Radar detection of objects

Abstract

Disclosed is a data processing method for processing measurement data obtained from a distributed target using a polarimetric monostatic radar. The method comprises inputting a measurement data set co

Description

BACKGROUND OF THE INVENTION The invention relates to acquiring and processing polarimetric radar data to identify objects. Over the past three decades, the microwave (0.3-30 GHz) and millimetre (30-300 GHz) wave bands have been explored extensively for radar security screening of persons. Radar is an active system that stimulates a target with artificial radiation and analyses the reflections. Clothing is transparent in this wave band whereas many threat items of interest, such as concealed weapons and explosives, generate significant scattering of the radar signal, which can be detected and analysed. Such radars may measure a single lateral pixel or multiple lateral pixels. Moreover, such radars may additionally include a range dimension, i.e., resolution at multiple different distances between the radar and the target. Some of the radars developed for security screening use polarimetric radar in reflection, in which the response to scattering of two orthogonal polarisation components are analysed. Polarimetric radar is the subject of the present invention. There are several published patent documents in the field of security screening which use polarimetric radar to screen persons of interest to detect concealed weapons, for example: • US7800527 • US7304603 • US7492303 • US10229328 • US10067226 • US11422252 • US2024111044 Some non-patent literature on this subject is: 1. D. A. Andrews, N. Bowring, N. D. Rezgui, M. Southgate, E. Guest, S. Harmer and A. Atiah, “A multifaceted active swept millimeter wave approach to the detection of concealed weapons,” in Proc. SPIE, Vol. 7117, 'Millimetre Wave and Terzhertz Sensors and Technology', Cardiff, 2008. 2. S. W. Harmer, N. Bowring, D. Andrews, N. Rezgui and M. Southgate, “Millimetre radar threat level evaluation (MiRTLE) at standoff ranges,” in Proc. SPIE 8188, Millimetre Wave and Terahertz Sensors and Technology IV, doi: 10.1117 / 12.902231 , Prague, 2011. 3. D. A. Andrews, S. W. Harmer, N. J. Bowring, N. D. Rezgui and M. J. Southgate, “Active Millimeter Wave Sensor for Standoff Concealed Threat Detection,” IEEE Sensors Journal, vol. 13, no. 12, pp. 4948-4954, 2013. 4. B. Y. Kapilevich, S. W. Harmer and N. J. Bowring, Non-Imaging Microwave and Millimetre-Wave Sensors for Concealed Object Detection, Boca Raton, FL: CRC Press, 2015. 5. M. J. Southgate, Remote Detection of Concealed Guns and Explosives, PhD Doctoral Dissertation, Manchester: Manchester Metropolitan University, 2013. 6. Andrews, David; Salmon, Neil A; Blackhurst, Eddie J; “Security screening FDTD simulations of the human body and enclosures in polarimetric radar and comparison with measurements,” in Proc. SPIE 12274, Emerging Imaging and Sensing Technologies for Security and Defence VII, Berlin, 2022. 7. E. Blackhurst, N. Salmon and M. Southgate, “Full polarimetric millimetre wave radar for stand-off security screening,” Proc. SPIE 10439, Millimetre Wave and Terahertz Sensors and Technology X, vol. 10439, p. 1043906, 2017, doi: 10.1117 / 12.2282564. 8. E. Blackhurst, N. Salmon and M. Southgate, “Experimental determination and simulations of the Huynen target parameters for full polarimetric millimetre wave concealed weapon recognition,” Proc. SPIE 10800, Millimetre Wave and Terahertz Sensors and Technology XI, vol. 10800, p. 1080007, 2018, doi: 10.1117 / 12.2324450. 9. E. Blackhurst and N. A. Salmon, “Full polarimetric radar for concealed weapons detection: Experimental determination and simulation of the Huynen target parameters for the human torso,” Proc. SPIE 11164, Millimetre Wave and Terahertz Sensors and Technology XII, vol. 11164, p. 111640D, 2019, doi: 10.1117 / 12.2547833. 10. D. O'Reilly, A feasibility study on the application of polarimetric decomposition algorithms to the detection of concealed weapons, PhD doctoral dissertation, Manchester: Manchester Metropolitan University, 2016. 11. E. J. Blackhurst, Development of techniques and technology for full polarimetric radar applied to concealed weapons detection, PhD doctoral dissertation, Manchester Metropolitan University, 2020. 12. Harmer, S. W.; Cole, S. E.; Bowring, N. J.; Rezgui, N. D.; Andrews, D., “On Body Concealed Weapon Detection Using a Phased Array Antenna,” Progress In Electromagnetics Research, vol. 124, pp. 187-210, 2012. Unfortunately, the performance of the above radars has been less than optimal and there has been no widespread adoption of security screening using the microwave and millimetre wave bands. Research and development effort in this area has dwindled to a low level in recent years. SUMMARY OF THE INVENTION According to the invention, a method is provided for processing radar data obtained from a full polarimetric radar, in particular in the microwave or millimetre wave bands. The radar data is in the form of Sinclair matrices, whose components are usually referred to as S-parameters. The radar data may be collected either in the frequency-domain or in the time-domain through use of an appropriate frequency-domain or time-domain radar respectively. The method is based on generating coherency matrices (or equivalent related by unitary matrix transformation, such as the covariance or Kennaugh matrices) from the acquired Sinclair matrices and then using the coherency or equivalent matrices as input into a machine learning algorithm which performs target classification. Using coherency or equivalent matrices as input to a machine learning algorithm appears to be a high performing combination, which may be attributable to the fact that the coherency matrix (or equivalent) fully characterises the polarimetric response of a distributed radar target. According to one aspect of the disclosure there is provided a data processing method for processing measurement data obtained from a distributed target using a full polarimetric monostatic radar to output an object classification, the method comprising: inputting a measurement data set in the time-domain or the frequency-domain comprising a set of Sinclair matrices collected over a data acquisition period from a distributed target using a full polarimetric monostatic radar, a Sinclair matrix being a 2 x 2 matrix comprising four parameter values, referred to as S-parameters; providing a trained machine learning algorithm configured to output a results matrix containing probabilities of the presence of each of a plurality of object classes in a distributed target that has been scanned by a full polarimetric monostatic radar, thereby representing an object classification; de-jittering the S-parameters in a time-domain representation of the measurement data set; generating a set of coherency matrices, or equivalent related by unitary matrix transformation, from the set of Sinclair matrices in either or both of a time-domain and a frequency-domain representation of the measurement data set; generating a plurality of real values from each of the coherency or equivalent matrices; and running the machine learning algorithm by inputting said real values as input matrices and receiving a results matrix as output, the results matrix containing the object classification. The above method operates on ‘live’ measurement data. However, the machine learning algorithm applied to ‘live’ measurement data will require prior training. A method according to another aspect of the disclosure thus provides a data processing method for training a machine learning algorithm to process measurement data obtained from a distributed target using a full polarimetric monostatic radar to output an object classification, the method comprising: providing a plurality of measurement data sets from a plurality of distributed targets using a full polarimetric monostatic radar, each measurement data set being in the timedomain or the frequency-domain and comprising a set of Sinclair matrices collected over a data acquisition period, a Sinclair matrix being a 2 x 2 matrix comprising four parameter values, referred to as S-parameters; providing a machine learning algorithm having a cost function with a plurality of weights which require optimization, the machine learning algorithm being configured to output a results matrix containing probabilities of presence of each of a plurality of object classes in a distributed target that has been scanned by a full polarimetric monostatic radar, thereby representing an object classification; providing a set of ground truth data indicating which object classes are present in which of the distributed targets; generating a set of coherency matrices, or equivalent related by unitary matrix transformation, from the set of Sinclair matrices in either or both of a time-domain and a frequency-domain representation of the measurement data set; generating a plurality of real values from each of the coherency or equivalent matrices; running the machine learning algorithm for each of the plurality of measurement data sets by inputting said real values as an input matrix and receiving the results matrix as output, each results matrix containing the object classification for the measurement data set it was obtained from; making a comparison between each results matrix and the ground truth data associated with the distributed target from which the measurement data set was obtained; adjusting the weights of the cost function in the machine learning algorithm according to said comparison; and iteratively running of the machine learning algorithm, making a comparison and adjusting the weights, in order to optimize the weights in the sense of converging the object classification made by the results matrices to the objects known to be present from the ground truth data. In some embodiments, said generating a plurality of real values is performed only on a time-domain representation of the measurement data set, and the machine learning algorithm is provided only with those real values. In other embodiments, said generating a plurality of real values is performed only on a frequency-domain representation of the measurement data set, and the machine learning algorithm is provided only with those real values. In still further embodiments, said generating a plurality of real values is performed both on a time-domain representation of the measurement data set and a frequency-domain representation of the measurement data set, and the machine learning algorithm is provided with real values generated from both the time-domain and frequency-domain representations of the measurement data set. When the machine learning algorithm receives frequency-domain input data, the frequencydomain representation of the measurement data set may be subjected to subsampling prior to being used to generate the set of coherency or equivalent matrices. Moreover, prior to subsampling, the frequency-domain representation of the measurement dataset is preferably smoothed. In practical implementations of the invention, the coherency matrices (or equivalent covariance or Kennaugh matrices or other matrices related by unitary matrix transform) are carefully prepared for input into the machine learning algorithm by appropriate pre-processing of the radar data to ensure the highest possible data integrity of the coherency matrix components (or equivalent matrices such as covariance or Kennaugh matrix components). The overall data processing pipeline thus commences with pre-processing of the measurement data and then uses the pre-processed measurement data to generate the coherency matrices (or equivalent matrices such as covariance or Kennaugh matrices), the values from which are then supplied as input to the machine learning algorithm. The pre-processing methods applied before generating the coherency matrices (or equivalent matrices such as covariance or Kennaugh matrices) are selected from one or more of: range gating, external calibration and, in the case of generating time-domain coherency matrices (or equivalent time-domain matrices, such as covariance or Kennaugh matrices), also de-jittering. Moreover, as described in the following, the type of machine learning algorithm is selected and configured to provide the highest possible classification accuracy with the training data set being used to train the machine learning algorithm. In some embodiments, the radar data is pre-processed by de-jittering the S-parameters in a time-domain representation of the measurement data set In some embodiments, the radar data is pre-processed by externally calibrating the S-parameters in a frequency-domain representation of the measurement data set. Moreover, if the measurement data has been obtained by a vector network analyser (VNA), it is also beneficial to perform an internal calibration prior to the external calibration by measuring reflections from short circuits, open circuits and matched loads at the ends of the cables (or waveguides if they are used) connected to the VNA ports and measuring transmission of a through connection between the cable (or waveguide) ends. In some embodiments, the radar data is pre-processed by range gating a time-domain representation of the measurement data set. If two or more of these three pre-processing measures are applied, the preferred order in which they are applied is range gating followed by external calibration followed by de-jittering. The data processing method, depending on whether the measurement data is collected in the time domain or the frequency domain and also depending which of the above pre-processing measures are employed, will require that the measurement data set is converted from a timedomain representation to a frequency-domain representation with a Fourier transform and / or from a frequency-domain representation to a time-domain representation with an inverse Fourier transform. Such conversions between the time- and frequency-domains will be performed by suitable numerical processing resource. It will be understood that the Fourier transforms and the inverse Fourier transforms will be digital. The machine learning algorithm may be a neural network algorithm or a classical machine learning algorithm. As is well known, classical machine learning is based on finding linear relationships between variables whereas neural networks with hidden layers of neurons have the ability to identify nonlinear relationships between variables, The invention in a further aspect relates to a computer program product comprising a computer-readable storage medium having computer-readable program code embodied therewith, the computer-readable program code configured to implement the above-described methods. The invention in a still further aspect provides a full polarimetric monostatic radar system, comprising: a monostatic antenna or antenna combination configured to direct a transmission radar beam onto a distributed target and in response collect a receiver radar beam; a measurement instrument configured to collect a measurement data set from the monostatic antenna; and a computer apparatus loaded with the above-specified computer program product for processing the measurement data set to obtain an object classification for the distributed target. The monostatic radar may be either true-monostatic or quasi-monostatic. The radar may be either of the frequency sweeping type to collect frequency-domain data or impulse type to collect time-domain data. The radar is operated to measure a target over one or a small number of lateral pixels. By lateral pixel, ‘cross-range’ is meant as opposed to ‘range’ which is depth. In practice, the easiest implementation is to acquire data over a single lateral pixel, since then the radar is realizable with standard radar head without the need to perform scanning. However, it is also possible to collect over multiple lateral pixels. This can be done using a multipixel radar head to collect data over multiple lateral pixels, or by moving a conventional radar head to collect data over multiple lateral pixels. The target of interest is a person who is to be subject to security screening. Operating the radar in each pixel obtains consecutive Sinclair matrices over a data acquisition period, which is typically of the order of 0.1 to 10 seconds. In the experimental results presented further below, integrating for a period of one second was sufficient to gather enough information from a nominally stationary target person. For moving persons, e.g., walking, it may be useful to shorten the integration times to a fraction of a second. Another approach to cope with moving target persons is to pan and tilt the radar sensor during a data acquisition to follow movement of the target. If a frequency-domain radar is used, this is operated to repeatedly sweep a frequency range to obtain multiple Sinclair matrices at each frequency of each lateral pixel on a distributed target. If a time-domain radar is used, this is operated to generate impulse responses directly, representing the co- and cross-polarisation responses from the target, thereby to provide the Sinclair matrices in the time-domain. The collected data can be Fourier transformed or inverse Fourier transformed between the frequency domain and the time domain as needed in the data processing pipeline. The consecutive Sinclair matrices in the acquired data set are processed to generate coherency matrices or equivalent such as covariance or Kennaugh matrices. It is noted that the information contained within a coherency matrix is the same as that contained in a covariance matrix or Kennaugh matrix or any other such matrix related by unitary matrix transformation. Conversion between these three matrix types is by a unitary matrix transformation. In the context of the invention, the use of coherency, covariance or Kennaugh matrices, or any other matrix created by a unitary matrix transformation of these, are equivalent. Data processing to de-jitter the data is performed using a cumulative cross-correlation technique in the time-domain. The Sinclair matrix components are thereby corrected for range movements of a target person. The de-jittering enables consecutive Sinclair matrices to be formed into a time-domain conjugate cross-product coherency matrix (or equivalent) with accurate content values. The coherency (or equivalent) matrices are then provided as input to a machine learning algorithm, which detects, recognises or identifies objects of interest on a target person by applying a classification of known objects on which the machine learning has been trained. The machine learning may either be by neural network or classical. Both machine learning approaches have shown to be successful in the context of the present invention. The machine learning is easily adaptable to handle either single pixel data or multipixel data. A significant benefit of the method of the invention is that the values within a coherency matrix (or equivalent matrix, such as covariance matrix or Kennaugh matrix) represent the maximum possible amount of information obtainable from a radar target, thus being the optimum data set to be supplied to a machine learning algorithm for target recognition. In the frequency-domain, a coherency matrix (or equivalent matrix such as covariance matrix or Kennaugh matrix) captures all spectral information from the target over the radiation band. In the time-domain, a coherency matrix (or equivalent matrix such as covariance matrix or Kennaugh matrix) captures all temporal information from the target. Another significant benefit of the method of the invention is that the coherency matrix (or equivalent matrix such as covariance matrix or Kennaugh matrix) acts as a speckle filter to reduce signal variation, thereby generating a higher quality signal for subsequent analysis by the machine learning. BRIEF DESCRIPTION OF THE DRAWINGS This invention will now be further described, by way of example only, with reference to the accompanying drawings. Figure 1 is a schematic view of a monostatic polarimetric radar system for screening a target person for concealed objects. Figures 2A and 2B are schematic drawings of two types of full polarimetric antennas. Figures 3A to 3C show different example single antenna beams as incident on a target person. Figure 4 is a schematic diagram of a monostatic (I, Q) dual-polarisation heterodyne swept frequency radar system for Sinclair matrix measurements. Figure 5 is a flow diagram of the signal processing pipeline used to identify items of interest from the measurement data set. Figure 6 shows graphs of the impulse responses of a plane reflector test object before external calibration (upper graph) and after external calibration (lower graph). Figure 7 is a flow diagram illustrating the cumulative cross-correlation de-jitter method operating on a group of Ng time-domain S-parameters. Figures 8A to 8F show in a graphical form the 9 time-domain averaged coherency matrix components for these six classes of security threat as function of time. Figures 9A to 9F show in a graphical form the 9 frequency-domain averaged coherency matrix components in a corresponding format to Figures 8A to 8F. Figure 10 shows a schematic of a two hidden layer FFN for processing the coherency matrix. Figure 11 shows a schematic of a single convolutional layer, single dense layer CNN. Figure 12 shows the normalised confusion matrix for six threat classes as obtained from an extra-trees classical machine learning algorithm working on the time-domain coherency matrix. Figure 13 shows the normalised confusion matrix for six threat classes as obtained from an FFN neural network machine learning algorithm working on the time-domain coherency matrix. Figure 14 shows a normalised confusion matrix for six threat classes as obtained from a 1DCNN. Figure 15 shows a normalised confusion matrix for six threat classes as obtained from a 2D CNN. Figure 16 is a block diagram of a tensor processing unit (TPU) which may be used for performing the computations involved in implementing the data processing method for training 5 or in a live system. Figure 17 is a block diagram of a computing apparatus that may be used for example as the host computer for the TPU of Figure 16 and / or as part of a radar system as shown in Figures 1 to 4. DETAILED DESCRIPTION In the following detailed description, for purposes of explanation and not limitation, specific details are set forth in order to provide a better understanding of the present disclosure. It will be apparent to one skilled in the art that the present disclosure may be practiced in other embodiments that depart from these specific details. Interaction of millimetre wave radiation with threat objects and the human body In the following detailed description, for purposes of explanation and not limitation, specific details are set forth in order to provide a better understanding of the present disclosure. It will be apparent to one skilled in the art that the present disclosure may be practiced in other embodiments that depart from these specific details. The security screening application of principal interest with the systems and methods presented herein is screening for threat items on a person, under clothing or another surface that is opaque to light in the visible (approx. 380-700 nm), for example surrogate skin, a prothesis or a wig. Other screening applications that could be addressed with the systems and method presented herein are by way of example detection of threat items in an enclosure that is opaque in the visible, under a wooden floor, inside a wall, in a bag or case, in a plastic drainpipe, or in a plastic dustbin. Many materials are transparent in the millimetre wave band. Specifically, paper, plastics and clothing (including leather) are very transparent in the lower frequency band of the millimetre wave band <30 GHz. On the other hand, other materials are reflective in the millimetre wave band and hence, in principle, detectable by screening when they are hidden from view by a transparent material. Specifically, metals are highly reflective with reflectivities up to 100% and water-containing (aqueous) items have an approximate 50% reflectivity at around 30 GHz, which falls off at higher frequencies. Dielectric materials are also detectable by millimetre wave band radar, having the property that they are semi-transparent and partially reflective. Materials that are dielectric include glass, plastic, many ceramics, the precise level of transparency and reflectivity being determined by their relative permittivities. Nitrogen-based explosives, such as RDX, TNT and PETN, are a particular class of dielectrics that are important for security screening. These materials are relatively transparent and as such present particular challenges for the security screening industry. These materials have a sufficiently low refractive index that they permit a millimetre wave beam to enter. In many of these materials the loss within is sufficiently low, that the wave may be totally or partially internally reflected, before exiting the material a short time later and propagating back to the radar. The additional time spent by the wave inside the material depends on the geometry of the bulk material and the relative permittivities. The threats which are screened for can be categorized at least in part by their reflectivity at the frequencies used by the millimetre radar of the system being used. A rough categorisation by reflectivity will have metal and ceramic items, such as guns and knives, with high reflectivity, and items made of a dielectric material, such as explosives, with a low reflectivity, and aqueous items with an intermediate reflectivity. Polarimetric radar and the Sinclair matrix Embodiments of the invention are based on full polarimetric radar. Full polarimetric radar uses two orthogonal polarisations which are transmitted separately, O and X, and the returns in these orthogonal polarisations are measured. Since the object being measured by a full polarimetric radar may convert a component of one polarisation into the orthogonal polarisation, a total of four scattering parameters are measured, these being Soo, Sox, Sxo and Sxx. The four parameters contain all the polarisation information that can be measured from an object. The group of these four numbers in a 2 x 2 matrix is referred to as the Sinclair Matrix: $00 $ox $xo $xx. (1) To measure the four scattering parameters of the Sinclair matrix a two-port instrument is used. A two-port instrument measures the fraction of radiation from port 1 that is reflected back into port 1 and reflected to port 2. A two-port instrument additionally measures the fraction of radiation from port 2 that is reflected back into port 2 and reflected to port 1. Since in-phase and quadrature receivers are used, the measured quantities are complex, i.e., contain both amplitude and phase information. As the antenna supports two orthogonal polarisation modes, the four scattering parameters represent the components of the Sinclair matrix, these components being referred to as the S-parameters. Generally, antenna and receiver components are easier to build for the transmission and reception of linear polarisations, so most full polarimetric radars use linear polarisations. However, it is in principle possible to use any other orthogonal pair of polarisations, such as left- and right-circular polarisations or orthogonal elliptical polarisations. Specifically, the experimental data presented in this document was collected using a linear polarisation full polarimetric radar having horizontal (H) and vertical (V) polarisations which were assigned to ports 1 and 2 of a VNA. When using a 2-port VNA as the instrument to make polarimetric radar measurements, the S-parameters recorded by the VNA become the components of the Sinclair matrix. When measuring using horizontal and vertical polarisations, the system is said to be measuring in the horizontal-vertical polarisation (HV) basis. For the convention used here the Sn scattering parameter refers to that response coming from stimulating the target in horizontal polarised radiation, whilst measuring the horizontal polarised radiation being returned from the target. For this reason, the Sn component of the Sinclair matrix is written as Shh, so it is clear which polarisation is involved. Likewise, the other components of the Sinclair matrix are, S12 = Shv, S21 = Svh and S22 = Sw. The components of the Sinclair matrix are measured in the frequency-domain by sweeping a source over a radiation bandwidth Brf and measuring the response using a receiver having a radio frequency resolution Af. This measures a whole series of Brf / Af Sinclair matrices. These measurements can be performed by either stepping the frequency in a stepped frequency continuous wave (SFCW) radar or by a continual ramping of the frequency in a frequency modulated continuous wave (FMCW) radar. The Sinclair matrix components in the time-domain can be found by taking the inverse Fourier transform of the components recorded in the frequency-domain. If the radar bandwidth swept, Brf, extends from DC up to a frequency fRF = Brf, the inverse Fourier transforms of the S-parameters can be constructed as purely real functions. This is because the measured S-parameters can be formed into Hermitian functions. However, if the radar sweeps between two frequencies, the lower of which is not DC, the Hermitian functions can only be formed by assumptions about the response from DC up to the lowest sweep frequency. A simpler solution, which is the approach taken in this analysis, is to neglect assumptions about the DC upward response, and just take the inverse Fourier transform of the measured swept frequencies. This results in a complex function in the time-domain. An alternative approach for data collection is to measure the time-domain Sinclair matrices directly using short bandwidthlimited polarised pulses from a pulsed radar (synonym: impulse radar). The benefit of measuring the Sinclair matrix is that it represents the full polarimetric response of a target. No further information can be collected by additional polarimetric probing; the Sinclair matrix represents the complete set of polarimetric information about a target. Mathematically, the Sinclair matrix represents a complete set, from which any other polarimetric response of a target can be derived. In a calibrated system, these reflection coefficients represent the response measured from the radar transmit antenna to the receive antenna. The phase of these complex reflection coefficients holds information about the target, including the range to the target. The magnitude of the reflection coefficients also holds information about the target. Any orthogonal polarisation pair (referred to as a basis) can be used to measure the Sinclair matrix, for example either horizontal and vertical linear polarisation, or right-hand and left-hand circular polarisation. Although the numerical values of a Sinclair matrix will be different, for different orthogonal pairs, the information content in the Sinclair matrix will be substantially the same. The Sinclair matrix from one orthogonal pair of measurements can be transformed into that which would have been measured by any other pair by a unitary matrix transformation, without loss or gain of information. The eigenvalues of the Sinclair matrices measured in different orthogonal polarisations are the same, but the eigenvectors are different. An important property of the Sinclair matrix for monostatic radar is that the matrix is symmetric, i.e., Sxo = Sox. This means that in a monostatic configuration there are only six pieces of information contained within the matrix, instead of eight for non-monostatic (so-called bistatic) radars. Since one of these pieces of information is the range of the target, in reality there are only five information pieces collected about the target itself. Given these five pieces of information and Brf / a / separate frequency measurement, a full polarimetric radar has the potential to collect 5SRp / Af independent pieces of information about a target from a single measurement. Full radar polarimetry is a term used to refer to measuring and using all the complex components of the Sinclair matrix. This involves sampling the electric fields of the transmit and receive radar beams. Full radar polarimetry differs from intensity polarimetry, the latter measuring only the intensities of the quantities {|Soo|2, |Sox|2, |Sxx|2} of the Sinclair matrix without any phase information. Intensity polarimetric radars therefore only collect a maximum of 3BRp / Af independent pieces of information from a target. Pure and distributed radar targets Radar theory distinguishes between pure and distributed targets. If there is no relative movement between the target and the radar, and if the target does not interact with its environment, repeated measurements of the Sinclair matrix will reveal the same numerical values for its components. In this case the target is classed as a ‘pure’ target. If there is relative movement between the target and the radar, or if the target interacts with the environment in a changing way, successive measurements of the Sinclair matrix will be different. In this case the target is classed as a ‘distributed’ target. Sometimes the term ‘extended’ target is used as a synonym for distributed target. The target according to embodiments of the invention is an object being carried by a person. Such a target is a distributed target. Even for a person who is standing still, their residual motion caused by biological factors such as breathing, beating of the heart and balance mechanisms introduce sufficient motion that the item being screened for is not a pure target. Distributed targets can be characterised by their measured coherency matrices (or equivalent matrices related by unitary matrix transformation, such as covariance or Kennaugh matrices), these being formed from a collection of Sinclair matrices. Distributed targets cannot be represented by a single Sinclair matrix. The rank of the coherency matrix of a distributed target will be greater than one. On the other hand, a pure target can be represented by a coherency matrix of unity rank and also by a single Sinclair matrix. Radar system set-up Figure 1 is a schematic view of a monostatic polarimetric radar 1 for screening a target person 2 for concealed objects according to an embodiment of the invention. The lateral extent of the radar beam on the target person is schematically illustrated with the circle 3. The radar 1 directs an interrogating transmission beam onto a subject under investigation from a monostatic antenna 4 connected to a measurement instrument 5. The radar 1 may be a true monostatic radar or a pseudo-monostatic radar. A true monostatic radar uses a single antenna for transmission and reception. A pseudo-monostatic radar uses two antennas, adjacently located, one for transmission and the other for reception. The gains of the transmitter beam and the receiver beam are nominally the same and they overlap on the subject, having a 3 dB width of approximately the width of the target person 2. The antenna beams are nominally horizontal, emanating from the radar 1 which is illustrated by way of example as being mounted on a tripod 6 to direct the antenna beam, generally horizontally, onto the target person. The radar 1 will typically have a range, i.e., effective distance from antenna to target, of somewhere between a metre or a few tens of metres. The radar 1 will be optimised for the intended range of effective distances by suitable choices of beam divergence and antenna gain, so that the beam diameter (or other lateral dimension) is matched to the width of a person’s body. The radar may be mounted in any manner appropriate for the screening environment, not just on a tripod as illustrated. For example, the radar can be wall mounted. This may be on an exterior wall of a building to monitor target persons walking on street or on the internal wall of a building to monitor target persons walking down a corridor or gathered in a room. The radar may also be mounted on a vehicle to monitor target persons in the environs of the vehicle. The radar may be mounted so that its beam is directed in a downward looking angle, e.g., from a ceiling mount, a streetlamp or other tall street furniture. The radar may be mounted so that its beam is directed at an upward looking angle, e.g. mounted on furniture. The radar may also be a hand-held unit which can be carried by security staff member and scanned over a target person. As mentioned above, for full polarimetric radar a two-port measuring instrument is used. Two specific examples are now described with reference to Fig. 2A and Fig. 2B Fig. 2A shows one specific implementation of a two-port measuring instrument in which the antenna 4 has two orthogonal ports in the form of a dual-ridged rectangular waveguide horn and is connected to the measurement instrument 5 via a suitable coaxial cable (or waveguide) 8. Fig. 2B shows another specific implementation of a two-port measuring instrument in which an orthomode transducer (OMT) 9 is arranged between the measurement instrument 5 and the antenna 4 with respective connections via sections of coaxial cable (or waveguide) 8, wherein the antenna 4 is a dual-polar circular waveguide horn. The OMT 9 has three ports. Connected to the measurement instrument 5 there is, an O-port and an X-port. Connected to the antenna 4, there is a dual-polarisation port. The OMT 9 has the property that O and X polarisations entering separately the O- and X-ports will exit the dual polarisation port together. The OMT 9 also operates in reverse, in that O and X polarisations entering the dual polarisation port together will exit separately from the O- and X-ports respectively. The polarimetric radar used to collect the data is now discussed. In its simplest form a generic radar can be considered as an instrument for measuring the scattering parameters of a network, whereby a signal is transmitted to a network and a return signal is measured. The scattering parameter, which represents the response of the network, is the ratio between the complex amplitude transmitted and the complex amplitude returned. The scattering parameter, normally designated with the upper-case letter ‘S’, contains both the phase and amplitude response of the network. In polarimetric radar it is the response to scattering of two orthogonal polarisation components that are analysed. Full polarimetry offers benefits to radar as it increases the information content of a single polarisation nine-fold by using coherency matrices (or equivalent matrices such as covariance or Kennaugh matrices). With a rapidly scanning radar, the data at any one given frequency in a frequency sweep can be accumulated at a time scale much shorter than a person’s normal movement while walking. A large number of frequency sweeps can thus be carried out on any given person as they move while being exposed to the radar beam, so in the process of screening a moving person, a large data set can be accumulated for the distributed target. This data set is then analysed to determine if a person is concealing items of interest under clothing. Figures 3A to 3C show different example single antenna beams as incident on a target person. Figure 3A shows a single circular antenna beam incident on the torso. Using a circular antenna beam on the body with a 3 dB full width half maximum of order of the body width is suitable for detecting items concealed on the torso. With a ~30 cm full half-power beam width, the region from the waist to the top of the chest can be screened. Figure 3B shows the same circular antenna beam as Figure 3A shifted downwards to detect between the legs. It will be understood that it may be desirable to move the beam to any area of interest on the target person (e.g., groin, legs, shoulders, head). To screen objects with smaller radar cross-sections it may be desirable to concentrate the beam by using an elliptical (fan-shaped) antenna pattern. Figure 3C shows such a fan beam, the illustrated example being an ellipse that is narrower in the vertical direction, meaning the whole front of the body may be screened by moving the beam in an up-down vertical motion. A fan beam offers a more localised measurement in the vertical direction, increasing detection probability and reducing false alarms. Frequency-domain radar Figure 4 is a schematic illustration of a monostatic radar using a dual-polarisation antenna as may be used for collecting data according to an embodiment of the invention. By way of example, this is a true monostatic configuration, where the same antenna is used to transmit and receive radar radiation. Moreover, this is a monostatic (I, Q) dual-polarisation heterodyne swept frequency radar which obtains data in the form of a Sinclair matrix. The antenna is as shown in Fig. 2A, namely a dual (orthogonal) polarisation antenna with a single output and two inputs, one for co-polarisation and the other for cross-polarisation. Alternatively, the antenna of Fig. 2B could be used, i.e., a dual-polarisation antenna with a single waveguide input, with an orthomode transducer having two orthogonal inputs to diplex the co-polarisation and crosspolarisation signal components into a single waveguide. The target person 2 is illuminated by a radar beam 3 emitted from an antenna 4. A millimetre wave voltage-controlled oscillator (VCO) 10 sweeps the frequency fvco over the radar bandwidth. A common local oscillator (LO) 12 with a frequency (4o), much lower in frequency than that of the VCO, ensures the intermediate frequency (IF) ftF = ko of the receiver is well away from DC in order to minimise 1 / f noise in the front-end of the receiver. A mixer M1 connected to receive the outputs of the VCO 10 and LO 12 generates a radar probe radiation at a frequency fvco + Flo which passes to a switch 14. The switch 14 directs the radiation alternately to a co-polarisation duplexer 15 and a cross-polarisation duplexer 16. The duplexers 15, 16 may for example be circulators or directional couplers. The duplexers 15, 16 pass radiation from the switch 14 to the antenna 4 for transmission of a radar beam 3 that propagates towards the target 2. Radar radiation is reflected from the target 2 back through the antenna 4 where the received signal is routed to respective mixers M2a and M2b for the co-polarised and cross-polarised signal components which form the inputs to an IF stage IT-22. Mixer M2a mixes the co-polarised signal component with the instantaneous VCO frequency fvco to shift the received frequency co-polarised signal component to the intermediate frequency ftF, the frequency shifted signal then being split into two and input to further mixers M3a and M3b which mix the frequency shifted signal at intermediate frequency fa down to a baseband frequency by mixing with the local oscillator frequency 4o supplied by a further local oscillator 17. The local oscillator signal at the local oscillator frequency ko supplied to mixer M3a is phase shifted by a quarter of a cycle by a phase shifter 19 whereas the local oscillator signal supplied to mixer M3b is not phase shifted. The outputs of mixers M3a, M3b are then sampled to digital values by respective analogue-to-digital converters 21,23 to obtain the in-phase (I) and quadrature (Q) signal components, which are the Soo and Sox entries of a Sinclair matrix 25. Mixer M2b mixes the cross-polarised signal component with the instantaneous VCO frequency fvco to shift the received frequency cross-polarised signal component to the intermediate frequency fF, the frequency shifted signal then being split into two and input to further mixers M3c and M3d which mix the frequency shifted signal at intermediate frequency f / pdown to a baseband frequency by mixing with the local oscillator frequency 4o supplied by a further local oscillator 18. The local oscillator signal at the local oscillator frequency 4o supplied to mixer M3d is phase shifted by a quarter of a cycle by a phase shifter 20 whereas the local oscillator signal supplied to mixer M3c is not phase shifted. The outputs of mixers M3c, M3d are then sampled to digital values by respective analogue-to-digital converters 22, 24 to obtain the I and Q signal components, which are the Sxoand Sxx entries of the Sinclair matrix 25. The two switch states of switch 14 are associated with the following two operational situations. When the switch 14 is positioned to cause the antenna 4 to transmit in co-polarisation (O), the receiver part of the circuit measures target reflected radiation in both the co-polarisation (0) and the cross-polarisation (X). Upon changing the switch state to cause the antenna 4 to transmit in cross-polarisation (X), the receiver part of the circuit measures in both the crosspolarisation (X) and the co-polarisation (0). These two switch states collectively allow all four components of the Sinclair matrix to be measured, labelled Soo, Sox, Sxo, Sxx- These are the so-called S-parameters. In an alternative notation, which assumes horizonal (H) and vertical (V) linear polarisations are used as the co- and cross-polarisations, these S-parameters are labelled Shh, Shv, Svh, Sw. The co-polarisation data and cross-polarisation data are thus processed to populate a Sinclair matrix 25. It will be understood that for each frequency sweep a Sinclair matrix is obtained at each of a large number of frequencies, typically at least several hundred frequencies, across the frequency range (bandwidth) that is swept over. The frequency sweep may be continuous or quasi-continuous (stepped). One variant of the circuit might use digital sampling and down-conversion in the IF stage. Another variant of the circuit might use a phase-locked loop for greater stability in the measurements. Amplifiers may optionally be provided to boost the radar output signal and thereby obtain greater radar range but these are omitted from the schematic for clarity. Similarly, amplifiers may also be provided at suitable places in the receiver to reduce noise effects but are also omitted for clarity. The millimetre wave band is used for security screening of persons for concealed items, since clothing is relatively transparent in this spectral region whereas the body is opaque, the penetration distance into the skin being sub-millimetre. At 20 GHz, almost all clothing is 100 % transparent. At 94 GHz, many clothing types are only semi-transparent as they begin to absorb more radiation and scatter radiation out of a beam. At frequencies much greater than this, typical clothing materials start to become opaque, so these are not suitable for security screening for weapons or other objects concealed by clothing. Typically, the frequency range of interest for security screening of persons through normal clothing is thus perhaps 10 GHz to 100 GHz with frequencies up to 200 GHz sometimes being used. Typically microwave or millimetre wave radars can have a sweep band of up to 40% of the radio frequency, if a well-designed waveguide horn antenna is used. The radar used for the measurements presented in this document was scanned with a sweep band from 18 GHz to 26.5 GHz which is a 39% bandwidth. The experimental data on which the examples presented herein are based were collected using a VNA that took around 340 ms to complete one frequency sweep. In a commercial screening system, the VNA would be replaced with a custom millimetre wave radar chip and, with current technology, the frequency sweep time would be reduced to about 1 ms. The experimental data analysed in this document were acquired at a 2 metre range from the antenna to the target person unless otherwise stated. The antenna gain used in these measurements was 25 dBi and the intermediate frequency bandwidth of the VNA was set at 100 kHz. One hundred frequency sweeps were made of each nominally motionless target person. The frequency sweeping radar of Figure 4 outputs a measurement data set in the frequency domain for a given target which comprises a large number of frequency sweeps, typically several hundred. For each frequency sweep across the bandwidth, a Sinclair matrix is obtained, each Sinclair matrix having 4 complex values; the so-called S-parameters. In the stepped frequency (VNA-based) radar used to collect the data presented herein, an 8.5 GHz frequency sweep (between 18 and 26.5 GHz) with a 5 MHz bandwidth collects 8.5 / 0.005 = 1,700 Sinclair matrices, one for each radio frequency, in a time window of 340 ms. Repeating this over an eleven second measurement period will result in approximately 11.0 / 0.34 ~ 32 frequency sweeps being performed, thereby collecting a total of 32 x 1,700 = 54,400 Sinclair matrices, amounting to 217,600 S-parameter values. Radar propagation times and signal integration times are now briefly mentioned. For security screening of people, the time scales associated with radiation propagation times over the target are typically from 0.1 ns to several nanoseconds. These are realisable with radar radiation bandwidths of a few GHz. The signal integration time is the time taken for the radar to sweep the target once and record the reflections, using either a pulsed (time domain) radar or a frequency swept (frequency domain) radar. The signal integration time is typically between 1 ms and 100 ms with today’s radar technology in the millimetre frequency band. The range resolution of the radar, Ar, is the smallest resolvable distance in the range direction between two scattering centres as the wave propagates from antenna to target and back, this being Ar = c / (2BRF), (2) where c is the speed of light. For example, a bandwidth of 10 GHz provides a range resolution of 15 mm. The unambiguous range of the radar is its maximum useable range, Ru, and is half the inverse of the radar frequency resolution (Af) multiplied by the speed of light. For a stepped frequency radar this is Ru = c / W). (3) For example, a frequency resolution of 5 MHz gives a maximum range of 30 metres and a range of 100 m would require a frequency resolution of 1.5 MHz. Radar returns from beyond the unambiguous range will be aliased and appear as originating from objects at ranges closer than this maximum range. If in the operational environment there are measurable reflections from beyond the unambiguous range, they should be reduced below the measurable level by the use of absorbers and / or reflectors. Various deployment scenarios can be envisaged for a polarimetric radar. The radar could be used like a hand-held proximity metal detector (at a range of 1-10 cm from the body surface), like a walk-through metal detector (at a range of 20-50 cm), for passageway or street surveillance (at a range of 2-10 m), or for long-range checkpoint screening (at a range of 100 metres mounted on a gimbal controlled by man or machine). Application scenarios include by way of example a sporting venue, shopping mall, public square, building entrance or building lobby area. The radar data collection could be coupled with simultaneous collection of other data, such as video image data of the target persons. Preparation of radar data sets for machine learning Figure 5 is a flow diagram of the signal processing pipeline used to train a machine and identify items of interest from the measurement data set. In Step S1, the measurement data set of a distributed target is inputted, i.e., all the S-parameter values of the Sinclair matrices captured by the frequency domain radar of Figure 4, collected over a period of one or two seconds, or less if a person is moving quickly. This means perhaps between 10 or 30 frequency sweeps are included, which may contain several tens of thousands of Sinclair matrices, to create a set of coherency matrices in the timedomain and a set of coherency matrices in the frequency domain. In Step S2, an inverse discrete Fourier transform (DFT1) is carried out on the data set to convert the data set from the frequency domain to the time domain. It will be understood that the inverse discrete Fourier transform will most likely be an inverse fast Fourier transform (FFT-1). In Step S3, a filtering operation on the time domain representation of the data set is carried out to remove radar signal that cannot be from the target, e.g., because the signal has arrived too late or too early. This step is one of range gating to remove clutter. Range gating in the time-domain removes clutter due to reflections from foreground and background objects. Targets at particular ranges can be selected and their data retained, whereas reflections from clutter at different ranges can be removed. This allows for rejection of reflections from objects or other people, in front of, and behind the subject being screened. The range gated signal then comprises the human body of the person being screened, any threats on their person, and any reflectors in the radar antenna beam at the same range as the subject. Range gating may be assisted through use of independently obtained measurement data. For example, the overall system may include a LiDAR imager which identifies and tracks the person being sampled by the radar beam, so the target-to-antenna distance is known, from which the time-of-flight can be determined. Range gating is used in the analysis of the measurement data examples presented in this document. Specifically, the gate window has a range of about 1 metre centred on the target person, so that the gate window extends from half a metre in front of the subject and half a metre behind the subject. In the experiments we conducted, the magnitude of the background clutter signal is several times that of the target signal, so range gating was important. In Step S4, a discrete Fourier transform (DFT) is carried out on the measurement data set -now range gated - to convert the measurement data set back into the frequency domain. It will be understood that the discrete Fourier transform will most likely be a fast Fourier transform (FFT). The range gating clutter rejection process is very noticeable in the frequency domain, as this spectrum now only contains components associated with the target. In Step S5, the S-parameters are calibrated. Calibration of the S-parameters is necessary to ensure reliability in the subsequent generation of the coherency matrix, whether that be in the time domain (Step S8) or the frequency domain (Step S11). Calibration involves a so-called external calibration by measuring metal targets of known polarimetric response, one which generates a purely co-polarimetric response (a perfectly flat plane surface or sphere) and a second which generates a purely cross-polarimetric response (a 90-degree dihedral orientated at 45 degrees to the horizontal). As this calibration uses no active sources it is referred to as a passive source radar calibration. These calibration sources belong to the class of pure targets, as repeated measurements of their S-parameters result in identical values. The external calibration calibrates both amplitude and phase of the radar antenna, orthomode transducer (if one is used), transmitter and receiver. It corrects for the dispersion in the antenna, the interconnecting cables and the orthomode transducer. It also corrects for polarisation conversion in the system (i.e. conversion from co-polarisation into crosspolarisation and vice versa). The calibration effectively zeros the phase at all measured frequencies to a single reference point in front of the antenna. Where possible, another more limited form of calibration is also made prior to external calibration, which is referred to as an internal calibration. This is possible when a VNA is used to obtain the measurement data. The internal calibration is done by measuring the S-parameters with short circuits, open circuits and matched loads and a through connection between cables (or waveguides) connected to the two VNA ports. Both amplitude and phase are calibrated and the system is then calibrated to the ends of the VNA cables (or waveguides). Calibration of the orthomode transducer and antenna of a polarimetric radar is not included in the internal calibration and as such the system is uncalibrated for measurements of targets in front of the antenna. A good external calibration can be demonstrated by measuring the S-parameters of a plane reflector which fills the radar antenna pattern and which is at normal incidence to the radar beam. A perfectly flat plane reflector should generate identical co-polarisation returns (Shh = Sw) and zero cross polarisation returns (Shv = Svh = 0). Making an inverse Fourier transform of the S-parameters into the time-domain, generates the impulse responses of the plane reflector, having a temporal width of the inverse of the radar radiation bandwidth (=1 / 8.5 GHz = 0.12 ns). Figure 6 shows graphs of the impulse responses of the plane reflector before applying an external calibration correction but after applying an internal calibration correction (upper graph) and after applying an external calibration correction (lower graph). The plot is of response time, t, against impulse response amplitude, A. There are four curves in each graph for each of the four S-parameters Shh, Shv, Svh, Sw. Each amplitude curve is in fact an average over many Sinclair matrices to improve the quality of these graphical representations. The lack of correct calibration in the S-parameters before external calibration is evident in that, in the upper graph, the two co-polarisation S-parameters Shh (solid line) and Sw (dotted line) peak at different times in the response. This is corrected for by the external calibration as is shown in the lower graph, where the curves for Shh (solid line) and Sw (dotted line) are almost perfectly superposed with the dotted line only being partially visible as a consequence of their near exact overlap. The co-polarised S-parameter measurement data after external calibration correction have a rise-time of 0.118 ns and a full width half maximum of 0.15 ns, which are faster and narrower than before the external calibration correction. Without the external calibration correction, the time difference between the two co-polarisation S-parameters represents a large phase error in the frequency domain which would significantly corrupt the values calculated for the elements of a coherency matrix. It is further noted that the narrowing of the co-polarisation S-parameter responses is an evident result of applying the external calibration correction, particularly in the wings of the responses; it is a result of the removal of dispersion in the OMT and the antenna, showing that this is a deconvolution that removes the response function of the measurement device. Namely, the response in the time-domain as generated by an inverse DFT of the measured frequency-domain data is a convolution of the effective transmitted pulse, the impulse response of the target and the impulse response of the radar receiver. The calibration correction procedure in the frequency-domain shifts the frequency component phases to effectively deconvolve the measurements from the instrument impulse response and removes the latter. In other words, the calibration synthesizes a bandwidthlimited pulse in the time-domain. If the measurement data were perfect, then the cross-polarisation components Shv (dashed line) and Svh (dash-dotted line) would be zero. In fact, they are not zero but nevertheless around two orders of magnitude lower in peak amplitude compared to the co-polarisation components. This is the case in both the internally calibrated data (upper graph) and the externally calibrated data (lower graph) - see inset maximum values. More specifically, the cross-polarisation response before external calibration is around 1% of the co-polarisation response. After the external calibration, this reduces to about 0.7% (0.0049 % in power, or -43 dB) showing that the external calibration is also improving signal integrity in respect of compensating for polarisation conversion in the transmitter and receiver of the radar. The nonzero response in cross-polarisation is probably attributable to small (fractions of a millimetre) deviations from flatness of the plane reflector and / or residual polarisation mode conversion in the OMT and antenna that cannot be removed by the external calibration. In Step S6, an inverse discrete Fourier transform (DFT-1) is carried out on the calibrated data set to convert it from the frequency domain to the time domain. In Step S7, the measured S-parameters are de-jittered to compensate for target range movements. This is referred to as range de-jittering. It is beneficial to perform range de-jittering in the time-domain response as a pre-processing step before generating time-domain coherency matrices, since the time-domain coherency matrix is sensitive to target range variations, so these should be removed. A number of different methods were investigated to perform the range de-jittering. Of the investigated methods, the method which generated the shortest averaged magnitude of the time-domain S-parameters was selected. This method is one using cross-correlations of the magnitudes of the S-parameters and is referred to as the cumulative cross-correlation de-jitter method. Figure 7 is a flow diagram illustrating the cumulative cross-correlation de-jitter method operating on a group of Ng time-domain S-parameters sweeps. In the processing, the S-parameters are stored in a 4-dimensional array, the first dimension being time (t), which is effectively range over the target, the second being sweep index (i) and the third and fourth dimensions (j,k) being the row and column indices of the 2-dimensional S-parameter matrix. In this de-jitter method, the summations of the magnitudes of the first two successive sweeps of the time-domain S-parameters in a group are cross-correlated. This is done by creating the first version of the cumulative function C from the time domain S-parameters of the first sweep, then cross-correlating this with the summations of the second sweep S-parameters, to create the first version of function D, as shown in the flow chart of Figure 7, where * is the crosscorrelation function. This enables determination of the time delay in the S-parameters of the second sweep that maximises the cross-correlation. This determined time delay is then used to time-shift all S-parameters of the second sweep, thereby de-jittering the second sweep S-parameters. An average of all of the magnitudes of the S-parameters in both sweeps are then made to generate a new version of the cumulative function C. This has the effect of averaging the speckle effects over the first and second sweeps, thereby creating a more precise representation of the S-parameter magnitudes. Then, moving on to the third sweep in the group, the newly generated cumulative function is cross-correlated with the S-parameters from this group, to create a new version of function D. The time delay in the third S-parameter sweep which maximises D is determined and then the third S-parameter sweep is time-shifted by this amount, thereby de-jittering the third sweep S-parameters. This process continues through the remaining S-parameter sweeps in the group, so all sweeps of the group become de-jittered. A variant of the above technique also works to some degree, whereby summations in Figure 7 are made of only the co-polarisation S-parameters (i.e. Shh and Sw) or only the crosspolarisation terms (Shv and Svh). However, the approach of making summations of all of the S-parameters in the Sinclair Matrix seems to produce consistently the better results. Another range de-jittering method which is also suitable is time-domain shifting to make the maxima or the moments (i.e. centres of gravities) of the S-parameters coincidental. However, a triangular profile in the magnitudes of the S-parameters results from using the maxima, which has a width wider than that from the cumulative cross-correlation method, which is not ideal. According to our results, the maxima method provides lower classification accuracies than the cumulative cross-correlation method, which may be because in the maxima method the speckle variations cause the maxima to shift back and forth in time, but the bulk of the time domain response does not always follow this. For this reason, it might then be expected that the centre of gravity method would be better, as it uses all of the samples in the time-domain response, not just the peak maximum value. However, according to our results, the centre of gravity shift method also provides lower classification accuracies than the cumulative crosscorrelation method. In Step S8 of Figure 5, the de-jittered Sinclair matrices of a single group are processed into a time-domain coherency matrix using Eq. (4): C3P =< f3P®f\P >(4) where ® is the vector outer product, t is the Hermitian transpose operator, the angle brackets <>denote an average and 1 (51 f^p = (^=) [Soo + $xx Soo — SXx 2SOX]T is the Pauli-based feature vector created from the Sinclair matrix components and Tis the transpose operator. For each time point of a sweep, the column-vector row-vector outer product of the equation creates a single 3x3 Hermitian matrix. This is repeated for each time point of a sweep and for each of the sweeps in the group. The resulting matrices are averaged over all the sweeps in a group, but not over the time dimension of each sweep. What results is the time-domain coherency matrix, a sequence of 3 x 3 Hermitian matrices separated in time by the radar time resolution of 1 / Brf generated from a group of Sinclair matrices acquired over a one or two second measurement period. This process captures all of the polarimetric information relating to the time response of a target, enabling the machine learning to distinguish parts of the body and threats on the body as a function of range. As an alternative to using the coherency matrix, the covariance matrix, Csl could be used, this being generated from elements of the Sinclair matrix by, C3L =< flL®^ >(6) where, f^L — [Soo Syx]T (^) is the lexicographic feature vector. The covariance matrix is directly related to the properties of the polarisations, whereas the coherency matrix is more closely related to the physical properties of the target. As a further alternative to the coherency matrix or the covariance matrix, the Kennaugh matrix could be used. All of these matrices contain essentially the same information and shown similar results when processed through the machine learning. Conversion from one of these matrices to any of the others is via unitary matrix transformation. In Step S9, the sequence of time-domain coherency matrices is converted into a data set for machine learning. The input data at this step is a sequence of coherency matrices separated in time by 1 / Brf, spanning about three nanoseconds, so essentially 3-D data. In the preparation of this data for machine learning it must be recognised that the coherency matrix is Hermitian. This means the on-diagonal components of the matrix are purely real quantities, and the upper off-diagonal components are complex conjugates of the lower off-diagonal components. As no redundant information should be passed to machine learning, only the following coherency matrix components are used in machine learning: the three on-diagonal quantities C3P(1,1), C3P(2,2), C3P(3,3); and the six off-diagonal components of Re C3P(1,2), Im C3P(1,2), Re C3P(1,3), Im C3P(1,3), Re C3P(2,3), Im C3P(2,3), where Re and Im refer to the real and imaginary parts. A total of nine values are taken from the coherency matrix and then flattened to form one dimension of a 2-D array, the other dimension being that of time. Considered as an image, the time may be taken as the x-dimension and the components of the coherency matrix as the y-dimension. Before describing the machine learning processing of the coherency matrices, we first describe the generation of the frequency-domain coherency matrices. This strand in the processing pipeline is indicated in Figure 5 with dashed arrows. Step S10 is a subsampling step in the frequency-domain strand of the process flow. Subsampling, sometimes referred to as decimating, is performed on a frequency-domain representation of the measurement data set after the range gating in the time-domain (Step S3) and subsequent Fourier transformation of the range-gated measurement data into the frequency domain (Step S4). The range gating of Step S3 shortens the time domain data to a length At, which has the effect of reducing the effective frequency resolution from the finer resolution necessary to avoid aliasing from reflections from beyond the unambiguous range to a much coarser resolution of ~1 / At. Subsampling is beneficial in the context of the subsequent machine learning applied to frequency-domain coherency or equivalent matrices, since the subsampling removes redundancy in the data. As is generally known in machine learning, input data should be devoid of redundancy, since redundancy in the input data damages the generalisation of the model and tends to reduce classification accuracy. Preferably, the subsampling at the frequency resolution ~1 / At is preceded by smoothing of the frequencydomain data, for example by using a Savitzky-Golay filter. Step S11 is similar to Step S7 but takes place in the frequency-domain. Starting with a single group of S-parameters in the frequency-domain, Eq.(4) is used to form the frequency-domain coherency matrix. The vector outer product of the equation generates a single 3x3 Hermitian matrix for each Sinclair matrix. The angle brackets of the equation indicate an averaging of each of the components in the matrix over multiple sweeps, but not over the frequency dimension of each sweep. What results is the frequency-domain coherency matrix, a sequence of 3 x 3 Hermitian matrices, one for each of the measured radio frequencies, generated from the same group of sweeps that generated the time-domain coherency matrix. The process captures all of the polarimetric information associated with the frequency response of the target, enabling machine learning to distinguish low quality-factor resonances associated with the body, clothing and concealed objects. In generating the frequency-domain coherency matrix it is not necessary to perform a prior de-jitter of the S-parameters. This is because the complex conjugate multiplication of the S-parameters in Eq.(4), (indicated by the dagger), cancels the phase shift associated with the path between the antenna and the target. This means any time-shift in the time domain S-parameters has no effect, when Fourier transformed back to the frequency domain and used to generate the frequency-domain coherency matrix. Furthermore, removing the phase shift between the antenna and target, by the complex conjugate multiplication of Eq. (4), reduces speckle variations arising from changes in the range of the target from the antenna. Step S12, is similar to Step S9, but takes place in the frequency domain. It takes a sequence of frequency-domain coherency matrices, each at a different radio frequency (3-D data) and turns them into a 2-D data set for machine learning. As in the time-domain, since the coherency matrix is Hermitian, the components of the frequency-domain coherency matrix C3P(1,1), C3P(2,2), C3P(3,3), Re C3P(1,2), Im C3P(1,2), Re C3P(1,3), Im C3P(1,3), Re C3P(2,3), Im C3P(2,3) are flattened to form the y-dimension of a 2-D array, and the radio frequencies become the x-dimension. Step S13 of the process takes either the time-domain coherency matrix components, or the frequency-domain coherency matrix components, or both, (which have been generated from a single group of sweeps from one to a few seconds of data acquisition) and processes them through machine learning algorithms described in the next section. (In the experiments using the time-domain or frequency-domain separately they both generated high (>0.9) classification accuracies, and sometimes when using both of these together they generated higher accuracies than when they were used separately.) Before passing data into the machine learning algorithm, the data features are scaled. Scaling was applied by subtracting from each of the features the mean over all samples of that feature, then dividing by the standard deviation over all samples of that feature. In the case of the 1D-CNN it was found that slightly higher classification accuracies could be achieved by only dividing by the standard deviation and omitting the subtraction of the mean. Omitting the scaling did not affect the performance of the classical machine learning algorithms that were tested. On the other hand, for the neural network machine learning algorithms, the inclusion of scaling improved the performance. The output from Step S13 is either a trained machine or a target classification. In the case of a target classification, a single group of S-parameters from an unknown target is processed through the flow diagram of Figure 5 to create the coherency matrices. The coherency matrices form the X-vector of machine learning, having Nf elements, the dimension Nf being the product of the number of elements used from coherency matrix (i.e. 9) and the number of time or frequency samples. This represents a single machine learning sample of data. This is then input to the trained machine to generate a target classification based on the closest match to the training data. To train the machine initially, Ms training samples (each one from a group of Mg Sinclair matrices) are processed sequentially through the flow diagram of Figure 5, each creating a number of features, Nf. This forms the X-matrix of machine learning, having dimensions of Ms rows by Nf columns. Accompanying the X-matrix into the training is the y-vector of machine learning, which contains Ms target label elements, which represent the ground truth of the training data. In the training process, a set of weights and biases for the features of the training set are identified by numerical processes which minimise a cost function. For neural networks, training is computationally more intensive than that of classical machine learning. In neural networks there are generally more weights and biases, there being a set of these for each of the layers of neurons in the network. Weights and biases are determined by a series of iterations (referred to as epochs) of forward propagation of the training data (the X-matrix) through the network, followed by a back propagation of the cost function errors through the network to adjust the weights and biases to make a better match to the training data (the y-vector). Processing data from a time-domain radar It is also possible to use time domain radar to collect the measurement data set. Time-domain radar generates the impulse responses directly, representing the co- and cross-polarisation responses from the target, to provide the S-parameters in the time-domain. If time domain radar is used for data acquisition, range gating can be performed directly on the input data. The subsequent process flow is the same as for frequency domain radar. This is shown schematically in Figure 5 with the dot-dashed alternative input path labelled Step ST. Experimental measurements in support of machine learning To assess the capability of our full polarimetric radar and its signal processing, six classes of target were selected for measurement on two subject persons; one male and one female. Five classes were threat objects placed against the skin on the front of the body, in the centre of the torso, covered by clothing of differing thicknesses. The sixth class was a divested subject (no threat or other items on the body, only clothing) thus serving as a control and simultaneously a test for false positives. The five representative threat classes were: kitchen knife (metal and ceramic, blade lengths 16-18 cm), diecast toy gun (pistol 17 cm long, revolver 20 cm long), surrogate nitrogen-based explosive sample (circular beeswax, diameter 18 cm x 1 cm thick and square 18 cm side length x 1 cm thick), surrogate pipe bomb (metal coated ceramic 15 cm x 10 cm x 10 cm) and a surrogate shrapnel weapon (metal tacks in candle wax, 33 cm x 13 cm x 2 cm thick). The clothing thicknesses varied from no clothing, through a vest and shirt, to vest, shirt and jumper (or fleece) covered by a leather coat. A polarimetric antenna having a gain of 25 dBi was set up to measure subjects at a range of two metres using a VNA. The VNA swept between 18 GHz and 26.5 GHz, with a 5 MHz step in frequency. The time between each frequency sweep of the four S-parameter measurements (of a single Sinclair matrix) was approximately 340 ms, with the time for a frequency sweep of a single S-parameter being in the region of 85 ms, using a 100 kHz intermediate frequency bandwidth. In the measurements of each target person, approximately 100 consecutive sweeps were recorded, which were then put into groups of ten sweeps to make up a total of 820 separate measurements for the six classes of item. The classes, and the number of samples of each class, are shown in the table below. In the language of machine learning, having differing numbers of samples in each class is referred to as class imbalance. Ideally, each target class would contain the same number of samples, but practicalities mean there is usually some class imbalance, as is the case here with our experimental data set. Class Number of samples of class Figure Divested 220 7A Pipe bomb 60 7B Explosive 170 7C Diecast gun 120 7D Kitchen knife 180 7E Shrapnel Weapon 70 7F Table 1 Figures 8A to 8F show in a graphical form the 9 time-domain averaged coherency matrix 5 components for these six classes of security threat as function of time, each row in the figure thus representing the input array for the machine learning as obtained at Step S9 of Figure 5. The averaging is for each class over all 820 samples. The y-axis association of the 9 independent components is as follows: Feature Number Parameter 0 C3P(1,1) 1 C3P(2,2) 2 C3P(3,3) 3 Re C3P(1,2) 4 Im C3P(1,2) 5 Re C3P(1,3) 6 Im C3P(1,3) 7 Re C3P(2,3) 8 Im C3P(2,3) Table 2 10 It can be seen that the averaged representations of the data for the different threat classes in Figures 8A to 8F have different overall patterns in their respective graphs, which at least makes it plausible that machine learning should or might be able to succeed in identifying the class. Closer examination of the time-domain representations indicates the signatures of subjects 15 carrying the various weapons and surrogate weapons reveals that the length of the impulse response is rarely greater than 3 ns. The number of features, Nf, is the product of nine (the number of independent components in the coherency matrix) and 32 (the number of timehistory values), which is 288. Figures 9A to 9F show in a graphical form the 9 frequency-domain averaged coherency matrix components in a corresponding format to Figures 8A to 8F thus representing the input array for the machine learning as obtained at Step S12 of Figure 5. The averaging is for each class over all 820 samples. The frequency axis spans 18.0 GHz to 26.5 GHz and is divided into pixel bins that are 330 MHz wide, as no frequency structure on a scale finer than this was observed. This is commensurate with the fact that the impulse response is rarely longer than the reciprocal of this value, which is 3 ns. This was considered sufficiently fine to resolve the low quality-factor resonance effects observed in the surrogate explosive material and that caused by the clothing against the human body. The y-axis association is the same but of course the x-axis shows frequency instead of time. Like for the time-domain representations in Figures 8A to 8F, the representation of the averaged data for the different threat classes in Figures 9A to 9F show different overall patterns, even though to a human interpreter the variations in the averaged frequency domain data probably look more like random noise than anything systematic. Machine learning The machine learning algorithms are now discussed. In the overall process flow of Figure 5, the machine learning algorithm is shown as Step S13. Two kinds of machine learning for threat recognition were tested against the experimental data: classical machine learning techniques and neural networks. Classical machine learning algorithms work only on linear relationships between measured variables and work well using hundreds to thousands of samples of data. On the other hand, neural networks with hidden layers of neurons have the ability to identify nonlinear relationships between variables, a capability referred to as an arbitrary function approximation. For many problems, this enables neural networks to surpass the performance of classical machine learning algorithms. However, to do this, they generally require many more samples of data to learn from, typically from the thousands to millions of samples. The classical machine learning algorithms that were tested with the experimental data were: adaboost, bagging, decision-tree, extra-trees, support vector machines (SVM) (of various types), Gaussian naive Bayes, k-nearest neighbours, linear discriminant analysis, logistic regression (with L1 and L2 regularisation), perceptron, quadratic discriminant analysis and random forest. Two of the neural network algorithms that were tested with the experimental data are now described. Figure 10 shows a schematic of a two hidden layer FFN for processing the coherency matrix, which is a fully filled (linear or dense) neural network. A rectified linear unit (ReLU) activation function was used as the nonlinear element on the output of each of the hidden neurons. Figure 11 shows a schematic of a single convolutional layer, ReLU activation function, single dense layer CNN, which may be one-dimensional or two-dimensional. It was noted that pooling on the ReLU outputs used in the CNNs tested at the time of writing did not make a significant difference to the classification accuracies, so it is not included in Figure 11. Pooling is a technique that is used to reduce memory size requirements, reduce the number of layers of neurons and thereby reduce overfitting. Since memory limitation and overfitting did not appear to be a problem during the testing, presumably because of the modest array sizes being processed here, pooling was omitted. However, pooling could be included in future tests to evaluate whether it provides higher classification accuracies. The neural network testing of each of these two types of neural network included exploring the effect of varying the number of hidden layers of neurons between one and three to establish what effect this had on accuracy. Overfitting is one of the main problems with machine learning. This happens when the number of samples of data are insufficient to generalise the data to the model, resulting in poor cross-validation classification accuracy. Overfitting is evident when the cross-validation cost function losses are significantly larger than the training losses. The solution is to either reduce the number of features of the model or learnable parameters in a neural network and / or increase the number of samples to train on. Generally, the number of learnable parameters in a neural network is related to the number of neurons in each layer and the number of layers. This number is usually larger than the number of features in classical machine learning algorithms, which is why neural networks require much larger data sets to function well in comparison to classical machine learning algorithms. The approach to be followed taking account of this general understanding is that the number of variables (or neurons) should be kept to a minimum and there should be a minimum correlation between different variables so that they are truly independent of each other. This is why coherency matrices (or equivalent, such as covariance or Kennaugh matrices) generated from full polarimetric radar data of a distributed target are an ideal choice for input, since they combine extraction of the maximum amount of information from the target and condensing this information into the minimum number of independent variables. This point is now described in more detail. The rank of the coherency matrix was found in all cases to be three. This indicates the 3 x 3 coherency matrix has full rank. This means the number of linearly independent rows and columns is three, showing there is no degeneracy in these elements of the matrix. This is important, as it means none of the elements of the matrix will be correlated, which in the language of machine learning shows there will be no collinearity of variables. Collinearity in machine learning needs to be avoided, as it leads to overfitting and compromises the classification accuracy. In this sense, the coherency matrix is ideally suited to machine learning. In the language of supervised machine learning, Xis the data matrix, having Ms rows and Nf columns and y is the label vector having m elements. Here Ms is the number of samples, which in the experiments conducted was 820 and Nf is the number of features. Working in the time-domain, the number of features is the time history of the nine time-domain coherency matrix components. Working in the frequency-domain, the number of features is the spectrum of the nine frequency-domain coherency matrix components. In the classical machine learning algorithms and the fully filled neural networks, the pixels from a single time or frequency-domain coherency matrix are flattened to make a column of the X-matrix. With the experimental data used here, there are 820 of these, one for each sample. Together with the y-vector which defines the sample label (i.e. the class of the threat), they are split to perform a training and cross-validation data set. For the cases of the one-dimensional and two-dimensional convolutional neural networks, the images are processed in the usual way for convolutional neural networks. This involves convolution of the image with kernels followed by array flattening, a fully filled neural network and a softmax activation function to select the class. The quality of the results of the machine learning testing were examined by cross-validation. Cross-validation is the method used to determine the accuracy of the classification. Although 820 samples might seem a large number, it is in reality quite a small number in the field of machine learning. For small numbers of samples, the accuracy is best determined using the largest number of samples as possible in the training data, and the smallest number in the cross-validation set. For this reason, the accuracy of the classical machine learning algorithms has been determined by the ‘leave-one-out cross-validation (LOOCV)’ method. In the case of the 820 samples, 820-1=819 samples are used in the training and one sample is used in the cross-validation. Each of these samples is then worked through in turn, making 820 iterations, to generate an average classification accuracy for the whole data set. For the neural network analysis, LOOCV was not used, as this would take too much time to process. Instead, the so-called k-fold cross validation was used. The 820 samples were split into k batches, each batch becoming the test sample and the remaining k-1 batches being the training set, with the accuracy formed by taking an average of the accuracy over all k batches. In the data presented here, a value of k=10 was selected. The results of the machine learning on the six classes are presented in the form of a normalised confusion matrix and the classification accuracy. The data set of 820 samples was analysed fully with four different types of machine learning one classical and three based on neural networks. The type of classical machine learning was extra-trees. The three types of neural network were: a fully filled (linear or dense) feed forward network (FFN), a one-dimensional convolutional neural network (1D-CNN) and a two-dimensional convolutional neural network (2D-CNN). Of the classical machine algorithms that were tested, the four most promising when applied to the time-domain coherency matrix (Step S8) were as follows with their accuracies quoted in parentheses. ExtraTrees (0.96), Poly Kernel SVM (0.91), Random Forest (0.93) and Logistic Regression using L2 regularisation (0.90). Figure 12 illustrates the normalised confusion matrix for the extra-trees classification working on the time-domain coherency matrix showing the individual classification accuracies for the different threat classes. The overall classification accuracy is 0.96. The results of the feed forward neural network (FFN) testing are now discussed. To find an optimum configuration for the FFN, the number of layers of neurons was varied between one and four. To avoid ambiguity about the neuron layer number in a network, the neuron is classed as a node in the network that has an activation function. (In some of the literature, the inputs are classed as a layer, but strictly speaking they are not.) This means in the language used in this document that a FFN with one layer of neurons has no hidden layer, and a FFN with two layers has one hidden layer of neurons, and so on. The number of neurons in each layer was varied between 5 and 100 to find the optimum number. In varying the number of layers of the FFN, the performance using two hidden layers was found to deliver marginally better classification accuracies than the other, with considerably better performance than that of the network with no hidden layers. The variation in the classification accuracy was not a strong function of the number of neurons in each layer, however, accuracies fell below 0.85 when the number of neurons dropped below ten. Other variables in the model tuned to optimise the accuracy were the learning rate and the weight decay. The learning rate is a step size in the learning process and the weight decay is a regularisation parameter. Figure 13 illustrates the normalised confusion matrix for one of the FFNs working on the timedomain coherency matrix. Specifically, these are the results for an FFN having two hidden layers of neurons, with 20 neurons in each, similar to that depicted in Figure 10. The overall classification accuracy is 0.93. One- and two-dimensional ON Ns were also tested on the experimental data. The structure of the CNN is one containing a number of convolutional layers, followed by a flattening of the array, then a number of dense, fully filled, feed forward layers of neurons. The 1D CNNs and 2D CNNs were investigated which had one and two convolutional layers and one and two fully filled layers, to determine which was optimal. However, the performance was not found to be a strong function of the numbers of these layers of neurons, so the minimum number was used, namely one convolutional layer and one dense layer, to minimise the possibilities of overfitting, as illustrated in Figure 11. In all configurations investigated, the performance was always less than that of the above FFN, with the 1-D CNN giving a slightly better classification accuracy of 0.87, than that of the 2-D CNN which gave a classification accuracy of 0.83, as illustrated in Figures 14 and 15 respectively. As just mentioned, the classification accuracies for six classes of target for classical machine learning and FFN has been found to be 0.96 and 0.93 respectively, with the values for the 1-D CNNs being 0.87 and the 2-D CNN being 0.83. The accuracies of the individual components of the coherency matrix are also large. These results are very encouraging, as these accuracy figures are far higher than the classification accuracy of a random selection of equally balance classes, which is 1 / 6 = 0.17. More precisely, considering the class imbalance of the number of samples, the random selection accuracy (RSA) given by yMc n2 (8) RS A = —classi 1 7 results in a value of 0.20, where N, are the number of samples in each class (given in Table 1), and Mc=Q is the number of classes. In summary of our testing, the two best performing machine learning approaches were the extra-trees classical machine learning algorithm and the FFN neural network algorithm. The accuracies achieved with both these algorithms are impressively high. The extra-trees classical machine learning algorithm performed marginally better than FFN neural network algorithm (0.96 vs 0.93 accuracy) but the difference is small. With larger data sets, it may be expected that neural networks will outperform classical machine learning, because neural networks are capable of arbitrary function approximation, while classical machine learning can only model linear functions. The above discussion of the testing with different machine learning algorithms relates to timedomain coherency matrix input (Steps S7 to S9). Further testing of machine learning algorithms was also done with frequency-domain coherency matrix input (Steps S10 to S12). The results were still good, but the classification accuracy is six percent less than for the time-domain coherency matrices. Still further testing was done in which the machine learning algorithm received as input both time-domain coherency matrix data (from Steps S7 to S9) and frequency-domain coherency matrix data (from Steps S10 to S12). The results were slightly more accurate compared to when only time-domain coherency matrices were used as input. The relative merits of time-domain versus frequency-domain coherency matrices generated from full polarimetric radar measurements as input to a machine learning algorithm are now discussed further. The coherency matrix in the frequency-domain contains information directly linked to the frequency response of the threat. Phenomena such as internal resonances from multiple internal reflections in low-loss dielectrics such as nitrogen-based explosives and standing waves formed around metal objects such as guns and knives will generate these signatures. These resonances are more a result of their geometry, rather than resonances arising from molecular properties. Given that resonances are due to geometry, it does open the possibility of object identification, if the resonant response of a particular target is known. A further benefit of using the frequency-domain coherency matrix is that range de-jittering is not necessary, as the frequency-domain coherency matrix is invariant to target range variations. This may be beneficial in some applications where the target is moving rapidly in range and de-jittering is not possible. The coherency matrix in the time-domain contains a time-history of how the radiation is reflected from the human body and threat item. For example, a threat on the front of the body will be observed at the beginning of the time-history, and this can be ‘gated out’ from reflections which come later from the arms. Likewise, a threat further around the side of the body will be observed to scatter later in the time-history than one on the front of the body. For the time-domain coherency matrix approach to work well for a range moving target, the data needs to be range de-jittered. Overall, it would seem best to generate both time-domain coherency matrices and frequencydomain matrices from any given measurement data set, at least for the training phase of the machine learning algorithm. In some scenarios, it may be that there is synergy if both are analysed by the machine learning algorithm, either independently or jointly. In other scenarios, it may be established that one of the time-domain and frequency-domain is significantly more reliable than the other. Decisions on which is the best approach to use in a live system for any particular screening application can be made based on performance when training the machine learning engine. The decision may also depend on the item(s) being screened for or perhaps even the cohort of persons being screened (e.g. according to age distribution, average adiposity, sex, winter clothing vs. summer clothing). The training phase is also an opportunity to train on a plurality of different machine learning algorithms as we have done in our experiments here in order to select the highest performing of these during training for the live system. Finally, no performance difference is expected if instead of coherency matrices, covariance or Kennaugh matrices are used as the inputs to the machine learning, since as mentioned above they each contain the same information. This is also true of the infinity of other matrices that may be created by a unitary matrix transformation of the coherency matrix, and these matrices may be generated directly from a group Ng of sweeps of the S-parameters. In overall summary, the changes in S-parameters due to physical movement of a person (whether concealing a threat item or not) shows the subject to belong to the class of distributed radar targets. In such circumstances, the integration of the conjugate S-parameter products in the coherency matrix captures extra information about the target that a single S-parameter measurement does not. The extra data captured in the coherency matrix (a total of nine independent measurements) provides additional discriminatory information over and above that provided in a single Sinclair matrix measurement (which only contains five independent pieces of information, or only three pieces when operating an intensity-based radar). In addition, the Sinclair matrix components cannot be integrated to improve measurement signal-to-noise ratio because they are phase sensitive, whereas integrations are possible in the coherency matrix, due to the conjugate phase cancelling the phase variation between radar antenna and target. However, the magnitudes of the Sinclair matrix components can be integrated, butthen that discards the phase information from the target. As mentioned further above, the coherency matrix from a monostatic radar measurement is a 3x3 Hermitian matrix C3P, containing nine pieces of information within the three purely real quantities, namely: C3P(1,1), C3P(2,2), C3P(3,3) along the diagonal, and the six off-axis quantities, Re C3P(1,2), Im C3P(1,2), Re C3P(1,3), Im C3P(1,3), Re C3P(2,3), Im C3P(2,3), where Re and Im refer to the real and imaginary parts. Notably, our experiments with machine learning found that using the real and imaginary components of the coherency matrix gives higher classification accuracies compared to using the amplitude and phase representation of these quantities as the input to the machine learning algorithm. That may have something to do with the phase being a circular quantity, meaningful for human interpretation, but not optimum for a machine. More generally, our selection of this set of independent pieces of information collected from a distributed target with a full polarimetric radar as the input for a machine learning algorithm would appear to be an ideal combination between radar measurement data and machine learning. At the very least, the experimental results presented herein are significantly more accurate at identifying concealed threat items than anything in the published literature of millimetre wave band security screening that is familiar to the inventor at the time of writing. The relative usefulness of the individual components of the coherency matrix has been assessed by determining the classification accuracy using the extra-trees machine learning algorithm. This shows that the on-axis individual components of the matrix were found to have classification accuracies of: 0.6 (C3p(1,1)), 0.7 (C3p(2,2) and 0.78 (C3p(3,3) for the targets in Table 1. The classification accuracies of the separate real and imaginary parts of the off-axis components were all ~0.6. The fact that these classification accuracies are far greater than the 0.20 for random selection, demonstrates that every component of the matrix is bringing useful information to the machine learning. Together with the fact that the matrix has rank three, meaning there is no duplication of data, the coherency matrix is the ideal input for machine learning. Computing Resource Figure 16 is a block diagram of a tensor processing unit (TPU) which may be used for performing the computations involved in implementing the data processing method fortraining or in a live system. The TPU 100 has a systolic matrix multiplication unit (MMU) 102 which contains an array of 256 x 256 multiplier-and-accumulators (MACs) that can perform 8-bit multiply-and-adds on signed or unsigned integers. The weights for the MMU are supplied through a weight FIFO buffer 104 that in turn reads the weights from a memory 106, in the form of an off-chip 8 GB DRAM, via a suitable memory interface 108. A unified buffer (UB) 110 is provided to store the intermediate results. The MMU 102 is connected to receives inputs from the weight FIFO interface 104 and the UB 110 (via a systolic data setup unit 112) and outputs the 16-bit products of the MMU processing to an accumulator unit 114. An activation unit 116 performs nonlinear functions on the data held in the accumulator unit 114. After further processing by a normalizing unit 118 and a pooling unit 120, the intermediate results are sent to the UB 110 for resupply to the MMU 102 via the data setup unit 112. The pooling unit 120 may perform maximum pooling (i.e. maxpooling) or average pooling as desired. A programmable DMA controller 122 transfers data to or from the TPU's host computer and the UB 110. The TPU instructions are sent from the host computer to the controller 122 via a host interface 124 and an instruction buffer 126. It will be understood that the computing power used for running the machine learning algorithm, whether it be based on CPUs, GPUs or TPUs, may be hosted locally in a computer network, e.g. the one described below, or remotely in a data centre which constitutes a network node. Moreover, an artificial intelligence (Al) processing node may correspond to a single piece of physical processing equipment, e.g. as arranged in one or more racks of a server, or may itself be distributed over two or more pieces of physical processing equipment. Figure 17 is a block diagram illustrating an example computing apparatus 500 that may be used in connection with various embodiments described herein. For example, computing apparatus 500 may be used as part of the radar system and / or a computing node, for example a host computer from which machine learning processing is carried out in conjunction with a suitable GPU, or the TPU shown in Figure 16. Computing apparatus 500 can be a server or any conventional personal computer, or any other processor-enabled device that is capable of wired or wireless data communication. Other computing apparatus, systems and / or architectures may be also used, including devices that are not capable of wired or wireless data communication, as will be clear to those skilled in the art. Computing apparatus 500 preferably includes one or more processors, such as processor 510. The processor 510 may be for example a CPU, GPU, TPU or arrays or combinations thereof such as CPU and TPU combinations or CPU and GPU combinations. Additional processors may be provided, such as an auxiliary processor to manage input / output, an auxiliary processor to perform floating point mathematical operations (e.g. a TPU), a specialpurpose microprocessor having an architecture suitable for fast execution of signal processing algorithms (e.g., digital signal processor, image processor), a slave processor subordinate to the main processing system (e.g., back-end processor), an additional microprocessor or controller for dual or multiple processor systems, or a coprocessor. Such auxiliary processors may be discrete processors or may be integrated with the processor 510. Processor 510 is connected to a communication bus 505. Communication bus 505 may include a data channel for facilitating information transfer between storage and other peripheral components of computing apparatus 500. Communication bus 505 further may provide a set of signals used for communication with processor 510, including a data bus, address bus, and control bus (not shown). Communication bus 505 may comprise any standard or non-standard bus architecture such as, for example, bus architectures compliant with industry standard architecture (ISA), extended industry standard architecture (EISA), Micro Channel Architecture (MCA), peripheral component interconnect (PCI) local bus, or standards promulgated by the Institute of Electrical and Electronics Engineers (IEEE) including IEEE 488 general-purpose interface bus (GPIB), IEEE 696 / S-100, and the like. Computing apparatus 500 preferably includes a main memory 515 and may also include a secondary memory 520. Main memory 515 provides storage of instructions and data for programs executing on processor 510, such as one or more of the functions and / or modules discussed above. It should be understood that computer readable program instructions stored in the memory and executed by processor 510 may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, configuration data for integrated circuitry, or either source code or object code written in and / or compiled from any combination of one or more programming languages. Main memory 515 is typically semiconductor-based memory such as dynamic random-access memory (DRAM) and / or static random-access memory (SRAM). The computer readable program instructions may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). Secondary memory 520 may optionally include an internal memory 525 and / or a removable medium 530. Removable medium 530 is read from and / or written to in any well-known manner. Removable storage medium 530 is a non-transitory computer-readable medium having stored thereon computer-executable code (i.e., software) and / or data. The computer software or data stored on removable storage medium 530 is read into computing apparatus 500 for execution by processor 510. The secondary memory 520 may include other similar elements for allowing computer programs or other data or instructions to be loaded into computing apparatus 500. Such means may include, for example, an external storage medium 545 and a communication interface 540, which allows software and data to be transferred from external storage medium 545 to computing apparatus 500. As mentioned above, computing apparatus 500 may include a communication interface 540. Communication interface 540 allows software and data to be transferred between computing apparatus 500 and external devices (e.g. printers), networks, or other information sources. For example, computer software or executable code may be transferred to computing apparatus 500 from a network server via communication interface 540. Software and data transferred via communication interface 540 are generally in the form of electrical communication signals 555. These signals 555 may be provided to communication interface 540 via a communication channel 550. In an embodiment, communication channel 550 may be a wired or wireless network, or any variety of other communication links. Communication channel 550 carries signals 555 and can be implemented using a variety of wired or wireless communication links including wire or cable, fibre optics, conventional phone line, cellular phone link, wireless data communication link, radio frequency ("RF") link, or infrared link, just to name a few. Computer-executable code (i.e., computer programs or software) is stored in main memory 515 and / or the secondary memory 520. Computer programs can also be received via communication interface 540 and stored in main memory 515 and / or secondary memory 520. Such computer programs, when executed, enable computing apparatus 500 to perform the various functions of the disclosed embodiments as described elsewhere herein. In this document, the term "computer-readable medium" is used to refer to any non-transitory computer-readable storage media used to provide computer-executable code (e.g., software and computer programs) to computing apparatus 500. Examples of such media include main memory 515, secondary memory 520 (including internal memory 525, removable medium 530, and external storage medium 545), and any peripheral device communicatively coupled with communication interface 540 (including a network information server or other network device). These non-transitory computer-readable media are means for providing executable code, programming instructions, and software to computing apparatus 500. In an embodiment that is implemented using software, the software may be stored on a computer-readable medium and loaded into computing apparatus 500 by way of removable medium 530, I / O interface 535, or communication interface 540. In such an embodiment, the software is loaded into computing apparatus 500 in the form of electrical communication signals 555. The software, when executed by processor 510, preferably causes processor 510 to perform the features and functions described elsewhere herein. Various embodiments may also be implemented primarily in hardware using, for example, components such as application specific integrated circuits (ASICs), programmable logic arrays (PLA), or field programmable gate arrays (FPGAs). Implementation of a hardware state machine capable of performing the functions described herein will also be apparent to those skilled in the relevant art. Various embodiments may also be implemented using a combination of both hardware and software. In this document, the term "computer-readable medium" is used to refer to any non-transitory computer-readable storage media used to provide computer-executable code (e.g., software and computer programs) to computing apparatus 500. I / O interface 535 provides an interface between one or more components of computing apparatus 500 and one or more input and / or output devices. Computing apparatus 500 also includes optional wireless communication components that facilitate wireless communication over a voice network and / or a data network. The wireless communication components comprise a radio system 565, and a baseband system 560. In computing apparatus 500, radio frequency (RF) signals are transmitted and received over the air under the management of radio system 565. Radio system 565 may comprise one or more radios that are configured to communicate over various frequencies. In an embodiment, radio system 565 may combine a demodulator (not shown) and modulator (not shown) in one integrated circuit (IC). The demodulator and modulator can also be separate components. In the incoming path, the demodulator strips away the RF carrier signal leaving a baseband receive audio signal, which is sent from radio system 565 to baseband system 560. If the received signal contains audio information, then baseband system 560 decodes the signal and converts it to an analogue signal. Then the signal is amplified and sent to a speaker. Baseband system 560 also receives analogue audio signals from a microphone. These analogue audio signals are converted to digital signals and encoded by baseband system 560. Baseband system 560 also codes the digital signals for transmission and generates a baseband transmit audio signal that is routed to the modulator portion of radio system 565. The modulator mixes the baseband transmit audio signal with an RF carrier signal generating an RF transmit signal. Baseband system 560 is also communicatively coupled with processor 510, which may be a central processing unit (CPU). Processor 510 has access to data storage areas 515 and 520. Processor 510 is preferably configured to execute instructions (i.e., computer programs or software) that can be stored in main memory 515 or secondary memory 520. Computer programs can also be received from baseband processor 560 and stored in main memory 510 or in secondary memory 520 or executed upon receipt. Such computer programs, when executed, enable computing apparatus 500 to perform the various functions of the disclosed embodiments. For example, data storage areas 515 or 520 may include various software modules. The computing apparatus further comprises a display 575 directly attached to the communication bus 505 which may be provided instead of or addition to any display connected to the I / O interface 535 referred to above. Various embodiments may also be implemented primarily in hardware using, for example, components such as application specific integrated circuits (ASICs), programmable logic arrays (PLA), or field programmable gate arrays (FPGAs). Implementation of a hardware state machine capable of performing the functions described herein will also be apparent to those skilled in the relevant art. Various embodiments may also be implemented using a combination of both hardware and software. Furthermore, those of skill in the art will appreciate that the various illustrative logical blocks, modules, circuits, and method steps described in connection with the above-described figures and the embodiments disclosed herein can often be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. Skilled persons can implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the invention. In addition, the grouping of functions within a module, block, circuit, or step is for ease of description. Specific functions or steps can be moved from one module, block, or circuit to another without departing from the invention. Moreover, the various illustrative logical blocks, modules, functions, and methods described in connection with the embodiments disclosed herein can be implemented or performed with a general-purpose processor, a digital signal processor (DSP), an ASIC, FPGA, or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general-purpose processor can be a microprocessor, but in the alternative, the processor can be any processor, controller, microcontroller, or state machine. A processor can also be implemented as a combination of computing devices, for example, a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. Additionally, the steps of a method or algorithm described in connection with the embodiments disclosed herein can be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module can reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium including a network storage medium. An exemplary storage medium can be coupled to the processor such that the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium can be integral to the processor. The processor and the storage medium can also reside in an ASIC. A computer readable storage medium, as referred to herein, is not to be construed as being transitory signals perse, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fibre-optic cable), or electrical signals transmitted through a wire. The computer readable program instructions may be provided to a processor of a general-purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and / or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function / act specified in the flowchart and / or block diagram block or blocks. The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device, implement the functions / acts specified in the flowchart and / or block diagram block or blocks. Apparatus and methods embodying the invention are capable of being hosted in and delivered by a cloud-computing environment. Cloud computing is a model of service delivery for enabling convenient, on-demand network access to a shared pool of configurable computing resources (e.g., networks, network bandwidth, servers, processing, memory, storage, applications, virtual machines, and services) that can be rapidly provisioned and released with minimal management effort or interaction with a provider of the service. This cloud model may include at least five characteristics, at least three service models, and at least four deployment models. Apparatus and methods embodying the invention are capable of being hosted in and delivered by a cloud-computing environment. Cloud computing is a model of service delivery for enabling convenient, on-demand network access to a shared pool of configurable computing resources (e.g., networks, network bandwidth, servers, processing, memory, storage, applications, virtual machines, and services) that can be rapidly provisioned and released with minimal management effort or interaction with a provider of the service. It will be clear to one skilled in the art that many improvements and modifications can be made to the foregoing exemplary embodiments without departing from the scope of the present disclosure.

Claims

1. A data processing method for processing measurement data obtained from a distributed target using a full polarimetric monostatic radar to output an object classification, the method comprising:inputting a measurement data set in the time-domain or the frequency-domain comprising a set of Sinclair matrices collected over a data acquisition period from a distributed target using a full polarimetric monostatic radar, a Sinclair matrix being a 2 x 2 matrix comprising four parameter values, referred to as S-parameters (S1, S1’);providing a trained machine learning algorithm configured to output a results matrix containing probabilities of presence of each of a plurality of object classes in a distributed target that has been scanned by a full polarimetric monostatic radar, thereby representing an object classification (S13);generating a set of coherency matrices, or equivalent related by unitary matrix transformation, from the set of Sinclair matrices in either or both of a time-domain and a frequency-domain representation of the measurement dataset (S8, S11);generating a plurality of real values from each of the coherency or equivalent matrices (S9, S12); andrunning the machine learning algorithm by inputting said real values as input matrices and receiving a results matrix as output, the results matrix containing the object classification.

2. A data processing method for training a machine learning algorithm to process measurement data obtained from a distributed target using a full polarimetric monostatic radar to output an object classification, the method comprising:providing a plurality of measurement data sets from a plurality of distributed targets using a full polarimetric monostatic radar, each measurement data set being in the timedomain or the frequency-domain and comprising a set of Sinclair matrices collected over a data acquisition period, a Sinclair matrix being a 2 x 2 matrix comprising four parameter values, referred to as S-parameters (S1, ST);providing a machine learning algorithm having a cost function with a plurality of weights which require optimization, the machine learning algorithm being configured to output a results matrix containing probabilities of presence of each of a plurality of object classes in a distributed target that has been scanned by a full polarimetric monostatic radar, thereby representing an object classification (S13);providing a set of ground truth data indicating which object classes are present in which of the distributed targets;generating a set of coherency matrices, or equivalent related by unitary matrix transformation, from the set of Sinclair matrices in either or both of a time-domain and a frequency-domain representation of the measurement data set (S8, S11);generating a plurality of real values from each of the coherency or equivalent matrices (S9, S12);running the machine learning algorithm for each of the plurality of measurement data sets by inputting said real values as an input matrix and receiving the results matrix as output, each results matrix containing the object classification for the measurement data set it was obtained from (S13);making a comparison between each results matrix and the ground truth data associated with the distributed target from which the measurement data set was obtained;adjusting the weights of the cost function in the machine learning algorithm according to said comparison; anditeratively running of the machine learning algorithm, making a comparison and adjusting the weights, in order to optimize the weights in the sense of converging the object classification made by the results matrices to the objects known to be present from the ground truth data.

3. The method of claim 1 or 2,wherein said generating a plurality of real values is performed only ona time-domain representation of the measurement data set (S9), andthe machine learning algorithm is provided with said real values generated from the time-domain representation of the measurement data set.

4. The method of claim 1 or 2,wherein said generating a plurality of real values is performed only on a frequencydomain representation of the measurement data set (S12), andthe machine learning algorithm is provided with said real values generated from the frequency-domain representation of the measurement data set.

5. The method of claim 1 or 2,wherein said generating a plurality of real values is performed both on a time-domain representation of the measurement data set (S9) and a frequency-domain representation of the measurement data set (S12), andthe machine learning algorithm is provided with said real values generated from both the time-domain and frequency-domain representations of the measurement data set.

6. The method of claim 4 or 5, wherein the frequency-domain representation of the measurement data set is subjected to subsampling prior to being used for said generating of a set of coherency or equivalent matrices.

7. The method of claim 6, wherein the frequency-domain representation of the measurement data set is subjected to smoothing prior to said subsampling.

8. The method of any one of the preceding claims, further comprising:de-jittering the S-parameters in a time-domain representation of the measurement data set (S7);9. The method of any one of the preceding claims, further comprising:externally calibrating the S-parameters in a frequency-domain representation of the measurement data set (S5);10. The method of any one of the preceding claims, further comprising:range gating a time-domain representation of the measurement data set (S3).

11. The method of any one of the preceding claims, further comprising:providing numerical processing resource to enable at least one of a Fourier transform and an inverse Fourier transform to be applied to the measurement data set to convert the measurement data set between a time-domain representation and a frequency-domain representation as required (S2, S4, S6).

12. The method of any one of claims 1 to 11, wherein the machine learning algorithm is a neural network algorithm.

13. The method of any one of claims 1 to 11, wherein the machine learning algorithm is a classical machine learning algorithm.

14. A computer program product comprising a computer-readable storage medium having computer-readable program code embodied therewith, the computer-readable program code configured to implement the method of any one of the preceding claims.

15. A full polarimetric monostatic radar system, comprising:a monostatic antenna or antenna combination configured to direct a transmission radar beam onto a distributed target and in response collect a receiver radar beam;a measurement instrument configured to collect a measurement data set from the monostatic antenna; anda computer apparatus loaded with a computer program product according to claim 14 for processing the measurement data set to obtain an object classification for the distributed target.

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