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.

CRAMER-RAO BOUND FOR BLIND CHANNEL ESTIMATION IN COMPLEX-VALUED CHANNEL

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 Cramer-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.

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.

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.

基于归一化CRB加权的宽带DOA估计方法

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。

高斯线性模型正则估计的Cramér-Rao下界

该文针对正则化高斯模型中参数估计的Cramér-Rao下界(CRB)开展研究,提出了一种新型CRB.在线性高斯模型的设计矩阵单位正交的假设下,给出L_1类正则估计的方差及CRB的显式表达,并进行数值计算.进一步地,推导了正则估计的CRB取等条件:在线性高斯模型中,取得CRB的估计均为线性估计量;在正则项可微的假设下,仅二次多项式正则项可令估计取得CRB.最后,针对带稀疏特征的估计提出sparse CRB,将其与现有的CRB比较,从理论和实践两方面说明了其优势.

实际伽利略搜救信号参数估计的Cramer-Rao界

考虑调制不对称度和信息位宽的不确定度,研究了实际伽利略搜救信号信息位宽、到达频率(FOA)、到达时间(TOA)估计的Cramer-Rao界(CRB).推导了伽利略搜救信号Fisher信息矩阵中各元素的计算表达式,利用单位冲激函数的性质和Parseval定理,将单位冲激函数的平方和转换到频域进行计算,得到了信息位宽、FOA和TOA估计的CRB的解析结果.数值分析和Monte Carlo仿真结果表明,CRB具有有效性,可以用于评估上述参数估计算法的性能.

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。

自适应雷达目标参数估计的Cramer-Rao下界

在窄带信号和窄带阵列假设下,分析了均匀面阵(UPA)自适应雷达中目标参数的最大似然估计.首先分析了UPA信号模型,随后给出了目标参数的最大似然估计和相应的CR下界.通过Jacobian矩阵给出了目标俯仰角、方位角、径向速度、模和相位的CRB.分析结果是1-D均匀线性阵列(ULA)到2-D(UPA)的推广,可用于空中运动目标参数估计的性能分析.

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.

基于STFAP的MIMO雷达运动目标参数估计的CRB研究

多发多收(Multiple-Input Multiple-Output,MIMO)雷达在目标检测、参数估计等方面具有显著优势。目标参数估值的CRB被证明是系统设计和空时自适应处理(STAP)性能分析中的有力工具。该文针对采用频分正交信号的共置天线MIMO雷达,首先建立基于MIMO雷达的目标和杂波空-时-频信号模型;在此基础上,研究基于空-时-频自适应处理(STFAP)的MIMO雷达地面运动目标角度和多普勒参数最大似然估值的克拉美-罗界(CRB);最后通过CRB性能仿真分析验证了MIMO雷达STFAP有效消除动目标检测盲速,提高目标参数估计精度的优势。

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.

ON MULTIPATH SIGNAL RESOLUTION AND ITS PERFORMANCE BOUNDS

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.

Optimal maneuvering strategy of spacecraft evasion based on angles-only measurement and observability analysis

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.

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.

Asymptotic Performance Limits of Vehicular Location and Velocity Detection Towards 6G mmWave Integrated Communication and Sensing

In this paper,joint location and velocity estimation(JLVE)of vehicular terminals for 6G integrated communication and sensing(ICAS)is studied.We aim to provide a unified performance analysis framework for ICAS-based JLVE,which is challenging due to random fading,multipath interference,and complexly coupled system models,and thus the impact of channel fading and multipath interference on JLVE performance is not fully understood.To address this challenge,we exploit structured information models of the JLVE problem to render tractable performance quantification.Firstly,an individual closedform Cramer-Rao lower bound for vehicular localization,velocity detection and channel estimation,respectively,is established for gaining insights into performance limits of ICAS-based JLVE.Secondly,the impact of system resource factors and fading environments,e.g.,system bandwidth,the number of subcarriers,carrier frequency,antenna array size,transmission distance,spatial channel correlation,channel covariance,the number of interference paths and noise power,on the JLVE performance is theoretically analyzed.The associated closed-form JLVE performance analysis can not only provide theoretical foundations for ICAS receiver design but also provide a perfor mance benchmark for various JLVE methods。

Parameter estimation of LFM signals based on time reversal

In this paper,parameter estimation of linear frequency modulation(LFM)signals containing additive white Gaussian noise is studied.Because the center frequency estimation of an LFM signal is affected by the error propagation effect,resulting in a higher signal to noise ratio(SNR)threshold,a parameter estimation method for LFM signals based on time reversal is proposed.The proposed method avoids SNR loss in the process of estimating the frequency,thus reducing the SNR threshold.The simulation results show that the threshold is reduced by 5 dB compared with the discrete polynomial transform(DPT)method,and the root-mean-square error(RMSE)of the proposed estimator is close to the Cramer-Rao lower bound(CRLB).

Performance Evaluation of Three-Dimensional UWB Real-Time Locating Auto-Positioning System for Fire Rescue

Fire rescue challenges and solutions have evolved from straightfor-ward plane rescue to encompass 3D space due to the rise of high-rise city buildings.Hence,this study facilitates a system with quick and simplified on-site launching and generates real-time location data,enabling fire rescuers to arrive at the intended spot faster and correctly for effective and precise rescue.Auto-positioning with step-by-step instructions is proposed when launching the locating system,while no extra measuring instrument like Total Station(TS)is needed.Real-time location tracking is provided via a 3D space real-time locating system(RTLS)constructed using Ultra-wide Bandwidth technology(UWB),which requires electromagnetic waves to pass through concrete walls.A hybrid weighted least squares with a time difference of arrival(WLS/TDOA)positioning method is proposed to address real path-tracking issues in 3D space and to meet RTLS requirements for quick computing in real-world applications.The 3D WLS/TDOA algorithm is theoretically constructed with the Cramer-Rao lower bound(CRLB).The computing complexity is reduced to the lower bound for embedded hardware to directly compute the time differential of the arriving signals using the time-to-digital converter(TDC).The results of the experiments show that the errors are controlled when the positioning algorithm is applied in various complicated situations to fulfill the requirements of engineering applications.The statistical analysis of the data reveals that the proposed UWB RTLS auto-positioning system can track target tags with an accuracy of 0.20 m.