Adaptive cubature Kalman filter with the estimation of correlation between multiplicative noise and additive measurement noise

Mobile robots are often subject to multiplicative noise in the target tracking tasks, where the multiplicative measurement noise is correlated with additive measurement noise. In this paper,first, a correlation multiplicative measurement noise model is established. It is able to more accurately represent the measurement error caused by the distance sensor dependence state. Then, the estimated performance mismatch problem of Cubature Kalman Filter(CKF) under multiplicative noise is analyzed. An i...     

Analysis of CA-CFAR processors for linear-law detection

A method for evaluating the performance of cell-averaging constant false alarm rate (CA-CFAR) processors which use the amplitude of echo signals rather than their squared amplitude is presented. Results for the case of Rayleigh clutter/noise statistics are given. Detection probabilities are evaluated for the case of a Rayleigh fluctuating target embedded in Rayleigh clutter/noise for linear-law CA-CFAR processors. These results are observed to be practically identical to those of square-law CA-CFAR processors for which analytical expressions are readily available. These observations are verified using Monte Carlo simulations. The same conclusion is reached in the case of a nonfluctuating target embedded in Rayleigh clutter/noise for which only simulation results are presented     

The Information Content of Synthetic Aperture Radar Images of Terrain

A statistical model is developed that portrays an imaging radar as a noisy communication channel with multiplicative noise, and the model is used to evaluate the average amount of information that can be extracted about a target from its radar image. The average information content is also used to define a measure of radiometric resolution for radar images. It is shown that the information content and the resolution capabilities of an imaging radar reach a limit beyond which an increase in scene dynamic range does not improve the information content or the resolution. This limitation results from the multiplicative nature of the noise introduced in the imaging process.     

Nonparametric Radar Extraction Using a Generalized Sign Test

A nonparametric procedure used in a constant false alarm rate (CFAR) radar extractor for detecting targets in a background of noise with unknown statistical properties is described. The detector is based on a generalization of the well-known two-sample sign test and thus requires a set of reference noise observations in addition to the set of observations being tested for signal presence. The detection performance against Gaussian noise is determined for a finite number of observations and asymptotically, for both nonfluctuating and pulse-to-pulse Rayleigh fluctuating target statistics. It is noted that the performance loss, as compared to the optimum parametric detector, depends critically on the number of reference noise observations available when the number of hits per target is not large. In the same case a much larger loss is also found for a pulse-to-pulse fluctuating target even though the asymptotic loss is the same as for a nonfluctuating target. A comparison is finally made with a detector based on the Mann-Whitney test, which usually is considered to be one of the better nonparametric procedures for the two-sample case.     

Pade approximations for detectability in K-clutter and noise

The Pade approximation (PA) method is used to analyze the detection performance of single and multiple pulse radar systems operating in K-distributed clutter and thermal noise. Simple approximations for false-alarm and detection probabilities are obtained, using lower order moments for the detection decision statistic. Both envelope and squaring detector laws are considered, with noncoherent integration, for independent and correlated K clutter. The target is assumed to be pulse-to-pulse Rayleigh fading. The methods are a substantial application of the PA methods we have previously published     

导航中单位矢量的二次旋转乘法观测模型

视线矢量观测是实现自主导航的重要方式。本文针对单位矢量的加法观测模型中观测矢量非单位化问题和乘法观测模型中测量噪声与实际情况不符的问题,提出二次旋转乘法观测模型。通过真实矢量在正交方向上进行的两次刚体旋转,获得了与现有乘法观测模型形式相同、但旋转角服从瑞利分布的正确观测方程。推导了测量误差的统计特性和双矢量观测的性质,并从空间几何角度给予了解释。数值仿真结果表明,二次旋转乘法观测模型弥补了由加法观测模型线性化所引起的问题,具有更精确的误差形式,由此给出了模型的潜在应用范围。     

包含乘性噪声自适应修正的非合作目标相对导航算法

无人机（UAV）态势感知的任务是利用机载传感器对未知环境进行目标识别和引导,针对无人机与非合作目标间中远距离的相对导航问题,提出了一种基于角度和距离量测的相对状态估计算法。在现有滤波算法的基础上,为了提高精度和稳定性,本文利用了列文伯格-马夸尔特（LM）优化的思想对迭代卡尔曼滤波（IEKF）算法进行改进,提出了一种LM-IEKF算法,并推导该算法在迭代过程中的状态更新方程及协方差阵的递推公式。在此基础上,考虑到距离传感器由于信号相关特性而引入的乘性噪声,现有的加性噪声模型难以适应,因此,进一步提出了基于量测噪声自适应修正的Modified LM-IEKF方法,通过在线实时更新噪声阵提高滤波的精度,并设置渐消记忆指数平滑估计结果。算法验证结果表明,与现有的EKF、IEKF算法相比,在仅含加性噪声的情况下,LM-IEKF算法具有更好的性能;在包含乘性噪声的情况下,Modified LM-IEKF可以有效地估计量测噪声,与目前广泛使用的EKF算法相比,在综合相对位置和相对速度精度上分别提高了10%和23%。     

M-correlated sweeps performance analysis of mean-level CFARprocessors in multiple target environments

This paper is devoted to the detection performance evaluation of the mean-level (ML) constant false-alarm rate (CFAR) detectors processing M-correlated sweeps in the presence of interfering targets. The consecutive pulses are assumed to be fluctuating according to the Swerling I model. Exact expressions are derived for the detection probability of the conventional mean-level detector (MLD) and its modified versions under Rayleigh fluctuating target model. Performance for independent sweeps can be easily obtained by setting the sweep-to-sweep correlation coefficient equal to zero. Results are obtained for both homogeneous and nonhomogeneous background environments. It is shown that for fixed M, the relative improvement over the single sweep case increases as the correlation between sweeps decreases. For the same parameter values, the minimum MLD has the best performance in the presence of extraneous target returns among the reference noise samples     

Monopulse tracking of Rayleigh targets: a simple approach

A simple derivation of the probability distribution of the monopulse ratio is presented. The derivation is based upon a conditional distribution and considers both Rayleigh targets and simple non-Rayleigh cases. The mean is obtained almost without calculation. The variance expression is given completely general noise and glint interpretation. Analytical expressions for angle error mean and spread, including noise, target width, and unresolved targets, are presented as functions of antenna position, in simple and comprehensive diagrams     

机动目标“当前”统计模型与自适应跟踪算法

本文提出机动目标“当前”统计模型的概念并建议用修正的瑞利-马尔科夫过程描述目标随机加速机动的统计特性。文中指出了在机动目标运动模型中状态（机动加速度）估值与状态噪声之间的内在联系。在此基础上提出了具有机动加速度均值及方差自适应的卡尔曼滤波算法。对一维和三维的情形进行了计算机模拟。计算结果表明,在仅对目标位置进行观测的情况下,这类自适应估值算法无论对高度机动或无机动的目标均可绘出较好的位置、速度及加速度估值。     

机动多目标跟踪问题中关联区域的研究

 本文研究了跟踪多个机动目标时,由滤波算法所获得的新息向量范数的统计性质,关联区域的大小以及接收正确回波的概率。借助拉蒙特卡洛方法,考察了不同的目标状态模型、目标机动加速度及状态噪声方差等因素对所研究的问题的影响。研究表明,文献[1]所提出的机动目标状态模型及相应的自适应算法具有较好的适应目标机动的能力,关联区域的大小及接收正确回波的概率均较为稳定。     

Detection of Target Multiplicity Using Monopulse Quadrature Angle

The feasibility of using the indicated quadrature angle of arrival of a monopulse radar to discriminate a single target from multiple targets, separated in angle within a radar resolution cell, is investigated. The analysis is performed for steady (fixed) and Rayleigh fluctuating targets which cover a broad range of target characteristics. In both cases, the interfering signals due to noise and clutter in the sum and difference monopulse channels are assumed to be independent, zero-mean Gaussian processes. Detection and false alarm probabilities are evaluated analytically and the receiver operating characteristics are obtained for both fixed and fluctuating target cases. It is shown that multiple targets can be discriminated from a single target condition by integrating the indicated monopulse quadrature angle of arrival from several independent pulses. It is also shown that the probability of detecting multiple targets increases as the fluctuation in the target radar cross section decreases, approaching the fixed amplitude case in the limit.     

CFAR for homogeneous part of high-resolution imagery

In high-resolution imaging, weak target pixel amplifiers may not be detected in the presence of clutter containing strong nonhomogeneities, when conventional approaches are used. The authors describe a constant false alarm rate (CFAR) approach that avoids the elimination of these significant target returns. The nonhomogeneous clutter as well as the weak target components are detected with this approach. The targets could then be discriminated from the homogeneities by discrimination techniques. It is shown how the lower amplitude components of the background noise and homogeneous clutter (which have Rayleigh statistics) can be detected in the presence of strong homogeneous clutter and targets. The average level of the homogeneous component is then determined using these lower-amplitude components. This CFAR approach avoids having a CFAR on the strong nonhomogeneities as well as the homogeneous component. The avoidance is what yields the ability to detect weak target pixel amplitudes     

Performances of order statistics CFAR

A previous analysis of order-statistics constant-false-alarm-rate (OS-CFAR) radar receiving a single pulse from a Rayleigh fluctuating target in a Rayleigh background is extended to a Rayleigh-plus-dominant target. The analysis includes effects of a multitarget environment. A detailed comparison of OS-CFAR, cell-averaging (CA) CFAR, and censored CA-CFAR is provided for a Rayleigh target in the presence of strongly interfering targets. The false-alarm analysis of OS-CFAR is extended to the more general case of a Weibull background. The deterioration of the CFAR property of OS as the shape factor, C, of a Weibull probability density function changes from Rayleigh (C=2) to a longer-tailed one (C<2) is evaluated. The analytic comparison between CA-CFAR and OS-CFAR is extended to an integration of pulses reflected from a Swerling II target. The OS-CFAR performance (with and without interfering targets) yields an integral equation that is solved numerically     

基于超短基线声传感器阵的高速目标轨迹估计

针对低空高速飞行目标跟踪问题,首先研究了某典型目标噪声信号的时频特性,发现其信号呈现宽带低频特征,难以从频域对目标轨迹进行估计。在此基础上,从各路接收信号的到达时延量入手,考虑到声基阵只能布设于有限空间内的制约,提出了一种基于超短基线阵时延估计的目标跟踪方法。该方法利用各个超短基线阵接收声强极值点分别估计目标运动轨迹垂线方向,计算多个垂线的叉乘向量实现对目标运动方向的估计,再利用多面交汇的方式获估计得到目标运动轨迹。分别对目标俯仰角、方位角及运动轨迹估计的理论误差进行了推导,根据理论估计误差,为能够实现对目标运动轨迹的估计,各个超短基线阵应尽量保证与目标运动轨迹不在同一平面上。根据仿真结果,在采用4个传感器基阵时,角度估计平均误差在4°以内,位置估计相对误差在5%左右。仿真结果验证了该方法的有效性。     

Layover solution in multibaseline SAR interferometry

In this work, spectral estimation techniques are used to exploit baseline diversity of a multichannel interferometric synthetic aperture radar (SAR) system and overcome the layover problem. This problem arises when different height contributions collapse in the same range-azimuth resolution cell, due to the presence of strong terrain slopes or discontinuities in the sensed scene. We propose a multilook approach to counteract the presence of multiplicative noise, which is due to the extended nature of natural targets; to this purpose we extend the RELAX algorithm to the multilook data scenario (M-RELAX). A thorough performance analysis of nonparametric (beamforming and Capon) and parametric (root MUSIC and M-RELAX) techniques is carried out based on Monte Carlo simulations and Cramer-Rao lower bounds (CRLB) calculation. The results suggest the superiority of parametric methods over nonparametric ones.     

Detection of a Distributed Target

The influence of increasing range resolution on the detectability of targets with dimensions greater than the resolution cell is studied. An N-cell target model is assumed, which contains k reflecting cells, each reflecting independently according to the same Rayleigh amplitude distribution. It will be referred to as the (N,k) target. Detection based on one transmitted pulse is performed against a background of white normal noise. Detection in stationary clutter is also considered. The optimum detector is obtained but, in view of its complexity, the performance of a simpler detector, the square-law envelope detector with linear integrator (SLEDLI), is analyzed, and a formula for the probability of detection is obtained. Graphs are presented which show the probability of detection as a function of signal-to-noise ratio (SNR) for various values of N k, and false alarm probability. For N/k not too large it is shown that the SLEDLI is near optimum.     

Exact Detection Probability for Partially Correlated Rayleigh Targets

The detection probability PD of a radar receiver which postdetection integrates N pulses of an expqnentially correlated signal from a Rayleigh target in thermal noise is determined. At the limiting correlation coefficients, p = 1 and p = 0, the analysis yields, respectively, the well known Swerling case 1 and case 2 formulas. The effect of partial (0 ? p ? 1) correlation is exhibited in a set of curves of PD versus signal-to-noise ratio, X, for various N and p. Additional curves compare the exact fluctuation loss determined from the above analysis with an approximate expression universally employed by radar system engineers.     

A new distributed constant false alarm rate detector

A new constant false alarm rate (CFAR) test termed signal-plus-order statistic CFAR (S+OS) using distributed sensors is developed. The sensor modeling assumes that the returns of the test cells of different sensors are all independent and identically distributed In the S+OS scheme, each sensor transmits its test sample and a designated order statistic of its surrounding observations to the fusion center. At the fusion center, the sum of the samples of the test cells is compared with a constant multiplied by a function of the order statistics. For a two-sensor network, the functions considered are the minimum of the order statistics (mOS) and the maximum of the order statistics (MOS). For detecting a Rayleigh fluctuating target in Gaussian noise, closed-form expressions for the false alarm and detection probabilities are obtained. The numerical results indicate that the performance of the MOS detector is very close to that of a centralized OS-CFAR and it performs considerably better than the OS-CFAR detector with the AND or the OR fusion rule. Extension to an N-sensor network is also considered, and general equations for the false alarm probabilities under homogeneous and nonhomogeneous background noise are presented.     

Lock threshold deterioration induced by antenna vibration and signal coupling effects in hypersonic vehicle carrier tracking system of Ka band

The envelope of a hypersonic vehicle is affected by severe fluctuating pressure, which causes the airborne antenna to vibrate slightly. This vibration mixes with the transmitted signals and thus introduces additional multiplicative phase noise. Antenna vibration and signal coupling effects as well as their influence on the lock threshold of the hypersonic vehicle carrier tracking system of the Ka band are investigated in this study. A vibration model is initially established to obtain phase noise in consideration of the inherent relationship between vibration displacement and electromagnetic wavelength. An analytical model of the Phase-Locked Loop(PLL), which is widely used in carrier tracking systems, is established. The coupling effects on carrier tracking performance are investigated and quantitatively analyzed by imposing the multiplicative phase noise on the PLL model. Simulation results show that the phase noise presents a Gaussian distribution and is similar to vibration displacement variation. A large standard deviation in vibration displacement exerts a significant effect on the lock threshold. A critical standard deviation is observed in the PLL of Binary Phase Shift Keying(BPSK) and Quadrature Phase Shift Keying(QPSK) signals. The effect on QPSK signals is more severe than that on BPSK signals. The maximum tolerable standard deviations normalized by the wavelength of the carrier are 0.04 and 0.02 for BPSK and QPSK signals,respectively. With these critical standard deviations, lock thresholds are increased from à12 andà4 d B to 3 and à2 d B, respectively.