Mean-Level Detection Utilizing a Digital First-Order Recursive Filter

The use of a simple digital first-order recursive filter for mean-level detection is described. Performance characteristics are derived for the case where the background noise is stationary, and detection results are given for Swerling Case 2 fluctuating signals. Equations are derived for computing false-alarm performance in nonstationary backgrounds, and results are given for some special cases. Comparisons are made with performance of a conventional mean-level circuit in stationary and nonstationary noise.     

An Adaptive Threshold System for Nonstationary Noise Backgrounds

The problem of detecting target signals in an ocean environment using active sonar is complicated by the nonstationary background which usually consists of both ambient ocean noise and reverberation. on. In this paper a signal processing system capable of detecting a signal in nonstationary noise is introduced. This system makes use of the mean and variance time functions of the nonstationary noise background in order to design estimation filters which will cope with the nonstationarity. Appropriate statistics of the noise and signal (tone burst) plus noise have been obtained and are used to determine the probabilities of false alarm and detection and the receiver operating characteristics.     

Transient Nonstationary Behavior of a Delay Line Discriminator

The development of numerical methods for studying the transient nonstationary behavior of a delay line discriminator is presented. Expressions are developed for the mean and the variance of the output noise process. For the cases where the output is stationary, power density spectra are found.     

Detection Performance of a Mean-Level Threshold

The problem of detecting signals in nonstationary clutter is met by presenting a mean-level or adaptive threshold which adjusts to the changing background level. Such a threshold performs better than a fixed threshold that must be set for the highest amplitude clutter. However, the mean-level threshold does not perform as well for stationary noise as a fixed threshold set at the proper value. One measure of effectiveness of an adaptive threshold is its performance in stationary noise (compared to the optimum fixed threshold) for a specified speed of response. For the mean-level threshold, a simple mathematical solution is found for the detection probability when the noise is stationary and the signal scintillates rapidly. The performance is evaluated for a wide range of mean-level-threshold time constants and for several false-alarm probabilities. The results are presented graphically. As an example, the mean-level threshold suffers 3 dB in detectability (equivalent signal-to-noise ratio) in the presence of stationary noise as compared to the optimum fixed threshold for 50-percent probability of detection, false-alarm probability of 10-8, and an adjustment time of 15 times the signal duration.     

A noncoherent adaptive detection technique

An adaptive detection technique suitable for both stationary and nonstationary noise environments based upon a generalized likelihood ratio test (GLRT) formulation is presented. The detector, which is statistically equivalent to a special form of the Wilks's lambda test, noncoherently combines the information contained in a pulse train of arbitrary length for decision-making purposes. The probability density function of the test under the noise only hypothesis is shown to be central χ². Under the signal plus noise hypothesis, an exact statistical characterization of the test cannot be obtained, and, therefore, a Chernoff bound is derived. Results in terms of the probability of detection versus signal-to-noise ratio (SNR) obtained from Monte Carlo simulation, the Chernoff bound, and the optimal matched filter case are examined. The performance of the noncoherent detector is shown to be a function of the covariance matrix estimate and the number of data samples     

Detection of Narrowband Signals Using Time-Domain Adaptive Filters

The detection performance of a conventional narrowband analyzer is compared with two adaptive processor mechanizations based on the Widrow least mean squares algorithm. Comparisons are based on both analysis and extensive digital simulation. With a narrowband signal in stationary, white background noise, the performance of the three systems is shown to be essentially the same. With nonstationary background noise, the performance of the conventional system degrades by an amount proportional to the processing time-bandwidth product. The adaptive systems appear to be less sensitive to the nonstationary background, resulting in a potential performance advantage relative to the conventional system.     

Adaptive Radar Detection in Doubly Nonstationary Autoregressive Doppler Spread Clutter

The problem of adaptive radar detection in clutter which is nonstationary both in slow and fast time is addressed. Nonstationarity within a coherent processing interval (CPI) often precludes target detection because of the masking induced by Doppler spreading of the clutter. Across range bins (i.e., fast time), nonstationarity severely limits the amount of training data available to estimate the noise covariance matrix required for adaptive detection. Such difficult clutter conditions are not uncommon in complex multipath propagation conditions where path lengths can change abruptly in dynamic scenarios. To mitigate nonstationary Doppler spread clutter, an approximation to the generalized likelihood ratio test (GLRT) detector is presented wherein the CPI from the hypothesized target range is used for both clutter estimation and target detection. To overcome the lack of training data, a modified time-varying autoregressive (TVAR) model is assumed for the clutter return. In particular, maximum likelihood (ML) estimates of the TVAR parameters, computed from a single snapshot of data, are used in a GLRT for detecting stationary targets in possibly abruptly nonstationary clutter. The GLRT is compared with three alternative methods including a conceptually simpler ad hoc approach based on extrapolation of quasi-stationary data segments. Detection performance is assessed using simulated targets in both synthetically-generated and real radar clutter. Results suggest the proposed GLRT with TVAR clutter modeling can provide between 5–8 dB improvement in signal-to-clutter plus noise ratio (SCNR) when compared with the conventional methods.     

Single Sidelobe Canceller: Theory and Evaluation

A sidelobe canceller (SLC) can be efficiently employed to reduce the undesirable effects of jammers on a search radar system. In this paper a functional block circuit is described for a single-sidelobe canceller (SSLC) apt to a single Jammer suppression; a detailed analysis is also presented. It is shown that the theory of stochastic differential equations and the covariance analysis describing function (CADET) technique can be used to evaluate the SSLC performances when two Gaussian colored and mutually correlated input processes are considered. The statistical properties of the weight can be obtained. The last results, which are very important in the case of nonstationary jammers, cannot be obtained without this theory. System implications can be drawn from the abovementioned analysis when the input process consists of one jammer or two jammers and/or thermal noise.     

A recursive multiple model approach to noise identification

Correct knowledge of noise statistics is essential for an estimator or controller to have reliable performance. In practice, however, the noise statistics are unknown or not known perfectly and thus need to be identified. Previous work on noise identification is limited to stationary noise and noise with slowly varying statistics only. An approach is presented here that is valid for nonstationary noise with rapidly or slowly varying statistics as well as stationary noise. This approach is based on the estimation with multiple hybrid system models. As one of the most cost-effective estimation schemes for hybrid system, the interacting multiple model (IMM) algorithm is used in this approach. The IMM algorithm has two desirable properties: it is recursive and has fixed computational requirements per cycle. The proposed approach is evaluated via a number of representative examples by both Monte Carlo simulations and a nonsimulation technique of performance prediction developed by the authors recently. The application of the proposed approach to failure detection is also illustrated     

A Superlimiting Phased-Array Receiving System in a Two-Source Environment

The performance of a uniformly spaced phased-steered line array with element channel superlimiting is studied for far-field sources consisting of 1) two sinusoidal signals with different frequencies and angular locations, and 2) a sinusoid and a noise signal at different angular locations. Attention is focused on the nonlinear case where internal noise is negligible compared to both input signals. The analysis for the two-sinusoid case gives the precise frequencies, positions, and amplitudes of all apparent sources. In addition to the two active sources, the array output has an array of images arranged symmetrically in sine space about the larger input, at intervals equal to the spacing between the two active sources. For the case of a separated sinusoid and a noise source, the analysis shows that the angular positions and average powers of the array outputs duplicate the double-sinusoid results, but the images have noise-like spectra. The analyses are confirmed by experimental results obtained with a 60-element superlimiting X-band array.     

Detection of Known Signals in Nonstationary Noise

The basic design of a nonlinear, time-invariant filter is postulated for detecting signal pulses of known shape imbedded in nonstationary noise. The noise is a sample function of a Gaussian random process whose statistics are approximately constant during the length of a signal pulse. The parameters of the filter are optimized to maximize the output signal-to-noise ratio (SNR). The resulting nonlinear filter has the interesting property of approximating the performance of an adaptive filter in that it weights each frequency band of each input pulse by a factor that depends on the instantaneous noise power spectrum present at that time. The SNR at the output of the nonlinear filter is compared to that at the output of a matched filter. The relative performance of the nonlinear system is good when the signal pulses have large time-bandwidth products and the instantaneous noise power spectrum is colored in the signal pass band.     

Distribution-Free Processors Based on the Theory of Runs

This correspondence describes distribution-free processors based on the theory of runs. No assumption about either the functional form of the distribution of noise or the nature of its distribution is made. Hence the processors described are expected to yield constant false alarm (CFA) irrespective of the nature of noise encountered in the system.     

Radar Detection of Correlated Targets in Clutter

This paper provides general models of radar echoes from a target. The rationale of the approach is to consider the echoes as the output of a linear dynamic system driven by white Gaussian noise (WGN). Two models can be conceived to generate N target returns: samples generated as a batch, or sequentially generated one by one. The models allow the accommodation of any correlation between pulses and nonstationary behavior of the target. The problem of deriving the optimum receiver structure is next considered. The theory of "estimator-correlator" receiver is applied to the case of a Gaussian-distributed time-correlated target embedded in clutter and thermal noise. Two equivalent detection schemes are obtained (i. e., the batch detector and the recursive detector) which are related to the above mentioned procedures of generating radar echoes. A combined analytic-numeric method has been conceived to obtain a set of original detection curves related to operational cases of interest. Finally, an adaptive implementation of the proposed processor is suggested, especially with reference to the problem of on-line estimation of the clutter covariance matrix and of the CFAR threshold. In both cases detection loss due to adaptation has been evaluated by means of a Monte Carlo simulation approach. In summary, the original contributions of the paper lie in the mathematical formulation of a powerful model for radar echoes and in the derivation of a large set of detection curves.     

An algorithm for detection of moving optical targets

An algorithm is described for detecting moving optical targets against spatially nonstationary Poisson background and noise. The algorithm has applications in optical detection of objects such as meteors, asteroids, and satellites against a stellar background. A maximum-likelihood approach is used which results in reducing interference from stars. It is shown that by choosing a detection threshold to provide a constant false alarm rate, the resulting algorithm is independent of the signal strength of the target. An analysis of this algorithm is presented, showing the probability of detection for several false-alarm rates     

Comments on "A Note on Satellite Dynamics"

Some details of the author's earlier derivation on gyrotorquer dynamics are worked out to confirm that Greensite's derivation failed to generate some important dynamic terms in the original motion equations, contrary to the claim of Guibord and Ahmed. In the above correspondence,1 it is claimed that erroneous terms were usm.     

Comments on "Bounds on Probability of Error in Decision Feedback Equalizers"

In the above paper1 a technique was proposed to derive an upper bound on the error probability of a decision feedback equalizer. It involves decomposition of the probability density function of residual intersymbol interference and derivation of Chebyshev-type bounds on the error functionals over the decomposed functions. In this correspondence, we demonstrate that the technique is not applicable in general. The result is not a bound in many cases.     

Error Performance of Two-Channel Phase-Measurement Systems

The problem of measuring a constant phase difference between two sinusoids which have been corrupted by two additive noise processes is investigated. For the case in which both noise processes are Gaussian and the signal-to-noise ratio is high, the variance of the time-averaged phase-difference estimate is found as a single integral over the noise power spectral densities and cross spectral density. Arbitrary cross correlation is allowed between the two noise processes. Two cases of practical interest are considered: 1) the noise processes have identical, rectangular power spectral densities and are statistically independent; 2) an idealized radio direction finding situation in which two spatially separated sensors are immersed in an isotropic, planar noise field. For the statistically independent case, a universal curve is presented which permits determination of phase-estimate standard deviation for arbitrary signal-to-noise ratio and for a wide range of bandwidths and integration times.     

Forced aeroelastic oscillations of a rotating anisotropic helicopter main rotor blade at hovering

Aeroelastic oscillations of a rotating blade as a thin-walled beam with restrained strains of bending, transverse shear, and torsion are considered. Aerodynamic loads on the blade performing the forced harmonic oscillations at helicopter hovering are determined according to the nonstationary theory of a two-dimensional flow past blade cross-sections without taking into account the vortex wake of other main rotor blades. The influence of blade anisotropy on its dynamic and propulsive characteristics is estimated in the case of prescribed variation of the root section angle of twist.     

Physical model of a hydrodynamically nonstationary turbulent flow

The influence of nonisothermality and hydrodynamic nonstationarity on turbulence generation and development is analyzed. A physical model of a hydrodynamically nonstationary turbulent flow is proposed, the model is created on the basis of previous experimental investigations on the structure of a nonstationary turbulent gas flow in the channel.     

不同飞行状态下施翼与大气湍流的干扰噪声

本文简述了一种直升机旋翼与大气湍流入流相干扰产生的噪声预估方法。这一方法考虑了桨叶上非定常载荷的弦向及展向非紧致性，桨叶－桨叶载荷之间的相关，通过结合大气湍流能量谱模型与快速畸变湍流收缩模型来确定旋翼平面处非均匀、各向异性湍流场的特性，使得这种方法可用于直升机在真实飞行状态下的旋翼与湍流场干扰噪声计算。利用文献中模型旋翼试验的结果，验证了本方法的可行性，并计算了某型直升机在六种飞行状态下的流场畸变情况及旋翼与湍流干扰的远场噪声谱，结果表明：在准悬停及低速爬升状态，湍流场的畸变较大，而在中、快速前飞状态，湍流场的畸变最小，在低速爬升状态，线性总声压级最小。