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 BOUNDS OF THE FREQUENCY ESTIMATION IN THE TIME SELECTIVE RADIO CHANNELS WITH DOPPLER SPREAD

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.

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.

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.

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.

Direction finding of bistatic MIMO radar in strong impulse noise

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.

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.

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.

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.

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.

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).

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.

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.

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。

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。

未知频偏下直扩信号的扩频序列估计

针对未知频偏下的直扩信号,通过将载频吸收至扩频波形中,提出了一种有效的基于协方差矩阵子空间分解的扩频序列估计算法。通过信号子空间分解,提高了含有未知频偏信息的扩频波形估计的信噪比,从而降低了载频估计难度。在随机信号模型条件下,还推导了扩频波形估计器的克拉美劳界。在低信噪比条件下,仿真验证了该算法的有效性。