The mobile channel is slow fading and time selective, thus the multiplicative and additive noise of the channel will smear the spectral line, or arouse Doppler spread. This spread will make the parameters estimation a...The mobile channel is slow fading and time selective, thus the multiplicative and additive noise of the channel will smear the spectral line, or arouse Doppler spread. This spread will make the parameters estimation accuracy degrade. The goal of this paper is to analytically assess this degradation when Carrier Frequency Offset (CFO) and Doppler shift exist jointly. Then the finite-sample Cramer-Rao Lower Bound (CRLB) is derived and close-form asymptotical expression is given for large-sample CRLB. These expressions give insights into the performance room for frequency estimation. Also the variance of Doppler shift estimator is simulated to illustrate the theoretical results.展开更多
The muitipath signal resolution is reviewed in this paper.The problemsexisted and to be studied are pointed out.Theoretical analysis of the performance ofthe resolution for deterministic signal in the cases where the ...The muitipath signal resolution is reviewed in this paper.The problemsexisted and to be studied are pointed out.Theoretical analysis of the performance ofthe resolution for deterministic signal in the cases where the signal known or unknownis made.Their corresponding Cramer-Rao lower bounds(CRLB)are obtained.展开更多
Time-delay and Doppler shift estimation is a basic task for pulse-Doppler radar processing. For low-rate sampling of echo signals, several kinds of compressive sampling(CS) pulse-Doppler(CSPD) radar are developed with...Time-delay and Doppler shift estimation is a basic task for pulse-Doppler radar processing. For low-rate sampling of echo signals, several kinds of compressive sampling(CS) pulse-Doppler(CSPD) radar are developed with different analog-to-information conversion(AIC) systems. However, a unified metric is absent to evaluate their parameter estimation performance. Towards this end, this paper derives the deterministic Cramer-Rao bound(CRB)for the joint delay-Doppler estimation of CSPD radar to quantitatively analyze the estimate performance. Theoretical results reveal that the CRBs of both time-delays and Doppler shifts are inversely proportional to the received target signal-to-noise ratio(SNR), the number of transmitted pulses and the sampling rate of AIC systems. The main difference is that the CRB of Doppler shifts also lies on the coherent processing interval. Numerical experiments validate these theoretical results. They also show that the structure of the AIC systems has weak influence on the CRBs, which implies that the AIC structures can be flexibly selected for the implementation of CSPD radar.展开更多
In this paper, Cramer-Rao Bound (CRB) is derived from phase-coding signal with additive white noise, where three important parameters are focused on: carrier frequency, chip width and amplitude. Simplified and close f...In this paper, Cramer-Rao Bound (CRB) is derived from phase-coding signal with additive white noise, where three important parameters are focused on: carrier frequency, chip width and amplitude. Simplified and close form expressions of CRB are obtained through complicated derivation, and then are applied to evaluate the performance of the cyclic estimator.The results are accurate enough and serve well as benchmark for evaluating the performance of parameter estimation method. Numerical simulations illustrate the accuracy and applicability of the derived CRB.展开更多
To achieve a high signal-to-noise ratio(SNR) while maintaining moderate radar antenna, a target-based calibration manner is available to coherently combine multiple radars. The key to this calibration manner is to est...To achieve a high signal-to-noise ratio(SNR) while maintaining moderate radar antenna, a target-based calibration manner is available to coherently combine multiple radars. The key to this calibration manner is to estimate coherence parameters(CPs), i.e., time and phase calibration values in transmission and reception estimation, by separating the target returns into monostatic and bistatic echoes. However, CPs estimations exist uncertainties, which will affect the performance gain after multiradar coherent combination. The principle of coherently combining multiple radars is elaborated and the signal probability model for CPs estimation is established. On this basis, CPs Cramer-Rao bound(CRB) is derived in the closed-form, according to which the non-tight and tight upper bounds for multiple radars coherent combination performance gain are derived in the closed-form and via Monte Carlo(MC) simulations, respectively. Simulations validate the correctness of the derived CRB and gain bounds.展开更多
This paper studies the estimation performance of the coherent processing parameter （CPP）, including time delay differences and phase synchronization errors among different apertures of the distributed coherent apert...This paper studies the estimation performance of the coherent processing parameter （CPP）, including time delay differences and phase synchronization errors among different apertures of the distributed coherent aperture radar （DCAR）. Firstly, three architectures of signal processing in the DCAR are introduced. Secondly, the closed-form Cramer-Rao bound （CRB） of the CPP estimation is derived and compared. Then, the closed-form CRB is verified by numerical simulations. Finally, when the next generation radar works in a fully coherent mode, the closed-form signal-to-noise ratio （SNR） gain of the three architectures is presented.展开更多
The optimal estimation performance of target parameters is studied. First, the general form of Cramer-Rao bound （CRB） for joint estimation of target location and velocity is derived for coherent multiple input multi...The optimal estimation performance of target parameters is studied. First, the general form of Cramer-Rao bound （CRB） for joint estimation of target location and velocity is derived for coherent multiple input multiple output （MIMO） radars. To gain some insight into the behavior of the CRB, the CRB with a set of given orthogonal waveforms is studied as a specific case. Second, a maximum likelihood （ML） estimation algorithm is proposed. The mean square error （MSE） of the ML estimation of target location and velocity is obtained by Monte Carlo simulation and it approaches CRB in the high signal-to-noise ratio （SNR） region.展开更多
For the problem of deterministic parameter estimate, the theoretical lower bound of esti- mate error is the Cramér-Rao bound; while for random parameter, the lower bound of estimate error is generally termed by P...For the problem of deterministic parameter estimate, the theoretical lower bound of esti- mate error is the Cramér-Rao bound; while for random parameter, the lower bound of estimate error is generally termed by Posterior Cramér-Rao Bound (PCRB). Under the background of passive tracking where the target's state can be seen as a time-varying random parameter, PCRB of the state estimate error is analyzed in this paper, and the relation between PCRB and varied condition is also fully in- vestigated using different simulation examples. The presented analytical method provides a theoretical base for performance assessment of all kinds of suboptimal estimate algorithms used in practice.展开更多
This paper delves into the problem of optimal placement conditions for a group of agents collaboratively localizing a target using range-only or bearing-only measurements.The challenge in this study stems from the unc...This paper delves into the problem of optimal placement conditions for a group of agents collaboratively localizing a target using range-only or bearing-only measurements.The challenge in this study stems from the uncertainty associated with the positions of the agents,which may experience drift or disturbances during the target localization process.Initially,we derive the Cramer-Rao lower bound(CRLB)of the target position as the primary analytical metric.Subsequently,we establish the necessary and sufficient conditions for the optimal placement of agents.Based on these conditions,we analyze the maximal allowable agent position error for an expected mean squared error(MSE),providing valuable guidance for the selection of agent positioning sensors.The analytical findings are further validated through simulation experiments.展开更多
With the rapid development of commercial communications,the research on Radar-Communication Coexistence(RCC)systems is becoming a hot spot.The resource allocation techniques play a crucial role in the RCC systems.A pe...With the rapid development of commercial communications,the research on Radar-Communication Coexistence(RCC)systems is becoming a hot spot.The resource allocation techniques play a crucial role in the RCC systems.A performance-driven Joint Radar-target and Communication-user Assignment,along with Power and Subchannel Allocation(JRCAPSA)strategy,is proposed for an RCC network.The optimization model aims to minimize the sum of weighted Bayesian Cramer-Rao Lower Bounds(BCRLBs)of target state estimates for radar purpose.This is subject to constraints such as the Communication Data Rate(CDR)for communication purpose,the total power budget in each RCC system,assignment relationships,and the number of available subchannels.Considering that such a problem falls into the realm of Mixed Integer Programming(MIP),a Three-stage Iteratively Augment-based Optimization Method(TIAOM)is developed.The Communication-User Assignment(CUA),Communication Subchannel Allocation(SCA),and Radar-Target Assignment(RTA)feasible solution domains are iteratively expanded based on their importance,leading to the efficient acquisition of a suboptimal solution.Simulation results show the outperformance of the proposed JRCAPSA strategy,compared to the other benchmarks and the OPTI toolbox.The results also imply that the Bayesian Cramer-Rao Lower Bound(BCRLB)is a more stringent optimization metric for the achieved Mean Square Error(MSE),compared to Mutual Information(MI)and Signal-to-Interference-Noise Ratio(SINR).展开更多
Since the features of low energy consumption and limited power supply are very impor- tant for wireless sensor networks （WSNs）, the problems of distributed state estimation with quan- tized innovations are investiga...Since the features of low energy consumption and limited power supply are very impor- tant for wireless sensor networks （WSNs）, the problems of distributed state estimation with quan- tized innovations are investigated in this paper. In the first place, the assumptions of prior and posterior probability density function （PDF） with quantized innovations in the previous papers are analyzed. After that, an innovative Gaussian mixture estimator is proposed. On this basis, this paper presents a Gaussian mixture state estimation algorithm based on quantized innovations for WSNs. In order to evaluate and compare the performance of this kind of state estimation algo- rithms for WSNs, the posterior Cram6r-Rao lower bound （CRLB） with quantized innovations is put forward. Performance analysis and simulations show that the proposed Gaussian mixture state estimation algorithm is efficient than the others under the same number of quantization levels and the performance of these algorithms can be benchmarked by the theoretical lower bound.展开更多
In order to solve the problem that the performance of traditional localization methods for mixed near-field sources(NFSs)and far-field sources(FFSs)degrades under impulsive noise,a robust and novel localization method...In order to solve the problem that the performance of traditional localization methods for mixed near-field sources(NFSs)and far-field sources(FFSs)degrades under impulsive noise,a robust and novel localization method is proposed.After eliminating the impacts of impulsive noise by the weighted out-lier filter,the direction of arrivals(DOAs)of FFSs can be estimated by multiple signal classification(MUSIC)spectral peaks search.Based on the DOAs information of FFSs,the separation of mixed sources can be performed.Finally,the estimation of localizing parameters of NFSs can avoid two-dimension spectral peaks search by decomposing steering vectors.The Cramer-Rao bounds(CRB)for the unbiased estimations of DOA and range under impulsive noise have been drawn.Simulation experiments verify that the proposed method has advantages in probability of successful estimation(PSE)and root mean square error(RMSE)compared with existing localization methods.It can be concluded that the proposed method is effective and reliable in the environment with low generalized signal to noise ratio(GSNR),few snapshots,and strong impulse.展开更多
针对无线传感器网络中如何准确获取节点位置信息的问题,研究了多径传播条件下基于到达时间(Time-of-Arrival,TOA)并兼顾路径时延的目标定位问题。所提算法在高斯噪声假设基础上,首先根据时间-距离观测模型推导出包含目标位置坐标及时延...针对无线传感器网络中如何准确获取节点位置信息的问题,研究了多径传播条件下基于到达时间(Time-of-Arrival,TOA)并兼顾路径时延的目标定位问题。所提算法在高斯噪声假设基础上,首先根据时间-距离观测模型推导出包含目标位置坐标及时延的测量方程;然后基于加权最小二乘(Weighted Least Squares,WLS)准则,计算出在目标坐标估计性能上严密逼近Cramér-Rao下界(CRLB)的解;最后通过理论分析得出位置和时延的误差方差及算法开销。仿真测试了单节点及多节点场景下测距误差对定位和延时性能的影响,结果表明,所提出算法的估计性能非常接近CRLB的估计性能,明显优于两步加权最小二乘(Two Step Weighted Least Squares,TSWLS)方法。展开更多
由于共形载体曲率的影响,共形阵列天线中各阵元单元方向图具有不同的指向,使得共形阵列天线具有了多极化特性(Polarization Diversity),为了描述共形阵列天线的多极化特性,通常在共形阵列天线的快拍数据模型中引入阵列入射信号的极化参...由于共形载体曲率的影响,共形阵列天线中各阵元单元方向图具有不同的指向,使得共形阵列天线具有了多极化特性(Polarization Diversity),为了描述共形阵列天线的多极化特性,通常在共形阵列天线的快拍数据模型中引入阵列入射信号的极化参数,因此共形阵列天线的DOA(Direction-Of-Arrival)估计需要与阵列入射信号极化参数联合估计.本文提出了一种盲极化DOA估计算法,通过在锥面共形阵列天线中设置三对特殊子阵,利用ESPRIT(Estimationof Signal Parameters via Rotational Invariance Techniques)算法,将入射信号极化参数与二维角参数去耦合,在入射信号极化参数未知条件下实现了高分辨DOA估计,并对估计性能进行了理论分析与推导,给出了参数估计的CRB(Cramer-RaoBound),通过Monte Carlo仿真实验验证了DOA估计算法的有效性.展开更多
文摘The mobile channel is slow fading and time selective, thus the multiplicative and additive noise of the channel will smear the spectral line, or arouse Doppler spread. This spread will make the parameters estimation accuracy degrade. The goal of this paper is to analytically assess this degradation when Carrier Frequency Offset (CFO) and Doppler shift exist jointly. Then the finite-sample Cramer-Rao Lower Bound (CRLB) is derived and close-form asymptotical expression is given for large-sample CRLB. These expressions give insights into the performance room for frequency estimation. Also the variance of Doppler shift estimator is simulated to illustrate the theoretical results.
文摘The muitipath signal resolution is reviewed in this paper.The problemsexisted and to be studied are pointed out.Theoretical analysis of the performance ofthe resolution for deterministic signal in the cases where the signal known or unknownis made.Their corresponding Cramer-Rao lower bounds(CRLB)are obtained.
基金supported by the National Natural Science Foundation of China(6140121061571228)
文摘Time-delay and Doppler shift estimation is a basic task for pulse-Doppler radar processing. For low-rate sampling of echo signals, several kinds of compressive sampling(CS) pulse-Doppler(CSPD) radar are developed with different analog-to-information conversion(AIC) systems. However, a unified metric is absent to evaluate their parameter estimation performance. Towards this end, this paper derives the deterministic Cramer-Rao bound(CRB)for the joint delay-Doppler estimation of CSPD radar to quantitatively analyze the estimate performance. Theoretical results reveal that the CRBs of both time-delays and Doppler shifts are inversely proportional to the received target signal-to-noise ratio(SNR), the number of transmitted pulses and the sampling rate of AIC systems. The main difference is that the CRB of Doppler shifts also lies on the coherent processing interval. Numerical experiments validate these theoretical results. They also show that the structure of the AIC systems has weak influence on the CRBs, which implies that the AIC structures can be flexibly selected for the implementation of CSPD radar.
文摘In this paper, Cramer-Rao Bound (CRB) is derived from phase-coding signal with additive white noise, where three important parameters are focused on: carrier frequency, chip width and amplitude. Simplified and close form expressions of CRB are obtained through complicated derivation, and then are applied to evaluate the performance of the cyclic estimator.The results are accurate enough and serve well as benchmark for evaluating the performance of parameter estimation method. Numerical simulations illustrate the accuracy and applicability of the derived CRB.
基金supported by the National Natural Science Foundation of China(61471372)
文摘To achieve a high signal-to-noise ratio(SNR) while maintaining moderate radar antenna, a target-based calibration manner is available to coherently combine multiple radars. The key to this calibration manner is to estimate coherence parameters(CPs), i.e., time and phase calibration values in transmission and reception estimation, by separating the target returns into monostatic and bistatic echoes. However, CPs estimations exist uncertainties, which will affect the performance gain after multiradar coherent combination. The principle of coherently combining multiple radars is elaborated and the signal probability model for CPs estimation is established. On this basis, CPs Cramer-Rao bound(CRB) is derived in the closed-form, according to which the non-tight and tight upper bounds for multiple radars coherent combination performance gain are derived in the closed-form and via Monte Carlo(MC) simulations, respectively. Simulations validate the correctness of the derived CRB and gain bounds.
基金supported by the National Natural Science Foundation of China(61171120)the Key National Ministry Foundation of China(9140A07020212JW0101)+2 种基金the Foundation of Tsinghua University(20101081772)the Foundation of National Laboratory of Information Control Technology for Communication System of Chinathe Foundation of National Information Control Laboratory
文摘This paper studies the estimation performance of the coherent processing parameter （CPP）, including time delay differences and phase synchronization errors among different apertures of the distributed coherent aperture radar （DCAR）. Firstly, three architectures of signal processing in the DCAR are introduced. Secondly, the closed-form Cramer-Rao bound （CRB） of the CPP estimation is derived and compared. Then, the closed-form CRB is verified by numerical simulations. Finally, when the next generation radar works in a fully coherent mode, the closed-form signal-to-noise ratio （SNR） gain of the three architectures is presented.
基金supported by the National Natural Science Foundation of China(61171120)the Key National Ministry Foundation of China(9140A07020212JW0101)the Foundation of Tsinghua University(20101081772)
文摘The optimal estimation performance of target parameters is studied. First, the general form of Cramer-Rao bound （CRB） for joint estimation of target location and velocity is derived for coherent multiple input multiple output （MIMO） radars. To gain some insight into the behavior of the CRB, the CRB with a set of given orthogonal waveforms is studied as a specific case. Second, a maximum likelihood （ML） estimation algorithm is proposed. The mean square error （MSE） of the ML estimation of target location and velocity is obtained by Monte Carlo simulation and it approaches CRB in the high signal-to-noise ratio （SNR） region.
文摘For the problem of deterministic parameter estimate, the theoretical lower bound of esti- mate error is the Cramér-Rao bound; while for random parameter, the lower bound of estimate error is generally termed by Posterior Cramér-Rao Bound (PCRB). Under the background of passive tracking where the target's state can be seen as a time-varying random parameter, PCRB of the state estimate error is analyzed in this paper, and the relation between PCRB and varied condition is also fully in- vestigated using different simulation examples. The presented analytical method provides a theoretical base for performance assessment of all kinds of suboptimal estimate algorithms used in practice.
文摘This paper delves into the problem of optimal placement conditions for a group of agents collaboratively localizing a target using range-only or bearing-only measurements.The challenge in this study stems from the uncertainty associated with the positions of the agents,which may experience drift or disturbances during the target localization process.Initially,we derive the Cramer-Rao lower bound(CRLB)of the target position as the primary analytical metric.Subsequently,we establish the necessary and sufficient conditions for the optimal placement of agents.Based on these conditions,we analyze the maximal allowable agent position error for an expected mean squared error(MSE),providing valuable guidance for the selection of agent positioning sensors.The analytical findings are further validated through simulation experiments.
基金supported by the National Natural Science Foundation of China(Nos.62071482,62471485,62471348)Shaanxi Association of Science and Technology Youth Talent Support Program Project,China(No.20230137)+1 种基金Innovative Talents Cultivate Program for Technology Innovation Team of ShaanXi Province,China(No.2024RS-CXTD-08)Youth Talent Lifting Project of the China Association for Science and Technology(No.2021-JCJQ-QT-018)。
文摘With the rapid development of commercial communications,the research on Radar-Communication Coexistence(RCC)systems is becoming a hot spot.The resource allocation techniques play a crucial role in the RCC systems.A performance-driven Joint Radar-target and Communication-user Assignment,along with Power and Subchannel Allocation(JRCAPSA)strategy,is proposed for an RCC network.The optimization model aims to minimize the sum of weighted Bayesian Cramer-Rao Lower Bounds(BCRLBs)of target state estimates for radar purpose.This is subject to constraints such as the Communication Data Rate(CDR)for communication purpose,the total power budget in each RCC system,assignment relationships,and the number of available subchannels.Considering that such a problem falls into the realm of Mixed Integer Programming(MIP),a Three-stage Iteratively Augment-based Optimization Method(TIAOM)is developed.The Communication-User Assignment(CUA),Communication Subchannel Allocation(SCA),and Radar-Target Assignment(RTA)feasible solution domains are iteratively expanded based on their importance,leading to the efficient acquisition of a suboptimal solution.Simulation results show the outperformance of the proposed JRCAPSA strategy,compared to the other benchmarks and the OPTI toolbox.The results also imply that the Bayesian Cramer-Rao Lower Bound(BCRLB)is a more stringent optimization metric for the achieved Mean Square Error(MSE),compared to Mutual Information(MI)and Signal-to-Interference-Noise Ratio(SINR).
基金jointly supported by the National Natural Science Foundation of China(No.61175008)State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System of China(No.CEMEE2014K0301A)the Natural Science Foundation of Jiangsu Province of China(No.BK20140896)
文摘Since the features of low energy consumption and limited power supply are very impor- tant for wireless sensor networks （WSNs）, the problems of distributed state estimation with quan- tized innovations are investigated in this paper. In the first place, the assumptions of prior and posterior probability density function （PDF） with quantized innovations in the previous papers are analyzed. After that, an innovative Gaussian mixture estimator is proposed. On this basis, this paper presents a Gaussian mixture state estimation algorithm based on quantized innovations for WSNs. In order to evaluate and compare the performance of this kind of state estimation algo- rithms for WSNs, the posterior Cram6r-Rao lower bound （CRLB） with quantized innovations is put forward. Performance analysis and simulations show that the proposed Gaussian mixture state estimation algorithm is efficient than the others under the same number of quantization levels and the performance of these algorithms can be benchmarked by the theoretical lower bound.
基金supported by the National Natural Science Foundation of China(62073093)the initiation fund for postdoctoral research in Heilongjiang Province(LBH-Q19098)the Natural Science Foundation of Heilongjiang Province(LH2020F017).
文摘In order to solve the problem that the performance of traditional localization methods for mixed near-field sources(NFSs)and far-field sources(FFSs)degrades under impulsive noise,a robust and novel localization method is proposed.After eliminating the impacts of impulsive noise by the weighted out-lier filter,the direction of arrivals(DOAs)of FFSs can be estimated by multiple signal classification(MUSIC)spectral peaks search.Based on the DOAs information of FFSs,the separation of mixed sources can be performed.Finally,the estimation of localizing parameters of NFSs can avoid two-dimension spectral peaks search by decomposing steering vectors.The Cramer-Rao bounds(CRB)for the unbiased estimations of DOA and range under impulsive noise have been drawn.Simulation experiments verify that the proposed method has advantages in probability of successful estimation(PSE)and root mean square error(RMSE)compared with existing localization methods.It can be concluded that the proposed method is effective and reliable in the environment with low generalized signal to noise ratio(GSNR),few snapshots,and strong impulse.
文摘针对无线传感器网络中如何准确获取节点位置信息的问题,研究了多径传播条件下基于到达时间(Time-of-Arrival,TOA)并兼顾路径时延的目标定位问题。所提算法在高斯噪声假设基础上,首先根据时间-距离观测模型推导出包含目标位置坐标及时延的测量方程;然后基于加权最小二乘(Weighted Least Squares,WLS)准则,计算出在目标坐标估计性能上严密逼近Cramér-Rao下界(CRLB)的解;最后通过理论分析得出位置和时延的误差方差及算法开销。仿真测试了单节点及多节点场景下测距误差对定位和延时性能的影响,结果表明,所提出算法的估计性能非常接近CRLB的估计性能,明显优于两步加权最小二乘(Two Step Weighted Least Squares,TSWLS)方法。
文摘由于共形载体曲率的影响,共形阵列天线中各阵元单元方向图具有不同的指向,使得共形阵列天线具有了多极化特性(Polarization Diversity),为了描述共形阵列天线的多极化特性,通常在共形阵列天线的快拍数据模型中引入阵列入射信号的极化参数,因此共形阵列天线的DOA(Direction-Of-Arrival)估计需要与阵列入射信号极化参数联合估计.本文提出了一种盲极化DOA估计算法,通过在锥面共形阵列天线中设置三对特殊子阵,利用ESPRIT(Estimationof Signal Parameters via Rotational Invariance Techniques)算法,将入射信号极化参数与二维角参数去耦合,在入射信号极化参数未知条件下实现了高分辨DOA估计,并对估计性能进行了理论分析与推导,给出了参数估计的CRB(Cramer-RaoBound),通过Monte Carlo仿真实验验证了DOA估计算法的有效性.
