Kalman Filter Divergence and Aircraft Motion Estimators

1978 ◽  
Vol 1 (1) ◽  
pp. 71-79 ◽  
Author(s):  
Arthur E. Bryson
Keyword(s):  
Kalman Filter ◽  
Aircraft Motion ◽  
Filter Divergence

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.

Review of the Ensemble Kalman Filter for Atmospheric Data Assimilation

2016 ◽  
Vol 144 (12) ◽  
pp. 4489-4532 ◽  
Author(s):  
P. L. Houtekamer ◽  
Fuqing Zhang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Hybrid Systems ◽  
Ensemble Kalman Filter ◽  
Satellite Observations ◽  
General Description ◽  
System Error ◽  
Radar Observations ◽  
Atmospheric Data ◽  
Filter Divergence

Abstract This paper reviews the development of the ensemble Kalman filter (EnKF) for atmospheric data assimilation. Particular attention is devoted to recent advances and current challenges. The distinguishing properties of three well-established variations of the EnKF algorithm are first discussed. Given the limited size of the ensemble and the unavoidable existence of errors whose origin is unknown (i.e., system error), various approaches to localizing the impact of observations and to accounting for these errors have been proposed. However, challenges remain; for example, with regard to localization of multiscale phenomena (both in time and space). For the EnKF in general, but higher-resolution applications in particular, it is desirable to use a short assimilation window. This motivates a focus on approaches for maintaining balance during the EnKF update. Also discussed are limited-area EnKF systems, in particular with regard to the assimilation of radar data and applications to tracking severe storms and tropical cyclones. It seems that relatively less attention has been paid to optimizing EnKF assimilation of satellite radiance observations, the growing volume of which has been instrumental in improving global weather predictions. There is also a tendency at various centers to investigate and implement hybrid systems that take advantage of both the ensemble and the variational data assimilation approaches; this poses additional challenges and it is not clear how it will evolve. It is concluded that, despite more than 10 years of operational experience, there are still many unresolved issues that could benefit from further research. Contents Introduction...4490 Popular flavors of the EnKF algorithm...4491 General description...4491 Stochastic and deterministic filters...4492 The stochastic filter...4492 The deterministic filter...4492 Sequential or local filters...4493 Sequential ensemble Kalman filters...4493 The local ensemble transform Kalman filter...4494 Extended state vector...4494 Issues for the development of algorithms...4495 Use of small ensembles...4495 Monte Carlo methods...4495 Validation of reliability...4497 Use of group filters with no inbreeding...4498 Sampling error due to limited ensemble size: The rank problem...4498 Covariance localization...4499 Localization in the sequential filter...4499 Localization in the LETKF...4499 Issues with localization...4500 Summary...4501 Methods to increase ensemble spread...4501 Covariance inflation...4501 Additive inflation...4501 Multiplicative inflation...4502 Relaxation to prior ensemble information...4502 Issues with inflation...4503 Diffusion and truncation...4503 Error in physical parameterizations...4504 Physical tendency perturbations...4504 Multimodel, multiphysics, and multiparameter approaches...4505 Future directions...4505 Realism of error sources...4506 Balance and length of the assimilation window...4506 The need for balancing methods...4506 Time-filtering methods...4506 Toward shorter assimilation windows...4507 Reduction of sources of imbalance...4507 Regional data assimilation...4508 Boundary conditions and consistency across multiple domains...4509 Initialization of the starting ensemble...4510 Preprocessing steps for radar observations...4510 Use of radar observations for convective-scale analyses...4511 Use of radar observations for tropical cyclone analyses...4511 Other issues with respect to LAM data assimilation...4511 The assimilation of satellite observations...4512 Covariance localization...4512 Data density...4513 Bias-correction procedures...4513 Impact of covariance cycling...4514 Assumptions regarding observational error...4514 Recommendations regarding satellite observations...4515 Computational aspects...4515 Parameters with an impact on quality...4515 Overview of current parallel algorithms...4516 Evolution of computer architecture...4516 Practical issues...4517 Approaching the gray zone...4518 Summary...4518 Hybrids with variational and EnKF components...4519 Hybrid background error covariances...4519 E4DVar with the α control variable...4519 Not using linearized models with 4DEnVar...4520 The hybrid gain algorithm...4521 Open issues and recommendations...4521 Summary and discussion...4521 Stochastic or deterministic filters...4522 The nature of system error...4522 Going beyond the synoptic scales...4522 Satellite observations...4523 Hybrid systems...4523 Future of the EnKF...4523 APPENDIX A...4524 Types of Filter Divergence...4524 Classical filter divergence...4524 Catastrophic filter divergence...4524 APPENDIX B...4524 Systems Available for Download...4524 References...4525

Vision-based terrain referenced navigation of aerial vehicles using an adaptive extended Kalman filter

2017 ◽  
Vol 232 (8) ◽  
pp. 1584-1597 ◽  
Author(s):  
Sung-Hoon Mok ◽  
Youngjoo Kim ◽  
Hyochoong Bang
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Least Squares Method ◽  
New Approach ◽  
Terrain Referenced Navigation ◽  
Digital Terrain ◽  
Highly Nonlinear ◽  
Noise Covariance ◽  
Adaptive Extended Kalman Filter ◽  
Filter Divergence

This paper addresses a vision-based terrain referenced navigation of an aircraft. A digital terrain map, in the surroundings of the aircraft, is compared with the camera measurements to estimate the aircraft position. Generally, the measurement equation in the terrain referenced navigation is highly nonlinear due to the sharp changes of terrain. Thus, the conventional extended Kalman filter could lead to unstable navigation solutions. In this paper, a new approach using an adaptive extended Kalman filter is proposed to cope up with the nonlinearity problem. A least squares method is utilized to derive the linearized measurement equations. The Jacobian matrix and sensor noise covariance are modified as a means of smoothing the sharp changes of terrain. Monte Carlo simulations verify that the proposed filter gives the stable navigation solutions, even when there is a large initial error, which is the primary reason for the filter divergence. Moreover, the proposed adaptation barely requires additional computational burden, whereas the high-order filters such as particle filter generally needs higher computational power.

scholarly journals The Robust Passive Location Algorithm for Maneuvering Target Tracking

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Xiaojun Yang ◽  
Gang Liu ◽  
Jinku Guo ◽  
Hongqiao Wang ◽  
Bing He
Keyword(s):  
Kalman Filter ◽  
Fuzzy Filter ◽  
Passive Location ◽  
Maneuvering Target Tracking ◽  
New Approach ◽  
Maneuvering Target ◽  
Change Of State ◽  
Location Algorithm ◽  
Filter Divergence ◽  
Location Methods

With the advantages such as high security and far responding distance, the passive location has a broad application in military and civil domains such as radar and aerospace. However, most of the current passive location methods are based on the framework of the probability theory and cannot be used to deal with fuzzy uncertainty in the passive location systems. Though the fuzzy Kalman filter can be used in the uncertainty systems, it could not deal with the abrupt change of state like the maneuvering target which will lead to the filter divergence. Therefore, in order to track the maneuvering target in the fuzzy passive system, we proposed a robust fuzzy extended Kalman filter based on the orthogonality principle and the fuzzy filter in the paper. Conclusion can be made based on the simulation result that this new approach is more precise and more robust than the fuzzy filter.

scholarly journals Sampling Errors in Ensemble Kalman Filtering. Part I: Theory

2008 ◽  
Vol 136 (8) ◽  
pp. 3035-3049 ◽  
Author(s):  
William Sacher ◽  
Peter Bartello
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
Test Case ◽  
Sampling Errors ◽  
Background Error ◽  
Theoretical Understanding ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Filter Divergence

Abstract This paper discusses the quality of the analysis given by the ensemble Kalman filter in a perfect model context when ensemble sizes are limited. The overall goal is to improve the theoretical understanding of the problem of systematic errors in the analysis variance due to the limited size of the ensemble, as well as the potential of the so-called double-ensemble Kalman filter, covariance inflation, and randomly perturbed analysis techniques to produce a stable analysis—that is to say, one not subject to filter divergence. This is achieved by expressing the error of the ensemble mean and the analysis error covariance matrix in terms of the sampling noise in the background error covariance matrix (owing to the finite ensemble estimation) and by comparing these errors for all methods. Theoretical predictions are confirmed with a simple scalar test case. In light of the analytical results obtained, the expression of the optimal covariance inflation factor is proposed in terms of the limited ensemble size and the Kalman gain.

scholarly journals Study of RobustH∞Filtering Application in Loosely Coupled INS/GPS System

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Lin Zhao ◽  
Haiyang Qiu ◽  
Yanming Feng
Keyword(s):  
Kalman Filter ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Lmi Approach ◽  
Model Case ◽  
Loosely Coupled ◽  
Filter Divergence ◽  
Gps System ◽  
The Relationship ◽  
Uncertain Dynamic System

Since a celebrate linear minimum mean square (MMS) Kalman filter in integration GPS/INS system cannot guarantee the robustness performance, aH∞filtering with respect to polytopic uncertainty is designed. The purpose of this paper is to give an illustration of this application and a contrast with traditional Kalman filter. A game theoryH∞filter is first reviewed; next we utilize linear matrix inequalities (LMI) approach to design the robustH∞filter. For the special INS/GPS model, unstable model case is considered. We give an explanation for Kalman filter divergence under uncertain dynamic system and simultaneously investigate the relationship betweenH∞filter and Kalman filter. A loosely coupled INS/GPS simulation system is given here to verify this application. Result shows that the robustH∞filter has a better performance when system suffers uncertainty; also it is more robust compared to the conventional Kalman filter.

scholarly journals Multi-Sensor Combined Measurement While Drilling Based on the Improved Adaptive Fading Square Root Unscented Kalman Filter

Sensors ◽  
2020 ◽  
Vol 20 (7) ◽  
pp. 1897
Author(s):  
Yi Yang ◽  
Fei Li ◽  
Yi Gao ◽  
Yanhui Mao
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Unscented Kalman Filter ◽  
Computational Method ◽  
Attitude Measurement ◽  
Square Root ◽  
Drilling Tool ◽  
Measurement While Drilling ◽  
Fading Factor ◽  
Filter Divergence

In the process of the attitude measurement for a steering drilling system, the measurement of the attitude parameters may be uncertain and unpredictable due to the influence of server vibration on bits. In order to eliminate the interference caused by vibration on the measurement and quickly obtain the accurate attitude parameters of the steering drilling tool, a new method for multi-sensor dynamic attitude combined measurement is presented. Firstly, by using a triaxial accelerometer and triaxial magnetometer measurement system, the nonlinear model based on the quaternion is established. Then, an improved adaptive fading square root unscented Kalman filter is proposed for eliminating the vibration disturbance signal. In this algorithm, the square root of the state covariance matrix is used to replace the covariance matrix in the classical unscented Kalman filter (UKF) to avoid the filter divergence caused by the negative definite state covariance matrix. The fading factor is introduced into UKF to adjust the filter gain in real-time and improve the adaptive ability of the algorithm to mutation state. Finally, the computational method of the fading factor is optimized to ensure the self-adaptability of the algorithm and reduce the computational complexity. The results of the laboratory test and the field-drilling data show that the proposed method can filter out the interference noise in the attitude measurement sensor effectively, improve the solution accuracy of attitude parameters of drilling tools in the case of abrupt changes in the measuring environment, and thus ensuring the dynamic stability of the well trajectory.

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