Multi-band discontinuous frequency synthesis for localization and tracking applications

Abstract

Embodiments of the present disclosure can perform more accurate localization and tracking in various applications where wireless signals are employed while overcoming bandwidth limitations in the realm of precise wireless ranging. In one aspect, a method of performing wireless contactless sensing is provided. The method can include: filtering a received signal using a filter to select non-contiguous frequency bands, determining phase information for the selected non-contiguous frequency bands, determining a time domain response of the determined phase information for the selected non-contiguous frequency bands, and determining a location of a target based on the determined time domain response.

Description

MULTI-BAND DISCONTINUOUS FREQUENCY SYNTHESIS FOR LOCALIZATION AND TRACKING APPLICATIONSCross-Reference to Related Applications

[0001] This application claims priority to and the benefit of U.S. Provisional Application No. 63 / 578,970, titled “MULTI-BAND DISCONTINUOUS FREQUENCY SYNTHESIS FOR LOCALIZATION AND TRACKING APPLICATIONS,” filed on August 25, 2023, the content of which is hereby incorporated by reference herein in its entirety.Background

[0002] Contactless sensing can use radiofrequency (RF) signals to detect the position and orientation of objects, as well as the movement of those objects. Contactless sensing can be limited by bandwidth and signal processing challenges. These challenges can include computational limitations, regulations on bandwidth allocation, and the design of physical contactless sensing systems. Contactless sensing can be used in a wide range of contexts including healthcare, automobiles, manufacturing, retail, and logistics. Improvements in contactless sensing can benefit these and other applications.Summary

[0003] Embodiments of the present disclosure can enhance ranging accuracy and resolution by synthesizing discontinuous frequency bands while keeping physical and computational implementation costs low and ensuring compliance with regulations governing bandwidth usage. In comparison to continuous measurements with the same effective bandwidth, the example embodiment outperforms them and achieves sub-millimeter accuracy within a given range.

[0004] An example embodiment can leverage the distinctive propagation characteristics found in sparse frequency bands. Additionally, the example embodiment can use information derived from analyzing the signal reflections at different frequencies within a fixed bandwidth. Based on these properties, the example embodiment can overcome the limitations imposed by bandwidth, which can be a significant factor in achieving precise localization and tracking through wireless signals. This innovative approach represents a significant advancement in the field, as it capitalizes on the use of multiple frequency bands to tackle the challenge of limited bandwidth. By intelligently synthesizing these non-continuous frequency bands, the example embodiment can significantly enhance the accuracy and resolution of ranging measurements.The example embodiment can optionally strike a balance between improved performance and practical considerations such as cost and regulatory compliance.

[0005] Embodiments of the present disclosure can perform more accurate localization and tracking in various applications where wireless signals are employed. Embodiments of the present disclosure can likewise overcome bandwidth limitations and unlock new possibilities in the realm of precise wireless ranging.

[0006] The present disclosure presents an overview of the innovative approach of noncontiguous bandwidth integration for wireless sensing and range finding applications. Traditional methods of distance estimation in contact-less systems have relied on continuous bandwidths, which often lead to regulatory restrictions and increased implementation costs. To address these challenges, a method is proposed that intelligently combines information from non-contiguous frequency bands. The disclosure explores the fundamental principles of wireless ranging, including phase interferometry and round-trip time of flight (ToF) methods. We highlight the critical role of bandwidth in determining the accuracy and resolution of distance measurements and discuss the limitations of ultra-high bandwidth systems. The proposed method employs a frequency domain filter to select non-contiguous frequency bands, substantially reducing the decision space for target localization. Additionally, we leverage phase information from the lowest frequency band to improve accuracy and discrimination capability.

[0007] In some implementations, a method for performing contactless sensing is provided. The method can include: receiving a signal, wherein the signal is associated with a target and includes multifrequency phase information for each of a plurality of frequencies received by a reader; filtering the received signal using a filter to select non-contiguous frequency bands; determining phase information for the selected non-contiguous frequency bands; determining a time domain response of the determined phase information for the selected non-contiguous frequency bands; and determining a location of the target based on the determined time domain response.

[0008] In some implementations, determining the location of the target includes convolving a time domain representation of the filter with the determined time domain response.

[0009] In some implementations, filtering the received signal further includes: defining a frequency domain filter.

[0010] In some implementations, the frequency domain filter defines a set of active bands and a set of notched bands.

[0011] In some implementations, the method further includes: calibrating an initial phase of the target's response by selecting phase information from a lowest frequency band of the selected non-contiguous frequency bands.

[0012] In some implementations, filtering the received signal includes eliminating phase information that is incoherent with the phase information for the lowest frequency band.

[0013] In some implementations, calibrating the initial phase of the target's response includes applying a linearization filter to the phase response of the target.

[0014] In some implementations, the time domain response is determined using an Inverse Discrete Fourier Transform (IDFT).

[0015] In some implementations, the reader is a passive or semi-passive tag.

[0016] In some implementations, a system is provided. The system can include: a reader configured to capture multifrequency phase information; a processor; and a memory having instructions stored thereon, wherein execution of the instructions by the processor causes the processor to perform non-contact sensing by executing a set of processes to: receive a signal, wherein the signal is associated with a target and includes multifrequency phase information for each of a plurality of frequencies received by a reader; filter the received signal using a filter to select non-contiguous frequency bands; determine phase information for the selected non-contiguous frequency bands; determine a time domain response of the determined phase information for the selected non-contiguous frequency bands; and determine a location of the target based on the determined time domain response.

[0017] In some implementations, a non-transitory computer readable medium is provided. The non-transitory computer readable medium can include a memory having instructions stored thereon to cause a processor to: receive a signal, wherein the signal is associated with a target and includes multifrequency phase information for each of a plurality of frequencies received by a reader; filter the received signal using a filter to select non-contiguous frequency bands; determine phase information for the selected non-contiguous frequency bands; determine a time domain response of the determined phase information for the selected noncontiguous frequency bands; and determine a location of the target based on the determined time domain response.

[0018] Additional advantages will be set forth in part in the description which follows or may be learned by practice. The advantages will be realized and attained by means of the elements and combinations particularly pointed out in the appended claims. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive, as claimed.Brief Description of Drawings

[0019] FIG. 1A is a flowchart of an example method according to embodiments of the present disclosure.

[0020] FIG. IB is a flowchart of another example method according to embodiments of the present disclosure.

[0021] FIG. 2 shows an example system according to embodiments of the present disclosure.

[0022] FIG. 3 A illustrates particle convergence for a low SNR (signal-to-noise ratio) case.

[0023] FIG. 3B is a graph tracking performance for the low SNR case.

[0024] FIG. 4A illustrates a frequency domain representation of ideal point target at distance, R., according to embodiments of the present disclosure.

[0025] FIG. 4B illustrates time domain representation of a point target, according to embodiments of the present disclosure.

[0026] FIG. 4C illustrates frequency domain representation of ideal point target at distance, R, according to embodiments of the present disclosure.

[0027] FIG. 4D illustrates a frequency domain filter response for two band case, according to embodiments of the present disclosure.

[0028] FIG. 4E illustrates an example time domain representation of filter structure, according to embodiments of the present disclosure.

[0029] FIG. 4F illustrates an example filtered response of a target, according to embodiments of the present disclosure.

[0030] FIG. 4G illustrates a filtered response of target with phase information applied, according to embodiments of the present disclosure.

[0031] FIGS. 5A-5D show distributions for high SNR for Full Band, Single Contiguous Band, Non-Contiguous Band, and Non-Contiguous Band with Phase, respectively

[0032] FIGS. 6A-6D show distributions for medium SNR for Full Band, Single Contiguous Band, Non-Contiguous Band, and Non-Contiguous Band with Phase, respectively.

[0033] FIGS. 7A-7D show distributions for low SNR case for Full Band, Single Contiguous Band, Non-Contiguous Band, and Non-Contiguous Band with Phase, respectively.

[0034] FIG. 8 is a schematic for a measurement setup that was utilized in a conducted study.

[0035] FIG. 9 and FIG. 10 are graphs demonstrating beneficial effects of applying the phase center calibration step.

[0036] FIG. 11 are graphs showing samples of the processed magnitude and phase data for various bandwidth conditions.

[0037] FIGS. 12A-12D showtime domain reconstruction for Full Band, Single Contiguous Band, Non-Contiguous Band, and Non-Contiguous Band with Phase, respectively.

[0038] FIGS. 13A-13D show measurement results for 0 dB attenuation, 8 dB attenuation, 14dB attenuation, and 17 dB attenuation.

[0039] FIG. 14 illustrates an example computing device.Detailed Description

[0040] The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings and from the claims.

[0041] Throughout the description and claims of this specification, the word “comprise” and other forms of the word, such as “comprising” and “comprises,” means including but not limited to, and is not intended to exclude, for example, other additives, components, integers, or steps.

[0042] To facilitate an understanding of the principles and features of various embodiments of the present invention, they are explained hereinafter with reference to their implementation in illustrative embodiments.

[0043] An example embodiment of the present disclosure was designed and studied. The example embodiment includes a system and method for integrating non-contiguous frequency bands.Example Method

[0044] FIG. 1A is a flowchart of an example method 100 for integrating non-contiguous frequency bands. In some implementations, the method 100 can be at least partially performed using the system 200 described in connection with FIG. 2 below. Additionally, and or alternatively, the method 100 can be at least partially performed by a processing circuitry (for example, but not limited to, an application-specific integrated circuit (ASIC), or a central processing unit (CPU)). In some examples, the processing circuitry may be electrically coupled to and / or in electronic communication with other circuitries of an example computing device, such as, but not limited to, the example computing device 1400 described in connection with FIG. 14. In some examples, embodiments may take the form of a computer program product on a non-transitory computer-readable storage medium storing computer-readable program instruction (e.g., computer software). Any suitable computer-readable storage medium may beutilized, including non-transitory hard disks, CD-ROMs, flash memory, optical storage devices, or magnetic storage devices. This disclosure contemplates that the example operations can be performed using one or more computing devices (e.g., at least the basic configuration illustrated in FIG. 14 by box 1402).

[0045] At step 110, the method 100 includes receiving (e.g., by a reader such as a passive or semi-passive tag) a signal associated with a target.

[0046] At step 120, the method 100 includes filtering the received signal using a filter to select non-contiguous frequency bands. In some embodiments, filtering the received signal further comprises defining a frequency domain filter. In some examples, the frequency domain filter can define a set of active bands and a set of notched bands.

[0047] At step 130, the method 100 includes determining phase information for the selected non-contiguous frequency bands. In some implementations, the method 100 further includes calibrating an initial phase of the target’s response by selecting phase information from the lowest frequency band of the selected non-contiguous frequency bands and eliminating phase information that is incoherent with the phase information for the lowest frequency band. In some examples, calibrating the initial phase of the target’s response comprises applying a linearization filter to the phase response of the target.

[0048] At step 140, the method 100 includes determining a time domain response of the determined phase information for the selected non-contiguous frequency bands, for example using an Inverse Discrete Fourier Transform (IDFT).

[0049] At step 150, the method 100 includes determining a location and / or orientation of the target based on the determined time domain response. In some implementations, determining the location of the target comprises convolving a time domain representation of the filter with the determined time domain response. In some examples, the method 100 described above can be performed in an iterative fashion on order to track the location of the target.

[0050] FIG. IB is a flowchart of signal processing and pre-processing steps for a noncontiguous sub-band integration method 160 in accordance with certain embodiments of the present disclosure. It should be understood that at least a portion of the steps described can be combined with any of the steps described in relation to FIG. 1 A above. The example method 160 can be performed using some or all of the components of the measurement setup described in connection with FIG. 8 and / or one or more computing devices (e.g., at least the basic configuration illustrated in FIG. 14 by box 1402).

[0051] At step 170, the method 160 includes importing data, for example, but not limited to, signal data associated with a given target from a Vector Network Analyzer (VNA).

[0052] At step 172, the method 160 includes a first pre-processing step. The first preprocessing step can comprise employing an environmental calibration which is achieved by subtracting the frequency domain response of the environment without the target present from that with the target in order to improve the signal detectability.

[0053] At step 174, the method 160 includes a second pre-processing step that comprises phase center calibration / alignment. The second pre-processing step can ensure that the phase centers of all the bands in use are correctly aligned thus mitigating the effects of dispersion in the antennas. In some implementations, aligning the phase centers is done by simply applying a linearization filter to the phase response of the target. This is achieved by using reference data taken at the initial position of the target before any displacements then obtaining a first order linear fit of the phase response of this measurement. The difference between the fitted response and the initial measured response represents the linearization filter that can be applied to all subsequent measurements.

[0054] At step 176, after the phase center calibration, the method 160 includes calibrating the initial phase of the target response. This is important so that the phase at all distances spanned by the process is well known and can be used to reduce the decision space. In some embodiments, the initial phase calibration is done by using the linear fitted phase of the reference measurement and multiplying this response with each subsequent measurement so that the reference measurement now becomes the origin of phase. After the calibration steps, the next step is to extract the subsets of the data that will be processed and compared. Similar to the simulated cases, a comparison is done between the full bandwidth case, a single continuous band and the non-contiguous case both before and after application of the additional phase information.

[0055] To facilitate this comparison, at step 178, a frequency domain filter is applied over the collected data for different bandwidth conditions.

[0056] At step 180, the final step in the signal processing flow is the application of an Inverse Fast Fourier Transform (IFFT) to the frequency domain data.

[0057] From the time domain representation, at step 182 and step 184, a simple maximum peak search can then be applied to find the most likely range. This process is repeated for the N observations at each displacement step and level of attenuation.Example System

[0058] FIG. 2 shows an example system 200 configured for integrating non-contiguous frequency bands in accordance with an illustrative embodiment. As shown, the system 200 includes a non-contiguous sub-bands transmitter 202 and a receiver 204 in electronic communication with a tag 206. In various implementations, the non-contiguous sub-bands transmitter 202 and receiver 204 can be, define, or include a reader, network analyzer, or another tag. In some aspects, the non-contiguous sub-bands transmitter 202 and receiver 204 are configured to determine frequency and phase information of transmitted and received signals to and from a target (e.g., tag 206) in order to determine and / or track the location of the target.

[0059] FIG. 3 A illustrates particle convergence for a low SNR case and FIG. 3B is a graph tracking performance for the low SNR case and provides estimates compared to Ground Truth. A low SNR case may refer to a signal that is difficult to detect or distinguish due to noise whereas a high SNR case may refer to a signal that is relatively easier to detect or distinguish. Embodiments of the present disclosure can consider some point target at some unknown distance, R which can be modelled by the impulse function 6(t — T) as shown in FIG. 4B. Generally, the target will be observed in frequency domain by some reader that sends out a series of evenly spaced frequencies and recording the magnitude and phase received at each frequency. For a frequency range starting atminand ending atmax, the frequency domain representation including magnitude and phase can be seen in FIG. 4A which shows frequency domain representation of ideal point target at distance, R. FIG. 4B shows a time domain representation of a point target.

[0060] A continuous swept bandwidth allows some level of reconstruction of the time domain profile of the target which allows the determination of the range. Embodiments of the present disclosure include a process for integrating a set of non-contiguous frequency bands.

[0061] In an aspect, embodiments of the present disclosure include defining a Filtering Structure. Integrating information from a set of non-contiguous frequency bands can include defining a frequency domain filter, which would indicate which bands in a continuous frequency vector are active and which bands are notched. The definition of this filter is given in Equation 1, where fnand Bnare the lowest frequency and bandwidth of the nth sub-band, respectively.

[0062] Taking the base case of two bands active with no information present in between, the filter response can be represented as shown in FIG. 4D which shows the frequency domain filter response for two band cases. This filter can then be applied to the frequency response of the ideal target to get the non-continuous frequency domain data that is then processed. An example result of this is shown in FIG. 4E which shows the time domain representation of the filter structure.

[0063] Embodiments of the present disclosure can include an Inverse Discrete Fourier Transform (IDFT), which produces the corresponding time-domain response. Ordinarily, for a simple high-pass or lowpass filter structure, the output of the IDFT is expected to be a simple Sine function. However, for the structure described by Equation 1, and owing to the fact that there is a set of discontinuous frequency bands in play, there can be a different result after applying an Inverse Fast Fourier Transform (IFFT). The time-domain spectra show an enveloped Sine function with periodically repeating peaks that are almost discrete in nature. This discretization of the spectral peaks in the time domain is one of the features of the described process that is to be leveraged by the example embodiment of the present disclosure. The spacing between and the distribution of the spectral peaks are a function of the chosen start frequencies for each sub-band as well as the available bandwidth. The time domain representation of the filter structure shows the function with which the time-domain response of a target can be convolved in order to determine its location, while the nature of the spectrum would allow for better discrimination of a target. Optionally, the example embodiment can make use of additional available information in the phase of the lowest frequency sub-band in order to achieve our desired accuracy.

[0064] As noted above, embodiments of the present disclosure can utilize additional phase information. At first glance, the phase of the discontinuous multi-band signal can appear ambiguous and not well known. Embodiments of the present disclosure show that it follows that of the lowest measured frequency. For example, a filter structure, H f), as defined in Equation 1 and shifting it in frequency to H f — / 0) such that some frequency, f0is the lowest frequency in the first sub-band, then Equation 2 shows that the phase of the time domain spectrum of H f — / 0) follows that of f0over time.IFFT [H(f - / o)] = e'^^lFFT [H( )] (2)

[0065] Once the initial phase is known, it can be combined with knowledge of the spectra in order to improve the degree of accuracy of the process. For ranging done via round-trip time ct of flight, each t in Equation 2 is correspondent to a range, r, which is given by The phase isthen multiplied by the time-domain spectra of the filter, and then the real part of that quantity is added to the magnitude of the time-domain spectra of the filter, as shown in Equation 3. In doing this, the portions of the spectra that are not phase coherent with the target can be eliminated, and the parts that are phase coherent amplified so that there is now an increased ability to discriminate which of the peaks represent the target range in a noisy environment.G = abs(IFFT[H(f ]') + real (ej2^ot / FFT[H( / )]) (3)

[0066] The main operating principle here is the fact that given the knowledge of the initial phase of the interrogation sequence and the use of a sparse non-continuous set of bandwidths, the decision space of the location of a given target can be significantly reduced and thus yield higher accuracy and a greater ability to discriminate between different ranges in the presence of noise. This reduction in space is illustrated in FIG. 4F which shows the filtered response of the target with phase information applied.

[0067] It is to be understood that the methods and systems are not limited to specific synthetic methods, specific components, or particular compositions. It is also to be understood that the terminology used herein is for the purpose of describing particular implementations only and is not intended to be limiting.Discussion

[0068] Over the past few years there has been an increasing interest in the uses and applications of contact-less sensing systems for the detection of either stationary or moving objects. A typically investigated parameter in these sensing systems is the distance between the object of interest and the sensor. A variety of methods exist for distance estimation in contactless systems including but not limited to interferometry, round-trip time of flight-based methods and combinations thereof.

[0069] Phase interferometry techniques are applied generally in the measurement of small distances with high accuracy and in low multi-path environments where the target of interest represents the most dominant signal received. The resolution of this technique is dependent on the frequency of operation such that higher frequencies can give better estimates of the phase of the signal over a smaller range which represents a particular distance however that is at the cost of a lower unambiguous range due to the shorter wavelengths at higher frequencies [1],

[0070] Round-trip time of flight-based techniques for distance estimation involve the measurement of the total time taken for a particular signal to travel from a source to the target of interest and back. Frequency Modulated Continuous Wave (FMCW) radar and ultrawideband (UWB) methods have been thoroughly investigated and presented asparticularly robust in determining the distance of a target with sensitivity and accuracy relative to system parameters such as bandwidth, signal-to-noise ratio and operating frequency.

[0071] The specific limiting factor for important parameters such as resolution and accuracy of the distance measurement of the target has been found to be dependent largely on the bandwidth over which the available signal information is integrated. Fundamentally the resolution limit is given strictly by the relation in Equation 1 where c is the speed of light in the medium and B is the available bandwidth.

[0072] The expression relating accuracy and bandwidth is slightly more intricate and is shown via the well known Cramer-Rao bound for an unbiased frequency estimate and is defined for an FMCW radar in [2] and shown in Equation 2 where r is the target range, v is the group velocity, N is the number of samples, B is the available bandwidth and TJ is the SNR.

[0073] Given the high dependency of range resolution and accuracy of the measured range on the total available bandwidth, a variety of methods have been proposed to achieve relatively high accuracy, resolution and unambiguous range but while using a very high bandwidth in excess of thousands of MHz [3]-[8], This presents an unfeasible solution for the majority of contact-less sensing and range finding applications for two primary reasons: (1) Regulatory agencies restrict bandwidth usage for electronics to the Industrial, Scientific and Medical (ISM) bands (which are typically only allotted in hundreds of MHz). (2) Use of ultra-high bandwidths for these systems inadvertently drive up both the physical and computational costs of implementation of the system.

[0074] Wireless Ranging-. As previously discussed, ranging through the use of wireless signals is achieved by processing the round-trip time of flight of the propagating signal, measuring the received signal strength or some combination of both. This can be achieved either completely passively or with the deployment of some set of RFID tags or other transponder to improve accuracy, range, and resolution. For the purposes of the work done and the methods described herein, we will consider passive targets and hone in on the phase evaluation and roundtrip time of flight methods of ranging that have been demonstrated in literature to be the preferred solution for applications desiring high accuracy.

[0075] Phase Evaluation'. When an electromagnetic wave propagates in some media (free space, loss media), it experiences changes to its amplitude and phase. The measure of the change experienced by this wave is given by the propagation constant given in Equation 3where the real part, a is the attenuation constant and the imaginary part, P is the phase constant. For non-conductive media, the attenuation constant is negligible and only the phase constant which represents the phase change per unit length over the distance traversed by the wave. For Transverse Electro-Magnetic (TEM) waves in lossless media, the phase constant is given by equation Equation 4 where is the wavelength of the propagating wave. The phase constant is defined such that when a wave traverses a distance Z, it accumulates a phase equivalent to 0 as defined by Equation 5. y = a + ip (3)P = T (4) e = pi (5)

[0076] Now, considering some point target at a distance R from a reader. In order to determine its range, a signal is first generated and sent out towards the target. The target reflects this signal, modulating its amplitude and phase. The reflected signal is processed at the reader to determine the distance R. The interrogating signal, Z(t) is defined in Equation 6 with amplitude, A, frequency, fcand some random initial phase (p0.I(t) = A ■ (2nfct + (po) (6)

[0077] As the signal / (t) propagates towards the target and then back towards the reader, it experiences accumulating phase following Equation 5 such that the reflected signal processed at the reader, Z?(t) can be represented by Equation 7 where q is the amplitude scaling factor, p is the phase constant as defined above and R is the distance between the reader and the target.Z?(t) = A ■ q ■ (2nfct + (po+ 2 / ? / ?) (7)

[0078] Thus, from Equation 7 the phase of Z?(t) can be monitored to extract the range of the target. Given the initial phase of the interrogating signal is known, this can be de-embedded on the received signal and the 2pR piece can be used to solve for the range of the target. This method proves to be very sensitive as fractional changes in R result in larger changes in the received signal phase. However, a problem persists in that the phase of the received signal is ambiguous about 2n; thus for the round trip propagation the range determined is ambiguous about Taking Equation 4 and Equation 5 and solving for the unknown distance that the signal travels yields Equation 8. Given that 0 is ambiguous about 2n, then 0 = 0 + n ■ 2n where n is some positive integer which indicates the number of full periods of the signal that has elapsed. 0 R - -2 2TT

[0079] Consequently, higher frequencies translate to a shorter unambiguous range but higher accuracy and sensitivity while lower frequencies yield a longer unambiguous range with reduced sensitivity. The target application use typically informs the chosen signal frequency.

[0080] Multi-frequency Phase Ranging: A relatively straightforward approach to resolving the phase ambiguity in the method described above is in the employment of more than one frequency to interrogate the target and extract the range. This concept rests on the idea that signals at different frequencies that travels the same amount of time would experience different phase shifts. For example, considering a system where the reader first transmits a signal with frequency, and then measures the phase of the returned signal for a target at some distance R. The phase, 0Xis given by Equation 9. A signal with frequency, f2is also transmitted and its phase is given by equation Equation 10.

[0081] Equation 9 and Equation 10 can be combined to solve unambiguously for the unknown distance, R. The result of this combination is given in equation Equation 11.

[0082] In actual real-world implementations, the employment of only two frequencies to measure the received signal phase results in poor accuracy in the ranging process. Thus, the phase is commonly measured at more than two frequencies thus improving the system resolution and accuracy. The resolution and accuracy of the system is dependent on the bandwidth of the frequencies in use which is defined here as the difference between the largest and smallest frequencies. Given that the maximum difference in phase that can be measured is 2TT, this can be substituted into Equation 11 to give Rmaxwhich is the maximum unambiguous range for the multi -frequency phase ranging process.

[0083] When a set of more than two frequencies that are necessarily evenly spaced is used to range some target at an unknown distance, the resulting magnitude and phase measured at each of these frequencies can be integrated to generate a representative time-domain signal.This is done by the application of an Inverse Discrete Fourier Transform (IDFT) across the magnitude and phase information for each frequency sample which reveals the time-domain representation of the round-trip signal propagation. Ranging can then be done in the timedomain context via the relationship between the signal propagation speed, target range, and the time it takes the signal to propagate to the target and back. This relationship is represented in Equation 13 where c is the speed of propagation and T is the round-trip time of flight. In the time domain signal, the response of the target will be centered at T.R = T (13)

[0084] Underlying this is still the idea of using multi -frequency phase-based ranging however the Fourier analysis approach simplifies the interpretation of results from integration across multiple frequencies. With the time-domain analysis, the ability to discriminate between two or more closely spaced targets (resolution) and the alias-free distance observable (unambiguous range) are of importance. These quantities are governed by the total bandwidth in use and the spacing between the frequency samples. Equation 1 and Equation 2 show more explicitly that the resolution and accuracy of the ranging method is strongly dependent on bandwidth. This is easily understandable and quite apparent through the lens of Fourier analysis and its properties. It is known that a signal that has finite support in the time / frequency domain must have infinite support in the opposite domain. This means that a band-limited (finite support in frequency domain) signal must have infinite support in time domain and a timelimited signal (finite support in time domain) must have infinite support in frequency domain. Intuitively, if we consider some point target at a distance, R which can be modelled by an impulse delta function, 6(t — T) where T is the roundtrip time of flight to the target given by 2.RT = — . This would represent a signal with finite support as the function 6(t — T) is zero everywhere except t = T. From standard Fourier transform properties, the frequency domain representation of the point target will be a complex exponential with infinite bandwidth. Ideally, it is possible to reconstruct the time domain signal from a frequency domain observation by applying the IDFT. However, for a time-limited signal such as this an infinite bandwidth would be required for perfect reconstruction. Although perfect reconstruction of the target response is not needed to extract its range with reasonable accuracy, it stands to reason that the accuracy of the obtained range and ability to resolve more closely spaced targets would experience positive correlation with the quality of the reconstruction achieved. This idea is summarized in FIG. 4A which shows the simulated time domain response reconstruction for a point target observed with varying bandwidth. As can be seen on the plot, as the bandwidth ofthe target observation is increased the response resembles more that of a delta function as would be expected.

[0085] Non-Contiguous Bandwidth Integration

[0086] To this point, wireless ranging via the use of evenly spaced frequency samples has been discussed and it has been shown that the bandwidth over which a target of interest is observed couples directly into the achievable accuracy and resolution of the overall system. However, as alluded to above, governmental regulations on bandwidth usage and increased implementation costs of deploying ultra-wide bandwidth systems necessitates the development of an alternative means of realizing high accuracy in ranging while working within the confines of those limitations. This brings about the question that the present disclosure aims to answer - is it possible to integrate information across a set of non-contiguous frequency bands in order to yield higher accuracy in ranging?

[0087] Experimental Results and Additional Examples

[0088] The performance benefits realized by the application of this method were evaluated in a conducted study by numerical simulation in MATLAB. To validate the performance of the developed method and show its utility in a realistic scenario, a measurement campaign was also carried out to test the performance and limits of the method.

[0089] The use of the non-contiguous bands with the additional information from the initial phase proves extremely useful in solving that problem, as the peaks that previously were being selected are now found to be incoherent and unable to be selected. The response of this method falls almost exactly in line with that of the full bandwidth despite the utilization of only a fraction of that bandwidth. This method also overcomes the limitation of the single continuous band method as it is able to discriminate between small displacements very accurately and with low variance.

[0090] Description of Approach: As mentioned earlier, we can consider some point target at some unknown distance, R which can be modelled by the impulse function 8(t — T) as shown in FIG. 4B. Generally, the target will be observed in frequency domain by some reader that sends out a series of evenly spaced frequencies and recording the magnitude and phase received at each frequency. For a frequency range starting at fminand ending at fmax, the frequency domain representation including magnitude and phase can be seen in FIG. 4C. As discussed earlier and as demonstrated in FIG. 4A, a continuous swept bandwidth allows some level of reconstruction of the time domain profile of the target which allows the determination of the range. However we are interested in a process that allows us to integrate a set of noncontiguous frequency bands.

[0091] 1) Defining a Filtering Structure: The first step in the process of integrating information from a set of non-contiguous frequency bands is to define a frequency domain filter which would indicate which bands in a continuous frequency vector are active and which bands are notched. The definition of this filter is given in Equation 14 where fnand Bnare the lowest frequency and bandwidth of the nth sub-band respectively. / / ( / ) (14)> fl fo f fo + Bo, . . fn< f < fn+ Bnt 0 otherwise

[0092] Taking the base case of two bands active with no information present in between, the filter response is represented as shown in FIG. 4E. This filter can then be applied to the frequency response of the ideal target to get the non-continuous frequency domain data that is then processed. The result of this is shown in FIG. 4F which shows the filtered response of the target.

[0093] The frequency response of the filter as described is not particularly interesting; however, the key to the procedure described here lies in its Inverse Discrete Fourier Transform (IDFT) which produces the corresponding time-domain response. Ordinarily, for a simple high-pass or low-pass filter structure, the output of the IDFT is expected to be a simple Sine function. However for the structure described by Equation 14, and owing to the fact that there is a set discontinuous frequency bands in play we get a more interesting result after applying an Inverse Fast Fourier Transform (IFFT). The time-domain spectra shows an enveloped Sine function with periodically repeating peaks that are almost discrete in nature. This discretization of the spectral peaks in the time domain is one of the features of the described process that is to be taken advantage of. The spacing between and the distribution of the spectral peaks are a function of the chosen start frequencies for each sub-band as well as the available bandwidth. The time domain representation of the filter structure shows the function with which the timedomain response of a target would be convolved with in order to determine its location and while the nature of the spectrum would allow for better discrimination of a target, we can make use of additional available information in the phase of the lowest frequency sub-band in order to achieve our desired accuracy.

[0094] 2) Utilizing Additional Phase Information: At first glance, the phase of the discontinuous multi-band signal may seem to be ambiguous and not well known but it can be shown that it follows that of the lowest measured frequency. Taking for example a filter structure, H(f) as defined in Equation 14 and shifting it in frequency to H f — / 0) such thatsome frequency, f0is the lowest frequency in the first sub-band then Equation 15 shows that the phase of the time domain spectrum of H f — / 0) follows that of f0over time.IFFT[H(f - / o)] = e^^lFFT H^ (15)

[0095] Once the initial phase is known, it can be combined with knowledge of the spectra in order to improve the degree of accuracy of the process. For ranging done via round-trip time ct of flight, each t in 15 is correspondent to a range, r which is given by — . The phase is then multiplied with the time-domain spectra of the filter and then the real part of that quantity is added into the magnitude of the time domain spectra of the filter as shown in Equation 16. In doing this, the portions of the spectra that aren’t phase coherent with the target can be eliminated and the parts that are phase coherent amplified so that there is now increased ability to discriminate which of the peaks represent the target range in a noisy environment.G = abs(IFFT[H( ])' + rea\(ej2nf°tIFFT[H(J)' ]') (16)

[0096] The main operating principle here is the fact that given the knowledge of the initial phase of the interrogation sequence and the use of a sparse non-continuous set of bandwidths, the decision space of the location of a given target can be significantly reduced and thus yield higher accuracy and a greater ability to discriminate between different ranges in the presence of noise. This reduction in space is illustrated in FIG. 4G which shows the filtered response of the target with phase information applied.

[0097] Simulation

[0098] As noted above, the performance benefits realized by the application of the proposed method were evaluated by numerical simulation in MATLAB. As was mentioned previously, the strength of the method of non-contiguous sub-band integration lies in its ability to greatly reduce the decision space for a given observation of the target in comparison to a single continuous bandwidth. When comparing the integration of multiple bands to a single continuous band, it is necessary to compare with the same total amount of bandwidth such that there is equal energy in either case. In MATLAB, a series of N noisy frequency domain observations of a point target are generated then the time-domain profile of the target is reconstructed using the method prescribed above both in the case of the additional phase information applied and in the case where that information is assumed to be unavailable. This reconstruction is then compared with one done using the full available bandwidth, a single continuous bandwidth equal to the sum of the non-contiguous bands in use. The comparisons are done in three cases of low, medium and high signal-to-noise ratio (SNR). The noise is modelled to be a complex Gaussian with a specified variance indicating the noise power. Ineach case considered, N = 10000 observations of the target at R = Im are realized for a given SNR. A frequency range spanning 5.725 GHz to 24.25 GHz is synthesized with known ISM bands centered at 5.8 GHz and 24 GHz chosen as the two non-contiguous bands. Histogram plots showing the distributions are shown in FIGS. 5A-5D, FIGS. 6A-6D, and FIGS. 7A-7D. Specifically, FIGS. 5A-5D show distributions for high SNR case for Full Band, Single Contiguous Band, Non-Contiguous Band, and Non-Contiguous Band with Phase, respectively. FIGS. 6A-6D show distributions for medium SNR for Full Band, Single Contiguous Band, Non-Contiguous Band, and Non-Contiguous Band with Phase, respectively. FIGS. 7A-7D show distributions for low SNR case for Full Band, Single Contiguous Band, Non-Contiguous Band, and Non-Contiguous Band with Phase, respectively.

[0099] For the high SNR case shown in FIGS. 5A-5D, the benefits of the use of a set of non-contiguous bands can start to be seen. High accuracy can be seen across all methods however the decision space in the multi -band method and the multi -band method with the phase information applied is smaller than in the case of a single continuous band. In the medium SNR case shown in FIGS. 6A-6D the true benefits of the non-contiguous integration approach can be seen. With the full band case representing a more ideal reconstruction and setting a reference point, the single continuous band case has worse performance as expected and sees a higher degree of variance in its relatively normal distribution. The multiband method shows a significant reduction in the decision space and even more so after the initial phase is applied to the time domain representation. Finally, in the low SNR distributions shown in FIGS. 7A-7D, the full band case still sees good performance; however that of the single continuous band has deteriorated significantly with greater variance around the mean true range. The ability of the non-contiguous sub-band integration method to clean up the distribution and increase the likelihood of selecting the correct range is demonstrated.

[0100] Measurements

[0101] To validate the performance of the developed method and show its utility in a realistic scenario, a measurement campaign was carried out to test the performance and limits of the method.

[0102] 1) Measurement Setup: The measurement setup was comprised of a two-port VectorNetwork Analyzer (VNA) used to synthesize a set of signals spanning the range 2 GHz to 24.25 GHz. This band was chosen as it includes a set of ISM bands centered at 2.4, 5.8 and 24.125 GHz each with different bandwidths. Each port of the VNA was connected to a wide-band antenna that was able to cover this range of frequencies to create the transmit and receive paths. A voltage controlled variable attenuator is added to the transmit path which enables the signalto noise ratio of the system to be dynamically adjusted in order to evaluate the performance of the system under a set of different conditions. The attenuator used was the RFVAT0050A17 which enabled up to 17 dB of attenuation. The pair of transmit and receive antennas are mounted on a tripod to ensure stability. The target used for these measurements was a flat rectangular metal plate. This target was chosen as it closely resembles the response of that of a unit point target. The metal plate was mounted on a millimeter scale track to evaluate a set of small distances. The target was initially displaced from the interrogator setup at a distance of approximately R = 1.1m. The target was then displaced by 1mm, 2mm, 5mm and 10mm with N = 100 measurements taken at each step. These measurements are repeated with the attenuator set to 0 dB, 8 dB, 14 dB and 17 dB.

[0103] 2) Data Collection and Signal Processing:

[0104] FIG. 8 shows a schematic for the measurement setup 800 utilized. The Anritsu 37369A VNA used to synthesize and collect the transmit and received signals is aided by an IQ down conversion process that enables the device to output magnitude and phase information over the desired range of frequencies. The data collected by the VNA was then imported into MATLAB for post-processing. The first pre-processing step is the employment of an environmental calibration which is achieved by subtracting the frequency domain response of the environment without the target present from that with the target in order to improve the signal detectability.

[0105] Given the nature of the measurement setup and the employment of wide-band antennas spanning multiple GHz as well as our interest in integrating information from frequency bands many GHz apart, the next pre-processing step is to ensure that the phase centers of all the bands in use are correctly aligned thus mitigating the effects of dispersion in the antennas. Aligning the phase centers is done by simply applying a linearization filter to the phase response of the target. This is achieved by using reference data taken at the initial position of the target before any displacements then obtaining a first order linear fit of the phase response of this measurement. The difference between the fitted response and the initial measured response represents the linearization filter that can be applied to all subsequent measurements. FIGS. 9 and 10 show the beneficial effects of applying the phase center calibration step. Specifically, FIG. 9 illustrates Before and after effects of phase center calibration shown in the time domain response. FIG. 10 illustrates before and after initial phase calibration.

[0106] After the phase center calibration there is an additional piece of calibration that is vital for the prescribed method which is the calibration of the initial phase of the targetresponse. As demonstrated in FIG. 10, this is important so that the phase at all distances spanned by the process is well known and can be used to reduce the decision space as explained previously. The initial phase calibration is done by using the linear fitted phase of the reference measurement and multiplying this response with each subsequent measurement so that the reference measurement now becomes the origin of phase then the method as described in Equation 16 shows the time domain representation of the reference measurement before and after the initial phase calibration showing the change so that the initial position of the target is now at r = 0m.

[0107] After the calibration steps the next step is to extract the subsets of the data that will be processed and compared. Similar to the simulated cases, a comparison is done between the full bandwidth case, a single continuous band and the non-contiguous case both before and after application of the additional phase information. To facilitate this comparison, a frequency domain filter is applied over the collected data for the different bandwidth conditions. FIG. 11 shows samples of the processed magnitude and phase data for each bandwidth condition.

[0108] The final step in the signal processing flow is the application of the IFFT to the frequency domain data as represented in FIGS. 12A-12D. Specifically, FIGS. 12A-12D illustrate time domain reconstruction for Full Band, Single Contiguous Band, Non-Contiguous Band, and Non-Contiguous Band with Phase, respectively. From the time domain representation, a simple maximum peak search can then be applied to find the most likely range. This process is repeated for the N observations at each displacement step and level of attenuation.

[0109] 3) Results: FIGS. 13A-13D show measurement results for 0 dB attenuation, 8 dB attenuation, 14dB attenuation, and 17 dB attenuation, respectively. The figures show the performance of each of the outlined methods of extracting the displacement of the target. As a result of the initial phase calibration step, the first measurement position has been zeroed out and now serves as the reference position so the range extracted for each subsequent position is relative to the initial position. Across all levels of attenuation, the range extraction with the full available bandwidth maintains strong performance as is expected given the large amount of information available across multiple GHz of bandwidth.

[0110] With increasing attenuation, range extraction using a single continuous bandwidth suffers in accuracy specifically in the ability to discriminate between displacements of 1mm and 2mm in the 14 dB and 17 dB attenuation cases. The initial case of the non-contiguous bands suffers from an inability to discern which of the discretized peaks in the vicinity of thetrue displacement is correct so there are predictable jumps in the estimated range that correlate with the distance between the peaks in the time-domain representation.[OHl] The use of the non-contiguous bands with the additional information from the initial phase proves extremely useful in solving that problem as the peaks that previously were being selected are now found to be incoherent and unable to be selected. The response of this method falls almost exactly in line with that of the full bandwidth despite the utilization of only a fraction of that bandwidth. This method also overcomes the limitation of the single continuous band method as it is able to discriminate between small displacements very accurately and with low variance.CONCLUSION

[0112] This disclosure has delved into the realm of wireless sensing systems for contactless distance estimation, focusing on phase interferometry and round-trip time of flight techniques. The investigation revealed the critical significance of bandwidth in determining distance measurement accuracy and resolution, while highlighting the challenges associated with limited bandwidth availability due to regulatory constraints and implementation costs.

[0113] To tackle these challenges, we proposed an innovative approach of non-contiguous bandwidth integration. This method amalgamates information from distinct frequency bands, drastically narrowing down the decision space for target localization. Leveraging phase information from the lowest frequency band, the method achieves remarkably higher accuracy and discrimination ability, competing with traditional full-bandwidth systems. The validity and potential of the proposed approach were verified through extensive simulations and real-world measurements. The results speak volumes, showcasing the practicality and cost-effectiveness of this method in real-life scenarios. By sidestepping the reliance on impractical ultra-high bandwidths, the method proves itself adaptable within regulatory constraints and significantly simplifies implementation complexities, broadening its applicability across a wide spectrum of scenarios.

[0114] In conclusion, the non-contiguous bandwidth integration technique demonstrated in this study holds exceptional promise for advancing wireless ranging systems. It presents a fresh perspective on achieving remarkable accuracy and resolution while adhering to bandwidth limitations. As we venture into diverse industrial, scientific, and medical domains, where precise distance measurements are of utmost importance, this innovative approach may become the beacon that illuminates the way forward.Example Computing Device

[0115] FIG. 14 shows an example computing device that may be configured to execute the operation described herein.

[0116] Referring to FIG. 14, an example computing device 1400 upon which the exemplary system and methods (e.g., for a part searcher) described herein may be implemented is illustrated. It should be understood that the example computing device 1400 is only one example of a suitable computing environment upon which the methods described herein may be implemented. Optionally, the computing device 1400 can be a well-known computing system including, but not limited to, personal computers, servers, handheld or laptop devices, multiprocessor systems, microprocessor-based systems, network personal computers (PCs), minicomputers, mainframe computers, embedded systems, and / or distributed computing environments including a plurality of any of the above systems or devices. Distributed computing environments enable remote computing devices, which are connected to a communication network or other data transmission medium, to perform various tasks. In the distributed computing environment, the program modules, applications, and other data may be stored on local and / or remote computer storage media.

[0117] In its most basic configuration, computing device 1400 typically includes at least one processing unit 1406 and system memory 1404. Depending on the exact configuration and type of computing device, system memory 1404 may be volatile (such as random-access memory (RAM)), non-volatile (such as read-only memory (ROM), flash memory, etc.), or some combination of the two. This most basic configuration is illustrated in FIG. 14 by dashed line 1402. The processing unit 1406 may be a standard programmable processor that performs arithmetic and logic operations necessary for operation of the computing device 1400. The computing device 1400 may also include a bus or other communication mechanism for communicating information among various components of the computing device 1400.

[0118] Computing device 1400 may have additional features / functionality. For example, computing device 1400 may include additional storage such as removable storage 1408 and non-removable storage 1410 including, but not limited to, magnetic or optical disks or tapes. Computing device 1400 may also contain network connection(s) 1416 that allow the device to communicate with other devices. Computing device 1400 may also have input device(s) 1414 such as a keyboard, mouse, touch screen, etc. Output device(s) 1412 such as a display, speakers, printer, etc. may also be included. The additional devices may be connected to the bus in order to facilitate communication of data among the components of the computing device 1400. All these devices are well known in the art and need not be discussed at length here.

[0119] The processing unit 1406 may be configured to execute program code encoded in tangible, computer-readable media. Tangible, computer-readable media refers to any media that is capable of providing data that causes the computing device 1400 (i.e., a machine) to operate in a particular fashion. Various computer-readable media may be utilized to provide instructions to the processing unit 1406 for execution. Example tangible, computer-readable media may include, but is not limited to, volatile media, non-volatile media, removable media and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. System memory 1404, removable storage 1408, and non-removable storage 1410 are all examples of tangible, computer storage media. Example tangible, computer-readable recording media include, but are not limited to, an integrated circuit (e.g., field-programmable gate array or application-specific IC), a hard disk, an optical disk, a magneto-optical disk, a floppy disk, a magnetic tape, a holographic storage medium, a solid-state device, RAM, ROM, electrically erasable program read-only memory (EEPROM), flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices.

[0120] In an example implementation, the processing unit 1406 may execute program code stored in the system memory 1404. For example, the bus may carry data to the system memory 1404, from which the processing unit 1406 receives and executes instructions. The data received by the system memory 1404 may optionally be stored on the removable storage 1408 or the non-removable storage 1410 before or after execution by the processing unit 1406.

[0121] It should be understood that the various techniques described herein may be implemented in connection with hardware or software or, where appropriate, with a combination thereof. Thus, the methods and apparatuses of the presently disclosed subject matter, or certain aspects or portions thereof, may take the form of program code (i.e., instructions) embodied in tangible media, such as floppy diskettes, CD-ROMs, hard drives, or any other machine-readable storage medium wherein, when the program code is loaded into and executed by a machine, such as a computing device, the machine becomes an apparatus for practicing the presently disclosed subject matter. In the case of program code execution on programmable computers, the computing device generally includes a processor, a storage medium readable by the processor (including volatile and non-volatile memory and / or storage elements), at least one input device, and at least one output device. One or more programs may implement or utilize the processes described in connection with the presently disclosed subject matter, e.g., through the use of an application programming interface (API), reusable controls,or the like. Such programs may be implemented in a high-level procedural or object-oriented programming language to communicate with a computer system. However, the program(s) can be implemented in assembly or machine language, if desired. In any case, the language may be a compiled or interpreted language and it may be combined with hardware implementations.

[0122] As used in the specification and the appended claims, the singular forms “a,” “an” and “the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another implementation includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another implementation. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint.

[0123] “Optional” or “optionally” means that the subsequently described event or circumstance may or may not occur, and that the description includes instances where said event or circumstance occurs and instances where it does not.

[0124] Throughout the description and claims of this specification, the word “comprise” and variations of the word, such as “comprising” and “comprises,” means “including but not limited to,” and is not intended to exclude, for example, other additives, components, integers or steps. “Exemplary” means “an example of’ and is not intended to convey an indication of a preferred or ideal implementation. “Such as” is not used in a restrictive sense, but for explanatory purposes.

[0125] Disclosed are components that can be used to perform the disclosed methods and systems. These and other components are disclosed herein, and it is understood that when combinations, subsets, interactions, groups, etc. of these components are disclosed that while specific reference of each various individual and collective combinations and permutation of these may not be explicitly disclosed, each is specifically contemplated and described herein, for all methods and systems. This applies to all aspects of this application including, but not limited to, steps in disclosed methods. Thus, if there are a variety of additional steps that can be performed it is understood that each of these additional steps can be performed with any specific implementation or combination of implementations of the disclosed methods.

[0126] The following patents, applications and publications as listed below and throughout this document are hereby incorporated by reference in their entirety herein.[1] T. Liu, M. Hsu, and Z. Tsai, “High ranging accuracy and wide detection range interferometry based on Frequency- Sweeping technique with vital sign sensing function,” IEEE Trans. Microw. Theory Tech., vol. 66, no. 9, pp. 4242-4251, Sep. 2018.[2] S. Scherr, S. Ayhan, M. Pauli, and T. Zwick, “Accuracy limits of a k-band FMCW radar with phase evaluation,” in 2012 9th European Radar Conference, Oct. 2012, pp. 246-249.[3] D. Vasisht, S. Kumar, and D. Katabi, “Decimeter-level localization with a single wifi access point,” in 13th {USENIX} Symposium on Networked Systems Design and Implementation ({NSDI} 16), 2016, pp. 165-178.[4] P. Caldero, M. Gareis, and M. Vossiek, “Saw rfid tag spatial division multiple access based on 3d reflector response localization using a wideband holographic approach,” IEEE Journal of Microwaves, vol. 2, no. 3, pp. 461-469, 2022.[5] J. Heidrich, D. Brenk, J. Essel, G. Fischer, R. Weigel, and S. Schwarzer, “Local positioning with passive uhf rfid transponders,” in 2009 IEEE MTT-S International Microwave Workshop on Wireless Sensing, Local Positioning, and RFID, 2009, pp. 1-4.[6] D. Amitz, K. Witrisal, and U. Muehlmann, “Multifrequency continuous-wave radar approach to ranging in passive uhf rfid,” IEEE Transactions on Microwave Theory and Techniques, vol. 57, no. 5, pp. 1398-1405, 2009.[7] L. Piotrowsky, T. Jaeschke, S. Kuppers, and N. Pohl, “An unambiguous phase-based algorithm for single-digit micron accuracy distance measurements using fmcw radar,” in 2019 IEEE MTT-S International Microwave Symposium (IMS), 2019, pp. 552-555.[8] L. Piotrowsky, T. Jaeschke, S. Kueppers, J. Siska, and N. Pohl, “Enabling high accuracy distance measurements with fmcw radar sensors,” IEEE Transactions on Microwave Theory and Techniques, vol. 67, no. 12, pp. 5360-5371, 2019.

Claims

What is claimed:

1. A method for performing contactless sensing, the method comprising: receiving a signal, wherein the signal is associated with a target and includes multifrequency phase information for each of a plurality of frequencies received by a reader; filtering the received signal using a filter to select non-contiguous frequency bands; determining phase information for the selected non-contiguous frequency bands; determining a time domain response of the determined phase information for the selected non-contiguous frequency bands; and determining a location of the target based on the determined time domain response.

2. The method of claim 1, wherein determining the location of the target comprises convolving a time domain representation of the filter with the determined time domain response.

3. The method of claim 1 or 2, wherein filtering the received signal further comprises: defining a frequency domain filter.

4. The method of claim 3, wherein the frequency domain filter defines a set of active bands and a set of notched bands.

5. The method of any one of claims 1-4, further comprising: calibrating an initial phase of the target’s response by selecting phase information from a lowest frequency band of the selected non-contiguous frequency bands.

6. The method of claim 5, wherein filtering the received signal comprises eliminating phase information that is incoherent with the phase information for the lowest frequency band.

7. The method of claim 5 or 6, wherein calibrating the initial phase of the target’s response comprises applying a linearization filter to the phase response of the target.

8. The method of any one of claims 1-7, wherein the time domain response is determined using an Inverse Discrete Fourier Transform (IDFT).

9. The method of any one of claims 1-8, wherein the reader is a passive or semi-passive tag.

10. A system comprising: a reader configured to capture multifrequency phase information; a processor; and a memory having instructions stored thereon, wherein execution of the instructions by the processor causes the processor to perform non-contact sensing by executing a set of processes to: receive a signal, wherein the signal is associated with a target and includes multifrequency phase information for each of a plurality of frequencies received by the reader; filter the received signal using a filter to select non-contiguous frequency bands; determine phase information for the selected non-contiguous frequency bands; determine a time domain response of the determined phase information for the selected non-contiguous frequency bands; and determine a location of the target based on the determined time domain response.

11. The system of claim 10, wherein execution of the instructions by the processor causes the processor to further: determine the location of the target by convolving a time domain representation of the filter with the determined time domain response.

12. The system of claim 10 or 11, wherein execution of the instructions by the processor causes the processor to filter the received signal by defining a frequency domain filter.

13. The system of any one of claims 10-12, wherein the frequency domain filter defines a set of active bands and a set of notched bands.

14. The system of any one of claims 10-13, wherein execution of the instructions by the processor causes the processor to further: calibrate an initial phase of the target’s response by selecting phase information from a lowest frequency band of the selected non-contiguous frequency bands.

15. The system of claim 14, wherein execution of the instructions by the processor causes the processor to filter the received signal by: eliminating phase information that is incoherent with the phase information for the lowest frequency band.

16. The system of claim 14 or 15, wherein execution of the instructions by the processor causes the processor to calibrate the initial phase of the target’s response by: applying a linearization filter to the phase response of the target.

17. The system of any one of claims 10-16, wherein execution of the instructions by the processor causes the processor to determine the time domain response using an Inverse Discrete Fourier Transform (IDFT).

18. The system of any one of claims 10-17, wherein the reader is a passive or semipassive tag.

19. A non-transitory computer readable medium comprising a memory having instructions stored thereon to cause a processor to: receive a signal, wherein the signal is associated with a target and includes multifrequency phase information for each of a plurality of frequencies received by a reader; filter the received signal using a filter to select non-contiguous frequency bands; determine phase information for the selected non-contiguous frequency bands; determine a time domain response of the determined phase information for the selected non-contiguous frequency bands; and determine a location of the target based on the determined time domain response.

20. The non-transitory computer readable medium of claim 19, wherein the memory having instructions stored thereon cause the processor to further: determine the location of the target by convolving a time domain representation of the filter with the determined time domain response.

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