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
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
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
针对宽带信号频域波达方向(direction of arrivals,DOA)估计方法在各子频带能量存在差异时性能下降的问题,提出一种基于归一化克拉美-罗界(Cramer-Rao bound,CRB)加权宽带DOA估计方法。首先在各子频带分别计算DOA估计值,然后根据信号在...针对宽带信号频域波达方向(direction of arrivals,DOA)估计方法在各子频带能量存在差异时性能下降的问题,提出一种基于归一化克拉美-罗界(Cramer-Rao bound,CRB)加权宽带DOA估计方法。首先在各子频带分别计算DOA估计值,然后根据信号在各子频带的归一化克拉美罗界值,对相应子频带的DOA估计值进行加权,从而提高DOA估计精度以及分辨率。仿真实验验证了所提方法的有效性。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
For bistatic multiple-input multiple-output(MIMO)radar,this paper presents a robust and direction finding method in strong impulse noise environment.By means of a new lower order covariance,the method is effective in ...For bistatic multiple-input multiple-output(MIMO)radar,this paper presents a robust and direction finding method in strong impulse noise environment.By means of a new lower order covariance,the method is effective in suppressing impulse noise and achieving superior direction finding performance using the maximum likelihood(ML)estimation method.A quantum equilibrium optimizer algorithm(QEOA)is devised to resolve the corresponding objective function for efficient and accurate direc-tion finding.The results of simulation reveal the capability of the presented method in success rate and root mean square error over existing direction-finding methods in different application situations,e.g.,locating coherent signal sources with very few snapshots in strong impulse noise.Other than that,the Cramér-Rao bound(CRB)under impulse noise environment has been drawn to test the capability of the presented method.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
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
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
The Cramer-Rao bound(CRB)for two-dimensional(2-D)direction of arrival(DOA)estimation in multiple-input multiple-output(MIMO)radar with uniform circular array(UCA)is studied.Compared with the uniform linear array(ULA),...The Cramer-Rao bound(CRB)for two-dimensional(2-D)direction of arrival(DOA)estimation in multiple-input multiple-output(MIMO)radar with uniform circular array(UCA)is studied.Compared with the uniform linear array(ULA),UCA can obtain the similar performance with fewer antennas and can achieve DOA estimation in the range of 360°.This paper investigates the signal model of the MIMO radar with UCA and 2-D DOA estimation with the multiple signal classification(MUSIC)method.The CRB expressions are derived for DOA estimation and the relationship between the CRB and several parameters of the MIMO radar system is discussed.The simulation results show that more antennas and larger radius of the UCA leads to lower CRB and more accurate DOA estimation performance for the monostatic MIMO radar.Also the interference during the 2-D DOA estimation will be well restrained when the number of the transmitting antennas is different from that of the receiving antennas.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
Spacecraft orbit evasion is an effective method to ensure space safety. In the spacecraft’s orbital plane, the space non-cooperate target with autonomous approaching to the spacecraft may have a dangerous rendezvous....Spacecraft orbit evasion is an effective method to ensure space safety. In the spacecraft’s orbital plane, the space non-cooperate target with autonomous approaching to the spacecraft may have a dangerous rendezvous. To deal with this problem, an optimal maneuvering strategy based on the relative navigation observability degree is proposed with angles-only measurements. A maneuver evasion relative navigation model in the spacecraft’s orbital plane is constructed and the observability measurement criteria with process noise and measurement noise are defined based on the posterior Cramer-Rao lower bound. Further, the optimal maneuver evasion strategy in spacecraft’s orbital plane based on the observability is proposed. The strategy provides a new idea for spacecraft to evade safety threats autonomously. Compared with the spacecraft evasion problem based on the absolute navigation, more accurate evasion results can be obtained. The simulation indicates that this optimal strategy can weaken the system’s observability and reduce the state estimation accuracy of the non-cooperative target, making it impossible for the non-cooperative target to accurately approach the spacecraft.展开更多
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.
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.
文摘针对宽带信号频域波达方向(direction of arrivals,DOA)估计方法在各子频带能量存在差异时性能下降的问题,提出一种基于归一化克拉美-罗界(Cramer-Rao bound,CRB)加权宽带DOA估计方法。首先在各子频带分别计算DOA估计值,然后根据信号在各子频带的归一化克拉美罗界值,对相应子频带的DOA估计值进行加权,从而提高DOA估计精度以及分辨率。仿真实验验证了所提方法的有效性。
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.
基金This work was supported by the National Natural Science Foundation of China(62073093)the Postdoctoral Scientific Research Developmental Fund of Heilongjiang Province(LBH-Q19098)+1 种基金the Heilongjiang Provincial Natural Science Foundation of China(LH2020F017)the Key Laboratory of Advanced Marine Communication and Information Technology,Ministry of Industry and Information Technology.
文摘For bistatic multiple-input multiple-output(MIMO)radar,this paper presents a robust and direction finding method in strong impulse noise environment.By means of a new lower order covariance,the method is effective in suppressing impulse noise and achieving superior direction finding performance using the maximum likelihood(ML)estimation method.A quantum equilibrium optimizer algorithm(QEOA)is devised to resolve the corresponding objective function for efficient and accurate direc-tion finding.The results of simulation reveal the capability of the presented method in success rate and root mean square error over existing direction-finding methods in different application situations,e.g.,locating coherent signal sources with very few snapshots in strong impulse noise.Other than that,the Cramér-Rao bound(CRB)under impulse noise environment has been drawn to test the capability of the presented method.
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 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.
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.
基金supported by the National Natural Science Foundation of China(Nos.61071163,61071164,61471191)project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘The Cramer-Rao bound(CRB)for two-dimensional(2-D)direction of arrival(DOA)estimation in multiple-input multiple-output(MIMO)radar with uniform circular array(UCA)is studied.Compared with the uniform linear array(ULA),UCA can obtain the similar performance with fewer antennas and can achieve DOA estimation in the range of 360°.This paper investigates the signal model of the MIMO radar with UCA and 2-D DOA estimation with the multiple signal classification(MUSIC)method.The CRB expressions are derived for DOA estimation and the relationship between the CRB and several parameters of the MIMO radar system is discussed.The simulation results show that more antennas and larger radius of the UCA leads to lower CRB and more accurate DOA estimation performance for the monostatic MIMO radar.Also the interference during the 2-D DOA estimation will be well restrained when the number of the transmitting antennas is different from that of the receiving antennas.
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 Key R&D Program of China (2020YFA0713502)the Special Fund Project for Guiding Local Scientific and Technological Development (2020ZYT003)+1 种基金the National Natural Science Foundation of China (U20B2055,61773021,61903086)the Natural Science Foundation of Hunan Province (2019JJ20018,2020JJ4280)。
文摘Spacecraft orbit evasion is an effective method to ensure space safety. In the spacecraft’s orbital plane, the space non-cooperate target with autonomous approaching to the spacecraft may have a dangerous rendezvous. To deal with this problem, an optimal maneuvering strategy based on the relative navigation observability degree is proposed with angles-only measurements. A maneuver evasion relative navigation model in the spacecraft’s orbital plane is constructed and the observability measurement criteria with process noise and measurement noise are defined based on the posterior Cramer-Rao lower bound. Further, the optimal maneuver evasion strategy in spacecraft’s orbital plane based on the observability is proposed. The strategy provides a new idea for spacecraft to evade safety threats autonomously. Compared with the spacecraft evasion problem based on the absolute navigation, more accurate evasion results can be obtained. The simulation indicates that this optimal strategy can weaken the system’s observability and reduce the state estimation accuracy of the non-cooperative target, making it impossible for the non-cooperative target to accurately approach the spacecraft.