Asymptotic Behavior of the Estimation Error Covariance of Quaternion Estimators

2008 ◽  
Vol 31 (6) ◽  
pp. 1665-1676 ◽  
Author(s):  
Avishy Carmi ◽  
Yaakov Oshman
Keyword(s):  
Asymptotic Behavior ◽  
Estimation Error ◽  
Error Covariance

Improved square-root cubature information filter

2016 ◽  
Vol 39 (4) ◽  
pp. 579-588 ◽  
Author(s):  
Yulong Huang ◽  
Yonggang Zhang ◽  
Ning Li ◽  
Lin Zhao
Keyword(s):  
Large Scale ◽  
Estimation Error ◽  
Sampling Interval ◽  
Prediction Errors ◽  
Square Root ◽  
Sigma Point ◽  
Theoretical Comparison ◽  
Error Covariance ◽  
Information Filter ◽  
Scale Matrix

In this paper, a theoretical comparison between existing the sigma-point information filter (SPIF) framework and the unscented information filter (UIF) framework is presented. It is shown that the SPIF framework is identical to the sigma-point Kalman filter (SPKF). However, the UIF framework is not identical to the classical SPKF due to the neglect of one-step prediction errors of measurements in the calculation of state estimation error covariance matrix. Thus SPIF framework is more reasonable as compared with UIF framework. According to the theoretical comparison, an improved cubature information filter (CIF) is derived based on the superior SPIF framework. Square-root CIF (SRCIF) is also developed to improve the numerical accuracy and stability of the proposed CIF. The proposed SRCIF is applied to a target tracking problem with large sampling interval and high turn rate, and its performance is compared with the existing SRCIF. The results show that the proposed SRCIF is more reliable and stable as compared with the existing SRCIF. Note that it is impractical for information filters in large-scale applications due to the enormous computational complexity of large-scale matrix inversion, and advanced techniques need to be further considered.

scholarly journals Minimax Robust Optimal Estimation Fusion for Distributed Multisensor Systems with a Relative Entropy Uncertainty

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Hua Li ◽  
Jie Zhou
Keyword(s):  
Robust Estimation ◽  
Relative Entropy ◽  
Estimation Error ◽  
Optimal Estimation ◽  
Minimum Variance ◽  
Estimation Errors ◽  
Multisensor Systems ◽  
Error Covariance ◽  
Local Estimation ◽  
Estimation Fusion

This paper considers the robust estimation fusion problem for distributed multisensor systems with uncertain correlations of local estimation errors. For an uncertain class characterized by the Kullback-Leibler (KL) divergence from the actual model to nominal model of local estimation error covariance, the robust estimation fusion problem is formulated to find a linear minimum variance unbiased estimator for the least favorable model. It is proved that the optimal fuser under nominal correlation model is robust while the estimation error has a relative entropy uncertainty.

scholarly journals Fractional baud-length coding

2011 ◽  
Vol 29 (6) ◽  
pp. 1189-1196
Author(s):  
J. Vierinen
Keyword(s):  
Estimation Error ◽  
Estimation Accuracy ◽  
Target Range ◽  
Estimation Errors ◽  
Range Resolution ◽  
Error Covariance ◽  
Novel Approach ◽  
Amplitude Estimation ◽  
Radar Measurements ◽  
Low Altitude

Abstract. We present a novel approach for modulating radar transmissions in order to improve target range and Doppler estimation accuracy. This is achieved by using non-uniform baud lengths. With this method it is possible to increase sub-baud range-resolution of phase coded radar measurements while maintaining a narrow transmission bandwidth. We first derive target backscatter amplitude estimation error covariance matrix for arbitrary targets when estimating backscatter in amplitude domain. We define target optimality and discuss different search strategies that can be used to find well performing transmission envelopes. We give several simulated examples of the method showing that fractional baud-length coding results in smaller estimation errors than conventional uniform baud length transmission codes when estimating the target backscatter amplitude at sub-baud range resolution. We also demonstrate the method in practice by analyzing the range resolved power of a low-altitude meteor trail echo that was measured using a fractional baud-length experiment with the EISCAT UHF system.

scholarly journals Model-Based Clustering with Measurement or Estimation Errors

Genes ◽  
2020 ◽  
Vol 11 (2) ◽  
pp. 185 ◽  
Author(s):  
Wanli Zhang ◽  
Yanming Di
Keyword(s):  
Finite Mixture Models ◽  
Estimation Error ◽  
Covariance Matrices ◽  
Finite Mixture ◽  
Estimation Errors ◽  
Data Set ◽  
Component Distribution ◽  
Model Based Clustering ◽  
Model Based ◽  
Error Covariance

Model-based clustering with finite mixture models has become a widely used clustering method. One of the recent implementations is MCLUST. When objects to be clustered are summary statistics, such as regression coefficient estimates, they are naturally associated with estimation errors, whose covariance matrices can often be calculated exactly or approximated using asymptotic theory. This article proposes an extension to Gaussian finite mixture modeling—called MCLUST-ME—that properly accounts for the estimation errors. More specifically, we assume that the distribution of each observation consists of an underlying true component distribution and an independent measurement error distribution. Under this assumption, each unique value of estimation error covariance corresponds to its own classification boundary, which consequently results in a different grouping from MCLUST. Through simulation and application to an RNA-Seq data set, we discovered that under certain circumstances, explicitly, modeling estimation errors, improves clustering performance or provides new insights into the data, compared with when errors are simply ignored, whereas the degree of improvement depends on factors such as the distribution of error covariance matrices.

scholarly journals An Error Evaluation Method for the Ship Angular Flexure Measurement Based on the Principle of Relevance

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Yutong Zhang ◽  
Xianglu Ma ◽  
Shiqiao Qin ◽  
Wei Wu ◽  
Wenfeng Tan
Keyword(s):  
Measurement Error ◽  
Evaluation Method ◽  
Estimation Error ◽  
Good Prediction ◽  
Error Evaluation ◽  
Prediction Formula ◽  
Matching Method ◽  
Error Covariance ◽  
Velocity Matching ◽  
Flexure Angle

Due to the lack of true ship angular flexure data, it is difficult to evaluate its measurement error of the angular velocity matching method in practice. In this paper, the cause of the measurement error of the ship flexure angle is analyzed in theory, and an evaluation method for the ship angular flexure measurement error based on the principle of relevance is proposed. The proposed method provides a prediction formula to describe the estimation error of the static flexure angle based on the off-diagonal elements of the error covariance matrix P in Kalman filtering. In addition, the optimized coefficient F is introduced to make the prediction error range better describe the real error variation. The optimized coefficient F ensures that the proposed formula has good prediction effects in all three directions. Simulations based on the actual measured ship flexure data are carried out, and the simulation results verify the capability of the prediction formula. The proposed method can be used in the evaluation of the ship flexure measurement error.

scholarly journals Optimal Sensor and Relay Nodes Power Scheduling for Remote State Estimation with Energy Constraint

Sensors ◽  
2020 ◽  
Vol 20 (4) ◽  
pp. 1073
Author(s):  
Yufei Han ◽  
Mengqi Cui ◽  
Shaojun Liu
Keyword(s):  
State Estimation ◽  
Estimation Error ◽  
Relay Node ◽  
Estimation Accuracy ◽  
Average Error ◽  
Relay Nodes ◽  
Trade Off ◽  
Error Covariance ◽  
Power Scheduling ◽  
Remote State Estimation

We study the sensor and relay nodes’ power scheduling problem for the remote state estimation in a Wireless Sensor Network (WSN) with relay nodes over a finite period of time given limited communication energy. We also explain why the optimal infinite time and energy case does not exist. Previous work applied a predefined threshold for the error covariance gap of two contiguous nodes in the WSN to adjust the trade-off between energy consumption and estimation accuracy. However, instead of adjusting the trade-off, we employ an algorithm to find the optimal sensor and relay nodes’ scheduling strategy that achieves the smallest estimation error within the given energy limit under our model assumptions. Our core idea is to unify the sensor-to-relay-node way of error covariance update with the relay-node-to-relay-node way by converting the former way of the update into the latter, which enables us to compare the average error covariances of different scheduling sequences with analytical methods and thus finding the strategy with the minimal estimation error. Examples are utilized to demonstrate the feasibility of converting. Meanwhile, we prove the optimality of our scheduling algorithm. Finally, we use MATLAB to run our algorithm and compute the average estimation error covariance of the optimal strategy. By comparing the average error covariance of our strategy with other strategies, we find that the performance of our strategy is better than the others in the simulation.

scholarly journals UKF-Based Vehicle Pose Estimation under Randomly Occurring Deception Attacks

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Xinghua Liu ◽  
Dandan Bai ◽  
Yunling Lv ◽  
Rui Jiang ◽  
Shuzhi Sam Ge
Keyword(s):  
Kalman Filter ◽  
Pose Estimation ◽  
Upper Bound ◽  
Unscented Kalman Filter ◽  
Estimation Error ◽  
Accurate Estimation ◽  
Ground Vehicles ◽  
Ground Vehicle ◽  
Attack Model ◽  
Error Covariance

Considering various cyberattacks aiming at the Internet of Vehicles (IoV), secure pose estimation has become an essential problem for ground vehicles. This paper proposes a pose estimation approach for ground vehicles under randomly occurring deception attacks. By modeling attacks as signals added to measurements with a certain probability, the attack model has been presented and incorporated into the existing process and measurement equations of ground vehicle pose estimation based on multisensor fusion. An unscented Kalman filter-based secure pose estimator is then proposed to generate a stable estimate of the vehicle pose states; i.e., an upper bound for the estimation error covariance is guaranteed. Finally, the simulation and experiments are conducted on a simple but effective single-input-single-output dynamic system and the ground vehicle model to show the effectiveness of UKF-based secure pose estimation. Particularly, the proposed scheme outperforms the conventional Kalman filter, not only by resulting in more accurate estimation but also by providing a theoretically proved upper bound of error covariance matrices that could be used as an indication of the estimator’s status.

Polynomial Filtering Algorithm Applied to Navigation Data Processing under Quadratic Nonlinearities in System and Measurement Equations. Part 1. Description and Comparison with Kalman Type Algorithms

2021 ◽  
Vol 29 (3) ◽  
pp. 3-33
Author(s):  
О.А. Stepanov ◽  
◽  
Yu.A. Litvinenko ◽  
V.A. Vasiliev ◽  
A.B. Toropov ◽  
...  
Keyword(s):  
Data Processing ◽  
Estimation Error ◽  
Recursive Algorithm ◽  
Filtering Algorithm ◽  
Navigation Data ◽  
Error Covariance ◽  
Quadratic Nonlinearities ◽  
Measurement Equations ◽  
Polynomial Filtering ◽  
Previous Step

The paper considers the filtering problems solved in navigation data processing under quadratic nonlinearities both in system and measurement equations. A Kalman type recursive algorithm is proposed, where the predicted estimate and gain at each step are calculated based on the assumption on the Gaussian posterior proba-bility density function of the estimated vector at the previous step and minimization of estimation error covariance matrix using a linear procedure with respect to the current measurement. The similarities between this algorithm and other Kalman type algorithms such as extended and secondorder Kalman filters are discussed. The procedure for estimating the performance and comparing the algorithms is presented.

scholarly journals Optimal Waveform Selection for Robust Target Tracking

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Fengming Xin ◽  
Jinkuan Wang ◽  
Qiang Zhao ◽  
Yuhuan Wang
Keyword(s):  
Target Tracking ◽  
Estimation Error ◽  
Tracking Performance ◽  
Selection Algorithm ◽  
Error Covariance ◽  
Selection For ◽  
Zero Sum ◽  
Transmitted Waveform ◽  
Waveform Selection ◽  
State Error

This paper proposes a new optimal waveform selection algorithm for intelligent target tracking. In radar systems, optimal waveform is inspired by the improvements in performance. When the target is intelligent and tries to escape from detection, it will maximize the estimation error to degrade the target tracking performance. So the conventional tracking algorithms are not suitable for this situation. In this paper, we assume a one-dimension target model which will try to escape the radar detection to degrade the tracking performance. A new optimal waveform selection algorithm is proposed based on game theory for robust tracking. The robust received filter is first reviewed according to zero-sum game with the derivation of estimated state error covariance. The parameters for transmitted waveform that need to be optimized are found to be related to the robust filter. The optimal parameters for transmitted waveform are finally found by the minimization of the trace of the estimated state error covariance. Simulation results show the effectiveness of this new proposed algorithm for optimal waveform selection for intelligent target tracking.

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