On the optimality of two-stage Kalman filtering for systems with unknown inputs

2010 ◽  
pp. n/a-n/a ◽  
Author(s):  
Chien-Shu Hsieh
Keyword(s):  
Kalman Filtering ◽  
Two Stage ◽  
Unknown Inputs

scholarly journals Globally Optimal Distributed Kalman Filtering for Multisensor Systems with Unknown Inputs

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 2976 ◽  
Author(s):  
Yali Ruan ◽  
Yingting Luo ◽  
Yunmin Zhu
Keyword(s):  
State Estimation ◽  
Kalman Filtering ◽  
Optimal Algorithm ◽  
The State ◽  
Unknown Input ◽  
Initial Value ◽  
State Estimate ◽  
Multisensor Systems ◽  
Unknown Inputs ◽  
Augmented State

In this paper, the state estimation for dynamic system with unknown inputs modeled as an autoregressive AR (1) process is considered. We propose an optimal algorithm in mean square error sense by using difference method to eliminate the unknown inputs. Moreover, we consider the state estimation for multisensor dynamic systems with unknown inputs. It is proved that the distributed fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurement; therefore, it achieves the best performance. The computation complexity of the traditional augmented state algorithm increases with the augmented state dimension. While, the new algorithm shows good performance with much less computations compared to that of the traditional augmented state algorithms. Moreover, numerical examples show that the performances of the traditional algorithms greatly depend on the initial value of the unknown inputs, if the estimation of initial value of the unknown input is largely biased, the performances of the traditional algorithms become quite worse. However, the new algorithm still works well because it is independent of the initial value of the unknown input.

scholarly journals Two-Stage Cubature Kalman Filtering Based on T-Transform and Its Application

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Lu Zhang ◽  
Qiugen Xiao ◽  
Hailun Wang ◽  
Yinyin Hou
Keyword(s):  
Kalman Filtering ◽  
Equivalent Transformation ◽  
Block Diagonalization ◽  
Tracking Accuracy ◽  
Two Stage ◽  
Filtering Algorithm ◽  
Actual Application ◽  
Wheeled Robot ◽  
The Matrix ◽  
Kalman Filtering Algorithm

According to the actual application system model which has bias, this paper analyzes the shortage of the conventional augmented algorithm, the two-stage cubature Kalman filtering algorithm, which is presented on the basis of a two-stage nonlinear transformation. The core ideas of the algorithm are to obtain the block diagonalization of the covariance matrix using the matrix transformation and avoid calculating the covariance of the state and bias to reduce the amount of calculation and ensure a smooth filtering process. Then, the equivalence of the two-stage cubature Kalman filtering algorithm and the cubature Kalman filtering algorithm is proved by updating equivalent transformation. Through the experiment of trajectory tracking of a wheeled robot, it is verified that the two-stage cubature Kalman filtering algorithm can obtain good tracking accuracy and stability with the presence of unknown random bias. Simultaneously, the equivalence of the two-stage cubature Kalman filtering algorithm and cubature Kalman filtering algorithm is verified again using the contrast experiment.

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