Multiple Gaussian Targets: The Track-on-Jam Problem

When a radar with amplitude comparison monopulse arithmetic encounters signals from multiple Gaussian sources it will "point" to the centroid of the incident radiation. The probability density function (pdf) of the monopulse ratio when N independent samples of difference and sum signals are processed in a maximum likelihood receiver is derived. For finite jam-to-noise ratio the estimate has a bias which is independent of N. The variance in the estimate does however depend upon N. Central moments of order less than or equal 2N - 2 exist and are given by a simple formula. Plots of the pdf and its bias and variance for various jam-to-noise ratios, locations of the centroid with respect to the boresight direction, and number of samples processed are presented in the accompanying figures.     

Detection Performance of the Cell Averaging LOG/CFAR Receiver

The cell averaging LOG/CFAR receiver is a special implementation of a constant-false-alarm-rate (CFAR) receiver in which the noise level estimate is derived from a set of contiguous time samples of the output of a logarithmic (LOG) detector as obtained from a tapped delay line. This CFAR receiver is capable of operating over a larger dynamic range of noise levels than a conventional cell averaging CFAR receiver, but with somewhat poorer detectability. The performance in stationary Gaussian noise of the cell averaging LOG/CFAR receiver with no post-detection integration is determined in this paper. For a small number of reference noise samples, results were obtained by a Monte Carlo simulation using the technique of importance sampling. For a large number of reference noise samples, a second moment analysis gave the desired results. Both these results can be summarized in the following simple formula, NLOG = 1.65NLIN - 0.65, which relates the number of reference samples required by each of the two receivers for equivalent performance. Thus, for the cell averaging LOG/CFAR receiver to give the same detection performance as the conventional cell averaging CFAR receiver, the number of reference noise samples has to be increased by up to 65 percent.     

Spectral Moment Estimates from Correlated Pulse Pairs

Estimates statistics of the first two power spectrum moments from the pulse pair covariance are analyzed. The input signal is assumed to be colored Gaussian and the noise, white Gaussian. Perturbation formulas for the standard deviation of both mean frequency and spectrum width are applied to a Gaussian shaped power spectrum, and so is a perturbation formula for the bias in the width estimate. Mean frequency estimation from interlaced pulse pairs is presented. Throughout this study, estimators from independent, spaced, and contiguous pulse pairs are compared to provide a continuum of statistics from equispaced tightly correlated to statistically independent pulse pairs.     

Analysis of a signal starting time estimator based on the Page test statistic

Many signal processing applications require the detection of an abrupt change with subsequent estimation of the actual time of occurrence of the change. The time of the most recent reset to zero of the Page test statistic is proposed for this purpose. The probability mass function of the estimator is determined analytically subject to a quantization of the Page test statistic update. Closed-form results for the first three uncorrected moments of the estimator are presented. The analytical results are verified by comparison to simulation results and the fineness of the quantization required for accurate representation is investigated by evaluation of the Kolmogorov-Smirnov statistic. The bias, standard deviation, and skewness of the estimator as a function of the signal strength and detector threshold are evaluated for Gaussian shift-in-mean and noncentral chi-squared changes in signal type.     

Bias and Standard Deviation of the Estimator for the Underlying Probability in a Sequence of Bernoulli Trials with Preselected Number of Successes

In a sequence of Bernoulli trials which stops after a preselected number M of successes, the maximum likelihood estimator of the underlying probability is given by the ratio of M and the required number of observations. Closed-form expressions for the bias and standard deviation of this estimator are developed.     

基于“当前”统计模型的卡尔曼滤波在北斗单向授时中的应用

为了提高北斗单向授时的授时精度,提出了一种基于“当前”统计模型的卡尔曼滤波单向授时方法。将“当前”统计模型应用于接收机时钟频率漂移的建模以建立状态方程,使用经过卡尔曼滤波后的钟差和钟速对本地时钟进行修正。实验结果表明,在选取合适的机动频率和最大频率漂移的情况下,相比于未滤波修正,温补晶振时钟的峰峰值最多可以减小36.7%,标准差最多可以减小42.5%;恒温晶振时钟的峰峰值最多可以减小71.8%,标准差最多可以减小67.0%。基于“当前”统计模型的卡尔曼滤波单向授时方法,可以有效地降低观测量的误差与噪声对于接收机钟差与钟速的影响,从而提高授时精度。     

Postdetection Integration Loss for Logarithmic Detectors

The effect of a logarithmic receiver on the detection performance of a radar has been determined by Green by numerical computations for up to 100 pulses integrated. It was further suggested that the loss in decibels as compared to a square-law detector would appear to be proportional to the logarithm of the number of pulses integrated. In this correspondence we show that this ?conjecture? is false, and that the additional loss when N becomes very large approaches a constant value of 2.2 dB.     

用联合样本法确定直升机零件的疲劳分散性

在直升机型号的疲劳合格鉴定中,由于经费和时间的限制,同一种零部件的试件数通常不超过6个。由这些试验结果构成的样本在统计学上叫小样本。一般认为,由这种小样本确定的平均值还比较准确,但确定的标准差可能偏离真值甚远。本文介绍一种把小样本试验数据联合起来构成大样本,比较精确地确定标准差的方法。     

Loss in Single-Channel MTI with Post-Detection Integration

The detection performance of a single-channel MTI receiver with post-detection integration, for a Swerling I target, has been evaluated by a Monte Carlo simulation. It is shown that a fairly good approximation is obtained by applying the ?effective number of independent integrated samples? to the standard detection curves. The ?I-only? loss is about 2 dB for integration of more than 20 pulses; thus this receiver is acceptable if implementation constraints dictate it.     

Noncoherent Detection of Split-Phase FSK by Multiple Predetection Filtering

When the cumulative drift in the center frequency of a binary split-phase FSK signal exceeds the peak deviation of the signal, a conventional noncoherent receiver (i.e., one provided with only two IF filters) may be unable to achieve the probability of error per bit which the designer desires. This limitation may be overcome if the receiver is provided with a bank of more than two contiguous filters (each followed by an envelope detector) tospan the total IF band the instantaneous IF signal might occupy. It is shown that the probability of error per bit for such a receiver is a function of 1) the ratio F of peak frequency deviation to peak frequency drift, 2) the number M of IF filter/detectors, and 3) the signal-to-noise ratio ? in the output of the filter containing the signal. It is further shown thatfor a given value of F an increase in M reduces the amount of transmitter power the communication system designer must provide to yield a given probability of error per bit.     

北斗二号伪距偏差特性分析及其对定位的影响

伪距偏差是指因卫星下行导航信号非理想状态,导致不同技术状态的终端在接收同一卫星导航信号时产生不同的测距偏差,而现有伪距改正手段尚未考虑该偏差,甚至在双频定位时还会被进一步放大.基于Curtin GNSS研究中心设置的零基线接收机,使用接收机零基线差分解算多组观测终端下北斗二号卫星的伪距偏差,分析其特性,并采用标准单点定...     

Analysis of airborne GPS multipath effects using high-fidelity EM models

Airborne GPS systems are being upgraded to provide sufficient positioning accuracy to support automatic landing operations in low visibility conditions. This is made possible by differential GPS (DGPS), in which the errors common to the airborne receiver and ground station are removed by knowledge of the latter's precise location. However, errors specific to the airborne system remain, of which the dominant components are receiver noise and multipath. To support the assessment of the integrity of the signal in space, these residual errors are incorporated in a statistically based error model, designated as the "standard model." The standard model is defined as the standard deviation of a Gaussian distribution that overbounds the residual pseudo-range (PR) error. It relates the standard deviation of the overbounding distribution to the elevation angle of the satellite relative to the local level coordinate system. The international community is currently developing improved standards to enable DGPS systems to support landings in the worst visibility conditions (i.e., CAT III). As a part of this development, the standard model for multipath is being re-evaluated and an improved model is sought. In order to better characterize the residual multipath errors, tools for accurate calculation of the airframe scattering effects are needed. Development of such tools is the subject of this paper. A new method for accurately computing pseudo-range error, based on the use of high-fidelity EM models, is described. This approach provides new insight into the mechanisms causing multipath error.     

Sigma inflation for the local area augmentation of GPS

The Local Area Augmentation System (LAAS) is the differential satellite navigation architectural standard for civil aircraft precision approach and landing. While the system promises great practical benefit, a number of key technical challenges have been encountered in the definition of the architecture. Perhaps chief among these has been the need to ensure compliance with stringent requirements for navigation Integrity. In this context, this research investigates the sensitivity of integrity risk to statistical uncertainties in the knowledge of reference receiver error standard deviation (σ_{pr_gnd} ) and error correlation across the multiple reference receivers to be used in the LAAS ground segment. A new, detailed approach toward mitigating the integrity risk due to parameter statistical uncertainty is presented     

Studies of Logarithmic Radar Receiver Using Pulse-Length Discrimination

Using a logarithmic amplifier giving a detected output followed by a high-pass filter is a technique for reducing adverse effects of distributed clutter in radar receivers. A pulse-length discriminator (PLD) used as the high-pass filter is treated here. Theoretical and experimental results for the loss in detectability introduced by this receiver, as compared with a matched filter or a good approximation thereto, have been obtained. For the case of single-hit detection, losses of 4 to 8 dB are introduced by the logarithmic amplifier/pulse-length discriminator (LOG AMP/PLD) combination; for post-detection integration, the losses are reduced to 2 to 4 dB. The latter values would apply where the LOG AMP/PLD output is presented on a PPI (plan position indicator). Some experimental results of the ability of the LOG AMP/PLD receiver to reject signals of incorrect pulse length show that signals exceeding the design pulse length by more than 25 to 50 percent are effectively suppressed. No significant short-pulse discrimination is obtained from the receiver.     

Interference Effects of Pseudo-Random Frequency-Hopping Signals

When a pseudo-random frequency-hopping signal is intercepted by a conventional receiver operating within the same frequency band, the interfering signal has the form of a pulse-amplitude modulated signal. Each pulse amplitude is dependent upon the hopping frequency and the selectivity characteristic of the victim receiver. The probability density function for the interfering pulse amplitude prior to demodulation is determined when the probability density function for the hopping frequency is uniform and the victim-receiver characteristic is 1) ideal flat bandpass, 2) single tuned, and 3) Gaussian shaped. It is shown that the average interfering pulse amplitude and interference power decrease as the frequency-hopping bandwidth increases with respect to the victim-receiver bandwidth. Fast Fourier transform computer techniques are used to obtain the probability density function of the interference amplitude in a Gaussian receiver when several (from 2 to 10) pseudo-random frequency-hopping systems are simultaneously using the same frequency band. The probability that the interference exceeds a prescribed threshold value is computed from the derived probability density functions. This probability may be used in signal-to-interference ratio calculations, to describe the capture effect, or to compute the expected number of clicks produced in an FM discriminator.     

Exact Angular Accuracy of an Amplitude Comparison Sequential-Lobing Processor

Assume E1 and E2 are the squares of two sequential envelopes from the sequential lobing of an antenna in a given plane. Independent thermal noise is generally present in the envelopes. The statistic e = (E2 ? E1)/(E2 + E1) has been used as an estimate of the angle to a target for the significant region of small angles compared to a beamwidth. For a nonfading target, the probability density and characteristic function of e are obtained in closed form. Thence, the exact bias, standard deviation, and rms error in estimating the noise-free value e of e are obtained for all e and signal-to-noise ratios. The same type of statistic as e can be used to estimate time delay in a split range gate tracker.     

Receiver clock-based integrity monitoring for GPS precision approaches

The errors in the vertical position and clock bias estimates obtained from GPS pseudo-range measurements are highly correlated. Therefore, the error in a vertical position estimate can be predicted if we know the clock bias estimation error. The latter can be estimated if the clock bias changes smoothly and, therefore, predictably. The current technology appears capable of manufacturing clocks which can meet this smoothness requirement for airborne use within the constraints of size, weight, and cost. We discuss the theoretical basis and present empirical data from laboratory and field experiments with a commercial rubidium standard to explore the benefits of integrity monitoring for precision approaches based on the receiver clock.     

Adaptive Maximum Likelihood Receiver for Direct-Ranging Applications

Recent interest in direct-ranging navigation methods has prompted new research into practical receiver structures which provide improved signal processing. Maximum likelihood receivers are compared with conventional phase-locked receivers by theoretical and simulation methods as phase estimators based on signal measurements only. Signal-to-noise ratio (SNR) enhancement is examined and filter recommendations made. An adaptive maximum likelihood receiver is then developed which uses both signal measurements and a priori data to improve phase estimation accuracy. Simulation results indicate a 33.3 dB processing gain yielding a ranging error standard deviation of ±15 feet for zero dB received SNR. Nonadaptive and adaptive receivers are fabricated, flight tested, and experimental results reported.     

Angular Accuracy of a Scanning Radar Employing a Two-Pole Filter

A two-pole filter is proposed as a detector for a scanning radar. The optimum values of the filter coefficients are found and are approximated by a simple expression. The optimum two-pole filter requires a 0.15-dB increase in signal-to-noise ratio in order to provide the same detection capability as the optimum detector, and yields azimuth estimates whose standard deviation are within 15 percent of the Cramér-Rao lower bound. The estimator is simple to implement, avoiding the storage requirements of the moving window detector and the bias complications of the feedback integrator.     

截尾数据线性回归分析方法

提出一种新的回归分析方法,建立了截尾数据回归方程,给出回归系数和标准差的最佳无偏整体估计及其协方差矩阵。文中详细讨论了工程中最常见的正态分布截尾数据一元线性回归分析,给出其回归曲线的置信限和百分位值的置信区间估计,并将该方法推广到极值分布和威布尔分布的情况。传统回归分析只适用于来自正态分布的完全数据,对于截尾数据或威布尔分布数据则无能为力,目前工程上只能采用成组试验方法,结果导致试验量很大。本文方法能够很好地解决上述问题,与成组试验法相比,在试样数相同的条件下具有更高的精度,而在精度相同的情况下,则可以节省大量试样。