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As the pixel resolution of imaging equipment has grown larger, the images’ sizes and the number of pixels used to represent objects in images have increased accordingly, exposing an issue when dealing with larger images using the traditional deep learning models and methods, as they typically employ mechanisms such as increasing the models’ depth, which, while suitable for applications that have to be spatially invariant, such as image classification, causes issues for applications that relies on the location of the different features within the images such as object localization and change detection. This paper proposes an adaptive convolutional kernels layer (AKL) as an architecture that adjusts dynamically to images’ sizes in order to extract comparable spectral information from images of different sizes, improving the features’ spatial resolution without sacrificing the local receptive field (LRF) for various image applications, specifically those that are sensitive to objects and features locations, using the definition of Fourier transform and the relation between spectral analysis and convolution kernels. The proposed method is then tested using a Monte Carlo simulation to evaluate its performance in spectral information coverage across images of various sizes, validating its ability to maintain coverage of a ratio of the spectral domain with a variation of around 20% of the desired coverage ratio. Finally, the AKL is validated for various image applications compared to other architectures such as Inception and VGG, demonstrating its capability to match Inception v4 in image classification applications, and outperforms it as images grow larger, up to a 30% increase in accuracy in object localization for the same number of parameters.

The articles in this special issue focus on the applications supported by quantum radar. QUANTUM physics has had a large impact on our everyday life. Relevant examples range from transistors and Monolithic microwave-integrated circuit, or MMIC,1 that make most of our technological society, as well as to nuclear energy, and to the science of materials. Some of these technologies have met with indisputable success while others have not proven to be useful to date. It should be remembered that the idea of a clean energy coming from nuclear fusion is an unfulfilled promise: such technologies have always involved a change of paradigm that made them quite different from known expectations. Note that Von Neumann machines, the foundations of our computers, are based on hardware made from quantum mechanics effects but they are otherwise easy to understand. A quantum computer is a rather different object and not so easy to comprehend unless an extensive knowledge of quantum physics is achieved. The same applies to the quantum radar (QR), the main topic of this special issue, which is quite different from a classical radar, both in terms of the working principles and the kind of hardware to realize it. The today’s radars are based on the propagation of electromagnetic waves of the classical (nonquantum) physics. The QR promises to be a radical change. It should be said that we are yet at a pioneering stage and we cannot be certain yet if a goal will be achieved nor in what form we will see it, though, R&D is progressing.

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.

Geo-registration and geo-location of data collected by video sensors such as electro-optical and infrared cameras are two fundamental steps in the airborne surveillance of ground targets. With the availability of high-resolution imaging sensors and detailed mapping or terrain data sources, video data plays an increasingly important role in modern surveillance platforms like unmanned aerial vehicles and airborne, ground, or maritime surveillance systems. Surveillance systems without any compensation for the inevitable sensor registration errors, i.e., biases, may make geo-location erroneous and render the surveillance platform less effective for precision targeting. This article deals with the modeling of sensor biases in geo-location and proposes a method to estimate them. The proposed method leads to a minimization problem with a nonlinear cost function. Detailed derivation of the bias model is given along with an algorithm to find the bias parameters. The achievable lower bounds for debiased geo-location are provided and simulations are used to demonstrate the validity of the proposed method.

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.

We evaluate the feasibility of a quantum monopulse radar, focusing on quantum illumination (QI) radars and quantum two-mode squeezing (QTMS) radars. Based on their similarity with noise radar, for which monopulse operation is known to be possible, we find that QTMS radars can be adapted into monopulse radars, but QI radars cannot. We conclude that quantum monopulse radars are feasible.

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 derive a detector function for quantum two-mode squeezing (QTMS) radars and noise radars that is based on the use of a likelihood ratio (LR) test for distinguishing between the presence and absence of a target. In addition to an explicit expression for the LR detector, we derive a detector function which approximates the LR detector in the limit where the target is small, far away, or otherwise difficult to detect. When the number of integrated samples is large, we derive a theoretical expression for the receiver operating characteristic (ROC) curve of the radar when the LR detector is used. When the number of samples is small, we use simulations to understand the ROC curve behavior of the detector. One interesting finding is there exists a parameter regime in which a previously-studied detector outperforms the LR detector, contrary to the intuition that LR tests are optimal. This is because neither the Neyman-Pearson lemma, nor the Karlin-Rubin theorem which generalizes the lemma, hold in this particular problem. However, the LR detector remains a good choice for target detection., 7 pages, 8 figures

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.

The problem of nonlinear/non-Gaussian filtering has generated significant interest in the literature. The effectiveness of a nonlinear/non-Gaussian filtering algorithm depends on the accurate representation of the probability density function of the system state. The Extended Kalman Filter (EKF), the Approximate Grid Based methods (AGBM), and particle based filters have been developed to solve nonlinear/non-Gaussian problems. However, the EKF may not perform well with high nonlinearity due to its linear approximation; the AGBM often incurs extremely high storage/computational cost; particle filters provide weighted samples at discrete points in the state space instead of a continuous estimate of the probability density function of the system state, but most of them may suffer from the well-known degeneracy problem. In this paper, a comprehensive solution for nonlinear/non-Gaussian state estimation that can provide a continuous estimate of the probability density function of the system state is developed based on B-splines. The proposed spline filter is capable of modeling any arbitrary probability density function of the system state, and it is able to provide statistically the same estimation accuracy as the particle filter, but with only a few knots. It is also important to emphasize that, unlike most of the particle based algorithms (e.g., Sequential Important Sampling (SIS), Generic Particle Filter (GPF), and Sequential Monte Carlo (SMC) filter), the spline filter is free from degeneracy-like problems due to its continuous nature. In addition, by moving the knots dynamically, it ensures that the splines cover, and only cover, the regions where the probability of system state is significant so that the high efficiency of the spline filter is maintained. To make it applicable in common tracking applications, the spline filter is further extended to a multiple model one with the capability to handle systems with multiple maneuvering models. Besides theoretical derivations, simulation results are provided to verify the effectiveness of the proposed spline filter.

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 derived and verified for the general additive noise case (i.e., explicitly time-dependent state model and with state-independent rectangular diffusion vielbein). The solution is universal in the sense that the initial distribution may be arbitrary. The practical utility is demonstrated via some examples., Interdisciplinary, pedagogical, 37 pages, 2 figures

In this paper, the application of track-before-detect (TkBD) processing against airborne radar surveillance data is examined. The sensitivity of TkBD processing to the choice of clutter model was examined through processing of real and simulated data containing noncoherent radar echo amplitude returns of a small maritime target in sea clutter. The utilization of K- and KA-distributed clutter models in place of the simpler Rayleigh distribution was examined through analysis of simulated and real data. Significant shortcomings were identified. An alternate empirical approach, clutter event based characterization, is proposed for characterizing and simulating sea clutter based on the identification and grouping of so-called “clutter events”.

In conventional target tracking systems, human operators use the estimated target tracks to make higher level inference of the target behaviour/intent. This paper develops syntactic filtering algorithms that assist human operators by extracting spatial patterns from target tracks to identify suspicious/anomalous spatial trajectories. The targets' spatial trajectories are modeled by a stochastic context free grammar (SCFG) and a switched mode state space model. Bayesian filtering algorithms for stochastic context free grammars are presented for extracting the syntactic structure and illustrated for a ground moving target indicator (GMTI) radar example. The performance of the algorithms is tested with the experimental data collected using DRDC Ottawa's X-band Wideband Experimental Airborne Radar (XWEAR).

A new application for reflector antennas is proposed and developed. Using the aperture theory, a phase center on the reflector aperture is determined and shown that, its location is dependent on the field distribution. The proposed concept is, initially, verified by using a symmetric reflector. It is shown that the phase center is located at the aperture geometric center, when the reflector is illuminated symmetrically about its principal planes. Then, a dual mode feed, employing TE11 and TM01 modes, is used for generating different reflector illuminations, and causing displacement of its phase center. The concept is then extended to offset reflectors, and the influence of the reflector geometry on the phase center displacement and other reflector electrical parameters is investigated. Based on the established feed radiation pattern requirements, a feed horn is designed using circular waveguide that can propagate both modes. By modifying the amplitude and phase of the modes in the horn, a controlled asymmetric reflector aperture field is achieved. A prototype feed horn is fabricated and tested for its dual mode radiation patterns. The results are in good agreement with simulations. The reflector phase center properties are then investigated, by using the designed feed. A reflector-feed assembly, with its dual phase center capability, was developed for improving the performance of the ground moving target indicator radars. The concept allows the conversion of a single reflector to two or more reflectors, simply by modifying the mode excitation amplitudes and phases, in the feed alone

We show how a single reflector antenna with a multimode feed horn can be used in a ground moving target indication (GMTI) radar. In particular, we demonstrate the simultaneous detection and estimation of angular location of a ground moving target via adaptive cancellation of ground clutter

Adaptive cancellation of stationary clutter for a ground moving target indicator (GMTI) radar requires antenna sensing using multiple apertures. In essence, simultaneous independent observations of the target plus clutter are required. Conventionally, multiple antenna apertures can be achieved through the use of physically separated antennas, or antennas which can be controlled so that subsections are used to receive. Herein, the use of reflector antennas to effect multiple phase centres is described. Multiple feedhorns pointed laterally from the focal point of the reflector are first reviewed, with capabilities and limitations discussed. A new technique for achieving multiple phase centres with a reflector antenna is then introduced. This technique is based on the excitation and combination of TE and/or TM modes from a single antenna feedhorn. It is shown that, by proper combination of multiple TE modes from a single feedhorn, radiation patterns with separate phase centres can be produced from the same reflector. TE and TM modes can also be combined to effect the same, but this is omitted for brevity. The characteristics of the resulting radiation patterns are analysed with a view towards maximising the separation of the antenna phase centres while maintaining symmetry between the patterns and minimising the reduction in gain and constant phase beamwidth with respect to the reflector's conventional radiation pattern.