Reduction of prediction error sensitivity to parameters in Kalman filter

2021 ◽  
Author(s):  
Jaroslav Tabacek ◽  
Vladimir Havlena
Keyword(s):  
Kalman Filter ◽  
Prediction Error ◽  
Error Sensitivity

scholarly journals Iterative and Algebraic Algorithms for the Computation of the Steady State Kalman Filter Gain

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Nicholas Assimakis ◽  
Maria Adam
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Prediction Error ◽  
Covariance Matrices ◽  
Asymptotically Stable ◽  
System Parameters ◽  
Estimation And Prediction ◽  
Error Covariance ◽  
Algebraic Algorithms ◽  
Time Invariant

The Kalman filter gain arises in linear estimation and is associated with linear systems. The gain is a matrix through which the estimation and the prediction of the state as well as the corresponding estimation and prediction error covariance matrices are computed. For time invariant and asymptotically stable systems, there exists a steady state value of the Kalman filter gain. The steady state Kalman filter gain is usually derived via the steady state prediction error covariance by first solving the corresponding Riccati equation. In this paper, we present iterative per-step and doubling algorithms as well as an algebraic algorithm for the steady state Kalman filter gain computation. These algorithms hold under conditions concerning the system parameters. The advantage of these algorithms is the autonomous computation of the steady state Kalman filter gain.

scholarly journals Novel Soil Moisture Estimates Combining the Ensemble Kalman Filter Data Assimilation and the Method of Breeding Growing Modes

2020 ◽  
Vol 12 (5) ◽  
pp. 889 ◽  
Author(s):  
Yize Li ◽  
Hong Shu ◽  
B. G. Mousa ◽  
Zhenhang Jiao
Keyword(s):  
Soil Moisture ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Model Prediction ◽  
Ensemble Kalman Filter ◽  
Prediction Error ◽  
Model Error ◽  
Drought Monitoring ◽  
Estimation Accuracy ◽  
Initial Field

Soil moisture plays an important role in climate prediction and drought monitoring. Data assimilation, as a method of integrating multi-geographic spatial data, plays an increasingly important role in estimating soil moisture. Model prediction error, an important part of the background field information, occupies a position that could not be ignored in data assimilation. The model prediction error in data assimilation consists of three parts: forcing data error, initial field error, and model error. However, the influence of model error in current data assimilation methods has not been completely considered in many studies. Therefore, we proposed a theoretical framework of the ensemble Kalman filter (EnKF) data assimilation based on the breeding of growing modes (BGM) method. This framework used the BGM method to perturb the initial field error term w of EnKF, and the EnKF data assimilation to assimilate the data to obtain the soil moisture analysis value. The feasibility and superiority of the proposed framework were verified, taking into consideration breeding length and ensemble size through experiments. We conducted experiments and evaluated the accuracy of the BGM and the Monte Carlo (MC) methods. The experiment showed that the BGM method could improve the estimation accuracy of the assimilated soil moisture and solve the problem of model error which is not fully expressed in data assimilation. This study can be widely used in data assimilation and has a significant role in weather forecast and drought monitoring.

THE KALMAN FILTER AS A PREDICTION ERROR FILTER*

1972 ◽  
Vol 20 (3) ◽  
pp. 549-560 ◽  
Author(s):  
N. OTT ◽  
H. G. MEDER
Keyword(s):  
Kalman Filter ◽  
Prediction Error

scholarly journals Kalman Filter Riccati Equation for the Prediction, Estimation, and Smoothing Error Covariance Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Nicholas Assimakis ◽  
Maria Adam
Keyword(s):  
Kalman Filter ◽  
Riccati Equation ◽  
Discrete Time ◽  
Prediction Error ◽  
Estimation Error ◽  
Riccati Equations ◽  
Covariance Matrices ◽  
Linear Estimation ◽  
Solution Algorithms ◽  
Error Covariance

The classical Riccati equation for the prediction error covariance arises in linear estimation and is derived by the discrete time Kalman filter equations. New Riccati equations for the estimation error covariance as well as for the smoothing error covariance are presented. These equations have the same structure as the classical Riccati equation. The three equations are computationally equivalent. It is pointed out that the new equations can be solved via the solution algorithms for the classical Riccati equation using other well-defined parameters instead of the original Kalman filter parameters.

scholarly journals Adaptive Cultural Algorithm-Based Cuckoo Search for Time-Dependent Vehicle Routing Problem with Stochastic Customers Using Adaptive Fractional Kalman Speed Prediction

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
H. Xue
Keyword(s):  
Kalman Filter ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Prediction Error ◽  
Cuckoo Search ◽  
Urban Traffic ◽  
Time Dependent ◽  
Cultural Algorithm ◽  
Routing Problem ◽  
Speed Prediction

For the Time-Dependent Vehicle Routing Problem with Stochastic Customers (TDVRPSC), an adaptive Cultural Algorithm-Based Cuckoo Search (CACS) has been proposed in this paper. The convergence of the new algorithm is proved. An adaptive fractional Kalman filter (AFKF) for traffic speed prediction is proposed. An adaptive mechanism for choosing the covariance of state noise is designed. Its mathematical process is proved. Several benchmark instances with different scales are tested, and new solutions are discovered, which are better than the published solutions. The effects of the parameters on the convergence and the results are studied. According to cargo weight of customers to be delivered, the customers can be divided into large, small, and retail customers. The algorithm is tested with fixed demand probability and also different customer types with stochastic demand. The traffic speeds in different business districts in Xiamen at different times are predicted by AFKF. The results show that AFKF has smaller prediction error and better prediction accuracy than fractional Kalman filter and Kalman filter. The effect of different fractional orders on prediction error is compared. The performance of the new algorithm is compared with that of the cultural algorithm and the Cuckoo Search. The result shows that the new algorithm can efficiently and effectively solve DTVRPSC and improve the accuracy of vehicle routing planning of time-varying actual urban traffic road.

scholarly journals Replacing the spotlight with a Kalman filter: A prediction error model of multiple object tracking

2014 ◽  
Vol 14 (10) ◽  
pp. 358-358
Author(s):  
A. M. Sherman ◽  
T. F. Yago Vicente ◽  
G. J. Zelinsky
Keyword(s):  
Kalman Filter ◽  
Object Tracking ◽  
Prediction Error ◽  
Multiple Object Tracking ◽  
Error Model ◽  
Multiple Object

Using Conventional Articulation Tests With Highly Unintelligible Children

1992 ◽  
Vol 23 (1) ◽  
pp. 52-60 ◽  
Author(s):  
Pamela G. Garn-Nunn ◽  
Vicki Martin
Keyword(s):  
Test Results ◽  
Phonological Processes ◽  
Rule Based ◽  
Severity Level ◽  
Error Sensitivity ◽  
Conventional Tests ◽  
Severity Levels ◽  
Conventional Test ◽  
Impaired Children

This study explored whether or not standard administration and scoring of conventional articulation tests accurately identified children as phonologically disordered and whether or not information from these tests established severity level and programming needs. Results of standard scoring procedures from the Assessment of Phonological Processes-Revised, the Goldman-Fristoe Test of Articulation, the Photo Articulation Test, and the Weiss Comprehensive Articulation Test were compared for 20 phonologically impaired children. All tests identified the children as phonologically delayed/disordered, but the conventional tests failed to clearly and consistently differentiate varying severity levels. Conventional test results also showed limitations in error sensitivity, ease of computation for scoring procedures, and implications for remediation programming. The use of some type of rule-based analysis for phonologically impaired children is highly recommended.

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