Cramer-Rao bound and signal-to-noise ratio gain in distributed coherent aperture radar

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.

Cramer-Rao bound of joint estimation of target location and velocity for coherent MIMO radar

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.

Simulation study of passive target motion analysis

In this paper, the problem of underwater passive target motion analysis (TMA) in three dimensions is discussed using the measurements of passive bearings and elevation and frequency on the condition that acoustic source and observer are in different horizontal planes. Simulation results with both of the PLE (pseudo-linear estimation) and MLE (Maximum likelihood estimation) show that the TMA method is effective in oceanic environment. Its error covariance curves tend to its Cramer-Rao lower bounds.

Cramer-Rao bounds for the joint delay-Doppler estimation of compressive sampling pulse-Doppler radar

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.

Joint polarization and DOA estimation based on improved maximum likelihood estimator and performance analysis for conformal array

The conformal array can make full use of the aperture,save space,meet the requirements of aerodynamics,and is sensitive to polarization information.It has broad application prospects in military,aerospace,and communication fields.The joint polarization and direction-of-arrival(DOA)estimation based on the conformal array and the theoretical analysis of its parameter estimation performance are the key factors to promote the engineering application of the conformal array.To solve these problems,this paper establishes the wave field signal model of the conformal array.Then,for the case of a single target,the cost function of the maximum likelihood(ML)estimator is rewritten with Rayleigh quotient from a problem of maximizing the ratio of quadratic forms into those of minimizing quadratic forms.On this basis,rapid parameter estimation is achieved with the idea of manifold separation technology(MST).Compared with the modified variable projection(MVP)algorithm,it reduces the computational complexity and improves the parameter estimation performance.Meanwhile,the MST is used to solve the partial derivative of the steering vector.Then,the theoretical performance of ML,the multiple signal classification(MUSIC)estimator and Cramer-Rao bound(CRB)based on the conformal array are derived respectively,which provides theoretical foundation for the engineering application of the conformal array.Finally,the simulation experiment verifies the effectiveness of the proposed method.

CRAMER-RAO BOUNDS FOR PARAMETER ESTIMATION OF PHASE-CODING SIGNALS

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.

多分辨率匹配CRB分析中噪声估计方法

多分辨率目标匹配克拉美-罗界(CRB)分析中,CRB对噪声敏感,噪声估计尤为重要。采用不同阶次有限差分算子构成一组高通滤波器,分别对图像滤波处理,并将四分位间距(IQR)方法与中值滤波原理结合,估计CRB分析中的噪声方差,避免了残留轮廓信息的复杂处理,实验表明算法简单有效。

Performance gain bounds of coherently combining multiple radars in a target-based calibration manner

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.

CRB for 2-D DOA Estimation in MIMO Radar with UCA

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.

Localization for mixed near-field and far-field sources under impulsive noise

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.

多载频MIMO雷达的空时超分辨算法

该文建立了多载频MIMO(Multi-Carrier-Frequency MCF-MIMO)雷达的信号模型,指出信号预处理后在接收端形成一个阵元数为N t×Nr的等效阵列(N t,N r分别为发射和接收阵元数),推导出窄带情况下导向矢量是发射和接收导向矢量的kronecker积,并针对该特点提出了采用空时2维MUSIC方法来实现距离和角度的超分辨,从而提高在多目标环境中目标距离以及角度的估计精度。推导了距离和角度估计的Cramer-Rao界,并仿真研究了估计性能与信噪比、快拍数和波达方向的关系,最后给出了面阵情况下3维空时超分辨的仿真结果,验证了该算法在面阵多维情况下的有效性。

锥面共形阵列天线的极化-DOA估计

由于共形载体曲率的影响,锥面共形阵列中的阵元不仅具有不同指向的方向图,而且具有不同的极化特性,从而使得共形阵列呈现多极化特性。利用锥面共形阵列的多极化特性,针对现有共形阵列下空间超分辨算法对信号极化参数估计缺失这一问题,结合多重信号分类(multiple signal classification,MUSIC)算法实现了入射信号的极化参数与二维波达方向(direction of arrival,DOA)的联合估计。算法对阵列形式无特殊要求,不需要参数配对;在此基础上进一步对算法的估计性能进行了理论分析与推导,给出了算法多参数估计的克拉美-罗边界(Cramer-Rao bound,CRB)。最后通过计算机仿真验证了算法的有效性。

基于方位频率测量的水下被动目标运动分析及其特性研究

探讨了水下三维情形的被动 TMA(目标运动分析 )问题。以被动声纳容易测得的方位角、俯仰角和频率的数据量测为依据 ,在充分考虑水下复杂环境的前题下 ,首先建立动态系统模型 ,并验证了系统的可测性。然后采用伪线性估计和最大似然估计方法来研究它的 TMA问题。计算机仿真结果表明 :采用伪线性估计和最大似然估计方法均能实现水下被动 TMA。且随着测量数据的不断增加 ,定位误差椭圆不断缩小 ,伪线性估计的误差曲线向 CRB界逼近。该方法也适合于已知确定深度的三维情形及目标与本舰在同一平面的二维情形等情况。

非机动水下三维情形的纯方位目标运动分析

以无源声纳关于目标方位(包括方位角、高低角)的有噪测量为依据,探讨了水下三维无源TMA(目标运动分析)的实现及精度问题。文中应用伪线性——Kalman滤波结合方法、最大似然估计方法、扩展卡尔曼滤波方法(EKF),对三维情况[4] 下已知固定深度的的TMA问题进行了研究,并结合数据批处理手段,有效地改善了参数估计的性能,且给出了它们的CRB界。计算机仿真证明了上述算法的有效性。本文所提出的方法要求简单,精度较高,简易平台即可实现,具有一定的实际意义。

一种阵列互耦影响下的目标直接定位算法及其理论性能分析

相比传统的两步定位方法,以Weiss和Amar等人提出的目标位置直接确定方法具有定位精度高、目标分辨率高、可避免"目标-量测"匹配等优势.本文基于该类定位方法的思想,提出了一种利用单个运动天线阵列对目标辐射源的直接定位算法.与已有直接定位算法不同的是,文中新算法考虑了阵列互耦的影响,并且能够实现阵列互耦参量和目标位置参量的解耦合估计.此外,文中还基于矩阵特征值扰动理论,定量推导了新算法参数估计的理论方差(包括目标位置估计方差和互耦向量估计方差),并且给出了全部参量估计方差的克拉美罗界.最后,该文通过仿真实验验证了新算法的优越性和理论分析的有效性.

一种水下未知固定深度的被动目标运动分析

本文对水下三维情形的被动目标运动分析（ＴＭＡ）进行了探讨．文中使用的数据量测是关于 目标的方位角、俯仰角和多卜勒频移等，且运动目标与观测平台相对深度固定未知．这是水下一种常 见的三维情况．伪线性估计和最大似然估计方法的处理结果表明：由于增大了观测的信息量，运动参 数的估计方差收敛性较好，估计性能得到有效改善．伪线性方法的方差估计曲线向ＣＲＢ界逼近．最 后该方法也适合于分析已知固定深度的三维情形与同处一个水平面的二维情形等特殊情况．

时－空二维信号模型下波达方向估计的克拉美·罗界

本文讨论在时－空二维信号模型下信号波达方向估计问题．本文首先对时－空二维信号模型进行了描述，然后分析了在该模型了信号时域信息不能利用、时域信息可以利用以及时域信息完全已知等情形时波达方向估计的克拉美·罗界（ＣＲＢ），并讨论了这几种ＣＲＢ之间的关系，最后给出了几点主要结论．

A performance analysis of multi-satellite joint geolocation

Determining the position of an emitter on Earth by using a satellite cluster has many important applications, such as in navigation, surveillance, and remote sensing. However, in realistic situations, a number of factors, such as errors in the measurement of signal parameters, uncertainties regarding the position of satellites, and errors in the location of calibration sources, are known to degrade the accuracy of target localization in satellite geolocation systems. We systematically analyze the performance of multi-satellite joint geolocation based on time difference of arrival （TDOA） measurements. The theoretical analysis starts with Cramer Rao bound （CRB） derivations for four localization scenarios under an altitude constraint and Gaussian noise assumption. In scenario 1, only the TDOA measurement errors of the emitting source are considered and the satellite positions are assumed to be perfectly estimated. In scenario 2, both the TDOA measurement errors and satellite position uncertainties are taken into account. Scenario 3 assumes that some calibration sources with accurate position information are used to mitigate the influence of satellite position perturbations. In scenario 4, several calibration sources at inaccurate locations are used to alleviate satellite position errors in target localization. Through comparing the CRBs of the four localization scenarios, some valuable＇s insights are gained into the effects of various error sources on the estimation performance. Two kinds of location mean-square errors （MSE） expressions under the altitude constraint are derived through first-order perturbation analysis and the Lagrange method. The first location MSE provides the theoretical prediction when an estimator assumes that the satellite locations are accurate but in fact have errors. The second location MSE provides the localization accuracy if an estimator assumes that the known calibration source locations are precise while in fact erroneous. Simulation results are included to verify the theoretical analysis.

Extended ambiguity function for bistatic MIMO radar

This paper derives the extended ambiguity function for a bistatic multiple-input multiple-output （MIMO） radar system, which includes the whole radar system parameters： geometric sensor configuration, waveforms, range, range rate, target scattering and noise characteristics. Recent research indicates the potential pa- rameter estimate performance of bistatic MIMO radars. And this ambiguity function can be used to analyze the parameter estimate performance for the relationship with the Cramer-Rao bounds of the estimated parameters. Finally, some examples are given to demonstrate the good parameter estimate performance of the bistatic MIMO radar, using the quasi-orthogonal waveforms based on Lorenz chaotic systems.

ESTIMATION OF CARRIER FREQUENCY OFFSETS FOR MIMO SYSTEMS WITH DISTRIBUTED TRANSMIT ANTENNAS

The problem of estimating the carrier frequency offsets in Multiple-Input Multiple-Output (MIMO) systems with distributed transmit antennas is addressed. It is supposed that the transmit antennas are distributed while the receive antennas are still centralized, and the general case where both the time delays and the frequency offsets are possibly different for each transmit antenna is considered. The channel is supposed to be frequency flat, and the macroscopic fading is also taken into consideration. A carrier frequency offset estimator based on Maximum Likelihood (ML) is proposed, which can separately estimate the frequency offset for each transmit antenna and exploit the spatial diversity. The Cramer-Rao Bound (CRB) for synchronous MIMO (i.e., the time delays for each transmit antenna are all equal) is also derived. Simulation results are given to illustrate the per- formance of the estimator and compare it with the CRB. It is shown that the estimator can provide satisfactory frequency offset estimates and its performance is close to the CRB for the Signal-to-Noise Ratio (SNR) below 20dB.