Constrained Abridged Gaussian Sum Extended Kalman Filter: Constrained Nonlinear Systems with Non-Gaussian Noises and Uncertainties

Author(s):  
Mahshad Valipour ◽  
Luis A. Ricardez-Sandoval
Author(s):  
Jean Walrand

AbstractIn Chapter Tracking: A, we explained the estimation of a random variable based on observations. We also described the Kalman filter and we gave a number of examples. In this chapter, we derive the Kalman filter and explain some of its properties. We also discuss the extended Kalman filter.Section 10.1 explains how to update an estimate as one makes additional observations. Section 10.2 derives the Kalman filter. The properties of the Kalman filter are explained in Sect. 10.3. Section 10.4 shows how the Kalman filter is extended to nonlinear systems.


2020 ◽  
Vol 53 (1-2) ◽  
pp. 250-261
Author(s):  
B Omkar Lakshmi Jagan ◽  
S Koteswara Rao

The aim of this paper is to evaluate the performance of different filtering algorithms in the presence of non-Gaussian noise environment for tracking underwater targets, using Doppler frequency and bearing measurements. The tracking using Doppler frequency and bearing measurements is popularly known as Doppler-bearing tracking. Here the measurements, that is, bearings and Doppler frequency, are considered to be corrupted with two types of non-Gaussian noises namely shot noise and Gaussian mixture noise. The non-Gaussian noise sampled measurements are assumed to be obtained (a) randomly throughout the process and (b) repeatedly at some particular time samples. The efficiency of these filters with the increase in non-Gaussian noise samples is discussed in this paper. The performance of filters is compared with that of Cramer-Rao Lower Bound. Doppler-bearing extended Kalman filter and Doppler-bearing unscented Kalman filter are chosen for this work.


Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 293 ◽  
Author(s):  
Zhiyu Zhang ◽  
Jinzhe Qiu ◽  
Wentao Ma

Monitoring the current operation status of the power system plays an essential role in the enhancement of the power grid for future requirements. Therefore, the real-time state estimation (SE) of the power system has been of widely-held concern. The Kalman filter is an outstanding method for the SE, and the noise in the system is generally assumed to be Gaussian noise. In the actual power system however, these measurements are usually disturbed by non-Gaussian noises in practice. Furthermore, it is hard to get the statistics of the state noise and measurement noise. As a result, a novel adaptive extended Kalman filter with correntropy loss is proposed and applied for power system SE in this paper. Firstly, correntropy is used to improve the robustness of the EKF algorithm in the presence of non-Gaussian noises and outliers. In addition, an adaptive update mechanism of the covariance matrixes of the measurement and process noises is introduced into the EKF with correntropy loss to enhance the accuracy of the algorithm. Extensive simulations are carried out on IEEE 14-bus and IEEE 30-bus test systems to verify the feasibility and robustness of the proposed algorithm.


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