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Radar detection of small drones in presence of noise and clutter is considered from a differential geometry viewpoint. The drone detection problem is challenging due to low radar cross section (RCS) of drones, especially in cluttered environments and when drones fly low and slow in urban areas. This paper proposes two detection techniques, the Riemannian-Brauer matrix (RBM) and the angle-based hybrid-Brauer (ABHB), to improve the probability of drone detection under small sample size and low signal-to-clutter ratio (SCR). These techniques are based on the regularized Burg algorithm (RBA), the Brauer disc (BD) theorem, and the Riemannian mean and distance. Both techniques exploit the RBA to obtain a Toeplitz Hermitian positive definite (THPD) covariance matrix from each snapshot and apply the BD theorem to cluster the clutter-plus-noise THPD covariance matrices. The proposed Riemannian-Brauer matrix technique is based on the Riemannian distance between the Riemannian mean of clutter-plus-noise cluster and potential targets. The proposed angle-based hybrid-Brauer technique uses the Euclidean tangent space and the Riemannian geodesical distances between the Riemannian mean, the Riemannian median and the potential target point. The angle at the potential target on the manifold is computed using the law of cosines on the manifold. The proposed detection techniques show advantage over the fast Fourier transform, the Riemannian distance-based matrix and the Kullback-Leibler (KLB) divergence detectors. The validity of both proposed techniques are demonstrated with real data.

Quantum two-mode squeezing (QTMS) radars and noise radars perform matched filtering of the received signal using a reference signal stored within the radar. Their target detection performance depends on the correlation between the received and reference signals, and the improved detection performance of QTMS radars over noise radars is due to the fact that it has an increased correlation. In this paper, we present a novel way of understanding how detection performance depends on the correlation by relating the correlation to the integration time. Concretely, we prove that increasing the correlation by a given factor is equivalent to increasing the integration time by the square of that factor. We apply this result to a recent QTMS radar experiment where the increase in correlation was approximately a factor of 3. This was found to be equivalent to increasing the integration time by a factor of 9, thus confirming the validity of our result and approximation.

The most important task of any radar is to detect targets. From this perspective, they are machines for distinguishing between two hypotheses: target absent and target present. The test statistic—or detector function—used by the radar is clearly of primary importance. In this paper, we explore the properties of a detector function for quantum two-mode squeezing radar and noise radar. This detector is derived from a second-order approximation of the likelihood ratio, and is attractive because it has a simple mathematical form. In order to analyze the performance of this detector function, we derive an expression for the receiver operating characteristic curve and verify it via simulations.

We analyze the potential application of a generalized likelihood ratio (GLR)-based detector function to quantum two-mode squeezing (QTMS) radars and standard noise radars. We give an expression for the likelihood ratio (LR) in terms of the maximum-likelihood estimate of the correlation coefficient between the received and reference signals of the radar. Interestingly, we found that a previously-studied detector function outperforms the GLR detector, though not in all parameter regimes. This runs counter to the intuition, based on the Neyman-Pearson lemma, that the LR test is optimal. We discuss why the lemma does not hold in this particular case and why the search for detector functions for QTMS radars and noise radars remains open. However, the GLR detector is a good choice when the correlation coefficient is high, the number of integrated samples is low, and appropriate computational resources are available.

Micro-Doppler methods of detecting and classifying small UAVs are limited in range due to the weak radar returns from their plastic propellers. Smaller windows of data instead of longer windows are used for detection as stationarity assumptions often fail for longer windows. Traditional non-parametric methods may be inadequate as they have limited spectral resolution with smaller windows and may provide false detection when radar returns are weak. A rotary drone detector using the number of Helicopter Rotation Modulation (HERM) lines is considered in this paper. Two parametric methods for estimating the number of HERM lines, Minimum Description Length (MDL) and Akaike Information Criterion (AIC), are considered for detection purposes. Experiments using real data acquired using a micro-helicopter drone and a commercial ultra-wide band radar reveal that MDL performs significantly better than AIC and the traditional Fourier-based non-parametric estimation methods.

Broadly speaking, in quantum illumination we can say that a proposed protocol has a “quantum advantage” if it outperforms all possible classical protocols. In the optical domain of LIDAR, this is the most useful metric as lasers can routinely produce nearly ideal classical states of light at room temperature (RT). This is not the case in the microwave domain of RADAR where the photon energy is much less than the 300K thermal energy, meaning that a real RT microwave source will always be contaminated by significant thermal noise. Thus, it is not clear if it is technologically possible to produce an ideal classical microwave signal at RT. It is therefore interesting to ask if a microwave quantum illumination protocol can have a “practical advantage” compared to the best technologically feasible RT microwave source. In this paper, we look to frame this question more precisely. As a concrete example, we present experimental results showing that, contrary to recent claims in the literature [1], an entangled microwave source amplified by a cryogenic HEMT amplifier fails to obtain any performance advantage over a simply constructed RT source and, in facts, performs significantly worse. We present a simple theory which explains the experimental results and which offers guidance on how a practical advantage might be achieved.

A detector function for a newly proposed quantum radar known as quantum two-mode squeezing (QTMS) radar is analyzed in this paper. The detector function proposed in this paper behaves like a normal distribution function when the number of radar samples integrated for the detection is over 500 samples. A closed form expression for the receiver operating characteristic (ROC) curve for QTMS radar is derived under the assumption that the radar integrates more than 500 samples to detect the presence or absence of a target. The detector function can also be applied to noise radar.

The detection and parametric estimation of low-SNR radar signals, particularly linear frequency modulated (LFM) radar signals, is a problem of considerable interest. In prior work, this problem has been investigated using various signal processing techniques, such as maximum likelihood estimation, fractional Fourier transform and Wigner-Ville-based methods, to analyze the signal parameters of a complex linear frequency modulated signal. Other work has focused on applying deep learning to automatically recognize various radar waveform types and their features, such as linear frequency modulation (LFM), Barker code and rectangular waveforms. In this paper, we investigate this problem from a machine learning perspective for multiple LFM radar signals given a priori information. We explore the use of naive Bayes, support vector machine and neural network classifiers to identify the LFM chirp rate, out of a set of known chirp rates, from a specific radar emitter under varying SNR conditions. Simulation results demonstrate the viability of this technique to identify the radar LFM mode in very low signal-to-noise ratio conditions down to -20 dB where using existing approaches (e.g., Wigner-Ville) fail.

The detection of objects under large background conditions is a problem of fundamental interest in sensing. In this talk we theoretically analyze a prototype target detection protocol, the quantum time correlated (QTC) detection protocol, with spontaneous parametric down-converted photon-pair sources. The QTC detection protocol only requires time-resolved photon counting detection, which is phase-insensitive and therefore suitable for optical target detection. As a comparison to the QTC detection protocol we also consider a classical phase-insensitive target detection protocol based on intensity detection. We formulated the target detection problem as a total probe photon transmission estimation problem. We carry out experiments using a semiconductor waveguide source. The experimental results agree very well with the theoretical prediction. In particular, we find that in a high-level environment noise and loss, the QTC detection protocol is able to achieve comparable to the classical protocol target detection performance but with 10–100 fold lower required time on target detection in terms of ROC curve metric. The performance of the QTC detection experiment setup could be further improved with a higher transmission of the reference photon and better detector time uncertainty. Furthermore, unlike classical target detection and ranging protocol, the probe photons in our QTC detection protocol are completely indistinguishable from the background noise and therefore useful for covert ranging applications. Finally, our technological platform is highly scalable and tunable and thus amenable to large scale integration necessary for practical applications.

We analyze the signal-to-noise ratio (SNR) metric in the context of quantum two-mode squeezing (QTMS) radar and find that there are actually two SNRs associated with a QTMS radar, one for the received signal and another for a signal retained inside the radar. Definitions for these SNRs are proposed which are simpler than those hitherto used in the quantum radar literature. We plot receiver operating characteristic (ROC) curves for varying values of these two SNRs. These plots show that the quality of the matched filtering performed by the radar, as quantified by the SNR of the retained signal, can have a strong impact on detection performance.

Most research on drone detection and classification focus on using features from micro-Doppler signatures with blade flashes. However, these methods are limited in range and require radars with high pulse repetition frequency (PRF)–at least twice the maximum tip velocity. A different method to detect and classify drones at longer ranges using a low PRF radar is desired. In the literature, the cepstrum method was shown to be able to estimate the rotation rate when the PRF is insufficient. An alternative way of analyzing micro-Doppler is by using a long windowed Short-time Fourier transform (STFT) to generate HElicopter Rotation Modulation (HERM) lines. HERM lines exhibit similar behavior to a cepstrogram, with spectral lines separated in frequency by a value related to the rotation rate. In this paper, the separation frequency of HERM lines was estimated using a log harmonic summation algorithm. The proposed algorithm was tested on a simple HERM line model and also on real data obtained from two blade single rotor micro-helicopter drone. The algorithm was shown to be more resilient than cepstrum under Gaussian noise.

The estimation of interference plus noise covariance (INC) matrix for beamforming applications is considered from a Riemannian space perspective. A new INC estimation technique based on regularized Burg algorithm (RBA), Riemannian mean and Riemannian distance is proposed to maintain a stable performance in presence of angle of arrival mismatch and small sample size with high and low signal to interference plus noise ratio (SINR). The RBA is exploited to generate Toeplitz Hermitian positive definite (THPD) covariance matrices from the estimates of the reflection coefficients for each radar snapshot. The estimated INC is formulated as a linear combination of THPD covariance matrices of the interference plus noise excluding potential target snapshots. The weights of the linear combination operation are based on the Riemannian distance between the Riemannian mean and each THPD covariance matrix. The largest distance (potential target) will have zero weight and the smallest distance will have maximum weight. Simulation results demonstrate the performance of the proposed technique in comparison with sample covariance and Riemannian mean covariance under steering vector mismatch and small sample size in presence of high and low SINR.

For target detection, quantum two-mode squeezing (QTMS) radars and noise radars require estimation of a covariance matrix. A scalar function of the covariance matrix is then used for deciding the presence or absence of a target. In this paper, estimation of the covariance matrix is carried out by minimizing the Frobenius norm between the sample covariance matrix and the theoretically expected form of the matrix. Two scalars, a normalized correlation coefficient and an unnormalized cross-correlation, are used for detecting the target. Their performances are compared and found to be the same. Probability distributions are then fit to the histograms of these estimated correlations. Using these fitted distributions, expressions are obtained for receiver operating characteristic (ROC) curves that predict the performance of these functions in the task of deciding whether a target is present or not. This work is a first step toward understanding and modeling target detection performance of a QTMS radar or noise radar when using correlation-related measures as detector functions.

Recently, a quantum-enhanced radar transmitter operating at microwave frequencies, called a quantum two-mode squeezing radar (QTMS radar), was demonstrated in the laboratory. Inspired by this, we discuss the possibility of building an array of quantum radars. In order for quantum radars to be practically relevant, it is important that an array can be built. We find that it is indeed possible to build such an array, but that the details matter. A quantum illumination radar array may not be very effective, but a QTMS radar array is quite amenable to array signal processing. We also briefly discuss the practical aspects of building a quantum radar array.

Detection of objects from a moving platform is a challenging problem. When detection of ships is attempted with data acquired from electro-optical (EO) and infrared (IR) sensors on an airborne platform, state-of-the-art algorithms fail. This paper provides a solution for detection of ships from EO/IR video dataset obtained from an airborne platform. A recently proposed statistical thresholding method called N-Modal Discrete (NMD) method that was successfully applied to synthetic aperture radar (SAR) datasets, is modified and applied to the EO/IR video datasets of interest. Results are presented to demonstrate the ability of the proposed method to detect objects in a single-frame.

The problem of direction of arrival (DOA) estimation is considered from a geometric point of view. In particular, a new Riemannian geometry direction of arrival (RGDOA) estimation technique based on regularized Burg algorithm (RBA) and Riemannian mean and distance is proposed to maintain robust estimation under low signal-to-noise ratio (SNR) and small sample size. The RBA is exploited on generated Toeplitz Hermitian positive definite (THPD) covariance matrices from the estimates of the reflection coefficients for each radar snapshot. In addition, the Karcher Barycenter is used to calculate the Riemannian mean of THPD covariance matrices. The RGDOA technique is formulated as an optimization problem by minimizing the Riemannian distance between the Riemannian mean and the steering vector Hermitian positive definite covariance matrix. Simulation results indicate the robustness of the RGDOA technique in comparison with MUSIC and MVDR estimation techniques under low SNR and small sample size.

We have built and evaluated a prototype quantum radar in the laboratory which operates at microwave frequencies. Because the signal generation process relies on quantum mechanical principles, the system is considered to contain a quantum-enhanced radar transmitter. This transmitter generates a pair of entangled microwave signals and transmits one of them through free space, where the one-way signal is measured using a simple and rudimentary receiver. The type of entanglement used is called two-mode squeezed vacuum (TMSV), so we may call our radar a quantum two-mode squeezing radar (QTMS radar). At the heart of the transmitter is a device called a Josephson parametric amplifier (JPA), which generates the entangled microwave beams; these are then sent through a chain of amplifiers. One beam passes through 0.5 m of free space; the other is measured directly. The two measurement results are correlated in order to distinguish noise from signal. We compare this quantum-enhanced transmitter to a similar one using only conventional components, and find that there is a significant gain when the two systems broadcast signals at approximately the same power.

Compressive sensing (CS) is a signal processing technique for acquiring sparse signals at sampling rates much lower than the Nyquist rate. Traditionally to avoid generation of large sensing matrices for 2D signals or images, individual rows or columns of the images are compressed in the sensing phase. This increases the number of matrix multiplication operations and results in a compressed image with a different aspect ratio than the original uncompressed image. To overcome these issues, in this paper, we investigate a 2D deterministic sensing technique that maintains both the aspect ratio and the morphology of the image. We use a linear filtering-based measurement matrix. Through this paper, we demonstrate that deterministic CS will preserve the features and there by enable analysis of the images such as detection and identification of objects in the compressed domain without the need to perform a computationally expensive reconstruction. In order to demonstrate this, images obtained by infra-red electro-optic camera on an airborne platform (low resolution), LandSat (medium resolution) and multispectral images (high resolutions) are chosen. Features of chosen objects from an uncompressed image are compared with those corresponding objects in the compressed image using template matching to demonstrate that such image analysis can be done in the compressed domain. Frobenius norm-based structural similarity analysis for the images at different levels of compression is presented to demonstrate the similarity in structure. Robustness of the deterministic CS technique is shown by performing template matching based image analysis on noisy compressed images.

With the rise of inexpensive, commercially available UAVs (drones) it has become possible to collect data from multiple UAVs equipped with optical sensors. This possibility has enabled tracking and data fusion with multiple airborne platforms. The addition of multiple airborne sensors allows for more robust tracking that is less susceptible to clutter and track proliferation. This paper demonstrates the air-to-ground tracking capabilities of two airborne sensors following a moving ground target using the centralized fusion Extended Kalman Filter and Probabilistic Data Association Filter implemented in the Python library pystemlib. The result of adding multiple airborne sensors is a reduced state estimation error and more robust target state predictions evidenced by a reduced root-mean-square error and smaller area of probabilities. A validation of this approach is demonstrated with real data.

Quantum illumination is an idea for detection of targets in the presence of a noisy background using a photon pair that is entangled in some degree of freedom, such as frequency. This paper provides a simple and illustrative proof-of-concept setup of a quantum illumination investigation. Detection and imaging is investigated in the optical regime using a correlated source and the performance of classical illumination and quantum illumination are compared for detection and imaging experiments. The quantum advantage is demonstrated in the acquired data and possible application spaces and technological requirements are identified for developing practical systems.

Quantum radar has been proposed in the quantum information science literature as a novel approach to sensing that can offer a substantial gain over existing, classical sensors. In particular, a quantum radar based on quantum entanglement, termed quantum illumination radar, has been theoretically shown to demonstrate superiority over the optimal classical sensor, and there have been some experimental validation. However, all of the existing literature in the subject is in language, terminology and metrics that are completely unfamiliar (or relevant) to classical radar experts, and as a result there is understandable skepticism among the radar experts. This paper attempts to bridge the large gap between practical radar scientists and quantum information science (QIS) experts working in the field. We review the theoretical state-of-the-art in field and examine some of the claims in the literature in terms of metrics of relevance to radar detection, tracking and sensor fusion. We also discuss some possible technological routes to building such a radar across the electromagnetic spectrum.

We describe an experiment which comes very close to implementing a quantum radar based on entangled microwaves. A pair of entangled microwave beams are generated using a Josephson parametric amplifier (JPA) and measured by a pair of digitizers after amplification. We present a receiver operating characteristic (ROC) curve for the case where the signal power at the digitizers is −83.84 dBm (corresponding to a JPA power output, before amplification, of −148.26 dBm), as well as for a classically correlated source which attempts to approximate the covariance structure of the entangled JPA signals. The entangled signals are seen to be clearly superior to the classically correlated signals. Although the latter is still interesting from a noise radar perspective, this demonstrates that attempting to simulate entanglement with classical signals causes a measurable decrease in correlation. Our experiment validates the feasibility and desirability of a microwave quantum radar.

In multiple input multiple output (MIMO) radar systems, choosing a proper orthogonal waveform is a critical task. A new hybrid spread spectrum (HSS) technique is proposed to maintain orthogonality at the transmit and receive ends. The HSS technique is a combination of direct-sequence spreading and frequency hopping schemes. In the context of MIMO radar, the transmitted signals are first spread using Hadamard-Walsh orthogonal codes and in every pulse repetition period, each signal hops to a different center frequency. The transmitted HSS signals are orthogonal in frequency and code domains. Simulation results show that the proposed HSS technique can achieve sharper auto ambiguity response and lower sidelobe cross ambiguity response with a gain of over 10 dB and better probability of detection in comparison with frequency orthogonality technique. The proposed HSS technique has the potential to resolve closely spaced targets and provide better immunity against narrowband interferences.

Hybrid beamforming for multiple input multiple output (MIMO) radar systems in a jamming enviroment is inves­tigated. A new hybrid beamforming (HB) technique is proposed to reduce the dimensionality of the covariance matrix and to have a better jamming and interference mitigation capability. HB consists of two stages. The first stage decodes, phase shifts the received signals and adds signals decoded by the same code from different antenna elements. The second stage exploits digital beamforming techniques such as Minimum Variance Distortionless Response (MVDR) or convex optimization beamforming to determine the complex weights using N × N covariance matrix where N is the number of transmitting antennas. Simulation results show that the proposed HB technique can achieve better interference and jamming suppression results in comparison with other radar configurations. In addition, the HB technique has the potential to reduce the complexity of MIMO radar signal processing such as space-time adaptive processing.

The estimation of covariance matrix is of fundamental importance in radar signal processing. Recent work has shown that information geometry provides a novel approach to estimating the covariance matrix. Prior work has shown that an information geometry inspired covariance matrix estimator provides significant gains (in SINR loss terms) over several standard estimators, such as the loaded sample matrix inversion (LSMI). In this paper, some techniques for computing the covariance matrix, inspired by information geometry, are presented. It is found that some algorithms provide superior performance when the number of samples is small.

The continuous-discrete filtering problem requires the solution of a partial differential equation known as the Fokker-Planck-Kolmogorov forward equation(FPKfe). In this paper, the path integral formula for the fundamental solution of the FPKfe is presented for the case the signal model noise is additive. The simplest approximation of the path integral formula leads to the Dirac-Feynman algorithm for continuous-discrete filtering. The practical utility of the proposed Dirac-Feynman algorithm is demonstrated in a fully nonlinear filtering problem where it is shown that it leads to highly accurate and reliable results. The Feynman path integral approach to nonlinear filtering has several advantages, especially in terms of ease in practical implementation.

The sensitivity of track before detect processing to the choice of clutter model in the measurement correction stage was examined through processing of real and simulated data containing radar echo returns of a small maritime target in sea clutter. The potential for achieving significant detection performance improvements by utilizing K and KA distributed clutter models in place of the simpler Rayleigh distribution was demonstrated through analysis of simulated data representing spiky sea clutter. In contrast, additional analysis using real data revealed that a more accurate clutter model does not imply better performance. Specifically, significantly degraded performance is observed when K and KA based processing is used in place of a Rayleigh based processor utilizing a simple likelihood limiting step to compensate for model mismatches due to sea clutter spikes.

Real radar data containing a small manoeuvring boat in sea clutter is processed using a grid based finite difference implementation of continuous-discrete filtering. Both two dimensional diffusion and four dimensional constant velocity models are implemented using Gaussian and Rayleigh sea clutter models. Superior performance is observed for the constant velocity model and significant sensitivity is noted due to mismatches between actual clutter characteristics and Gaussian and Rayleigh models. A simple likelihood ratio thresholding technique is shown to provide a significant performance improvement.

This paper presents the results of an investigation of the vertical plane beam scanning of an offset reflector antenna by lateral displacements of the multimode feed horns array, which was earlier shown to have multiple phase centres in the horizontal plane. The antenna was found to have both multiple phase centres, as well as, the beam scan. It is suitable for the space borne radar application at X-band frequency

An orthogonally polarized polarimetric radar feed horn was designed and developed. The radar feed showed 1.20 GHz bandwidth and very low port isolation at X-band frequency and acceptable radiation characteristics. A very complex elliptical aperture feed would be another design option meeting the edge illumination required for the elliptic aperture reflector. When this horn was employed as a feed source for the offset reflector, it showed acceptable radiation characteristics with the peak gain, peak cross-polarization and sidelobe levels of 36.90 dBi, -25 dB and -24 dB, respectively, for the both orthogonally polarized port excitations at 9.75 GHz. The prototype feed horn has been fabricated and was experimentally verified

The phase centre is a theoretical point along the axis of an antenna and is the centre of curvature of the phase fronts of the spherical waves. L.I. Basilio et al. (see Proc. 9th Int. Symp. on Antenna Tech. and App. Electromagnetics, p.455-8, 2002) presented investigations on defining an effective point of radiation, or phase centre, for the dominant mode of a rectangular microstrip patch antenna for Global Positioning System (GPS) applications. The determination of the phase centre and its control provides further important applications in radar systems. The paper presents the results of an investigation of a multimode microstrip patch antenna. They reveal that a single multimode patch shows a movement of the phase centre with variation in the amplitude and phase of the modes. By controlling the amplitude, the phase centre displacement is controlled, whereas by changing the phase between two modes, the direction of the phase centre movement may be controlled. The study was further extended to a finite linear array. It was seen that there is control of the phase centre movement by controlling the amplitude and phase of individual multimode patches.

The investigation results of multimode feed horns are presented, which provide multi-phase centre radiation performance with the reflector. These feed horns with reflector assembly are suitable for radar systems, where ground moving target indicator (GMTI) mode implementation is desired. The simulations were carried out using Ansoft Corporation's HFSS v8.5 for feed horn, and Ticra's GRASP v7.0 for the reflector.

The phase centre of a feed horn is a theoretical point along the axis of the horn which is the centre of curvature of the phase fronts of the spherical waves. In most feeds, there is a phase centre region rather than a single point because radiation is due to a summation of spherical waves, which seems to emanate from the aperture [1]. Determination of the feed phase centre helps, its location relative to the focal point of the reflector. Different techniques to compute and determine the phase centre location in single and dual reflector geometries are reported in [1-3]. However, when the feed horn has a multimode excitation, the amplitude and phase control of modes provide different constant phase centre locations, which in turn helps to conceptualize a virtual array on the reflector antenna aperture [4].

In ground surveillance from an airborne or space-based radar it is desirable to be able to detect small and slowly moving targets, within severe ground clutter. For operational moving target indication (MTI) systems the clutter filter coefficients have to be updated frequently due to rapidly changing interference environment. This paper examines the small sample size performance of different fast fully adaptive space-time processors (STAP) and compares it to the optimum-detector performance. These previously proposed techniques, named matrix transformation based projection (MTP) and lean matrix inversion (LMI), were originally developed to provide fast jammer suppression in phased array radars with many elements. For this application they have been proven to operate with near-optimum performance, yet with a computational expense extremely reduced from that of the optimum detector in most practical cases. The investigation herein focuses on the performance achieved when only a very few data samples are available to adapt (update) the clutter filter coefficient.