We construct an improved and distribution-free quantile estimator (called IBQ estimator) with representation as a linear combination of order statistics. The IBQ estimator can estimate quantiles of any scale-invariant population by using censored samples. Taking Exponential population as an example, we derive the mean squared error (MSE) of IBQ estimator under small sample case. It is found that the IBQ estimator exhibits higher estimation efficiency when estimating large quantiles compared with other two existing estimators. Applying IBQ estimator to create the clutter level, we establish the IBQ constant false alarm rate (CFAR) processor. We investigate the performance of IBQ-CFAR in homogeneous background and multiple target scenario. The theoretical analyses show that the IBQ-CFAR exhibits outstanding detection performance and false alarm control ability in multiple target scenario.

Realistically simulating spatial–temporal correlated complex sea clutter using statistical model-based methods is very challenging because the intricate interplay of various physical mechanisms in both space and time poses significant obstacles for clutter modeling. In this article, to overcome this challenge, we propose a data-driven method based on the 2-D amplitude and phase matching optimization (APMO) with two steps. First, the simulated clutter amplitudes with desired distribution and correlation characteristics are generated by performing the frequency-domain inverse transform and correlation transfer techniques on the measured clutter. Second, an optimization strategy is developed to acquire the well-matched phases for the simulated clutter amplitudes by constraining the phases to the simulated clutter amplitudes and the desired Doppler and range spectra. Two different algorithms are separately adopted to implement the optimization strategy, and their advantages and disadvantages are compared theoretically and experimentally. The APMO method is direct in the analysis of the measured clutter’s statistical characteristics and universal to different radar and environmental conditions. It is shown that the simulation results can reproduce the distribution and spatial–temporal correlation features of the real-world X-band complex sea clutter. The relative mean-squared deviation (RMSD) between the measured and simulated clutter’s Doppler and range spectra can be notably reduced to 0.0499 and 0.1237, respectively.

The order statistic (OS) constant false alarm rate (CFAR) detector is designed from a perspective of quantile estimation and uses the sample quantile (SQ) estimator to estimate background level. Following this idea, we find a more efficient quantile estimator, i.e. Kaigh-Lachenbruch quantile (KLQ) estimator, to construct a robust CFAR detector, which is referred to as KLQ-CFAR. We prove that the KLQ estimator is an asymptotic unbiased estimator to the quantile function and derive the asymptotic variance of KLQ estimator in Exponential case. It is shown that the KLQ estimator has more efficient estimation efficiency than SQ estimator. Subsequently, we explore the performance of KLQ-CFAR in Exponential clutter. In homogeneous background, the KLQ-CFAR conquers the shortcoming of large detection loss of OS-CFAR, and exhibits comparable performance with trimmed mean (TM) CFAR. The superiority of KLQ-CFAR is also reflected in multiple-target scenario, especially in the case where the number of interferences exceeds the preset parameters of KLQ- and TM-CFAR. In this case, the detection performance and false alarm control ability of KLQ-CFAR have significant improvement compared with TM-CFAR. Then, we extend the KLQ-CFAR from Exponential background to non-Gaussian clutter via transformation approach, and obtain the transformed KLQ (TKLQ) CFAR. We take Weibull clutter as a specific example. It is found that the behavior of TKLQ-CFAR in Weibull background is very similar to that of the KLQ-CFAR in Exponential clutter, but the difference lies in that the performance of TKLQ-CFAR is related to Weibull shape parameter. The TKLQ-CFAR tends to have better detection performance with the increase of Weibull shape parameter. Finally, the validity of TKLQ-CFAR is verified in skywave over-the-horizon radar data.

The impulsive noise originated from regional lightning discharges can dramatically degrade the performance of skywave over-the-horizon radar (OTHR) target detection with generally 10–20-dB increase of noise level in the Doppler domain. As a result, it is necessary to excise impulsive noise in corrupted data while preserving the useful echo signal. Traditional techniques first locate the impulsive noise in slow-time data with a high-pass finite-duration impulse response (FIR) notch filter and then restore the contaminated samples by neighboring good data. However, the effect of impulsive noise is propagated into the subsequent filtered residuals, which will mislead the impulsive noise detection. Instead of the conventional detection-interpolation methods, we propose a novel impulsive noise excision approach based on robust smoothing. The proposed method can robustly smooth the corrupted data and determine the position of impulsive noise with a preset threshold against the residuals of corrupted data subtracting the smoothed signal. The contaminated data at last are replaced by the smoothed signal. Experimental results have demonstrated the effectiveness of our proposed method.

In this paper, the concept of quantile is introduced and elaborately related to the truncation depth, based on which quantile truncated statistics (QTS) is put forward. The QTS gives a reasonable explanation of truncation depth and makes the selection of truncation depth well-founded and controllable. In addition, maximum likelihood estimation based on QTS (QTS-MLE) for the probability density function (PDF) parameters is derived. We start the analysis from Weibull background assuming that the shape parameter is known, and then extend it to the case where the shape parameter is unknown. By analyzing the variance and mean square error (MSE) of the estimated parameters in Weibull background, it is found that QTS-MLE has better estimation performance than the MLE based on truncated statistics (TS-MLE). On this basis, the constant false alarm rate (CFAR) detector based on QTS-MLE, i.e. QTS-CFAR, is proposed. The analytic expressions of the false alarm rate and detection probability of QTS-CFAR are derived under the Weibull background with known shape parameter. The full CFAR characteristics of TS- and QTS-CFAR detectors in Weibull background with unknown shape parameter are proved by invariant theory. Monte Carlo simulations show that QTS-CFAR detector has better anti-interference performance and false alarm control ability in multiple-target environment. Furthermore, the superiority of QTS-CFAR detector is verified by the real data collected by skywave over-the-horizon radar. Finally, we present the expression of QTS-MLE for the scale parameter in the Gamma background.

This letter addresses the problem of signal detection in additive correlated noise whose covariance matrix is Toeplitz. Particularly, we design a novel detection approach in the framework of generalized likelihood ratio test, in which the maximum likelihood (ML) estimate of the Toeplitz covariance matrix is needed. Since there are no closed-form expressions for this ML estimate, we resort to the inverse iterative algorithm. The proposed detector surpasses existing methods in detection power and enjoys the constant false-alarm rate property. Besides, accurate asymptotic null and non-null distributions of the test statistic are derived. Numerical results are presented to validate our theoretical findings.

Constant false alarm rate (CFAR) is the desired property for automatic target detection in unknown and nonstationary background. In this letter, an analysis of the experimental data shows that gamma (GM) distribution is a promising model for sea clutter. Furthermore, a modified cell-averaging (CA) detector for GM-distributed clutter is proposed by using the maximum likelihood estimation method. Theoretical analysis demonstrates that the proposed detector maintains the CFAR property with respect to the scale parameter of the GM-distributed background. The proposed detector is verified to be optimal in homogenous GM-distributed clutter with a known shape parameter when compared with CA, greatest of selection, ordered statistic (OS), and weighted amplitude iteration (WAI) detectors. At clutter edges, the proposed method attains a similar false alarm rate control compared with the CA, OS, and WAI detectors. In multiple-target scenario, the proposed method works effectively and robustly, whereas the competitors suffer performance degradation in varying degree. Simulation and experimental results demonstrate the superiority and generality of the proposed method.

Extraction of ocean surface wind field from data collected by shipborne high-frequency surface wave radar (HFSWR) is an ongoing challenge because of the inherent directional ambiguity and the effect of complicated platform motion on radar Doppler spectra. Here, a method for extracting the wind direction and speed from the spreading first-order radar Doppler spectra is first presented. First, the mathematical model of the wind direction versus a variable spreading parameter is developed. Moreover, based on the spreading characteristic of the first-order spectra, an approach for simultaneously determining the unambiguous wind direction and the unique spreading parameter with a single receiving antenna is presented. Furthermore, the relationship between the wind speed and the spreading parameter is derived on the basis of the relationship between the drag coefficient and the spreading parameter, and the wind speed can be determined. Therefore, the wind field of ocean area covered by shipborne HFSWR can be measured by sequentially exploiting the presented method, which is more beneficial for shipborne HFSWR because of smaller installation space and less cost. Simulation results and discussions of basic applications show the feasibility of wind field measurement in shipborne HFSWR. Experimental results validate the presented method and evaluate the detection accuracy and distance limit. The range for wind field measurement is up to 120 km, which is the range for which the signal-to-noise ratio typically exceeds about 11 dB in the relevant first-order portions of the backscatter spectra. Comparisons between the radar-measured and forecasting or buoy-measured results show good agreement.

Usually, it is very difficult to determine the exact distribution for a test statistic. In this paper, asymptotic distributions of locally most powerful invariant test for independence of complex Gaussian vectors are developed. In particular, its cumulative distribution function (CDF) under the null hypothesis is approximated by a function of chi-squared CDFs. Moreover, the CDF corresponding to the non-null distribution is expressed in terms of non-central chi-squared CDFs for close hypothesis, and Gaussian CDF as well as its derivatives for far hypothesis. The results turn out to be very accurate in terms of fitting their empirical counterparts. Closed-form expression for the detection threshold is also provided. Numerical results are presented to validate our theoretical findings.

Shipborne high-frequency surface wave radar (SHFSWR) has exhibited great advantages over onshore HFSWR (OHFSWR) in ocean remote sensing. Unlike OHFSWR, SHFSWR suffers the problem of Doppler spectrum spread owing to platform movement, which is a great challenge preventing the extraction of ocean surface parameters for SHFSWR. To address this challenge, in this letter, the mathematical model of ocean surface wind direction is first investigated based on the first-order SHFSWR cross section. Furthermore, a method for the wind direction inversion without ambiguity from the spread Doppler spectrum is proposed using a single receiving antenna. Meanwhile, the wind directions of the sea area covered by radar can be obtained by sequentially utilizing the proposed method, which is more appropriate for the application of SHFSWR with limited deck space and less cost. Experimental results of the real data collected in Taiwan Strait preliminarily verify the detection accuracy and the distance limit of the wind direction inversion, as the root-mean-square error and the detection range are 9.85° and 120 km, respectively.

John's test, which is also known as the locally most invariant test for sphericity of Gaussian variables, is one of the most frequently used methods in multichannel signal detection. The application of John's test requires closed-form and accurate formula to set threshold according to a prescribed false alarm rate. Asymptotic expansion is a powerful method in deriving the threshold expressions of detectors for large samples. However, the existing asymptotic analysis of John's test in the real-valued Gaussian case is not accurate, causing the obtained false alarm rate to deviate from the preset value. This work first corrects a miscalculation in the existing results. Then this accurate approach is extended to the complex-valued case. In this scenario our result is as accurate as the state-of-the-art scheme but enjoys higher computational efficiency.

Sea clutter has a major impact on the detection performance of a shipborne high-frequency surface wave radar (HFSWR) system. Due to the platform motion of shipborne HFSWR, the Doppler spectrum of the first-order sea clutter suffers from some broadening so that the targets submerged in this broadening Doppler spectrum can be hardly detected. In this letter, an improved oblique projection (IOP) method, combining the oblique projection (OP) algorithm and the method of sea clutter suppression in the Doppler domain, is proposed to suppress sea clutter in both Doppler domain and spatial domain for shipborne HFSWR. Compared with the OP and the orthogonal weighting algorithms, the proposed IOP algorithm is shown to give far superior suppression results in the Doppler domain and can achieve better azimuth estimation results based on real data.