The paper is concerned with the basic properties of multivariate extreme value distribution (in the Logistic model). We obtain the characteristic function and recurrence formula of the density function. The explicit a...The paper is concerned with the basic properties of multivariate extreme value distribution (in the Logistic model). We obtain the characteristic function and recurrence formula of the density function. The explicit algebraic formula for Fisher information matrix is indicated. A simple and accurate procedure for generating random vector from multivariate extreme value distribution is presented.展开更多
The tracking of maneuvering targets in radar networking scenarios is studied in this paper.For the interacting multiple model algorithm and the expected-mode augmentation algorithm,the fixed base model set leads to a ...The tracking of maneuvering targets in radar networking scenarios is studied in this paper.For the interacting multiple model algorithm and the expected-mode augmentation algorithm,the fixed base model set leads to a mismatch between the model set and the target motion mode,which causes the reduction on tracking accuracy.An adaptive grid-expected-mode augmentation variable structure multiple model algorithm is proposed.The adaptive grid algorithm based on the turning model is extended to the two-dimensional pattern space to realize the self-adaptation of the model set.Furthermore,combining with the unscented information filtering,and by interacting the measurement information of neighboring radars and iterating information matrix with consistency strategy,a distributed target tracking algorithm based on the posterior information of the information matrix is proposed.For the problem of filtering divergence while target is leaving radar surveillance area,a k-coverage algorithm based on particle swarm optimization is applied to plan the radar motion trajectory for achieving filtering convergence.展开更多
Fault detection caused by single event effect( SEE) in system was studied,and an improved fault detection algorithm by fusing multi-information entropy for detecting soft error was proposed based on multi-objective de...Fault detection caused by single event effect( SEE) in system was studied,and an improved fault detection algorithm by fusing multi-information entropy for detecting soft error was proposed based on multi-objective detection approach and classification management method. In the improved fault detection algorithm, the analysis model of posteriori information with corresponding multi-fault alternative detection points was formulated through correlation information matrix, and the maximum incremental information entropy was chosen as the classification principle for the optimal detection points. A system design example was given to prove the rationality and feasibility of this algorithm.This fault detection algorithm can achieve the purpose of fault detection and resource configuration with high efficiency.展开更多
Intrusion detection is critical to guaranteeing the safety of the data in the network.Even though,since Internet commerce has grown at a breakneck pace,network traffic kinds are rising daily,and network behavior chara...Intrusion detection is critical to guaranteeing the safety of the data in the network.Even though,since Internet commerce has grown at a breakneck pace,network traffic kinds are rising daily,and network behavior characteristics are becoming increasingly complicated,posing significant hurdles to intrusion detection.The challenges in terms of false positives,false negatives,low detection accuracy,high running time,adversarial attacks,uncertain attacks,etc.lead to insecure Intrusion Detection System(IDS).To offset the existing challenge,the work has developed a secure Data Mining Intrusion detection system(DataMIDS)framework using Functional Perturbation(FP)feature selection and Bengio Nesterov Momentum-based Tuned Generative Adversarial Network(BNM-tGAN)attack detection technique.The data mining-based framework provides shallow learning of features and emphasizes feature engineering as well as selection.Initially,the IDS data are analyzed for missing values based on the Marginal Likelihood Fisher Information Matrix technique(MLFIMT)that identifies the relationship among the missing values and attack classes.Based on the analysis,the missing values are classified as Missing Completely at Random(MCAR),Missing at random(MAR),Missing Not at Random(MNAR),and handled according to the types.Thereafter,categorical features are handled followed by feature scaling using Absolute Median Division based Robust Scalar(AMDRS)and the Handling of the imbalanced dataset.The selection of relevant features is initiated using FP that uses‘3’Feature Selection(FS)techniques i.e.,Inverse Chi Square based Flamingo Search(ICS-FSO)wrapper method,Hyperparameter Tuned Threshold based Decision Tree(HpTT-DT)embedded method,and Xavier Normal Distribution based Relief(XavND-Relief)filter method.Finally,the selected features are trained and tested for detecting attacks using BNM-tGAN.The Experimental analysis demonstrates that the introduced DataMIDS framework produces an accurate diagnosis about the attack with low computation time.The work avoids false alarm rate of attacks and remains to be relatively robust against malicious attacks as compared to existing methods.展开更多
This article investigates the optimal observation configuration of unmanned aerial vehicles(UAVs) based on angle and range measurements, and generalizes predecessors' researches in two dimensions into three dimens...This article investigates the optimal observation configuration of unmanned aerial vehicles(UAVs) based on angle and range measurements, and generalizes predecessors' researches in two dimensions into three dimensions. The relative geometry of the UAVs-target will significantly affect the state estimation performance of the target, the cost function based on the Fisher information matrix(FIM) is used to derive the FIM determinant of UAVs' observation in three-dimensional space, and the optimal observation geometric configuration that maximizes the determinant of the FIM is obtained. It is shown that the optimal observation configuration of the UAVs-target is usually not unique, and the optimal observation configuration is proved for two UAVs and three UAVs in three-dimension. The long-range over-the-horizon target tracking is simulated and analyzed based on the analysis of optimal observation configuration for two UAVs. The simulation results show that the theoretical analysis and control algorithm can effectively improve the positioning accuracy of the target. It can provide a helpful reference for the design of over-the-horizon target localization based on UAVs.展开更多
A new method is presented for prioritizing sensor locations for structural health monitoring (SHM). In view of the needs of SHM and damage detection,sensor locations are optimized for the purpose of both sensitivity f...A new method is presented for prioritizing sensor locations for structural health monitoring (SHM). In view of the needs of SHM and damage detection,sensor locations are optimized for the purpose of both sensitivity for local damages and independence of the target mode. However,the two different optimization criterions lead to an inconsistency of the optimal result. Considering the structural response changes that result from damage,the relationship between the structural response and damage is deduced from the structural motion equation by a quasi-analytical mode. Based on the harmony between damage identifiability and mode observability,an object function is set up,including the information of mode independence and damage sensitivity. Utilizing the technique of singular value decomposition,an interior algorithm for the optimum sensor placement is proposed with the multiple objective criterions of minimizing the condition number of coefficient matrix and maximizing the fisher information matrix. A numerical example shows that this approach can effectively avoid the contradiction between the two different optimization criterions. Comparing with the result of single object,the result of damage detection from the optical sensor locations is much more accurate.展开更多
In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become i...In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become its special cases. The statistical properties of the new distribution are studied in detail, its moment generating function, skewness coefficient, kurtosis coefficient, Fisher information matrix, maximum likelihood estimators are derived. Moreover, a random simulation study is carried out for test the performance of the estimators, the simulation results show that with the increase of sample size, the mean value of maximum likelihood estimators tends to the true value. The new distribution family provides a better fit compared with other known skew distributions through the analysis of a real data set.展开更多
Wavefront coding (WFC) is used to extend the field depth of an incoherent optical system by employing a phase mask on the pupil. We uses a Fisher information (FI) metric based optimization method to design a phase...Wavefront coding (WFC) is used to extend the field depth of an incoherent optical system by employing a phase mask on the pupil. We uses a Fisher information (FI) metric based optimization method to design a phase mask by taking the modulation transfer function (MTF) of the practical optical system into consid- eration. This method can modulate the wavefront so that the point spread function and optical transfer function are insensitive to the object distance. The simulation results show that the optimized phase mask based on the proposed method can further improve the defocusing image quality while maintaining the focusing image quality.展开更多
In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling called moving extremes ranked s...In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling called moving extremes ranked set sampling(MERSS)is considered for the Fisher information matrix for the location-scale family.The Fisher information matrix for this model are respectively derived under simple random sampling and MERSS.In order to give more insight into the performance of MERSS with respect to simple random sampling,the Fisher information matrix for usual locationscale distributions are respectively computed under the two sampling.The numerical results show that MERSS provides more information than simple random sampling in parametric inference.展开更多
Based on the standard angular momentum theory, we create an experiment on preparing maximally path- entangled ([N, 0] + [0, N〉]2 (NOON) states of triphotons. In order to explain the error between the theoretical ...Based on the standard angular momentum theory, we create an experiment on preparing maximally path- entangled ([N, 0] + [0, N〉]2 (NOON) states of triphotons. In order to explain the error between the theoretical and experimental data, we consider the background events during the experiment, and observe their effect on the uncertainty in S1- Afterwards, we calculate the quantum Fisher information (QFI) of the states to evaluate their potential applications in quantum metrology. Our results show that by adding the appropriate background terms, the theoretical data of the produced states matches well with the experimental data. In this case, the QFI of the states is lower than maximally entangled NOON states, but still higher than a classical state.展开更多
Target tracking using wireless sensor networks requires efficient collaboration among sensors to tradeoff between energy consumption and tracking accuracy. This paper presents a collaborative target tracking approach ...Target tracking using wireless sensor networks requires efficient collaboration among sensors to tradeoff between energy consumption and tracking accuracy. This paper presents a collaborative target tracking approach in wire- less sensor networks using the combination of maximum likelihood estimation and the Kalman filter. The cluster leader converts the received nonlinear distance measurements into linear observation model and approximates the covariance of the converted measurement noise using maximum likelihood estimation, then applies Kalman filter to recursively update the target state estimate using the converted measurements. Finally, a measure based on the Fisher information matrix of maximum likelihood estimation is used by the leader to select the most informative sensors as a new tracking cluster for further tracking. The advantages of the proposed collaborative tracking approach are demonstrated via simulation results.展开更多
For the purpose of structural health monitoring, a damage detection method combined with optimum sensor placement is proposed in this paper. The back sequential sensor placement (BSSP) algorithm is introduced to opt...For the purpose of structural health monitoring, a damage detection method combined with optimum sensor placement is proposed in this paper. The back sequential sensor placement (BSSP) algorithm is introduced to optimize the sensor locations with the aim of maximizing the 2-norm of information matrix, since the EI method is not suitable for optimum sensor placement based on eigenvector sensitivity analysis. Structural damage detection is carried out based on the respective advantages of mode shape and frequency. The optimized incomplete mode shapes yielded from the optimal sensor locations are used to localize structural damage. After the potential damage elements have been preliminarily identified, an iteration scheme is adopted to estimate the damage extent of the potential damage elements based on the changes in the frequency. The effectiveness of this method is demonstrated using a numerical example of a 31-bar truss structure.展开更多
The wavefront coding technique is used to enlarge the depth of field(DOF)of incoherent imaging systems. The key to wavefront coding lies in the design of suitable phase masks.To date,numerous kinds of phase masks ar...The wavefront coding technique is used to enlarge the depth of field(DOF)of incoherent imaging systems. The key to wavefront coding lies in the design of suitable phase masks.To date,numerous kinds of phase masks are proposed.However,further understanding is needed regarding phase mask with its phase function being in a standard sinusoidal form.Therefore,the characteristics of such a phase mask are studied in this letter.Deriving the defocused optical transfer function(OTF)analytically proves that the standard sinusoidal phase mask is effective in extending the DOF,and actual experiments confirm the numerical results.At the same time,with the Fisher information as a criterion,the standard sinusoidal phase mask shows a higher tolerance to focus errors(especially severe focus errors)than the classical cubic phase mask.展开更多
Non-random missing data poses serious problems in longitudinal studies. The binomial distribution parameter becomes to be unidentifiable without any other auxiliary information or assumption when it suffers from ignor...Non-random missing data poses serious problems in longitudinal studies. The binomial distribution parameter becomes to be unidentifiable without any other auxiliary information or assumption when it suffers from ignorable missing data. Existing methods are mostly based on the log-linear regression model. In this article, a model is proposed for longitudinal data with non-ignorable non-response. It is considered to use the pre-test baseline data to improve the identifiability of the post-test parameter. Furthermore, we derive the identified estimation (IE), the maximum likelihood estimation (MLE) and its associated variance for the post-test parameter. The simulation study based on the model of this paper shows that the proposed approach gives promising results.展开更多
An observation-driven method for coordinated standoff target tracking based on Model Predictive Control(MPC)is proposed to improve observation of multiple Unmanned Aerial Vehicles(UAVs)while approaching or loitering o...An observation-driven method for coordinated standoff target tracking based on Model Predictive Control(MPC)is proposed to improve observation of multiple Unmanned Aerial Vehicles(UAVs)while approaching or loitering over a target.After acquiring a fusion estimate of the target state,each UAV locally measures the observation capability of the entire UAV system with the Fisher Information Matrix(FIM)determinant in the decentralized architecture.To facilitate observation optimization,only the FIM determinant is adopted to derive the performance function and control constraints for coordinated standoff tracking.Additionally,a modified iterative scheme is introduced to improve the iterative efficiency,and a consistent circular direction control is established to maintain long-term observation performance when the UAV approaches its target.Sufficient experiments with simulated and real trajectories validate that the proposed method can improve observation of the UAV system for target tracking and adaptively optimize UAV trajectories according to sensor performance and UAV-target geometry.展开更多
文摘The paper is concerned with the basic properties of multivariate extreme value distribution (in the Logistic model). We obtain the characteristic function and recurrence formula of the density function. The explicit algebraic formula for Fisher information matrix is indicated. A simple and accurate procedure for generating random vector from multivariate extreme value distribution is presented.
基金the Joint Fund of Advanced Aerospace Manufacturing Technology Research(No.2017-JCJQ-ZQ-031)。
文摘The tracking of maneuvering targets in radar networking scenarios is studied in this paper.For the interacting multiple model algorithm and the expected-mode augmentation algorithm,the fixed base model set leads to a mismatch between the model set and the target motion mode,which causes the reduction on tracking accuracy.An adaptive grid-expected-mode augmentation variable structure multiple model algorithm is proposed.The adaptive grid algorithm based on the turning model is extended to the two-dimensional pattern space to realize the self-adaptation of the model set.Furthermore,combining with the unscented information filtering,and by interacting the measurement information of neighboring radars and iterating information matrix with consistency strategy,a distributed target tracking algorithm based on the posterior information of the information matrix is proposed.For the problem of filtering divergence while target is leaving radar surveillance area,a k-coverage algorithm based on particle swarm optimization is applied to plan the radar motion trajectory for achieving filtering convergence.
文摘Fault detection caused by single event effect( SEE) in system was studied,and an improved fault detection algorithm by fusing multi-information entropy for detecting soft error was proposed based on multi-objective detection approach and classification management method. In the improved fault detection algorithm, the analysis model of posteriori information with corresponding multi-fault alternative detection points was formulated through correlation information matrix, and the maximum incremental information entropy was chosen as the classification principle for the optimal detection points. A system design example was given to prove the rationality and feasibility of this algorithm.This fault detection algorithm can achieve the purpose of fault detection and resource configuration with high efficiency.
文摘Intrusion detection is critical to guaranteeing the safety of the data in the network.Even though,since Internet commerce has grown at a breakneck pace,network traffic kinds are rising daily,and network behavior characteristics are becoming increasingly complicated,posing significant hurdles to intrusion detection.The challenges in terms of false positives,false negatives,low detection accuracy,high running time,adversarial attacks,uncertain attacks,etc.lead to insecure Intrusion Detection System(IDS).To offset the existing challenge,the work has developed a secure Data Mining Intrusion detection system(DataMIDS)framework using Functional Perturbation(FP)feature selection and Bengio Nesterov Momentum-based Tuned Generative Adversarial Network(BNM-tGAN)attack detection technique.The data mining-based framework provides shallow learning of features and emphasizes feature engineering as well as selection.Initially,the IDS data are analyzed for missing values based on the Marginal Likelihood Fisher Information Matrix technique(MLFIMT)that identifies the relationship among the missing values and attack classes.Based on the analysis,the missing values are classified as Missing Completely at Random(MCAR),Missing at random(MAR),Missing Not at Random(MNAR),and handled according to the types.Thereafter,categorical features are handled followed by feature scaling using Absolute Median Division based Robust Scalar(AMDRS)and the Handling of the imbalanced dataset.The selection of relevant features is initiated using FP that uses‘3’Feature Selection(FS)techniques i.e.,Inverse Chi Square based Flamingo Search(ICS-FSO)wrapper method,Hyperparameter Tuned Threshold based Decision Tree(HpTT-DT)embedded method,and Xavier Normal Distribution based Relief(XavND-Relief)filter method.Finally,the selected features are trained and tested for detecting attacks using BNM-tGAN.The Experimental analysis demonstrates that the introduced DataMIDS framework produces an accurate diagnosis about the attack with low computation time.The work avoids false alarm rate of attacks and remains to be relatively robust against malicious attacks as compared to existing methods.
基金supported by the National Natural Science Foundation of China(61703419)。
文摘This article investigates the optimal observation configuration of unmanned aerial vehicles(UAVs) based on angle and range measurements, and generalizes predecessors' researches in two dimensions into three dimensions. The relative geometry of the UAVs-target will significantly affect the state estimation performance of the target, the cost function based on the Fisher information matrix(FIM) is used to derive the FIM determinant of UAVs' observation in three-dimensional space, and the optimal observation geometric configuration that maximizes the determinant of the FIM is obtained. It is shown that the optimal observation configuration of the UAVs-target is usually not unique, and the optimal observation configuration is proved for two UAVs and three UAVs in three-dimension. The long-range over-the-horizon target tracking is simulated and analyzed based on the analysis of optimal observation configuration for two UAVs. The simulation results show that the theoretical analysis and control algorithm can effectively improve the positioning accuracy of the target. It can provide a helpful reference for the design of over-the-horizon target localization based on UAVs.
基金Sponsored by the National Key Natural Science Foundation of China(Grant No.50439010)Key Project of Chinese Ministry of Education(Grant No.305003)
文摘A new method is presented for prioritizing sensor locations for structural health monitoring (SHM). In view of the needs of SHM and damage detection,sensor locations are optimized for the purpose of both sensitivity for local damages and independence of the target mode. However,the two different optimization criterions lead to an inconsistency of the optimal result. Considering the structural response changes that result from damage,the relationship between the structural response and damage is deduced from the structural motion equation by a quasi-analytical mode. Based on the harmony between damage identifiability and mode observability,an object function is set up,including the information of mode independence and damage sensitivity. Utilizing the technique of singular value decomposition,an interior algorithm for the optimum sensor placement is proposed with the multiple objective criterions of minimizing the condition number of coefficient matrix and maximizing the fisher information matrix. A numerical example shows that this approach can effectively avoid the contradiction between the two different optimization criterions. Comparing with the result of single object,the result of damage detection from the optical sensor locations is much more accurate.
文摘In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become its special cases. The statistical properties of the new distribution are studied in detail, its moment generating function, skewness coefficient, kurtosis coefficient, Fisher information matrix, maximum likelihood estimators are derived. Moreover, a random simulation study is carried out for test the performance of the estimators, the simulation results show that with the increase of sample size, the mean value of maximum likelihood estimators tends to the true value. The new distribution family provides a better fit compared with other known skew distributions through the analysis of a real data set.
基金supported by the National Natural Science Foundation of China(No.60777002)Ningbo Science and Technology Bureau(No.2008A610035).
文摘Wavefront coding (WFC) is used to extend the field depth of an incoherent optical system by employing a phase mask on the pupil. We uses a Fisher information (FI) metric based optimization method to design a phase mask by taking the modulation transfer function (MTF) of the practical optical system into consid- eration. This method can modulate the wavefront so that the point spread function and optical transfer function are insensitive to the object distance. The simulation results show that the optimized phase mask based on the proposed method can further improve the defocusing image quality while maintaining the focusing image quality.
基金supported by the National Natural Science Foundation of China under Grant No.11901236Fund of Hunan Provincial Science and Technology Department under Grant No.2019JJ50479+1 种基金Fund of Hunan Provincial Education Department under Grant No.18B322Young Core Teacher Foundation of Hunan Province under Grant No.[2020]43。
文摘In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling called moving extremes ranked set sampling(MERSS)is considered for the Fisher information matrix for the location-scale family.The Fisher information matrix for this model are respectively derived under simple random sampling and MERSS.In order to give more insight into the performance of MERSS with respect to simple random sampling,the Fisher information matrix for usual locationscale distributions are respectively computed under the two sampling.The numerical results show that MERSS provides more information than simple random sampling in parametric inference.
基金supported by the National Innovation Experiment Program for University Students under Grant No. BJTU 150170042
文摘Based on the standard angular momentum theory, we create an experiment on preparing maximally path- entangled ([N, 0] + [0, N〉]2 (NOON) states of triphotons. In order to explain the error between the theoretical and experimental data, we consider the background events during the experiment, and observe their effect on the uncertainty in S1- Afterwards, we calculate the quantum Fisher information (QFI) of the states to evaluate their potential applications in quantum metrology. Our results show that by adding the appropriate background terms, the theoretical data of the produced states matches well with the experimental data. In this case, the QFI of the states is lower than maximally entangled NOON states, but still higher than a classical state.
基金supported by the National Natural Science Foundation for Distinguished Young Scholars of China (No. 60825304)the National Basic Research Development Program of China (973 Program) (No. 2009cb320600)the Open Project of State Key Laboratory of Industrial Control Technology (ICT1006)
文摘Target tracking using wireless sensor networks requires efficient collaboration among sensors to tradeoff between energy consumption and tracking accuracy. This paper presents a collaborative target tracking approach in wire- less sensor networks using the combination of maximum likelihood estimation and the Kalman filter. The cluster leader converts the received nonlinear distance measurements into linear observation model and approximates the covariance of the converted measurement noise using maximum likelihood estimation, then applies Kalman filter to recursively update the target state estimate using the converted measurements. Finally, a measure based on the Fisher information matrix of maximum likelihood estimation is used by the leader to select the most informative sensors as a new tracking cluster for further tracking. The advantages of the proposed collaborative tracking approach are demonstrated via simulation results.
基金Project supported by the National Basic Research Program of China(973 Program)(No.2011CB13804)
文摘For the purpose of structural health monitoring, a damage detection method combined with optimum sensor placement is proposed in this paper. The back sequential sensor placement (BSSP) algorithm is introduced to optimize the sensor locations with the aim of maximizing the 2-norm of information matrix, since the EI method is not suitable for optimum sensor placement based on eigenvector sensitivity analysis. Structural damage detection is carried out based on the respective advantages of mode shape and frequency. The optimized incomplete mode shapes yielded from the optimal sensor locations are used to localize structural damage. After the potential damage elements have been preliminarily identified, an iteration scheme is adopted to estimate the damage extent of the potential damage elements based on the changes in the frequency. The effectiveness of this method is demonstrated using a numerical example of a 31-bar truss structure.
基金supported by the West Light Foundation of the Chinese Academy of Sciences under GrantNo.J11-002
文摘The wavefront coding technique is used to enlarge the depth of field(DOF)of incoherent imaging systems. The key to wavefront coding lies in the design of suitable phase masks.To date,numerous kinds of phase masks are proposed.However,further understanding is needed regarding phase mask with its phase function being in a standard sinusoidal form.Therefore,the characteristics of such a phase mask are studied in this letter.Deriving the defocused optical transfer function(OTF)analytically proves that the standard sinusoidal phase mask is effective in extending the DOF,and actual experiments confirm the numerical results.At the same time,with the Fisher information as a criterion,the standard sinusoidal phase mask shows a higher tolerance to focus errors(especially severe focus errors)than the classical cubic phase mask.
基金Supported by the National Natural Science Foundation of China(No.10801019)the Fundamental ResearchFunds for the Central Universities(BUPT2012RC0708)
文摘Non-random missing data poses serious problems in longitudinal studies. The binomial distribution parameter becomes to be unidentifiable without any other auxiliary information or assumption when it suffers from ignorable missing data. Existing methods are mostly based on the log-linear regression model. In this article, a model is proposed for longitudinal data with non-ignorable non-response. It is considered to use the pre-test baseline data to improve the identifiability of the post-test parameter. Furthermore, we derive the identified estimation (IE), the maximum likelihood estimation (MLE) and its associated variance for the post-test parameter. The simulation study based on the model of this paper shows that the proposed approach gives promising results.
基金supported in part by the National Natural Science Foundation of China(Nos.62022092 and 61790550).
文摘An observation-driven method for coordinated standoff target tracking based on Model Predictive Control(MPC)is proposed to improve observation of multiple Unmanned Aerial Vehicles(UAVs)while approaching or loitering over a target.After acquiring a fusion estimate of the target state,each UAV locally measures the observation capability of the entire UAV system with the Fisher Information Matrix(FIM)determinant in the decentralized architecture.To facilitate observation optimization,only the FIM determinant is adopted to derive the performance function and control constraints for coordinated standoff tracking.Additionally,a modified iterative scheme is introduced to improve the iterative efficiency,and a consistent circular direction control is established to maintain long-term observation performance when the UAV approaches its target.Sufficient experiments with simulated and real trajectories validate that the proposed method can improve observation of the UAV system for target tracking and adaptively optimize UAV trajectories according to sensor performance and UAV-target geometry.