Quantization and Saturation Noise Due to Analog-to-Digital Conversion of Radar Returns from Targets with Log-Normal Radar Cross-Section Distributions

An analysis of the saturation and quantization noise generated by analog-to-digital (A/D) conversion of radar returns from targets with log-normal radar cross sections is presented. The results of the analysis show that the high-cross-section tails of the log-normal distribution require higher saturation levels to be set in the A/D converter. The setting of the higher saturation level in the converter results in an increase in quantization noise. Thus the minimum achievable distortion in the output of the A/D converter signal is considerably higher than that for radar targets if their radar cross section had an exponential power distribution.     

A Kalman Filter Based Tracking Scheme with Input Estimation

Beginning with the derivation of a least squares estimator that yields an estimate of the acceleration input vector, this paper first develops a detector for sensing target maneuvers and then develops the combination of the estimator, detector, and a "simple" Kalman filter to form a tracker for maneuvering targets. Finally, some simulation results are presented. A relationship between the actual residuals, assuming target maneuvers, and the theoretical residuals of the "simple" Kalman filter that assumes no maneuvers, is first formulated. The estimator then computes a constant acceleration input vector that best fits that relationship. The result is a least squares estimator of the input vector which can be used to update the "simple" Kalman filter. Since typical targets spend considerable periods of time in the constant course and speed mode, a detector is used to guard against automatic updating of the "simple" Kalman filter. A maneuver is declared, and updating performed, only if the norm of the estimated input vector exceeds a threshold. The tracking sclheme is easy to implement and its capability is illustrated in three tracking examples.     

Comments on "Optimum Bandwidth of a Low-Pass Filter for Detection of a Pulse in Nonstationary Noise"

In a recent correspondence1 a calculation of the optimum bandwidth of a low-pass RC filter for the detection of a pulse signal in nonstationary noise was presented. The purpose of this correspondence is: 1) to point out additional references to the work which has been conducted in the stationary noise case, and 2) to present an interesting alternate derivation of the expected output noise power for the nonstationary noise case.     

异常值和未知观测噪声鲁棒的非线性滤波器

针对含异常观测值的非线性系统滤波问题,以Huber损失函数替代推导滤波器最大后验准则中观测误差的l₂范数,构造出了一种新的优化准则函数,从而给出了一种对异常值鲁棒的非线性后验线性化滤波器。分析表明：由于Huber损失函数兼具l₁和l₂范数的性质,从而使得由这个新准则推导出的滤波器,不仅具有l₂范数的低误差拟合性,也具备l₁范数对异常值的鲁棒性。而当观测噪声的分布未知时,通过引入箱线图法检测异常值,并对噪声统计分布的参数进行估计,进一步提出了对异常值和未知观测噪声分布鲁棒的非线性后验线性化滤波器。仿真实验验证了分析结果的有效性,并表明本文算法的性能优于现有文献报道的非线性滤波算法。     

Feedback Realization of a Continuous-Time Optimal Filter

Another derivation of a continuous-time optimal linear filter is presented. Using this result as a point of departure, a feedback version of this continuous filter is postulated and shown to be optimal in the limit as the ``feedback gain' becomes infinite. It is then demonstrated that the need for this infinite feedback gain can frequently be eliminated. This feedback realization of the continuous optimal filter has application to the problem of optimally mixing two or more redundant signals, each contaminated by random noise. The feedback configuration has the advantages of simplicity and the bounding of otherwise troublesome very large errors. A simple example is given of the mixing of two (velocity) references each having exponentially correlated error.     

Some Properties and Effects of Reverberation in Acoustic Surveillance

Following the work of Van Trees,[1] the effect of wide-sense stationary clutter on signal detectability with a matched filter is determined. The improvement to be gained by a high time-bandwidth product in the transmitted waveform for the detection of low-velocity targets is clearly shown. The additional noise contributed by the clutter is reduced by a factor equal to the time-bandwidth product. This reducing effect occurs provided that the transmitted waveform is adjusted properly. The optimum transmitted waveform for detection of low-velocity targets turns out to be one whose energy density spectrum is flat over the bandwidth of interest. This derivation is made by a simple application of Schwarz's inequality rather than the application of the calculus of variations that was done by Manasse.[14] Computations were made of the loss encountered by a narrow-band single-frequency waveform and by a wide-band linear FM waveform, each used in a matched-filter detector. The contrast is especially marked for very low target speeds where the narrow-band waveform is very bad. Its loss drops off sharply with target speed while the loss of the wide-band waveform drops off very slowly in comparison. Beyond a certain small target speed, the narrow-band loss is negligible. However, with enough bandwidth, the wide-band waveform can be made to have acceptable loss at all target speeds.     

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。     

Phased array of large reflectors for deep-space communication

In this paper the problem of uplink array calibration for deep-space communication is considered. A phased array of many modest-size reflectors antennas is used to drastically improve the uplink effective isotropic radiated power of a ground station. A radar calibration procedure for the array phase distribution is presented using a number of in-orbit targets. Design of optimal orbit and the number of calibration targets is investigated for providing frequent calibration opportunities needed for compensating array elements phase center movements as the array tracks a spacecraft. Array far-field focusing based on the near-filed in-orbit (low Earth orbit (LEO)) calibration targets is also presented and array gain degradation analysis based on the position error of the array elements and in-orbit targets has been carried out. It is shown that errors in the in-orbit targets positions significantly degrade the far-field array gain while the errors in array elements positions are not very important. Analysis of phase errors caused by thermal noise, system instability, and atmospheric effects show insignificant array gain degradation by these factors     

Target racking with glint noise

In tracking targets, there can be an uncertainty associated with the measurements in addition to their inaccuracy, which is usually modeled by aDditive Gaussian noise. However, the Gaussian modeling of the noise may not be true. Noise can be non-Gaussian. The non-Gaussian noise arising in a radar system is known as glint noise. The distribution of glint noise is long tailed and will seriously affect the tracking performance. An algorithm is developed which can significantly improve the tracking performance when glint noise is present     

Recursive Methods for Computing Detection Probabilities

Recursive methods are drived for computing detection probabilities for general fluctuating targets in Gaussian noise. For the generalized chi-square family of fluctuating targets, very simple and convenient recursive algrithms result. The methods are also extended to cell-averaging CFAR. Although the detection probability is expressed iw: terms of an infinite series, a convenient expression is derived for the resulting error when the series is truncated. Cell-averaging CFAR results are computed for nonfluctuating, Swering case I, and Swerling case II fluctuating targets.     

Composite Bound on Arrival Time Estimation Errors

Time of arrival (TOA) estimation of narrowband signals is a problem of considerable practical interest in radar and sonar applications. A new technique is presented to analyze the mean square error (MSE) performance of TOA estimation schemes, based on recently developed lower bound. We obtain a complete characterization of the MSE as a function of the signal and noise parameters. The results are given in a simple closed-form analytical expression.     

Linear Quadratic Differential Games Guidance Law for Dual Controlled Missiles

A novel guidance law designed specifically for a missile having forward and aft control systems is presented. For the derivation a linear quadratic differential games formulation of the end-game interception scenario is used. Conditions for achieving perfect intercept are given and new game spaces are presented. It is also shown that increasing the direct lift associated with the canard control allows intercepting targets with higher maneuvering capability, while for the tail control the effect is opposite.     

A morphological approach to automatic mine detection problems

We consider the problem of detecting mines and minelike targets imaged by multispectral sensors. We propose an algorithm, based on mathematical morphology (MM), that yields accurate detection results in moderately cluttered environments. For targets in heavily cluttered environments, a preprocessing step is employed, based on the maximum noise fraction (MNF) transform, in order to reduce the effect of clutter and enhance the presence of targets. The algorithm is simple, performs well, and requires only approximate knowledge of target size     

False alarm effects on estimation in multitarget trackers

An analysis of false alarm effects on tracking filter performance in multitarget track-while-scan radars, using variable correlation gates, is presented. The false alarms considered originate from noise, clutter, and crossing targets. The dimensions of the correlation gates are determined by filter prediction and measurement error variances. Track association is implanted either by means of a distance weighted average of the observations or by the nearest neighbor rule. State estimation is performed by means of a second-order discrete Kalman filter, taking into consideration random target maneuvers. Measurements are made in polar coordinates, while target dynamics are estimated in Cartesian coordinates, resulting in coupled linear filter equations. the effect of false alarms on the observation noise covariance matrix, and hence on state estimation errors, is analyzed. A computer simulation example, implementing radar target tracking with a variable correlation gate in the presence of false alarms, is discussed     

Graphical Interpretation of Chirp Echoes from Complex Targets

Echoes from complex targets due to chirp waveforms show different time responses for different chirp rates, because of the ambiguity of range and radial velocity information. A graphical method is described which enables the derivation of the time response for an arbitrary chirp rate when the scattering cross-section distribution in the range and radial velocity plane is known for complex targets. The graphical method can also be used to generate an approximately realistic scattering cross-section distribution when the time responses for two different chirp rates are given. An example is shown which applies to the computer simulation of the radar echo from a waking reentry space vehicle.     

Adaptive Radar Beacon Forming

Propagation errors along paths between an array radar and a distribution of targets cause degradations in angle measurements and detection range. The overall objective of the research described in this paper was to analyze and demonstrate the use of conjugate reflections for compensating adverse effects of path errors. The effect of reflecting the conjugate of an incident wave is described mathematically and is demonstrated by computer simulation. Repeated conjugate reflections are shown to result in the formation of a single beam usually focussed on a target highlight. Echoes from this spatial reference, or "beacon" are shown to provide the means by which aperture phase errors may be effectively compensated. Results of radar simulations include two-way patterns computed for an example involving a distribution of three-point targets and half-wave-length Gaussian aperture errors. Without compensation a gain loss of 12 dB is computed; with error correction, based on echoes from an adaptively focussed beam, the two-way pattern is within a small fraction of a dB of the ideal pattern. The effect of noise on adaptive beacon forming was considered for a case involving one target. Repeated conjugate reflections improve signal-to-noise ratio as long as the effect of noise is less than the effect of aperture dephasing on the power reflected back to the target. An example is presented in which signal-to-noise ratio at the output of the receiver combining network is increased from 4 to 11.8 dB.     

Detection Probabilities for Log-Normally Distributed Signals

The amplitude and power of a large family of radio signals are observed to have log-normal probability density functions. Among these are signals propagated through random inhomogeneous media, a notable example being low frequency atmospheric radio noise. Of greater importance are certain radar targets that have been observed to have essentially log-normal density functions. Both ships and space vehicles may fall into this category. Curves of probability of detection vs. signal-to-noise ratio for the case of log-normal signals in Gaussian noise have been computed and are presented in this paper. The curves apply for square-law detection with varying degrees of postdetection linear integration. Both fully correlated and completely uncorrelated fluctuating signals are considered. It is shown that for log-normal signal distributions having large variances, the probability of detection differs significantly from that obtained using curves based on an assumed Rayleigh signal distribution.     

Improved target classification using optimum polarimetric SARsignatures

We present a new method for automatic target/object classification by using the optimum polarimetric radar signatures of the targets/objects of interest. The state-of-the-art in radar target recognition is based mostly either on the use of single polarimetric pairs or on the four preset pairs of orthogonal polarimetric signatures. Due to these limitations, polarimetric radar processing has been fruitful only in the area of noise suppression and target detection. The use of target separability criteria for the optimal selection of radar signal state of polarizations is addressed here. The polarization scattering matrix is used for the derivation of target signatures at arbitrary transmit and receive polarization states (arbitrary polarization inclination angles and ellipticity angles). Then, an optimization criterion that minimizes the within-class distance and maximizes the between-class metrics is used for the derivation of optimum sets of polarimetric states. The results of the application of this approach on real synthetic aperture radar (SAR) data of military vehicles are obtained. The results show that noticeable improvements in target separability and consequently target classification can be achieved by the use of the optimum over nonoptimum signatures     

An Interleaved-Trace Time-Compression Radar Display

Detection information from conventional surveillance radars is frequently presented in the form of a display known as the plan position indicator map. In this display, new data are displayed while data from previous scans fade from the display. Target blips typically persist for several scans, making possible operator integration or correlation. However, the noise from previous scans often masks signals from small moving targets. To avoid the loss in signal-to-noise ratio caused by the addition of noise to signal plus noise, a digital signal processing display unit has been designed and is presented here.     

Effect of Monopulse Signal Thresholding on Tracking Multiple Targets

The monopulse angle of arrival measured from two targets may wander far beyond the angular separation of the targets. In order to remove large errors, angle of arrival measurements are passed through a threshold detector and the measurements which do not satisfy the threshold are rejected. Thresholding has the tendency to move the mean indicated angle of arrival away from the stronger target and toward the power centroid of the targets, which may be undesirable in some applications. Expressions for the probability density function, the mean, and the variance of the in-phase angle of arrival are developed in this paper as a function of the threshold setting. Background noise and interfering signals are neglected in the analysis.