Flexible polarization demultiplexing method based on an adaptive process noise covariance Kalman filter

2018 ◽  
Vol 16 (6) ◽  
pp. 060601
Author(s):  
Jun Ge Jun Ge ◽  
Lianshan Yan Lianshan Yan ◽  
Anlin Yi Anlin Yi ◽  
Yan Pan Yan Pan ◽  
Lin Jiang Lin Jiang ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Process Noise ◽  
Adaptive Process ◽  
Noise Covariance

Detection of power quality disturbances using an adaptive process noise covariance Kalman filter

2018 ◽  
Vol 76 ◽  
pp. 34-49 ◽  
Author(s):  
Yanhui Xi ◽  
Zewen Li ◽  
Xiangjun Zeng ◽  
Xin Tang ◽  
Qiao Liu ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Power Quality ◽  
Process Noise ◽  
Adaptive Process ◽  
Noise Covariance ◽  
Power Quality Disturbances

scholarly journals Novel Process Noise Model for GNSS Kalman Filter Based on Sensitivity Analysis of Covariance with Poor Satellite Geometry

Sensors ◽  
2021 ◽  
Vol 21 (18) ◽  
pp. 6056
Author(s):  
Yoji Takayama ◽  
Takateru Urakubo ◽  
Hisashi Tamaki
Keyword(s):  
Kalman Filter ◽  
Estimation Error ◽  
Conventional Technique ◽  
Urban Environments ◽  
Analysis Of Covariance ◽  
Noise Model ◽  
Process Noise ◽  
Satellite Geometry ◽  
Noise Covariance ◽  
Filter Divergence

One of the great unsolved GNSS problems is inaccuracy in urban canyons due to Non-Line-Of-Sight (NLOS) signal reception. Owing to several studies about the NLOS signal rejection method, almost all NLOS signals can be excluded from the calculation of the position. However, such precise NLOS rejection would make satellite geometry poor, especially in dense urban environments. This paper points out, through numerical simulations and theoretical analysis, that poor satellite geometry leads to unintentional performance degradation of the Kalman filter with a conventional technique to prevent filter divergence. The conventional technique is to bump up process noise covariance, and causes unnecessary inflation of estimation-error covariance when satellite geometry is poor. We propose a novel choice of process noise covariance based on satellite geometry that can reduce such unnecessary inflation. Numerical and experimental results demonstrate that performance improvement can be achieved by the choice of process noise covariance even for a poor satellite geometry.

GDOP, Ridge Regression and the Kalman Filter

1990 ◽  
Vol 43 (03) ◽  
pp. 409-427 ◽  
Author(s):  
R. J. Kelly
Keyword(s):  
Kalman Filter ◽  
Ridge Regression ◽  
Navigation Systems ◽  
Process Noise ◽  
Navigation Problem ◽  
Navigation Signal ◽  
Noise Covariance ◽  
Regression Techniques ◽  
Signal Processors ◽  
Parameter Estimators

Multicollinearity and its effect on parameter estimators such as the Kalman filter is analysed using the navigation application as a special example. All position-fix navigation systems suffer loss of accuracy when their navigation landmarks are nearly collinear. Nearly collinear measurement geometry is termed the geometric dilution of position (GDOP). Its presence causes the errors of the position estimates to be highly inflated. In 1970 Hoerl and Kennard developed ridge regression to combat near collinearity when it arises in the predictor matrix of a linear regression model. Since GDOP is mathematically equivalent to a nearly collinear predictor matrix, Kelly suggested using ridge regression techniques in navigation signal processors to reduce the effects of GDOP. The original programme intended to use ridge regression not only to reduce variance inflation but also to reduce bias inflation. Reducing bias inflation is an extension of Hoerl's ridge concept by Kelly. Preliminary results show that ridge regression will reduce the effects of variance inflation caused by GDOP. However, recent results (Kelly) conclude it will not reduce bias inflation as it arises in the navigation problem, GDOP is not a mismatched estimator/model problem. Even with an estimator matched to the model, GDOP may inflate the MSE of the ordinary Kalman filter while the ridge recursive filter chooses a suitable biased estimator that will reduce the MSE. The main goal is obtaining a smaller MSE for the estimator, rather than minimizing the residual sum of squares. This is a different operation than tuning the Kalman filter's dynamic process noise covariance Q, in order to compensate for unmodelled errors. Although ridge regression has not yielded a satisfactory solution to the general GDOP problem, it has provided insight into exactly what causes multicollinearity in navigation signal processors such as the Kalman filter and under what conditions an estimator's performance can be improved.

Improving Adaptive Kalman Estimation in GPS/INS Integration

2007 ◽  
Vol 60 (3) ◽  
pp. 517-529 ◽  
Author(s):  
Weidong Ding ◽  
Jinling Wang ◽  
Chris Rizos ◽  
Doug Kinlyside
Keyword(s):  
A Priori ◽  
Optimal Solution ◽  
Window Size ◽  
Stochastic Modelling ◽  
Process Noise ◽  
Stringent Requirement ◽  
Adaptive Process ◽  
Covariance Matching ◽  
Noise Covariance ◽  
Optimal Window

The central task of GPS/INS integration is to effectively blend GPS and INS data together to generate an optimal solution. The present data fusion algorithms, which are mostly based on Kalman filtering (KF), have several limitations. One of those limitations is the stringent requirement on precise a priori knowledge of the system models and noise properties. Uncertainty in the covariance parameters of the process noise (Q) and the observation errors (R) may significantly degrade the filtering performance. The conventional way of determining Q and R relies on intensive analysis of empirical data. However, the noise levels may change in different applications. Over the past few decades adaptive KF algorithms have been intensively investigated with a view to reducing the influence of the Q and R definition errors. The covariance matching method has been shown to be one of the most promising techniques. This paper first investigates the utilization of an online stochastic modelling algorithm with regards to its parameter estimation stability, convergence, optimal window size, and the interaction between Q and R estimations. Then a new adaptive process noise scaling algorithm is proposed. Without artificial or empirical parameters being used, the proposed adaptive mechanism has demonstrated the capability of autonomously tuning the process noise covariance to the optimal magnitude, and hence improving the overall filtering performance.

Kalman Filter With Recursive Covariance Estimation—Sequentially Estimating Process Noise Covariance

2014 ◽  
Vol 61 (11) ◽  
pp. 6253-6263 ◽  
Author(s):  
Bo Feng ◽  
Mengyin Fu ◽  
Hongbin Ma ◽  
Yuanqing Xia ◽  
Bo Wang
Keyword(s):  
Kalman Filter ◽  
Covariance Estimation ◽  
Process Noise ◽  
Noise Covariance

The Selection of Process Noise Covariance Q and Measurement Noise Covariance R on Kalman Filter

2014 ◽  
Vol 513-517 ◽  
pp. 4342-4345 ◽  
Author(s):  
Chao Yi Wei ◽  
Shu Jian Ye ◽  
Xu Guang Li ◽  
Mei Zhi Xie ◽  
Feng Yan Yi
Keyword(s):  
Kalman Filter ◽  
Simulation Model ◽  
Dynamic Model ◽  
Measurement Noise ◽  
State Estimator ◽  
Process Noise ◽  
Measurement Noise Covariance ◽  
High Measurement ◽  
Noise Covariance ◽  
Selection Of

At first, a seven degree of freedom dynamic model of tractor semi-trailer was established, and a simulation model with the Matlab/Simulink software was established too. Based on the model, a state estimator based on Kalman theory was designed, using easily measured parameters to estimate the parameters that are difficultly measured or have high measurement cost, after that, compared estimated values and simulation measurements and analyzed the influence with changes of process noise covariance Q and measurement noise covariance R.

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