-Gaussian noise environments. Also, many systems include equality or inequality state constraints that are not directly included in the system model, and thus are not incorporated in the Kalman filter. To address these combined issues, we propose a robust Kalman-type filter in the presence of non-Gaussian noise that uses information from state constraints. The proposed filter, called the maximum correntropy criterion constrained Kalman filter (MCC-CKF), uses a correntropy metric to quantify not only second-order information but also higher-order moments of the non-Gaussian process and measurement noise, and also enforces constraints on the state estimates. We analytically prove that our newly derived MCC-CKF is an unbiased estimator and has a smaller error covariance than the standard Kalman filter under certain conditions. Simulation results show the superiority of the MCC-CKF compared with other estimators when the system measurement is disturbed by non-Gaussian noise and when the states are constrained.

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