Usually, only the Cramer-Rao lower bound （CRLB） of single target is taken into consideration in the state estimate of passive tracking systems. As for the case of multitarget, there are few works done due to its com...Usually, only the Cramer-Rao lower bound （CRLB） of single target is taken into consideration in the state estimate of passive tracking systems. As for the case of multitarget, there are few works done due to its complexity. The recursion formula of the posterior Cramer-Rao lower bound （PCRLB） in multitarget bearings-only tracking with the three kinds of data association is presented. Meanwhile, computer simulation is carried out for data association. The final result shows that the accuracy probability of data association has an important impact on the PCRLB.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
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 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 functio...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 multistatic Cramér-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
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
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
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
文摘Usually, only the Cramer-Rao lower bound （CRLB） of single target is taken into consideration in the state estimate of passive tracking systems. As for the case of multitarget, there are few works done due to its complexity. The recursion formula of the posterior Cramer-Rao lower bound （PCRLB） in multitarget bearings-only tracking with the three kinds of data association is presented. Meanwhile, computer simulation is carried out for data association. The final result shows that the accuracy probability of data association has an important impact on the PCRLB.
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(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.
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 multistatic Cramér-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.
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(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.
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.
