A sensor and system and methods using the sensor

Abstract

A sensor comprising two or more resonators 702,704,706,708 is provided in an array. Each of the two or more resonators is associated with a base resonant frequency (e.g. microwave) and is physically arranged such that each resonator is spaced apart from each of the other resonator(s) by a physical distance 710,712, 714, 716, 718, 720 determined based on the base resonant frequency. Each resonator couples electromagnetically differently relative to each other resonator(s) based on characteristics and / or situation of different artefacts to which they are exposed causing exhibition of different types of resonance. A type of resonance exhibited (e.g. Fano resonance, EIT resonance, Lorentz resonance) and an associated phase value are usable in detecting an artifact to which the resonators are exposed. The sensor may be embedded in a vehicle such as a UAV and used to map underground obstacles in a trenching operation.

Description

CROSS-REFERENCE(S) TO RELATED APPLICATIONS This application claims priority from United Kingdom provisional patent applications numbered 2316462.7 and 2317499.8, filed on 27 October 2023 and 15 November 2023, respectively, both of which are incorporated by reference herein. FIELD The field of the invention relates to sensors, such as microwave sensors, and systems and methods using the sensors. BACKGROUND Underground conduits for the provisions of oil, gas, water, power and communication lines are commonly used. Trenches for the conduits are typically dug by heavy machinery such as bucket wheel trenchers and chain saw trenchers. Prior to commencing with the trenching, a comprehensive land survey is conducted to determine the ideal path for the trench. Once the survey has been completed and the ideal path determined, the trenches are dug and specialised equipment for laying pipes or cables in the trenches are utilized, after which the trenches are closed again. The incorporation of heavy machinery into trenching processes has substantially improved efficiency, but the process of trenching remains time-consuming and expensive. A major drawback in the process lies in the lack of prior underground surveying which results in an informational void about underground conditions. Trenching becomes extremely difficult in rugged and mountainous terrains where rocks that are buried underground evade detection through surface surveys. Such environments often present scenarios where these underground rocks unexpectedly obstruct the trencher's path requiring an abrupt halt to trenching operations and redefining the predetermined trajectory. This deviation in the path significantly increases the project costs and timeframes and disrupts the continuity of the path of trenching operation. Should the hidden rocks remain undetected, they can cause significant damage to the trencher’s blade thus further increasing costs and delaying the trenching operations. A number of techniques have been developed and deployed to locate and map underground utilities and manmade obstacles. The two primary mapping practices are active and passive systems. Active systems are those that have some physical contact with the utility, while passive systems are those that attempt to map without any physical connection or even prior knowledge of their existence. Active systems are problematic for various reasons, such as the difficulty and cost of physically accessing the utility and sensing non-conductive utilities. Passive systems currently in use often employ Ground Penetrating Radar (GPR). GPR surveys are conducted from the surface, and the location and relative depth to potential utilities are determined by analysing reflected energy. Imaging techniques are also used to detect subsurface obstacles. There is, however, room for improvement. The preceding discussion of the background of the invention is intended only to facilitate an understanding of the present invention. It should be appreciated that the discussion is not an acknowledgement or admission that any of the material referred to was part of the common general knowledge in the art as of the application's priority date. SUMMARY In accordance with an aspect of the invention there is provided a sensor comprising two or more resonators, each of the two or more resonators being associated with a base resonant frequency and being physically arranged such that each resonator is spaced apart from each of the other resonator(s) by a physical distance determined based on the base resonant frequency, wherein each resonator couples electromagnetically differently relative to each other resonator(s) based on characteristics and / or situation of different artefacts to which they are exposed causing exhibition of different types of resonance, and wherein a type of resonance exhibited and an associated phase value are usable in detecting an artifact to which the resonators are exposed. The sensor may include four resonators. The resonators may be arranged in an array. The array may be a two-by-two array. The base resonant frequency may be a resonant frequency of the resonator in air. The physical distance may be determined based on a wavelength determined from the base resonant frequency. The physical distance may be greater than or equal the wavelength over four. The sensor may output phase values. A change in phase value may indicate a change in situation of an artefact relative to each of the resonators. A change in phase value may indicate a change in characteristic of the artefact. The characteristic may be a permittivity of the artefact. The different types of resonance may include: Fano resonance; EIT resonance; and, Lorentz resonance. The sensor may include a front-end including an input. The input may be coupled to each of one or more of the resonators via respective switches configured for selectively coupling and decoupling each of the one or more resonators from the receiver. In accordance with a further aspect of the invention there is provided a sensor including two or more resonators, wherein a change in permittivity of different test samples influences a A / 4 size or distance of or between the two or more resonators, thereby changing phase trends of the sensors’ filters. A signature resonance type obtained by the sensor may be influenced by the effect of the sample under test. The sensor may obtain three types of resonances under the effect of the sample under test with different locations of the samples exhibiting different resonances instantaneously with no additional physical change required in sensor architecture. The signature response may include a slope of one or more of: EIT, Lorentz, and Fano resonators. The slopes may be compared and a change in nature of the phase trend of the resonators may be used to determine the presence of different obstacles / hurdles in surface and sub-surface terrain. Different resonances may be used for far-field sensing in such a way that minor exposure to the sample under test will produce an abrupt change from one signature resonance type to another. The sensor may be used to map the terrain surface and sub-surface profiles and determine an optimised path for trenching by incorporating permittivity fraction balancing. In this manner, the resonance type is changed under or due to the effect of the material under test. In accordance with another aspect of the invention there is provided a terrain mapping and path planning system for trenching operations, the system comprising: at least one Unmanned Aerial Vehicle (UAV) including sensors capable of mapping surface and sub-surface profiles of terrain and a processor capable of processing sensed information received from the sensors; and at least one trencher; wherein the UAV is configured to fly over terrain through which the trencher is to dig a trench, survey the terrain and locate any trenching obstacles, wherein the UAV’s processor is configured to determine an optimal trenching route for the trencher and to communicate information on the optimal trenching route to the trencher. Further features provide for the UAV to include a microwave-based obstacle-detecting sensor; for the UAV to include sensors making use of phase sensing for surveying sub-surface terrain. Phase sensing is preferred over magnitude sensing since it offers resistance to losses and generates a steady curve. With varying levels of losses, the phase curve remains stable; however, this does not happen with the magnitude curve. Further features provide for the UAV to include temperature and humidity sensors to enable the UAV to detect weather conditions and for the processor to utilize this information to contribute to work routine planning for the trencher; for the UAV to further include one more of: an ultrasonic sensor, an optical sensor, a GPS module, and a camera module. Still further features provide for the trencher to be capable of operating autonomously; for the trencher to include sensors and a processor in communication with the sensors to detect and avoid any trenching obstacles that may have been missed by the UAV; for a digital signal processor (DSP) module to be configured to control the trencher’s movement and display any sensor data on a panel for real-time monitoring; and for the DSP module to be capable of wirelessly transmitting date to web and mobile applications. BRIEF DESCRIPTION OF THE DRAWINGS In the drawings: Figure 1 is a graphical demonstration of normalised phase trends of various filters; Figure 2 shows a Lorentz resonator and its normalised phase and amplitude curves; Figure 3 depicts Fano resonators with their normalised phase and amplitude curves; Figure 4 shows the behaviour of EIT resonators' normalised phase and amplitude curves; Figure 5 demonstrates the importance of phase sensing by illustrating the normalised amplitude and phase curves when encountering different losses; Figure 6 shows the resonators placed at a specific distance and their corresponding phase profile; Figure 7A is a schematic diagram which illustrates an example sensor according to aspects of the present disclosure; Figure 7B is a schematic diagram which illustrates components of an example sensor according to aspects of the present disclosure; Figure 7C is a schematic diagram which illustrates a physical distance between resonators of an example sensor according to aspects of the present disclosure; Figure 8 is a chart plotting the normalised phase-shifting profile of the example sensor of Figure 7A; Figure 9 is a simplified depiction of terrain mapping through use of a low-flying UAV equipped with one or more sensors according to aspects of the present disclosure; Figure 10 is a block diagram which illustrates different sensors and control units installed on a UAV for mapping and planning an optimised path for a trencher according to aspects of the present disclosure; Figure 11 is the three-dimensional map of a terrain surface generated by surveying a UAV in a specified region; Figure 12 depicts the underground map of different hurdles and obstacles between two endpoints of the trencher operation; Figure 13 is a schematic diagram which illustrates a UAV manoeuvre for terrain mapping and obstacle detection based on fractional permittivity according to aspects of the present disclosure; Figure 14 illustrates the actual path followed by a UAV by incorporating permittivity fraction balance logic in path planning whilst mapping the terrain profile; Figure 15 is a schematic diagram which illustrates system logic for going around, above or through the obstacle depending upon the nature of the terrain surface; Figure 16 is a schematic diagram which illustrates terrain mapping method performed by a UAV equipped with a microwave sensor during its flight in a targeted region for underground obstacle detection and terrain sub-surface mapping; Figure 17 is a schematic diagram which illustrates system logic implemented in trencher path planning for going around or through the obstacle according to the disposition of hindrances in the terrain sub-surface; Figure 18 is a block diagram which illustrates different modules of a trencher; Figure 19 is a schematic diagram which illustrates an optimised path planned for a trencher in a region with irregular terrain profile; Figure 20 is conceptual representation of an optimal path planned for a trencher, contemplating economic factors and machine safety for smooth operations; Figure 21 is a chart plotting measured and simulated results showing Fano resonance curve from an experimental implantation of a sensor described herein; Figure 22 is a chart plotting a phase response for Fano resonance from the experimental implantation of the sensor; Figure 23 is a chart plotting measured and simulated response showing EIT resonance from the experimental implantation of the sensor; Figure 24 is a chart plotting phase response for EIT resonance from the experimental implantation of the sensor; Figure 25 is a chart plotting measured and simulated response showing Lorentz resonance from the experimental implantation of the sensor; and, Figure 26 is a chart plotting phase response of Lorentz resonance from the experimental implantation of the sensor. DETAILED DESCRIPTION WITH REFERENCE TO THE DRAWINGS A sensor and systems and methods using the sensor are described. The sensor may be an electromagnetic sensor, such as a microwave sensor. The sensor may include two or more resonators. Each of the two or more resonators is associated with a base resonant frequency. Each of the two or more resonators are physically arranged such that each resonator is spaced apart from each of the other resonator(s) by a physical distance determined based on the base resonant frequency. Each resonator couples (electromagnetically) differently relative to each other resonator(s) based on characteristics and / or situation of different artefacts (also termed “superstrate” or “sample under test”) to which they are exposed. This different, or varying, electromagnetic coupling may cause exhibition of different types of resonance. A type of resonance exhibited and / or an associated phase value may be usable in detecting, identifying and / or classifying an artifact to which the resonators are exposed. Further, a terrain mapping and path planning system using the sensor performing far-field sensing for trenching operations is disclosed. The sensor may be a microwave-based, highly efficient obstacle-detecting sensor. As will be explained in greater detail below, the sensor may switch between Electromagnetically Induced Transparency (EIT), Fano and Lorentz resonance. Slopes of the respective phase values may be compared to perform microwave imaging of terrain. The microwave sensor may be embedded in a vehicle, such as an unmanned aerial vehicle (UAV), optionally along with other sensors. The UAV, equipped with a microwave sensor, may be deployed to conduct a survey of a target area where trenching activities are planned, mapping the terrain profile. Other applications of the sensor described herein are also anticipated. Aspects of the present disclosure provide a sensor, which may be specialised for terrain surface and sub-surface mapping. The sensor may include four resonators and wherein a change in permittivity of different test samples (or artefacts) influences a A / 4 (quarter-wavelength) size or distance of or between the resonators, thereby changing phase trends of the sensors’ filters. A signature resonance of the sensor may thus change type under the effect of the sample under test. The sensor may obtain three types of resonances under the effect of the sample under test with different locations of the samples exhibiting different resonances instantaneously with no additional physical change required in sensor architecture. A slope of EIT, Lorentz, and Fano resonators can thus be compared. In some applications, a change in nature of the phase trend of the resonators determines the presence of different obstacles / hurdles in the surface and subsurface of the terrain. Different resonances may be used for far-field sensing in such a way that minor exposure to the sample under test may produce an abrupt change from one signature resonance type to another. The sensor may be used to map the terrain surface and sub-surface profiles and determine an optimised path for trenching by incorporating permittivity fraction balancing. A sensor which changes its signature resonance type under the effect of the sample under test is described. The sensor obtains three types of resonances under the effect of the test sample; no physical change is required. Different location of the samples gives different resonances. Instead of comparing the shape of resonances, a phase slope of EIT, Lorentz, and Fano resonance can be compared. The advantage of using different resonances is that minor exposure to the sample under test will produce an abrupt change from one signature resonance type to another. Fraction permittivity may therefore be used to determine an optimal path in trenching applications. The sensor may form a core part of the system along with multiple sensors, underground obstacle detection and far-field microwave imaging are possible. Most rock-forming minerals have a dielectric permittivity in the order of er = 3-10 F / m; higher values show, for example, sulphides and some oxides. The dielectric permittivity of water is about 80 F / m. This results in a strong correlation between permittivity and the water content of a rock. When implementing underground fraction permittivity balancing as described herein, a UAV may be controlled to maintain a uniform height from the ground while returning in a pre-calculated path. The shortest path will be used. For hard obstacles, the UAV will change the path. Aspects of the present disclosure provide a terrain mapping and path planning system for use in trenching operations. The system includes at least one UAV that has been fitted with a number of sensors capable of mapping surface and sub-surface profiles and a processor capable of processing information received from the sensor to determine an optimal trenching route through the terrain. In some examples, a UAV is in communication with a trencher and configured to, while flying over a terrain, survey the terrain and determine an optimal trenching route. Determination of the trenching route may be performed using artificial intelligence algorithms to thereby determine the most cost-effective and efficient route. As such, the system aims to avoid maximum trenching obstacles while minimising the distance trenched. The UAV may include a microwave-based obstacle detecting sensor that is designed to map the terrain profile. It may be important to understand the resonators’ general phase trend and to understand the filters’ behaviour in response to different frequencies. Depending upon the sensors’ response, i.e., Lorentz, Fano, or EIT, obstacle detection is done. The insights into the normalised amplitude and phase curves help better understand the Lorentz behaviour and exploit its unique characteristics to make an effective sensor. The Fano response occurs only when two stringent constraints are met. Firstly, the two resonators placed close to each other must match in dimensions and, secondly, they must lie within a specified range of d <-. Lastly, with EIT resonators, the key differentiating factor lies in the resonators' size, where a slight mismatch may exhibit an EIT filter’s response. It is crucial to understand the behaviour of an EIT filter to make complex decisions for a trencher, e.g., choosing an optimal path for a trencher. Preferably, for surveying sub-surface terrain, the sensor makes use of phase sensing rather than magnitude sensing since it offers resistance to losses and generates a steady curve. With varying losses, the phase curve remains stable while this does not happen with the magnitude curve. The resonator's phase profile changes based on the electrical distance between resonators, as determined by lambda over four, where lambda changes based on changing permittivity. The resonator's phase profile may further change based on the relative electrical sizes of resonators. Such properties can assist in detecting underground obstacles, with each phase trend corresponding to a distinct obstacle. By examining these profiles, the system proposed in the present disclosure can determine an optimal path for the trencher machine and make informed decisions about the trenching process. The sensors used for obstacle detection help trencher machines avoid collapse or damage by finding efficient routes. The permittivity values of the test sample strongly influence the electrical distance between each resonator, resulting in a particular filter phase response. By evaluating these phase profiles of the filters, the stated sensor enables a trencher machine to navigate effectively and safely through various terrains and optimise trenching operations. The sensor's phase-shifting profile displays a graph. Deviations in the phase curves of resonators indicate changes in their size or distance, signalling the detection of an obstacle. The microwave sensor, along with ultrasonic sensor, optical sensor, GPS module, temperature and humidity sensors, and camera module, are all embedded in the UAV for terrain surface and sub-surface mapping. Al algorithms process the data collected by these sensors for efficient path planning. Optimised route plans are stored in the cloud. This mapping is important for safe and effective trenching, as natural slope, rock, bedrock, and underground utilities can complicate the trenching operation. The route plan is then fed to the trencher through cloud communication. The UAV’s processor may be configured to receive data from the various sensors to then, using Al algorithms, determine an optimal trenching path which may then be wirelessly communicated to a remote location, typically a server. Once the optimal trenching route has been determined, taking into account natural slope, rock, bedrock and underground utilities, the trenching route may then be communicated to the trencher to commence trenching. The trencher may be configured to operate either manually, in which case an operator will operate the trencher to follow the determined optimal path, or the trencher may be able to operate autonomously. The trencher may thus receive the optimal route plan from the UAV or remote location and use its own camera, GPS module and obstacle detector to navigate along the determined route. The trencher may be provided with a DSP module that controls the trencher’s movement and preferably displays received sensor data on a display for real-time monitoring. The DSP module may also be configured to wirelessly transmit data to a web or mobile application for remote monitoring. In the following description, reference is made to the accompanying drawings that form a part of an example embodiment of a terrain profile mapping and path planning system for a trencher. Therefore, the drawings representing the embodiments are shown for illustrative purposes only in which the invention may be practised. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention, and it is to be understood that other embodiments may be utilised and that structural, logical, and electrical changes may be made without departing from the scope of the present invention. Therefore, the following description of example embodiments is not to be taken in a limited sense. Figure 1 illustrates the normalised phase trends of various filters. The demonstration provides a basic understanding of the general phase trend of the resonators. To accomplish this, a graph is plotted, with phase (in degrees) on the vertical axis (102) and a normalised frequency on the horizontal axis (104). Each filter generates its unique curve (106, 108) on the graph. The key distinguishing factor between these filters is the difference in slope of their respective curves. These curves demonstrate how the phase of a signal changes in response to the frequency of each filter. Understanding these phase trends in response to different frequencies is crucial for designing a filter-based obstacle detection device. The normalised phase and amplitude curve of a Lorentz resonator is shown in Figure 2. The plot provides a graphical representation of how the amplitude and phase of one of the three filters, i.e., the Lorentz filter, vary with respect to the normalised frequency. The amplitude curve (208) of a Lorentz resonator (202) is demonstrated with normalised frequency (206) taken along the x-axis and the magnitude (204) along the y-axis. In contrast, the phase curve (214) represents the phase of the Lorentz filter. The phase is measured in degrees and is plotted on the y-axis (210), while the normalised frequency (212) is taken along the x-axis. The unique phase and amplitude curves of the Lorentz resonator may be exploited to make an underground obstacle detector sensor device. A Fano resonator with its normalised phase and amplitude curve is illustrated in Figure 3. To exploit the unique phenomenon exhibited by the second type of filter, i.e., the Fano filter, it is imperative to have a basic understanding of its behaviour. The Fano response emerges when the width (310) and length (308) of the resonator R} (302) perfectly match with the dimensions (312, 314) of the resonator R2 (304). Additionally, the resonators (302, 304) must be positioned within A a specified range, being the distance d <-. The normalized Fano amplitude (316) and phase 4 (318) curves are obtained only when these stringent constraints are satisfied. Lastly, an EIT resonator with its phase and amplitude curve is depicted in Figure 4. It is essential to highlight the significance of the resonator's size since it is the key differentiating factor between the Fano and EIT resonators. A slight mismatch in the resonators' (402, 404) size, i.e., heights (408, 414) and widths (410, 412), leads to the manifestation of an EIT curve. The distance between the resonators (402, 404) must remain within a specified range (406). The respective amplitude (416) and phase (418) curves are disclosed. It is crucial to understand the behaviour of an EIT filter to utilise it in the trencher sensor effectively. The significance of phase sensing in scrutinising a terrain sub-surface profile is demonstrated in Figure 5. Phase sensing is preferred over amplitude sensing because it is more resilient to losses and generates a steady curve. Disturbances are visible in the magnitude profile of a filter when it faces different losses. The normalised magnitude curve of the filter shifts from its initial location (506) to new positions (508, 510) as a result of these disturbances. Nevertheless, the filter's phase curve (512) does not show these changes or shifts. Consequently, phase sensing seems to be a favourable option since, in contrast to the amplitude curves, the phase curves remain stable regardless of the losses. Thus, phase sensing proves to be a valuable tool for scrutinising terrain sub-surfaces. The resonators placed at specific distances with their corresponding phase profile are illustrated in Figure 6. The phase profile changes in response to the resonators’ varying size and distance. Underground obstacles can be detected by leveraging these unique behaviours of different filters, namely Lorentz, Fano, and EIT. Each obstacle corresponds to a particular phase profile, which assists in determining an optimal path for a trencher machine. If the distance between the resonators (602, 604) falls within the specified range of d >- (606), a Lorentz curve is obtained. On the other hand, if there are slight variations in the dimensions of the resonators or the distances between the resonators (within a specified range, i.e., d <-), either an EIT or a Fano curve is obtained. These variations observed in the phase profiles of filters enable the accurate inspection of an obstacle's location. Furthermore, it facilitates estimating a given terrain's cost-effective and efficient path. Accordingly, it is possible to make well-informed decisions about the trenching process by examining these phase profiles. An example sensor (722) utilizing the principles described in the foregoing figures is illustrated in Figures 7A to 7C. The sensor includes at least two (and, in the illustrated example, four) resonators (702, 704, 706, 708). Each resonator is associated with a base resonant frequency and is physically arranged such that each resonator is spaced apart from each of the other resonator(s) by a physical distance (710, 712, 714, 716, 718, 720) determined based on the base resonant frequency. The base resonant frequency may be a resonant frequency of the resonator in free space or in air. The sensor may be a microwave sensor in that the resonators may have a base resonant frequency that is in the range of: between 300 MHz and 3000 GHz; or between 300 MHz and 300 GHz; or between 1 and 100 GHz; or between 1 and 3000 GHz. The resonators may be arranged in an array (in the illustrated example being a two-by-two array). Referring now to Figure 7B, each resonator may include a feed via which electromagnetic signals are transmitted via and / or received from the resonator. Each feed of each resonator may be connected to a front-end (711) of the sensor via a feeding unit (713) connected to an input (or receiver port) (715) and an output (or transmitter port) (717) of the front-end. In some examples, some or all of the resonators are coupled to the feeding unit via a switch (719A-719C) for selectively coupling and decoupling individual resonators from the feeding unit. The feeding unit / path and resonators may be fabricated on the same substrate. The front-end may include bandpass filters (724, 726, 728, 730) interposed: between the input and a low noise amplifier (732) and between the output and a power amplifier (734), respectively; and between the low noise amplifier and a first local oscillator (736) and between the power amplifier and a second local oscillator (738). In some examples, the sensor includes a digital signal processor (DSP) (740), which may connect to the input via an analogue-to-digital converter (ADC) (742) and to the output via a digital-to-analogue converter (DAC) (744) respectively. The DSP may provide a phase output (746) for storing and / or displaying phase measurements obtained via the input and the ADC. Referring now to Figure 7C, as mentioned above, each resonator is associated with a base resonant frequency and is physically arranged such that each resonator is spaced apart from each of the other resonator(s) by a physical distance (710, 712, 714, 716, 718, 720) determined based on the base resonant frequency. The physical distance may be determined based on a wavelength (A) determined from the base resonant frequency, and may hence be termed a base wavelength. In particular, the physical distance may be determined to be greater than or equal to the wavelength over four (or quarter-wavelength). The base wavelength may therefore be an operating wavelength based on an operating frequency of the sensor (or of the resonators of the sensor) in certain predefined conditions. The base wavelength may for example be a wavelength at which the sensor operates air or in free space. The frequency and wavelength at which the sensor operates may depend on the environment in which the sensor locates and operates, and in particular the permittivity of that environment. Thus, changes in the environment (or the permittivity of the environment) may affect the resonant frequency and in turn the wavelength of the sensor. As mentioned, in some examples, each resonator is located at a physical distance which is greater than or equal to A / 4 from each other sensor, where A is the base wavelength of each resonator at the base frequency of each resonator. Thus, each resonator couples electromagnetically differently relative to each other resonator(s) based on characteristics and / or situation of different artefacts to which they are exposed, which may in turn cause the exhibition of different types of resonance. The type of resonance exhibited, and in particular sudden changes in resonance type, and / or an associated phase value may be usable in classifying an artifact to which the sensor is, and in turn the resonators are, exposed. The sensor may accordingly output phase values (e.g. via the phase output) for use in detecting, identifying and / or classifying artefacts. A change in phase value may indicate a change in situation of an artefact relative to each of the resonators. In some examples, a change in phase value may indicate a change in characteristic of the artefact (or, a change in the artefact itself). The characteristic of the artifact may be a permittivity of the artefact. The different types of resonance may include one or more of: Fano resonance; EIT resonance; and, Lorentz resonance, as described in greater detail in the foregoing. In some examples, the sensor includes a switch controller configured to control operation of the switches. In some examples, the switch controller switches between each of a second resonator (704) followed by a third resonator (706) followed by a fourth resonator (708) (or in any other order). The phase output may output phase measurements obtained during each of these states. Switching the resonators in this way may obtain different types of resonance based on the situation of the artefact relative to each of the different resonator pairs. For example, referring to Figures 2 to 6, different situations of the artefact in relation to each of the different resonator pairs may cause the resonator pairs to interact or couple with each other differently, thus causing different resonance types to be exhibited. The normalised phase-shifting profile of the sensor (722) is shown in the exemplary graph (800) of Figure 8. The different phase curves (806, 808, 810, 812) of the resonators (702, 704, 706, 708) are shown. The deviation of the curve from its original position indicates that there has been a change in either the distance or the size of the resonators, and therefore, an obstacle is detected. In some examples, a particular phase value and / or a particular type of resonance may, through calibration, be used to classify or identify an artifact. Permittivity differences may exist between different terrain profiles. These permittivity values obtained from different terrain profiles may alter the size or distances of resonators of the sensor, which in turn change a response type. Only when the test sample maintains an equal distance of d >A / 4 on all sides of the resonators a Lorentz curve is obtained. However, the phase profile may change depending on the test sample's permittivity value. If the permittivity value of the sample under the test alters the resonator size and, therefore, its distance, then an EIT curve is obtained. Conversely, a Fano plot is obtained if only the distance is changed to d <A / 4. By evaluating the phase profiles of the filters, this sensor provides an optimal solution for above and subsurface obstacle detection, enabling a trencher of any work vehicle to navigate effectively and safely through various terrains and optimise operations. In this manner, for example in the case of a trencher, a sudden encounter with an artefact in the form of an obstacle can lead to the collapse of a trencher machine, whereas a sharp obstacle may cause damage to the trencher's blade. To overcome these challenges, it is vital for the trencher machine to not only change its path but also find the most efficient and economical route to avoid such detrimental effects. Subsequently, attaining detailed information about the precise location and type of the obstacle plays a crucial role in planning an optimal path for a trencher machine. This information can be obtained by carefully examining the phase profile of filters. In some examples, referring now to Figure 9, a UAV (902) may be equipped with a sensor and other sensing and communication modules, surveying a region (912) where trenching operation is to be carried out. The rays (904, 906, 908, 910) emitted by sensors installed on the UAV (902) are used for obstacle detection and mapping of terrain surface as well as terrain sub-surface. Mapping terrain surface and sub-surface before trenching, using UAV, is important because of various factors. The natural slope of the terrain complicates trenching operations. Trenching on grade requires additional safety precautions, while steep slopes increase the risk of soil collapse. The presence of rock or bedrock also obscures trenching, as it may require specialised excavation equipment and techniques, such as rock trenching machines or explosives for rock removal. Additionally, existing underground utilities, like water, gas, or electrical lines, muddle trenching. Appropriate mapping of terrain sub-surface is essential to avoid damage and disruptions to these utilities during trenching. Figure 10 illustrates an exemplary block diagram of different sensing, processing, and implementing modules installed on the UAV (902). A sensor (722) may be provided for its use in obstacle detection in terrain sub-surfaces but also finds its use in surface mapping. The Digital Signal Processing unit (1002) communicates with a microwave sensor (722), ultrasonic sensor (1006), optical sensor (1008) and GPS module (1010) to map the terrain surface and sub-surface profile for smart path planning for the trencher while maintaining a breakeven between operational efficiency, cost and equipment safety using Al algorithms. It will be appreciated that in some cases it may be more time and cost effective to trench a longer route rather than trenching through a path filled with obstacles. The DSP may be configured to utilise the data received from the various sensors to effectively determine an optimal path. The temperature sensor (1012) and humidity sensor (1014) are used for weather monitoring to efficiently plan the work routines since heavy rains can lead to site flooding and soil instability. Monitoring and adapting to weather conditions is essential for maintaining trench stability and safety. The camera module (1004) is installed on the UAV, giving a live video feed of the terrain. The terrain data processed by DSP (1002) may be stored (1016) remotely, preferably in a cloud server and sent to the web server (1020) through loT communication (1018). Figure 11 illustrates an exemplary three-dimensional diagram of terrain surface mapping using a UAV (1102) according to the invention that is equipped with a number of sensors and which manoeuvres in a region (1104) where trenching operations are to be carried out. The natural slope of the terrain surface (1114) and the presence of rocky regions (1106, 1108, 1110, 1112) on the terrain surface are mapped using data collected through the sensors of the UAV. Figure 12 illustrates an exemplary diagram of underground mapping for obstacle detection in terrain sub-surface (1107) between endpoints (1103, 1105), using a UAV (1102) according to the invention. The presence of bedrock (1109) and underground utilities is detected through a microwave sensor (722) mounted on the low-flying UAV (1102). The terrain surface (1104) and sub-surface (1107) profile data are then sent to a web server (1020). The terrain data is processed using Al algorithms for efficient path planning, and optimised route plans are stored in the cloud (1016). The smart Al logic implemented during the UAV manoeuvre (1102) for mapping the terrain profile based on fractional permittivity is exhibited in embodiment (1200) of Figure 13. Assuming (1202) to be the far-field sensing range, a reference line (1204) along the x-axis (1224) for UAV manoeuvre is defined pre-emptively at an altitude where the detected permittivity fraction of air (1206) and soil (1214) is 1 / 2 each. The low-flying UAV manoeuvring along this reference line will decide a straight path for the trencher, according to the Al logic defined herein, as long as this specified permittivity fraction is not disturbed. To further elaborate this comprehension, an irregular terrain (1222) is selected. The surveying UAV (1102) equipped with a microwave sensor (722), manoeuvring along reference line (1204), will divide this uneven terrain profile into four regions (1226,1228,1230,1232) according to varying permittivity fractions of air and soil detected there. The permittivity fraction of air (1208, 1212) and soil (1216, 1220) in the second region and fourth region (1228, 1232) is detected to be 2 / 3 and 1 / 3, respectively, illustrating a steep dwell there. The permittivity fraction for air (1210) and soil (1218) in the third region is detected to be % and %, respectively, illustrating a grade rise there. The actual path followed by surveying UAV (1102) by incorporating fraction permittivity balance logic and Al in path planning is disclosed in embodiment (1300) of Figure 14. The microwave sensor (722) embedded in the UAV determines the nature of the obstacle / hurdle by examining the permittivity of the sample. The UAV adjusts its altitude (1310) in all four regions (1302, 1304, 1306, 1308) in such a way that the detected permittivity fraction of air and soil stays 1 / 2 each. The steeps and grades along the x-axis (1224) in the terrain profile (1222) are therefore mapped. In another exemplary embodiment (1400) of Figure 15, the smart system logic is disclosed for carrying trenching operation around (1412), above (1410) or through the obstacle (1408) in three-dimensional space (1402, 1404, 1406), depending upon the nature of terrain surface. As comprehended commonly, the natural slope of the terrain complicates trenching operations. Trenching on grade requires additional safety precautions, while steep slopes increase the risk of soil collapse. Additionally, most rock-forming minerals have a permittivity in the order of er = 3-10 F / m. The dielectric permittivity of water is about 80 F / m. This results in a strong correlation between permittivity and the water content of a rock. The nature of the soil, terrain gradient and presence of rocks or other hurdles can, therefore, be mapped based on permittivity fractions and relative permittivity of tested samples. The Al logic exploited by UAV (1102) equipped with a microwave sensor (722) during its flight in a targeted region for underground obstacle (1504) detection and terrain sub-surface mapping is disclosed in embodiment (1500) of Figure 16. The reference line for UAV manoeuvre (1502) is changed such that the air and soil permittivity fraction is initially kept at % and %, respectively, by adjusting the UAV flight’s altitude. This facilitates the in-depth mapping of the terrain sub-surface by detecting bedrocks, utility lines or any other hurdle in the terrain sub-surface that may hinder the trenching process. Owing to the obstacle detection and surface mapping carried out by a microwave sensor, the terrain surface and sub-surface profiles are mapped. The terrain data is then processed through Al algorithms to devise an optimised path for trenching. One such algorithm governing the decision-making process for the trencher to go through (1602) or around (1604) the obstacle (1504) in spatial terrain sub-surface (1402, 1404, 1406) is disclosed in embodiment (1600) of Figure 17. Firstly, the nature of the obstacle is detected. After that, the physical properties of the detected obstacle are computed to perform the decision-making on whether or not the trencher blade can withstand that specific obstacle’s impact. Conclusively, an optimised path is devised for trenching by simultaneously considering hindrances in terrain surface and sub-surface. Figure 18 illustrates a block diagram of an exemplary embodiment of a trencher (1700) including the numerous modules thereof. The trencher may be configured to operate autonomously, alternatively it may also operate manually and hence by an operator. The data for the optimised route plan (1016) from the UAV is fed to the control panel of the trencher for autonomous trenching. The camera module (1702), GPS module (1704) and obstacle detector (1706) may be used to navigate the trencher via communication with the DSP module (1710) in case of a sudden deterioration in the terrain profile of the mapped route. The DSP module (1710) controls the actuation of the trencher (1708) as well as displays the sensor data on the display panel (1712) of the trencher for real-time monitoring by an operator. It will be appreciated that even where the trencher is configured to operate autonomously, the DSP module (1710) will preferably be configured to transmit data to a web application (1716) or mobile application (1718) through WiFi communication (1714) to enable an operator to monitor the trenching operations remotely. Figure 19 illustrates an exemplary diagram in which the optimised path (1802) planned for the trencher (1804), operating between the start-point (1806) and endpoint (1808) in a terrain (1104) is depicted. Numerous obstacles (1106,1108, 1110, 1112, 1114) may be avoided in planning the optimal path. It will be appreciated that by incorporating Al algorithms in the sensor data processing, the system is able to determine a trenching route that follows the shortest path while avoiding the most obstacles. Figure 20 depicts three different routes planned for trenching (1904, 1906, 1908), based on displacement between start-point ‘A’ and endpoint ‘B’ whilst considering the obstacles in terrain surface and sub-surface, safety of the trench and operational cost. The first path (1904) constitutes the maximum distance between points A and B, after avoiding the slightest of obstacles and ensuring maximum trencher safety, but the operational cost in this case will typically be the highest. Similarly, the third path (1908) provides the shortest distance between points A and B thus providing the minimum operational costs, but at the same time exhibits minimum safety factors for the trencher because it avoids the minimum number of obstacles. Considering the obstacle avoidance, shortest path, operation cost, and safety factor for the trencher, the Al algorithm may suggest the optimum path (1906) for trenching operation. A sensor including two or more resonators is provided wherein a change in permittivity of different test samples (or artefacts) influences a A / 4 size or distance of or between the two or more resonators, thereby changing phase trends of the sensor. The sensor may in this manner obtain EIT, Fano, and / or Lorentz resonance under the effect of the sample. The slopes of the different resonances may be compared for conducting terrain surface and sub-terrain sensing to detect irregularities or obstacles within the terrain. In some examples, the sensor may be attached to a UAV by which the sensor monitors the permittivity of the air above the terrain surface and the sub-terrain material to detect terrain irregularities or obstacles. In some examples, the UAV is controlled over a sample region such that the region contains permittivity fractions indicating that half of the sample region is air, and the other half is sub-terrain material. In some examples, the sensor is used to detect water content in rock formations by monitoring the permittivity levels of water in a rock sample. In some examples, the UAV’s altitude is controlled to change such that air is a % of the test sample region so that the sensor can detect irregular permittivity in the rest of the region. In accordance with aspects of the present disclosure, a system implementing the sensor for terrain mapping and path planning for trenching operations is provided. Experimental results In an experimental implementation of the sensor described above with reference to Figures 7A-7C, a Pi-shaped structure containing two resonators in the feeding path was tested and measurements were obtained using a vector network analyser (VNA). The experimental results demonstrated that a microwave sensor can produce three distinct resonance types - Fano, Electromagnetically Induced Transparency (EIT), and Lorentz - through the manipulation of superstrate properties. The sensor, comprising two coupled resonators, demonstrates a unique ability to switch between resonance modes based on the dielectric properties and positioning of the superstrate material (e.g., being an artefact or sample under test). This versatility offers significant advantages in sensing applications. This example introduces a T-shaped sensor design that leverages the interaction between coupled resonators and a superstrate layer to achieve multiple resonance types within a single structure. The experimental sensor included two coupled resonators arranged in a T-shape configuration. The horizontal arm of the T forms the through arm, while the vertical arms are the two resonators. Through these two resonators, the type of resonator can be controlled. The sensor was tested using a VNA to measure S-parameters. Superstrate materials with specific dielectric properties were placed at different locations on top of the sensor to investigate their effects on the resonance characteristics. The superstrate layer was systematically varied in terms of Position relative to the T-shape sensor. Results and Discussion - Fano Resonance When the superstrate material partially covers both arms of the T-shape with a moderate dielectric constant, a Fano resonance is observed. This asymmetric line shape results from the interference between a narrow discrete resonance and a broad continuum. Our experiments revealed a Fano resonance centred at approximately 1.5 GHz, as shown in Figure 21. The transmission spectrum exhibits a characteristic asymmetric profile with a sharp transition from a transmission peak to a deep dip. The minimum transmission (S (1,2) S) reaches approximately -22 dB at 1.7 GHz, while a local maximum of about -1 dB is observed near 1.4 GHz. This asymmetry is a hallmark of Fano resonance. With reference to Figure 21, measured and simulated results show good agreement, with the measured response displaying a slightly less pronounced dip and a small frequency shift compared to the simulated data. This minor discrepancy could be attributed to fabrication tolerances and small variations in material properties. The quality factor (Q) of the resonance, estimated from the sharpness of the transition, is quite high, indicating the sensor's potential for high-sensitivity applications. The transmission coefficient S21 can be described by the Fano formula: 521 = 4 * (e + q)2 / (l + s2) where A is the maximum amplitude, s = 2( / - f^ / r is the reduced frequency, ( / 0) is the resonance frequency and F is the resonance width, and q is the asymmetry parameter. The observed asymmetry in the results suggests a q value between 0.5 and 1. Referring now to Figure 22, the phase response of the Fano resonance exhibits a distinctive behaviour characteristic of this type of resonance. The phase undergoes a rapid change of approximately 250 degrees within a narrow frequency range centred around 1.5 GHz. This abrupt phase transition corresponds to the asymmetric line shape observed in the magnitude response. Before the resonance, the phase remains relatively constant at about 150 degrees. As the frequency approaches 1.5 GHz, there is a sharp drop in phase, reaching approximately -100 degrees. Following this steep transition, the phase continues to decrease more gradually, reaching about -150 degrees at 2.5 GHz. The measured and simulated phase responses show excellent agreement, with only minor discrepancies in the steepness of the transition. This rapid phase change contributes significantly to the sensor's high sensitivity to small perturbations in the superstrate properties. The steepness of the phase curve reaches its maximum at the centre of the resonance, where the rate of phase change with respect to frequency (group delay) is highest. In this manner, the experimental data shows: a characteristic asymmetric peak-and-dip profile in the transmission spectrum; a rapid phase change near the resonance frequency; and, high sensitivity to small changes in the superstrate properties. Results and Discussion - Electromaqnetically Induced Transparency (EIT) EIT-like resonance is achieved when the superstrate material primarily covers one arm of the T-shape, typically one of the vertical arms. This configuration creates a coupling between the two resonators that mimics the quantum interference phenomenon of EIT. As illustrated in Figure 23, the experiments revealed an EIT-like spectrum with two distinct transmission dips flanking a transparency window. The two transmission dips are centred at approximately 1.1 GHz and 1.7 GHz, with the transparency window occurring between these frequencies. The depth of the transmission dips reaches about -24 dB for the simulated response and -21 dB for the measured response. The transparency window shows a local maximum in transmission of approximately -1.5 dB at around 1.6 GHz. The slight discrepancy between measured and simulated results, particularly in the depth of the dips and the exact frequency positions, can be attributed to fabrication tolerances and coupling variations in the physical structure. The quality factor of each resonance dip is relatively high, contributing to a well-defined transparency window. The EIT-like spectrum can be modelled using a coupled oscillator model: FF' Fr 521 = 11--+----------- 1 S + IF 8 + A + IF where F is the Fano parameter, F and P are the damping rates of the two resonators, 3 is the detuning from the resonance frequency, and A is the frequency separation between the two resonators. In the described experimentation, A is approximately 1 GHz, as evidenced by the separation between the two dips. The phase response of the EIT-like resonance, illustrated in Figure 24, reveals a complex behaviour that corresponds to the dual-dip structure seen in the magnitude response. The phase undergoes two distinct transitions over the frequency range of 0.5 to 2.5 GHz, aligning with the two transmission dips observed in the magnitude spectrum. Initially, the phase remains stable at around 160 degrees up to about 1.2 GHz. At this point, there is a sharp drop of approximately 260 degrees, corresponding to the first transmission dip. The phase then stabilizes briefly before undergoing a second, more gradual transition between 2 and 2.5 GHz, coinciding with the second transmission dip. Notably, the region between these two- phase transitions, where the phase remains relatively stable, corresponds to the transparency window in the magnitude response. This phase stability in the transparency window is a key feature of EIT-like phenomena, contributing to the potential for slow light applications. The measured and simulated phase responses show good overall agreement, with some minor differences in the exact positions and steepness of the transitions. These small discrepancies align with the variations observed in the magnitude response and can be attributed to fabrication tolerances and coupling variations in the physical structure. Key observations include: a sharp transparency window within a broader absorption spectrum; a steep slope in the phase response within the transparency window; an enhanced group delay, indicating potential for slow light applications. Results and Discussion - Lorentz Resonance Lorentz resonance is observed when the superstrate material uniformly covers the entire T-shape or when its dielectric constant is significantly higher than the substrate. Figure 25 shows the characteristic symmetric profile of a Lorentz resonance centred at about 1.5 GHz. The resonance manifests as a symmetric peak in the transmission spectrum, reaching a maximum of approximately -1 dB for the simulated response and -4.5 dB for the measured response. The full width at half maximum (FWHM) of the resonance is roughly 0.5 GHz, indicating a moderate quality factor Q of about 3 (calculated as the centre frequency divided by the FWHM). The transmission coefficient can be modelled using the Lorentz oscillator equation: "o 521 = 1 - A *—---7---- or — o>q + iyM where A is the oscillator strength, ai0 is the resonance frequency, w is the angular frequency, and y is the damping factor. The symmetry of the observed peak aligns well with this model. The measured response shows good agreement with the simulated results, with a slight reduction in peak amplitude and a minor broadening of the resonance. These small discrepancies can be attributed to additional losses in the fabricated structure and slight variations in material properties. The phase response of the Lorentz resonance, depicted in Figure 26, displays a characteristic smooth transition typical of classical resonant systems. Over the frequency range of 1 to 2 GHz, the phase undergoes a total shift of approximately 270 degrees. Starting from about 150 degrees at lower frequencies, the phase remains relatively constant until around 1.3 GHz. At this point, coinciding with the peak in the magnitude response, the phase begins a smooth and rapid descent. The transition is steepest around 1.5 GHz, where it drops by about 200 degrees over a narrow frequency range. After this main transition, the phase continues to decrease more gradually, eventually stabilizing at around -120 degrees for higher frequencies. The measured and simulated phase responses show excellent agreement throughout most of the frequency range. A slight discrepancy is observed in the transition region, with the measured response showing a slightly more gradual change compared to the simulated results. This minor difference is consistent with the slight broadening observed in the measured magnitude response and can be attributed to additional losses in the fabricated structure. The smoothness of this phase transition, in contrast to the sharp changes seen in the Fano and EIT responses, is characteristic of the Lorentz resonance. This behaviour results in a more moderate but consistent group delay across the resonance bandwidth, which can be advantageous for certain sensing and signal processing applications. It is notable that the Lorentz resonance exhibits a much broader response compared to the sharp features observed in the Fano and EIT cases. This broader response makes the Lorentz configuration less sensitive to small perturbations but potentially more robust for certain sensing applications where a wider detection range is desired. Characteristics of the Lorentz resonance include: a symmetric dip in the transmission spectrum; a 180-degree phase shift across the resonance frequency; and, a broader bandwidth compared to Fano and EIT resonances. The foregoing description has been presented for illustration; it is not intended to be exhaustive or limit the invention to the precise forms disclosed. Persons skilled in the relevant art can appreciate that many modifications and variations are possible in light of the above disclosure. The language used in the specification has been principally selected for readability and instructional purposes, and it may not have been selected to delineate or circumscribe the inventive subject matter. Therefore, it is intended that the invention's scope be limited not by this detailed description but rather by any claims on an application based hereon. Accordingly, the disclosure of the embodiments of the invention is intended to be illustrative, but not limiting, of the scope of the invention, which is set forth in the following claims. Finally, throughout the specification and accompanying claims, unless the context requires otherwise, the word 'comprise' or variations such as 'comprises' or 'comprising' will be understood to imply the inclusion of a stated integer or group of integers but not the exclusion of any other integer or group of integers.

Claims

1. A sensor comprising two or more resonators, each of the two or more resonators being associated with a base resonant frequency and being physically arranged such that each resonator is spaced apart from each of the other resonator(s) by a physical distance determined based on the base resonant frequency, wherein each resonator couples electromagnetically differently relative to each other resonator(s) based on characteristics and / or situation of different artefacts to which they are exposed causing exhibition of different types of resonance, and wherein a type of resonance exhibited and an associated phase value are usable in detecting an artifact to which the resonators are exposed.

2. The sensor as claimed in claim 1, wherein the sensor includes four resonators.

3. The sensor as claimed in claim 2, wherein the resonators are arranged in an array,wherein the array is a two-by-two array.

4. The sensor as claimed in any one of the preceding claims, wherein the base resonant frequency is a resonant frequency of the resonator in air.

5. The sensor as claimed in any one of the preceding claims, wherein the physical distance is determined based on a wavelength determined from the base resonant frequency.

6. The sensor as claimed in claim 5, wherein the physical distance is greater than or equal the wavelength over four.

7. The sensor as claimed in any one of the preceding claims, wherein the sensor outputs phase values, and wherein a change in phase value indicates a change in situation of an artefact relative to each of the resonators.

8. The sensor as claimed in any one of the preceding claims, wherein a change in phase value indicates a change in characteristic of the artefact, wherein the characteristic is a permittivity of the artefact.

9. The sensor as claimed in any one of the preceding claims, wherein the different types of resonance include: Fano resonance; EIT resonance; and, Lorentz resonance.

10. The sensor as claimed in any one of the preceding claims, wherein the sensor includes a front-end including an input, and wherein the input is coupled to each of one or more of the resonators via respective switches configured for selectively coupling and decoupling each of the one or more resonators from the receiver.

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