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The detection of objects in the presence of significant background noise is a problem of fundamental interest in sensing. In this article, we theoretically analyze a prototype target detection protocol, the quantum temporal correlation (QTC) detection protocol, which is implemented in this article utilizing 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 that is practical in the optical regime. We formulated the target detection problem as a total probe photon transmission estimation problem and obtain an analytical expression of the receiver operating characteristic (ROC) curves. We carry out experiments using a semiconductor waveguide source, which we developed and previously reported. 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 can achieve performance comparable to that of the classical protocol (that is practical in the optical regime) but with $\simeq\!\text{57}$ times lower detection time in terms of ROC curve metric. The performance of the QTC-detection protocol experiment setup could be further improved with a higher transmission of the reference photon and better detector time uncertainty. Furthermore, the probe photons in the QTC-detection protocol are completely indistinguishable from the background noise and therefore useful for covert ranging applications. Finally, our technological platform is highly scalable as well as tunable and thus amenable to large scale integration, which is necessary for practical applications.

For an airborne sensor, there is a pressing need to be able to detect/track submerged submarines, shipwrecks, sea mines, unexploded explosive ordnance, and buried drums during maritime surveillance. Traditional usage is the magnetic anomaly detection (MAD), where the small changes in the earth's magnetic field caused by the ferrous components of the targets are measured. The primary means of long-range detection and classification of targets are with passive and active acoustic sensors, and MAD is used for accurate final localization. MAD could also be used for land-based targets but this is not common. Knowing the relationship between the magnetic signature and the kinematic parameters, the tracking problem can be formulated under a Bayesian framework. In this article, multiple nonlinear filters are used for a real single surface-target tracking problem in maritime surveillance using an airborne total-field sensor. The posterior Cramer–Rao lower bound for MAD is derived. Given the total-field measurements, these filters can estimate the kinematic states as well as the permanent moments and induced moments effectively. Results demonstrate the effectiveness of the proposed nonlinear filters as well as the impact of using MAD as part of airborne surveillance.

Many quantum radars currently studied in the literature use a phenomenon called entanglement to address the problem of distinguishing signal from noise, which is one of the most important problems faced by any radar. Until recently, entanglement-based quantum radars at radio frequencies existed only in theory; their practicality was very much in doubt. The situation has changed with a recent experimental implementation of all the necessary components of a quantum two-mode squeezing (QTMS) radar, which operates at microwave frequencies and can be described as a quantum range finder. In this article, we lay out the exact problem solved by this prototype, namely quantum noise, and explain how entanglement can overcome the existence of this noise. By analyzing the QTMS radar prototype, we point out a technological route to an entanglement-based quantum radar that can, in principle, perform all tasks that radars can and must do, such as array processing, clutter suppression, and image processing (including synthetic aperture radar and inverse synthetic aperture radar).

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.

Recently, the authors have built and evaluated a prototype quantum radar in the laboratory which operates at microwave frequencies. This radar, which they call a quantum two-mode squeezing radar (QTMS radar), generates a pair of entangled microwave signals and transmits one of them through free space, using the other signal as a reference to perform matched filtering. The specific type of entanglement is called a two-mode squeezed vacuum, a type of continuous-variable entanglement between two frequencies. Motivated by the success of these experiments, they try to better understand the entangled QTMS radar signals in this study. They do so by comparing it to a simpler, more conventional radar system, which they call a two-mode noise radar (TMN radar). They also show how both types of radars are related to standard noise radars as described in the literature. They find that the signals for QTMS radar signals and TMN radar signals have the same mathematical form and that they are related to noise radar by a simple mathematical transformation. This shows that QTMS radar signals can be emulated by a fictional, idealised TMN radar and that it is possible to apply results from the noise radar literature to QTMS radar.

Reports on the IQC Workshop on Quantum Illumination: From Theory to Practice. The workshop was held 3–4 December 2019 at the Institute of Quantum Computing (IQC), University of Waterloo, a well-known research center for quantum information as well as home to the world’s first microwave quantum radar experiment that was published in the literature.

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 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.

In this article, we modify Mumford–Shah level-set model to handle speckles and blur in synthetic aperture radar (SAR) imagery. The proposed model is formulated using a non-local regularization framework. Hence, the model duly cares about local gradient oscillations (corresponding to the fine details/textures) during the evolution process. It is assumed that the speckle intensity is gamma distributed, while designing a maximum a posteriori estimator of the functional. The parameters of the gamma distribution (i.e. scale and shape) are estimated using a maximum likelihood estimator. The regularization parameter of the model is evaluated adaptively using these (estimated) parameters at each iteration. The split-Bregman iterative scheme is employed to improve the convergence rate of the model. The proposed and the state-of-the-art despeckling models are experimentally verified and compared using a large number of speckled and blurred SAR images. Statistical quantifiers are used to numerically evaluate the performance of various models under consideration.

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.

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.

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.

We have built and evaluated a prototype quantum radar, which we call a quantum two-mode squeezing radar (QTMS radar), in the laboratory. It operates solely at microwave frequencies; there is no downconversion from optical 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 signal is measured using a simple and rudimentary receiver. At the heart of the transmitter is a device called a Josephson parametric amplifier (JPA), which generates a pair of entangled signals called two-mode squeezed vacuum (TMSV) at 6.1445 GHz and 7.5376 GHz. These are then sent through a chain of amplifiers. The 7.5376 GHz beam passes through 0.5 m of free space; the 6.1445 GHz signal is measured directly after amplification. The two measurement results are correlated in order to distinguish signal from noise. We compare our QTMS radar to a classical radar setup using conventional components, which we call a two-mode noise radar (TMN radar), and find that there is a significant gain when both systems broadcast signals at -82 dBm. This is shown via a comparison of receiver operator characteristic (ROC) curves. In particular, we find that the quantum radar requires 8 times fewer integrated samples compared to its classical counterpart to achieve the same performance., 17 pages, 17 figures; submitted to IEEE Transactions on Aerospace and Electronic Systems

In this paper, the joint multitarget (JoM) estimator proposed for the joint target detection and tracking (JoTT) filter is reformulated for the Gaussian mixture (GM) implementations of the multitarget multi-Bernoulli (MeMBer) filters. For this purpose, a mode-finding algorithm is employed to search for the most significant mode of a GM density. Thus, the maximum a posterior (MAP) estimates of Bernoulli targets are determined. In addition, the multi-Bernoulli versions of the two conflicting objective functions for the Pareto-optimal value of the unknown JoM estimation constant are derived. Simulations compare the performance of the proposed JoM estimator with that of the marginal multitarget (MaM) estimator in a multitarget tracking scenario, where the probability of target detection is a function of target states. The simulation results demonstrate that the proposed JoM estimator outperforms the MaM estimator under moderately low-observable conditions. This is because the incomplete cost function of the MaM estimator is not adequate to obtain accurate cardinality estimates of targets without considering how well targets are localized. Nevertheless, the proposed JoM estimator may suffer from track termination latency more than the MaM estimator due to the definition of its cost function.

The cardinality-balanced multi-target multi-Bernoulli (CBMeMBer) filter removes the positive bias from the data-updated cardinality estimate in the multi-target multi-Bernoulli (MeMBer) filter. In this study, the relationship between the MeMBer corrector and the multi-Bernoulli random finite set (RFS) distribution is analysed. By utilising this relationship, a filter that offers a new statistical framework for the MeMBer data update process is proposed. Thus, the multi-Bernoulli RFS distribution is extended to model spurious targets arising from targets under the legacy track set with high probabilities of existence. Unlike the CBMeMBer filter, the proposed filter removes the bias observed in the MeMBer filter by distinguishing spurious targets from actual targets, and while doing this, it does not make any limiting assumption on the probability of target detection. In addition, the modelling of spurious targets allows the refinement of the existence probabilities of targets in light of measurements. As a result, the stability of the cardinality estimate is improved while removing the bias. The theoretical analysis performed on the joint detection and state estimation problem of a single target reveals the strengths and limitations of the proposed filter. In addition, numerical simulations are performed in a scenario involving targets with crossing trajectories to demonstrate the filter performance.

Detecting and identifying drones is of great interest due to the proliferation of highly manoeuverable drones with on-board sensors of increasing sensing capabilities. In this paper, we investigate the use of radars for tackling this problem. In particular, we focus on the problem of detecting rotary drones and distinguishing between single-propeller and multi-propeller drones using a micro-Doppler analysis. Two different radars were used, an ultra wideband (UWB) continuous wave (CW) C-band radar and an automotive frequency modulated continuous wave (FMCW) W-band radar, to collect micro-Doppler signatures of the drones. By taking a closer look at HElicopter Rotor Modulation (HERM) lines, the spool and chopping lines are identified for the first time in the context of drones to determine the number of propeller blades. Furthermore, a new multi-frequency analysis method using HERM lines is developed, which allows the detection of propeller rotation rates (spool and chopping frequencies) of single and multi-propeller drones. Therefore, the presented method is a promising technique to aid in the classification of drones.

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 ability to detect and unambiguously follow all moving entities in a state-space is important in multiple domains both in defence (e.g. air surveillance, maritime situational awareness, ground moving target indication) and the civil sphere (e.g. astronomy, biology, epidemiology, dispersion modelling). However, tracking and state estimation researchers and practitioners have difficulties recreating state-of-the-art algorithms in order to benchmark their own work. Furthermore, system developers need to assess which algorithms meet operational requirements objectively and exhaustively rather than intuitively or driven by personal favourites. We have therefore commenced the development of a collaborative initiative to create an open source framework for production, demonstration and evaluation of Tracking and State Estimation algorithms. The initiative will develop a (MIT-licensed) software platform for researchers and practitioners to test, verify and benchmark a variety of multi-sensor and multi-object state estimation algorithms. The initiative is supported by four defence laboratories, who will contribute to the development effort for the framework. The tracking and state estimation community will derive significant benefits from this work, including: access to repositories of verified and validated tracking and state estimation algorithms, a framework for the evaluation of multiple algorithms, standardisation of interfaces and access to challenging data sets. Keywords: Tracking