Compared with the traditional channel estimation methods, blind channel estimation methods can increase the bandwidth efficiency of the systems, but their precision is low and they converge slowly. In this paper, the ...Compared with the traditional channel estimation methods, blind channel estimation methods can increase the bandwidth efficiency of the systems, but their precision is low and they converge slowly. In this paper, the Cramér-Rao Bound （CRB） for blind channel estimation in complex-valued Single-Input Multiple- Output （SIMO） channel is derived. In the simulations, the correctness of the CRB is validated and some channel estimation methods are evaluated by using the CRB.展开更多
Most currently existing investigations on the observability of passive guidance systems can only provide a qualitative result. In this paper, a quantitative method, which utilizes Cramér-Rao lower bound in the es...Most currently existing investigations on the observability of passive guidance systems can only provide a qualitative result. In this paper, a quantitative method, which utilizes Cramér-Rao lower bound in the estimability analysis of closed-loop guidance systems with bearings-only measurements, is proposed. The new method provides an intuitive result for observability of the guidance system through graphical analysis. As a demonstration, a numerical example is presented, in which the degrees of observability of the guidance systems under two commonly used guidance laws are compared by using the new approach.展开更多
The primary goal of this work is to characterize the impact of weighting selection strategy and multistatic geometry on the multistatic radar performance. With the relationship between the multistatic ambiguity functi...The primary goal of this work is to characterize the impact of weighting selection strategy and multistatic geometry on the multistatic radar performance. With the relationship between the multistatic ambiguity function （AF） and the multistatie Cram6r-Rao lower bound （CRLB）, the problem of calculating the multistatic AF and the multistatic CRLB as a performance metric for multistatic radar system is studied. Exactly, based on the proper selection of the system parameters, the multistatic radar performance can be significantly improved. The simulation results illustrate that the multistatic AF and the multistatic CRLB can serve as guidelines for future multistatic fusion rule development and multistatic radars deployment.展开更多
本文推导了激光多普勒测速 (LDA)频率估计的Cram r Rao下限。得到了不同于目前LDA工作者广为使用的基于纯频谐波信号的分析结果。得出以下结论 :对大多数LDA测量而言 ,其频率估计的Cram r Rao下限将是同样情况下纯频谐波信号频率估计的 ...本文推导了激光多普勒测速 (LDA)频率估计的Cram r Rao下限。得到了不同于目前LDA工作者广为使用的基于纯频谐波信号的分析结果。得出以下结论 :对大多数LDA测量而言 ,其频率估计的Cram r Rao下限将是同样情况下纯频谐波信号频率估计的 2到 6倍。展开更多
In this paper,we study asymptotic properties of the approximated maximum likelihood estimator(MLE)for the drift coefficient in an Ornstein-Uhlenbeck process with discrete observations.By the change of measure method a...In this paper,we study asymptotic properties of the approximated maximum likelihood estimator(MLE)for the drift coefficient in an Ornstein-Uhlenbeck process with discrete observations.By the change of measure method and asymptotic analysis technique,we establish an exponential nonuniform Berry-Esseen bound of the approximated MLE.Then,the Cramér-type moderate deviation can be obtained.As applications,the global and local powers for the hypothesis test are shown to approach one at exponential rates.Simulation experiments are conducted to confirm the theoretical results.展开更多
Sixth Generation(6G)mobile communication networks will involve sensing as a new function,with the overwhelming trend of Integrated Sensing And Communications(ISAC).Although expanding the serving range of the networks,...Sixth Generation(6G)mobile communication networks will involve sensing as a new function,with the overwhelming trend of Integrated Sensing And Communications(ISAC).Although expanding the serving range of the networks,there exists performance trade-offbetween communication and sensing,in that they have competitions on the physical resources.Different resource allocation schemes will result in different sensing and communication performance,thus influencing the system’s overall performance.Therefore,how to model the system’s overall performance,and how to optimize it are key issues for ISAC.Relying on the large-scale deployment of the networks,cooperative ISAC has the advantages of wider coverage,more robust performance and good compatibility of multiple monostatic and multistatic sensing,compared to the non-cooperative ISAC.How to capture the performance gain of cooperation is a key issue for cooperative ISAC.To address the aforementioned vital problems,in this paper,we analyze the sensing accuracy gain,propose a unified ISAC performance evaluation framework and design several optimization methods in cooperative ISAC systems.The cooperative sensing accuracy gain is theoretically analyzed via Cramér Rao lower bound.The unified ISAC performance evaluation model is established by converting the communication mutual information to the effective minimum mean squared error.To optimize the unified ISAC performance,we design the optimization algorithms considering three factors:base stations’working modes,power allocation schemes and waveform design.Through simulations,we show the performance gain of the cooperative ISAC system and the effectiveness of the proposed optimization methods.展开更多
We study Berry-Esseen bounds and Cramér-type moderate deviations of a jump-type Cox-Ingersoll-Ross(CIR)process driven by a standard Wiener process and a subordinator.In the sub critical case,we obtain the best Be...We study Berry-Esseen bounds and Cramér-type moderate deviations of a jump-type Cox-Ingersoll-Ross(CIR)process driven by a standard Wiener process and a subordinator.In the sub critical case,we obtain the best Berry-Esseen bound of the sample mean and the MLE of the growth rate if the Lévy measure of the subordinator has finite third order moment.Under the Cramér condition,we establish the Cramér-type moderate deviations of the MLE of the growth rate.We first derive a Berry-Esseen bound,a deviation inequality and the Cramér-type moderate deviations for the sample mean of the CIR process by analyzing the asymptotic behaviors of the characteristic function and the moment generating function of the sample mean.Then we analyze a type of additive functional of the jump-type CIR process and use a transformation to study the Berry-Esseen bound and the Cramér-type moderate deviations for the MLE of the growth rate.展开更多
Due to the potential of quantum advantage to surpass the standard quantum limit(SQL),nonlinear interferometers have garnered significant attention from researchers in the field of precision measurement.However,many pr...Due to the potential of quantum advantage to surpass the standard quantum limit(SQL),nonlinear interferometers have garnered significant attention from researchers in the field of precision measurement.However,many practical applications require multiparameter estimation.In this work,we discuss the precision limit of multi-parameter estimation of pure Gaussian states based on nonlinear interferometers,and derive the Holevo Cramér–Rao bound(HCRB)for the case where both modes undergo displacement estimation.Furthermore,we compare our analytical results with the quantum Cramér–Rao bound based on the symmetric logarithmic derivative(SLD-CRB),and with the result of the dual homodyne measurement.Through numerical analysis,we find that the HCRB equals the result of the dual homodyne measurement,whereas SLD-CRB is not saturable at small squeezed parameters.Therefore,this indicates that the HCRB is tight.Additionally,we provide intuitive analysis and visual representation of our numerical results in phase space.展开更多
A mean squared error lower bound for the discrete-time nonlinear filtering with colored noises is derived based on the posterior version of the Cramér-Rao inequality. The colored noises are characterized by the a...A mean squared error lower bound for the discrete-time nonlinear filtering with colored noises is derived based on the posterior version of the Cramér-Rao inequality. The colored noises are characterized by the auto-regressive model including the auto-correlated process noise and autocorrelated measurement noise simultaneously. Moreover, the proposed lower bound is also suitable for a general model of nonlinear high order auto-regressive systems. Finally, the lower bound is evaluated by a typical example in target tracking. It shows that the new lower bound can assess the achievable performance of suboptimal filtering techniques, and the colored noise has a significantly effect on the lower bound and the performance of filters.展开更多
As an important parameter in the single airborne passive locating system, the rate of phase difference change contains range information of the radio emitter. Taking single carrier sine pulse signals as an example, th...As an important parameter in the single airborne passive locating system, the rate of phase difference change contains range information of the radio emitter. Taking single carrier sine pulse signals as an example, this article illustrates the principle of passive location through measurement of rates of phase difference change and analyzes the structure of measurement errors. On the basis of the Cramér-Rao lower bound (CRLB), an algorithm associated with time-chips is proposed to determine the rates of pha...展开更多
It is well known that the Two-step Weighted Least-Squares(TWLS) is a widely used method for source localization and sensor position refinement. For this reason, we propose a unified framework of the TWLS method for jo...It is well known that the Two-step Weighted Least-Squares(TWLS) is a widely used method for source localization and sensor position refinement. For this reason, we propose a unified framework of the TWLS method for joint estimation of multiple disjoint sources and sensor locations in this paper. Unlike some existing works, the presented method is based on more general measurement model, and therefore it can be applied to many different localization scenarios.Besides, it does not have the initialization and local convergence problem. The closed-form expression for the covariance matrix of the proposed TWLS estimator is also derived by exploiting the first-order perturbation analysis. Moreover, the estimation accuracy of the TWLS method is shown analytically to achieve the Cramér-Rao Bound(CRB) before the threshold effect takes place. The theoretical analysis is also performed in a common mathematical framework, rather than aiming at some specific signal metrics. Finally, two numerical experiments are performed to support the theoretical development in this paper.展开更多
We establish Berry-Esseen bounds and Cramér type large deviations for the eigenvalues of Wigner Hermitian matrices in the bulk and at the edge cases. Similar results are also obtained for covariance matrices.
For coping with the multiple target tracking in the presence of complex time-varying environments and unknown target information, a time resource management scheme based on chance-constraint programming（CCP） employi...For coping with the multiple target tracking in the presence of complex time-varying environments and unknown target information, a time resource management scheme based on chance-constraint programming（CCP） employing fuzzy logic priority is proposed for opportunistic array radar（OAR）. In this scheme,the total beam illuminating time is minimized by effective time resource allocation so that the desired tracking performance is achieved. Meanwhile, owing to the randomness of radar cross section（RCS）, the CCP is used to balance tracking accuracy and time resource conditioned on the specified confidence level. The adaptive fuzzy logic prioritization, imitating the human decision-making process for ranking radar targets, can realize the full potential of radar. The Bayesian Crame ′r-Rao lower bound（BCRLB） provides us with a low bound of localization estimation root-mean-square error（RMSE）, and equally important, it can be calculated predictively. Consequently, it is employed as an optimization criterion for the time resource allocation scheme. The stochastic simulation is integrated into the genetic algorithm（GA） to compose a hybrid intelligent optimization algorithm to solve the CCP optimization problem. The simulation results show that the time resource is saved strikingly and the radar performance is also improved.展开更多
基金Supported by Jiangsu Natural Science Fund (BK2003015) National Mobile Communications Research Laboratory Fund (N0302).
文摘Compared with the traditional channel estimation methods, blind channel estimation methods can increase the bandwidth efficiency of the systems, but their precision is low and they converge slowly. In this paper, the Cramér-Rao Bound （CRB） for blind channel estimation in complex-valued Single-Input Multiple- Output （SIMO） channel is derived. In the simulations, the correctness of the CRB is validated and some channel estimation methods are evaluated by using the CRB.
基金the National Natural Science Foundation of China (Grant No. 60104003 and 60374024).
文摘Most currently existing investigations on the observability of passive guidance systems can only provide a qualitative result. In this paper, a quantitative method, which utilizes Cramér-Rao lower bound in the estimability analysis of closed-loop guidance systems with bearings-only measurements, is proposed. The new method provides an intuitive result for observability of the guidance system through graphical analysis. As a demonstration, a numerical example is presented, in which the degrees of observability of the guidance systems under two commonly used guidance laws are compared by using the new approach.
基金Project(61271441)supported by the National Natural Science Foundation of ChinaProject(NCET-10-0895)supported by the Program for New Century Excellent Talents in Universities of China
文摘The primary goal of this work is to characterize the impact of weighting selection strategy and multistatic geometry on the multistatic radar performance. With the relationship between the multistatic ambiguity function （AF） and the multistatie Cram6r-Rao lower bound （CRLB）, the problem of calculating the multistatic AF and the multistatic CRLB as a performance metric for multistatic radar system is studied. Exactly, based on the proper selection of the system parameters, the multistatic radar performance can be significantly improved. The simulation results illustrate that the multistatic AF and the multistatic CRLB can serve as guidelines for future multistatic fusion rule development and multistatic radars deployment.
基金supported by the National Natural Science Foundation of China(Grant No.12471146)the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20231435)。
文摘In this paper,we study asymptotic properties of the approximated maximum likelihood estimator(MLE)for the drift coefficient in an Ornstein-Uhlenbeck process with discrete observations.By the change of measure method and asymptotic analysis technique,we establish an exponential nonuniform Berry-Esseen bound of the approximated MLE.Then,the Cramér-type moderate deviation can be obtained.As applications,the global and local powers for the hypothesis test are shown to approach one at exponential rates.Simulation experiments are conducted to confirm the theoretical results.
文摘Sixth Generation(6G)mobile communication networks will involve sensing as a new function,with the overwhelming trend of Integrated Sensing And Communications(ISAC).Although expanding the serving range of the networks,there exists performance trade-offbetween communication and sensing,in that they have competitions on the physical resources.Different resource allocation schemes will result in different sensing and communication performance,thus influencing the system’s overall performance.Therefore,how to model the system’s overall performance,and how to optimize it are key issues for ISAC.Relying on the large-scale deployment of the networks,cooperative ISAC has the advantages of wider coverage,more robust performance and good compatibility of multiple monostatic and multistatic sensing,compared to the non-cooperative ISAC.How to capture the performance gain of cooperation is a key issue for cooperative ISAC.To address the aforementioned vital problems,in this paper,we analyze the sensing accuracy gain,propose a unified ISAC performance evaluation framework and design several optimization methods in cooperative ISAC systems.The cooperative sensing accuracy gain is theoretically analyzed via Cramér Rao lower bound.The unified ISAC performance evaluation model is established by converting the communication mutual information to the effective minimum mean squared error.To optimize the unified ISAC performance,we design the optimization algorithms considering three factors:base stations’working modes,power allocation schemes and waveform design.Through simulations,we show the performance gain of the cooperative ISAC system and the effectiveness of the proposed optimization methods.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11971361,12371275)。
文摘We study Berry-Esseen bounds and Cramér-type moderate deviations of a jump-type Cox-Ingersoll-Ross(CIR)process driven by a standard Wiener process and a subordinator.In the sub critical case,we obtain the best Berry-Esseen bound of the sample mean and the MLE of the growth rate if the Lévy measure of the subordinator has finite third order moment.Under the Cramér condition,we establish the Cramér-type moderate deviations of the MLE of the growth rate.We first derive a Berry-Esseen bound,a deviation inequality and the Cramér-type moderate deviations for the sample mean of the CIR process by analyzing the asymptotic behaviors of the characteristic function and the moment generating function of the sample mean.Then we analyze a type of additive functional of the jump-type CIR process and use a transformation to study the Berry-Esseen bound and the Cramér-type moderate deviations for the MLE of the growth rate.
基金supported by the Shanghai Science and Technology Innovation Project(No.24LZ1400600)the Innovation Program for Quantum Science and Technology(No.2021ZD0303200)+4 种基金the National Natural Science Foundation of China(Grant Nos.U23A2075,12274132,11974111,12234014,11654005,11874152,and 91536114)Shanghai Municipal Science and Technology Major Project(Grant No.2019SHZDZX01)Innovation Program of Shanghai Municipal Education Commission(No.202101070008E00099)the National Key Research and Development Program of China(Grant No.2016YFA0302001)Fundamental Research Funds for the Central Universities.
文摘Due to the potential of quantum advantage to surpass the standard quantum limit(SQL),nonlinear interferometers have garnered significant attention from researchers in the field of precision measurement.However,many practical applications require multiparameter estimation.In this work,we discuss the precision limit of multi-parameter estimation of pure Gaussian states based on nonlinear interferometers,and derive the Holevo Cramér–Rao bound(HCRB)for the case where both modes undergo displacement estimation.Furthermore,we compare our analytical results with the quantum Cramér–Rao bound based on the symmetric logarithmic derivative(SLD-CRB),and with the result of the dual homodyne measurement.Through numerical analysis,we find that the HCRB equals the result of the dual homodyne measurement,whereas SLD-CRB is not saturable at small squeezed parameters.Therefore,this indicates that the HCRB is tight.Additionally,we provide intuitive analysis and visual representation of our numerical results in phase space.
基金supported in part by the Open Research Funds of BACC-STAFDL of China under Grant No.2015afdl010the National Natural Science Foundation of China under Grant No.61673282the PCSIRT16R53
文摘A mean squared error lower bound for the discrete-time nonlinear filtering with colored noises is derived based on the posterior version of the Cramér-Rao inequality. The colored noises are characterized by the auto-regressive model including the auto-correlated process noise and autocorrelated measurement noise simultaneously. Moreover, the proposed lower bound is also suitable for a general model of nonlinear high order auto-regressive systems. Finally, the lower bound is evaluated by a typical example in target tracking. It shows that the new lower bound can assess the achievable performance of suboptimal filtering techniques, and the colored noise has a significantly effect on the lower bound and the performance of filters.
基金Aeronautical Science Foundation of China (2007ZC53030)
文摘As an important parameter in the single airborne passive locating system, the rate of phase difference change contains range information of the radio emitter. Taking single carrier sine pulse signals as an example, this article illustrates the principle of passive location through measurement of rates of phase difference change and analyzes the structure of measurement errors. On the basis of the Cramér-Rao lower bound (CRLB), an algorithm associated with time-chips is proposed to determine the rates of pha...
基金co-supported by the National Natural Science Foundation of China (Nos. 61201381, 61401513 and 61772548)the China Postdoctoral Science Foundation (No. 2016M592989)+1 种基金the Self-Topic Foundation of Information Engineering University, China (No. 2016600701)the Outstanding Youth Foundation of Information Engineering University, China (No. 2016603201)
文摘It is well known that the Two-step Weighted Least-Squares(TWLS) is a widely used method for source localization and sensor position refinement. For this reason, we propose a unified framework of the TWLS method for joint estimation of multiple disjoint sources and sensor locations in this paper. Unlike some existing works, the presented method is based on more general measurement model, and therefore it can be applied to many different localization scenarios.Besides, it does not have the initialization and local convergence problem. The closed-form expression for the covariance matrix of the proposed TWLS estimator is also derived by exploiting the first-order perturbation analysis. Moreover, the estimation accuracy of the TWLS method is shown analytically to achieve the Cramér-Rao Bound(CRB) before the threshold effect takes place. The theoretical analysis is also performed in a common mathematical framework, rather than aiming at some specific signal metrics. Finally, two numerical experiments are performed to support the theoretical development in this paper.
基金supported by National Natural Science Foundation of China(Grant No.11171262)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130141110076)
文摘We establish Berry-Esseen bounds and Cramér type large deviations for the eigenvalues of Wigner Hermitian matrices in the bulk and at the edge cases. Similar results are also obtained for covariance matrices.
基金supported by the National Natural Science Foundation of China(6127132761671241)
文摘For coping with the multiple target tracking in the presence of complex time-varying environments and unknown target information, a time resource management scheme based on chance-constraint programming（CCP） employing fuzzy logic priority is proposed for opportunistic array radar（OAR）. In this scheme,the total beam illuminating time is minimized by effective time resource allocation so that the desired tracking performance is achieved. Meanwhile, owing to the randomness of radar cross section（RCS）, the CCP is used to balance tracking accuracy and time resource conditioned on the specified confidence level. The adaptive fuzzy logic prioritization, imitating the human decision-making process for ranking radar targets, can realize the full potential of radar. The Bayesian Crame ′r-Rao lower bound（BCRLB） provides us with a low bound of localization estimation root-mean-square error（RMSE）, and equally important, it can be calculated predictively. Consequently, it is employed as an optimization criterion for the time resource allocation scheme. The stochastic simulation is integrated into the genetic algorithm（GA） to compose a hybrid intelligent optimization algorithm to solve the CCP optimization problem. The simulation results show that the time resource is saved strikingly and the radar performance is also improved.
