Patent Description:
Unless otherwise indicated herein, the materials described herein are not prior art to the claims in the present application and are not admitted to be prior art by inclusion in this section.

Current operational weather radars operate within the radio frequency (RF) spectrum, a resource under increasing demand by various users and devices for, e.g., communications, remote sensing, and navigation. The increasing demand for and utilization of the RF spectrum has led to a significant increase in RFI for weather radar. RFI can significantly degrade the quality of weather radar observations, preventing the retrieval of desired meteorological information and presenting false data that might be mistaken for actual atmospheric observations.

Degradation of weather radar data resulting from RFI can occur in many radar systems, including those that use a solid-state power amplifier (SSPA) and/or pulse compression, due to the relatively short duty cycle and large receiver bandwidth used, respectively. Although regulations exist governing the use of the RF spectrum, the problem of RFI in weather radar observations continues to grow.

Document <CIT> discloses a precipitation estimation method based on an X-band all-solid-state dual-polarization rainfall radar. The method comprises computing ℓp norms of radials of weather radar data to construct an ℓp norm profile of the weather radar data as a function of azimuth angle, the weather radar data comprising Level <NUM> or higher weather radar data in polar format. The method further comprises determining that a given radial in the weather radar data is an RFI radial based on the ℓp norm profile of the weather radar data. Additionally, the method comprises displaying an image from the weather radar data in which at least one of: the RFI radial is identified in the image as including RFI, or the RFI radial is omitted from the image.

<NPL> further teach that electromagnetic disturbance (EMI) is an unpredictable event which often causes abnormal radar echo. EMI enables invariant radial interference echo existing in certain directions in radar echo charts at many radar stations. The interference echo and the precipitation echo overlap in many regions.

Additionally, document <CIT> describes that a Doppler radar apparatus includes a quadrature detection unit configured to quadrature-detect a received signal of a reflected pulse from an observation target, and generate time-series data including an in-phase component and a quadrature component, an interference judgment unit configured to judge whether an interference is mixed into the received signal based on the time-series data, a correction unit configured to correct a vector expressed by the in-phase component and the quadrature component such that variation with respect to time of a deviation angle of the vector continues when the interference judgment unit has judged than an interference signal is mixed into the received signal, and a calculation unit configured to calculate a Doppler velocity of the observation target based on an amount of variation with respect to time of the deviation angle of corrected vector.

Rather, this background is only provided to illustrate one example technology area where some embodiments described herein may be practiced.

According to a first aspect of the present invention, a method to mitigate RFI in weather radar data includes computing ℓp norms of radials of weather radar data to construct an ℓp norm profile of the weather radar data as a function of azimuth angle. The weather radar data includes Level <NUM> or higher weather radar data in polar format. Each ℓp norm comprises an ℓ<NUM> norm, a Manhattan Distance, or a Euclidian Norm. The method includes determining that a given radial in the weather radar data is an RFI radial based on the ℓp norm profile of the weather radar data. Determining that the given radial in the weather radar data is the RFI radial based on the ℓp norm profile of the weather radar data includes determining that a convolution of a derivative of the ℓp norm profile with a RFI kernel exceeds a threshold at an azimuth angle of the given radial, wherein the RFI kernel is a kernel that is associated with or indicative of RFI. The method includes displaying an image from the weather radar data in which at least one of: the RFI radial is identified in the image as including RFI; or the RFI radial is omitted from the image. According to the first aspect, Level <NUM> weather radar data refers to and includes data resulting from processing and creating data from Level <NUM> weather radar data and wherein Level <NUM> weather radar data refers to and includes time series of complex voltage samples of radar returns generated by a radar system.

According to a second aspect of the present invention, a non-transitory computer-readable medium has computer-readable instructions stored thereon that are executable by a processor to perform or control performance of various operations. The operations include computing ℓp norms of all radials of weather radar data to construct an ℓp norm profile of the weather radar data as a function of azimuth angle. The weather radar data includes Level <NUM> or higher weather radar data in polar format. Each ℓp norm comprises an ℓ<NUM> norm, a Manhattan Distance, or a Euclidian Norm. The operations include determining that a given radial in the weather radar data is an RFI radial based on the ℓp norm profile of the weather radar data. Determining that the given radial in the weather radar data is the RFI radial based on the ℓp norm profile of the weather radar data includes determining that a convolution of a derivative of the ℓp norm profile with a RFI kernel exceeds a threshold at an azimuth angle of the given radial, wherein the RFI kernel is a kernel that is associated with or indicative of RFI. The operations include displaying an image from the weather radar data in which at least one of: the RFI radial is identified in the image as including RFI; or the RFI radial is omitted from the image. According to the second aspect, Level <NUM> weather radar data refers to and includes data resulting from processing and creating data from Level <NUM> weather radar data and wherein Level <NUM> weather radar data refers to and includes time series of complex voltage samples of radar returns generated by a radar system.

According to an example, a method includes computing ℓp norms of radials of weather radar data to construct an ℓp norm profile of the weather radar data as a function of azimuth angle. The weather radar data may include Level <NUM> or higher weather radar data in polar format. The weather radar data in polar format may include, for each data point, a magnitude of the corresponding data point and a location of the corresponding data point, the location specified by a radial distance and azimuth angle. Each radial may include all data points that have an azimuth angle within a given range of azimuth angles across a radial distance range for each azimuth angle within the given range of azimuth angles. The method may include computing the derivative of the ℓp norm profile with respect to azimuth angle. The method may include obtaining an RFI kernel by one of: computing a template RFI kernel to use as the RFI kernel, the template RFI kernel including an approximation of typical radials in an azimuthal neighborhood of RFI; deriving a wavelet RFI kernel to use as the RFI kernel, the wavelet RFI kernel derived from data that represents an actual RFI radial and neighboring radials; or deriving an average wavelet RFI kernel to use as the RFI kernel, the average wavelet RFI kernel derived from data that represents multiple actual RFI radials and respective neighboring radials. The method may include computing a convolution of the derivative of the ℓp norm profile with the RFI kernel. The method may include determining that a given radial in the weather radar data includes an RFI radial based on the ℓp norm profile of the weather radar data, including determining that the convolution exceeds a threshold at an azimuth angle of the given radial. The method may include displaying an image from the weather radar data in which at least one of: the RFI radial is identified in the image as including RFI; or the RFI radial is omitted from the image.

Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by the practice of the invention. The features and advantages of the invention may be realized and obtained by means of the instruments and combinations particularly pointed out in the appended claims. These and other features of the present invention will become more fully apparent from the following description and appended claims, or may be learned by the practice of the invention as set forth hereinafter.

To further clarify the above and other advantages and features of the present invention, a more particular description of the invention will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings. The invention will be described and explained with additional specificity and detail through the use of the accompanying drawings in which:.

Some embodiments herein compute ℓp norms of radials of data in polar format. Each radial may include all data points having an azimuth angle within a given range of azimuth angles across a radial distance range for each azimuth angle within the range of azimuth angles. The range of azimuth angles may span a single degree or multiple degrees. Stated another way, a radial may include all data points across a radial distance range for a single-degree bin of azimuth angles or a multi-degree bin of azimuth angles. Where a given radial includes data points each having an azimuth angle within a multi-degree range of azimuth angles, the range of azimuth angles may include a center azimuth angle +/- some offset.

Some RFI mitigation techniques for weather radars are disclosed in <NPL> (hereinafter "Cho" or the "Cho paper"). Cho specifically describes three RFI mitigation techniques: (<NUM>) the "Vaisala-<NUM>" algorithm, (<NUM>) a 1D median filter, and (<NUM>) a 2D median filter. Of the three techniques, only the Vaisala-<NUM> algorithm is operational. The three techniques generally exhibit poor performance in the identification of RFI, particularly when coincident with precipitation, or are too computationally intense for real-time or near real-time identification of RFI in weather radar data.

Embodiments described herein generally mitigate RFI (e.g., identify and/or remove) better than the three techniques described in Cho and/or sufficiently quickly to be used in real-time or near real-time identification of RFI in weather radar data. In general, embodiments described herein identify RFI in Level <NUM> or higher weather radar data and optionally remove the RFI and/or impute the removed data. Because RFI is fundamentally characterized by a radially streaked nature that is apparent in images of Level <NUM> and Level <NUM> data, embodiments described herein may treat Level <NUM> and Level <NUM> data as images and thereby take an image processing approach to mitigate RFI.

As indicated, weather radar data may include at least Level <NUM> and Level <NUM> weather radar data, which is derived from Level <NUM> weather radar data. As used herein, Level <NUM> weather radar data refers to and includes a time series of complex voltage samples of radar returns generated by a radar system. In comparison, Level <NUM> weather radar data refers to and includes the data resulting from processing and creating data from the Level <NUM> weather radar data. Similarly, Level <NUM> weather radar data refers to and includes the data resulting from processing and creating data from the Level <NUM> weather radar data. Level <NUM> weather radar data may include data products such as reflectivity data, differential reflectivity data, normalized coherent power/signal quality index data, differential phase data, mean radial velocity data, correlation coefficient (ρhv) data, radar echo classification data, spectrum width data, total power data, linear depolarization ratio (LDR) data, specific differential phase (KDP) data, or other Level <NUM> data products. Level <NUM> weather radar data may include data products such as base and composite reflectivity data, storm relative velocity data, vertical integrated liquid data, echo tops and VAD wind profile data, precipitation products such as estimated ground accumulated rainfall amounts for one and three hour periods, storm totals, and digital arrays, or other Level <NUM> data products.

RFI may present differently in Level <NUM> (or higher) data products than it does in Level <NUM> data (e.g., the time series of complex voltage samples of radar returns), which is leveraged according to some embodiments herein for the identification of RFI. Although not required, some embodiments analyze multiple Level <NUM> data products to form a "consensus"; for example, if the analysis of a first Level <NUM> data product identifies RFI at first and second locations and the analysis of a different second Level <NUM> data product identifies RFI only at the first location, the consensus determination may be that only the RFI at the first location is identified as such. Accordingly, some embodiments herein provide "different looks" at the same underlying Level <NUM> data (e.g., through analysis of at least two different Level <NUM> data products generated from the same underlying Level <NUM> data). In such a consensus approach, different Level <NUM> (or higher) data products are used where each is based on weather radar data collected from a given area at a given time. Such a consensus approach may facilitate identification of RFI in weather radar data, including RFI that is coincident with precipitation, which is one of the most challenging scenarios for RFI identification.

Some embodiments herein may compute ℓp norms of radials of weather radar data to construct an ℓp norm profile of the weather radar data as a function of azimuth angle, where the weather radar data includes Level <NUM> or higher weather radar data in polar format. Such an ℓp norm profile may be referred to as a radial ℓp norm profile. In some embodiments, before computing the ℓp norms of the radials, one or more thresholds may be applied to the weather radar data to suppress noise and precipitation that may be coincident with the RFI. The ℓp norms according to embodiments herein may include the ℓ<NUM> norm, the Manhattan Distance, the Euclidian Norm, or other suitable ℓp norm.

Some embodiments may determine whether radials in the weather radar data include RFI, e.g., are RFI radials, based on the radial ℓp norm profile of the weather radar data. In this and other embodiments, a kernel may be computed that is associated with or indicative of RFI, a derivative of the radial ℓp norm profile with respect to azimuth angle may be computed, and a convolution of the derivative of the radial ℓp norm profile with the kernel may be computed. When the convolution exceeds a threshold at any given azimuth angle, the corresponding radial at the given azimuth angle may be determined to be or marked as an RFI radial. An image of the weather radar data may then be displayed in which any RFI radials are identified in the image as including RFI and/or are omitted from the image. In some cases where the RFI radials are omitted from the image, replacement data that replaces the omitted data may be completely or partially imputed from surrounding radials and may be displayed in the image. Alternatively or additionally, prior to displaying the image, the weather radar data may be despeckled and masked or otherwise processed to remove noise from the image.

Reference will now be made to the drawings to describe various aspects of example embodiments of the invention. It is to be understood that the drawings are diagrammatic and schematic representations of such example embodiments, and are not limiting of the present invention, nor are they necessarily drawn to scale.

<FIG> illustrates an example system <NUM> to generate weather radar data and mitigate RFI in the weather radar data, arranged in accordance with at least one embodiment described herein. The system <NUM> may include a radar system <NUM>, a computer device <NUM>, and a network <NUM>. The radar system <NUM> may generate weather radar data <NUM>. The computer device <NUM> may obtain the weather radar data <NUM> from the radar system <NUM> through the network <NUM> and may analyze it to identify RFI in the weather radar data <NUM>. Alternatively or additionally, the weather radar system <NUM> or other computer device or server may analyze the weather radar data <NUM> to identify RFI in the weather radar data <NUM>. If the weather radar data <NUM> is Level <NUM> weather radar data, the computer device <NUM> or the radar system <NUM> itself may convert the weather radar data <NUM> to or use it to generate one or more Level <NUM> or higher data products in polar format before the computer device <NUM> or the radar system <NUM> analyzes it to identify RFI therein.

Although illustrated with a single radar system <NUM> and a single computer device <NUM>, more generally the system <NUM> may include one or more radar systems <NUM> and one or more computer devices <NUM>. In some embodiments, the system <NUM> may further include one or more client devices that can access data and/or services available at or provided by the computer device <NUM>. For example, subscribers to a weather radar data service provided by the computer device <NUM> may use corresponding client devices to access the weather radar data <NUM> over the network <NUM> from the computer device <NUM>. In some embodiments, RFI may be identified in and/or removed from the weather radar data <NUM> by the computer device <NUM> (or other device) before being provided to the client devices.

In general, the network <NUM> may include one or more wide area networks (WANs) and/or local area networks (LANs) that enable the radar system <NUM>, the computer device <NUM>, and the client devices to communicate with each other. In some embodiments, the network <NUM> may include the Internet, including a global internetwork formed by logical and physical connections between multiple WANs and/or LANs. Alternately or additionally, the network <NUM> may include one or more cellular radio frequency (RF) networks, a voice over Internet Protocol (VOIP) network, a public switched telephone network (PSTN), and/or one or more wired and/or wireless networks such as <NUM>. xx networks, Bluetooth access points, wireless access points, Internet Protocol (IP)-based networks, or other wired and/or wireless networks. The network <NUM> may also include servers that enable one type of network to interface with another type of network.

In general, the radar system <NUM> may transmit electromagnetic waves (e.g., microwaves) towards a region of interest (e.g., an atmospheric region, an environmental region, etc.) or object of interest. The radar system <NUM> may receive reflections of the electromagnetic waves off of an object or objects, such as a storm system or precipitation <NUM> (e.g., rain, ice, sleet, hail, etc.) and may generate a time series of complex voltage samples from the received reflections. Such reflections may be referred to as reflectivity and the generated time series may be referred to as reflectivity data, which is a Level <NUM> data product. Any processing, filtering, or accumulation of the reflectivity data may be performed, for example, by the radar system <NUM> and/or the computer device <NUM>. The weather radar data <NUM> provided by the radar system <NUM> to the computer device <NUM> may include the reflectivity data and/or one or more Level <NUM> or higher data products generated from the reflectivity data.

<FIG> includes a weather radar image (hereinafter "image") <NUM> that represents weather radar data in polar format, arranged in accordance with at least one embodiment described herein. The weather radar data from which the image <NUM> is generated was part of a weather radar data set collected by a VAISALA dual-polarization C-band SSPA prototype <NUM> at Kumpula, Helsinki, Finland, on Mar <NUM>, <NUM>. The foregoing SSPA prototype is an example of the radar system <NUM> of <FIG> and is referred to hereinafter as radar system <NUM>. The foregoing weather radar data set is hereinafter referred to as the Kumpula data set. The Kumpula data set is an example of the weather radar data <NUM> of <FIG>. The image <NUM> has three readily identifiable RFI radials <NUM>, <NUM>, <NUM> respectively at the following azimuths: about <NUM> degrees (or about <NUM> o'clock), about <NUM> degrees (or about <NUM> o'clock), and about <NUM> degrees (about <NUM>:<NUM>).

With combined reference to <FIG> and <FIG>, the computer device <NUM>, the radar system <NUM>, <NUM>, or other computing resources may take one or more of the following actions to process and analyze the weather data <NUM> for RFI. For example, the computer device <NUM> may compute ℓp norms of radials of the weather radar data <NUM>, such as of the weather radar data used to generate the image <NUM>. In some embodiments, prior to computing the ℓp norms of the radials, the computer device <NUM> may convert the weather radar data <NUM> to one or more Level <NUM> or higher data products and/or may convert the weather radar data <NUM> to polar format if not already in the polar format.

In some embodiments, weather radar data in polar format may include, for each data point, a magnitude of the corresponding data point and a location of the corresponding data point specified by a radial distance from the radar system <NUM>, <NUM> and azimuth angle, where North may be considered an azimuth of <NUM> degrees. Computing the ℓp norms, and specifically the ℓ<NUM> norms, may include determining, for each radial, a number of data points in the corresponding radial that have a non-zero magnitude. In an example, each radial may include all data points with a given azimuth angle across a radial distance range. For example, the RFI radial <NUM> of <FIG> may include all data points of the weather radar data used to generate the image <NUM> that have an azimuth of about <NUM> degrees. More generally, each radial may include all data points having an azimuth angle within a given range of azimuth angles across a radial distance range for each azimuth angle within the range of azimuth angles. The radial distance range may extend from the radar system <NUM>, <NUM> (e.g., radial distance = <NUM>) or other minimum range to a resolution distance of the radar or other maximum range.

In some embodiments, the computer device <NUM> may apply a threshold to the weather radar data <NUM> to suppress noise and precipitation that may be coincident with the RFI prior to computing the ℓp norms. For example, each of the RFI radials <NUM>, <NUM> is coincident with precipitation in the image <NUM> of <FIG>; applying a threshold of about <NUM> decibels relative to Z (dBz) would suppress noise and precipitation that is coincident with the RFI radial <NUM> or applying a threshold of about <NUM> dBz would suppress noise and precipitation that is coincident with the RFI radial <NUM>. Alternatively or additionally, multiple thresholds may be iteratively applied to the weather radar data <NUM> with computation of ℓp norms to build a corresponding radial ℓp norm profile after application of each threshold. The application of multiple thresholds and building of multiple radial ℓp norm profiles may serve to identify RFI that manifests in the weather radar data <NUM> with different amplitudes that in some cases may be coincident with precipitation or other objects that also manifest in the weather radar data.

For example, a first threshold (e.g., of <NUM> dBz) may not suppress noise or precipitation relative to any of the RFI radials <NUM>, <NUM>, <NUM> but the RFI radial <NUM> would nevertheless be manifest in a corresponding first radial ℓp norm profile since it is generally not coincident with precipitation. A second threshold (e.g., of <NUM> dBz) may suppress noise or precipitation relative to the RFI radial <NUM>, while also suppressing the RFI radial <NUM> and without suppressing noise or precipitation relative to the RFI radial <NUM>, such that only the RFI radial <NUM> would be manifest in a corresponding second radial ℓp norm profile. A third threshold (e.g., of <NUM> dBz) may suppress noise or precipitation relative to the RFI radial <NUM>, while also suppressing the RFI radials <NUM>, <NUM>, such that only the RFI radial <NUM> would be manifest in a corresponding third radial ℓp norm profile. Thus, although the RFI radials <NUM>, <NUM>, <NUM> have different amplitudes in the image <NUM>, the iterative application of multiple thresholds to the weather radar data <NUM> may serve to suppress noise and precipitation relative to the RFI radials <NUM>, <NUM>, <NUM> so they may manifest in corresponding radial ℓp norm profiles and may be identified, e.g., by subsequent processing of the radial ℓp norm profiles as described herein.

Where multiple Level <NUM> data products are considered for a consensus, the computation of ℓp norms to build radial ℓp norm profiles and/or the iterative application of thresholds to build multiple radial ℓp norm profiles may be performed for each Level <NUM> data product. Where one or more radial ℓp norm profiles are generated for each of multiple Level <NUM> data products, the radial ℓp norm profiles of the multiple Level <NUM> data products may be averaged, e.g., by the computer device <NUM>, to form an average radial ℓp norm profile.

The computer device <NUM> may obtain an RFI kernel kRFI that is associated with or indicative of RFI. In an example, the RFI kernel kRFI may be obtained by computing a template RFI kernel to use as the RFI kernel kRFI, the template RFI kernel including an approximation of typical radials in an azimuthal neighborhood of RFI, where the azimuthal neighborhood is defined as a range of azimuth angles (e.g., on the order of a few degrees, such as +/- <NUM> degrees) adjacent to and on both sides of a radial identified as containing RFI. For instance, the template RFI kernel may be computed as kRFI(x) = ex - <NUM> (for x = <NUM>,. , <NUM>) and -ex + <NUM> (for x = <NUM>,. In another example, the RFI kernel kRFI may be obtained by deriving a wavelet RFI kernel to use as the RFI kernel kRFI, the wavelet RFI kernel derived from data that represents an actual RFI radial and neighboring radials (e.g., radials within the azimuthal neighborhood). In another example, the RFI kernel kRFI may be obtained by deriving an average wavelet RFI kernel to use as the RFI kernel kRFI, the average wavelet RFI kernel derived from data that represents multiple actual RFI radials and their respective neighboring radials.

The computer device <NUM> may compute a derivative with respect to azimuth angle of the radial ℓp norm profile computed previously to differentiate between RFI and precipitation. The radial ℓp norm profile for which the derivative is computed may include a single radial ℓp norm profile for a single Level <NUM> or higher data product, a set of radial ℓp norm profiles for the same Level <NUM> or higher data product (e.g., taken after application of different thresholds), an average of two or more single radial ℓp norm profiles for two or more Level <NUM> or higher data products, or an average of two or more sets of radial ℓp norm profiles for two or more Level <NUM> or higher data products. The radial ℓp norm profile for which the derivative is computed may be referred to as the radial ℓp norm profile B(θ). The derivative of the radial ℓp norm profile B(θ) may be referred to as the derivative B'(θ).

<FIG> includes first and second example radial ℓp norm (in this example, the ℓ<NUM> norm) profiles B(θ) <NUM>, <NUM> (or portions thereof), arranged in accordance with at least some embodiments described herein. The first radial ℓ<NUM> norm profile B(θ) <NUM> is for weather radar data with precipitation and an azimuthal angular resolution of <NUM> degrees. The second radial ℓ<NUM> norm profile B(θ) <NUM> is for weather radar data with RFI and no precipitation, or with precipitation suppressed, e.g., by application of a threshold as described above, also with an azimuthal angular resolution of <NUM> degrees. Other embodiments may use weather radar data with the same or different azimuthal angular resolution.

<FIG> also includes example derivatives B'(θ) <NUM>, <NUM>. The derivative B'(θ) <NUM> is the derivative with respect to azimuth angle of the first radial ℓ<NUM> norm profile B(θ) <NUM>. Similarly, the derivative B '(θ) <NUM> is the derivative with respect to azimuth angle of the second radial ℓ<NUM> norm profile B(θ) <NUM>.

The derivative B'(θ) <NUM> of the second radial ℓ<NUM> norm profile <NUM> exhibits a sharp updown spike pair, e.g., for the RFI observed by weather radar (e.g., the radar system <NUM>, <NUM>), which feature is generally absent for precipitation observed by weather radar as indicated by the derivative B'(θ) <NUM> of the first radial ℓ<NUM> norm profile B(θ) <NUM>. The RFI kernel kRFI obtained by the computer device <NUM> may be based on this feature such that a convolution of a derivative of a given radial ℓp norm profile with the RFI kernel kRFI grows very large, e.g., in excess of a threshold, at each azimuth angle associated with such a sharp updown spike pair. For example, as previously indicated, the RFI kernel kRFI may be computed as, e.g., kRFI(x) = ex - <NUM> (for x = <NUM>,. , <NUM>) and -ex + <NUM> (for x = <NUM>,.

Returning to <FIG> and <FIG>, the computer device <NUM> may then compute a convolution R(θ) of the derivative B'(θ) with the RFI kernel kRFI, e.g., R(θ) = B'(θ) * kRFI(θ). The radial associated with any azimuth angle θ at which the convolution R(θ) exceeds a threshold t may be marked as and/or determined to be an RFI radial rRFI.

The computer device <NUM> may delete all data of each RFI radial rRFI from the weather radar data <NUM>. Alternatively or additionally, the computer device <NUM> may further process the weather radar data <NUM> for general noise removal by despeckling and masking. In some embodiments, the computer device <NUM> may further impute the deleted data using surrounding data, e.g., surrounding radials, from the weather radar data <NUM> that are not identified as containing RFI, e.g., as being an RFI radial rRFI.

<FIG> further includes a weather radar image (hereinafter "image") <NUM> that generally represents the same weather radar data as the image <NUM>, but with the RFI radials <NUM>, <NUM>, <NUM> identified, their corresponding data removed from the weather radar data, replacement data imputed for each, and further processing for general noise removal, e.g., according to the foregoing process. It can be seen from the image <NUM> that embodiments described herein can identify (and optionally remove) both isolated RFI, such as the RFI radial <NUM>, as well as RFI that is coincident with precipitation, such as the RFI radials <NUM>, <NUM>.

<FIG> is a flowchart of an example method <NUM> to mitigate RFI in weather radar data, arranged in accordance with at least one embodiment described herein. The method <NUM> may be performed or controlled by, e.g., the computer device <NUM> of <FIG>, computer resources of the radar system <NUM>, or other device or system. Alternatively or additionally, the method <NUM> may be embodied by computer memory, storage, or other non-transitory computer-readable medium having computer-readable instructions stored thereon that are executable by a processor to perform or control performance of one or more operations of the method <NUM>. The method <NUM> may include one or more of blocks <NUM>, <NUM>, or <NUM>.

At block <NUM>, the method <NUM> may include computing ℓp norms of radials of weather radar data to construct an ℓp norm profile of the weather radar data as a function of azimuth angle. The weather radar data may include Level <NUM> or higher weather radar data in polar format. Block <NUM> may be followed by block <NUM>.

At block <NUM>, the method <NUM> may include determining that a given radial in the weather radar data is an RFI radial based on the ℓp norm profile of the weather radar data. Block <NUM> may be followed by block <NUM>.

At block <NUM>, the method <NUM> may include displaying an image from the weather radar data in which at least one of: the RFI radial is identified in the image as including RFI; or the RFI radial is omitted from the image. Thus, the method <NUM> may be implemented as an RFI filter.

One skilled in the art will appreciate that, for the method <NUM> and other processes and methods disclosed herein, the functions or operations performed in the processes and methods may be implemented in differing order. Furthermore, the outlined steps and actions are only provided as examples, and some of the steps and actions may be optional, combined into fewer steps and actions, or expanded into additional steps and actions without detracting from the essence of the disclosed embodiments.

For example, the method <NUM> may further include deleting data points of the RFI radial from the weather radar data before displaying the image to cause the RFI radial to be omitted from the image when the image is displayed. The RFI radial may be omitted altogether from the image.

Alternatively or additionally, the method <NUM> may further include imputing at least some replacement data points for the deleted data points from data points of two or more non-RFI radials in the weather radar data that are near a location of the RFI radial. Non-RFI radials may be considered to be near an RFI radial if they are within a threshold angular range of the radial, such as within <NUM> degrees, <NUM> degrees, <NUM> degrees, or other angular range of the RFI radial. Imputing at least some replacement data points for the deleted data points from data points of two or more non-RFI radials in the weather radar data that are near the location of the RFI radial may include interpolating from each side of the RFI radial.

In some embodiments, the method <NUM> may further include, prior to computing the ℓp norms, applying a threshold to the weather radar data to suppress noise and precipitation data. Applying the threshold to the weather radar data to suppress noise and precipitation data may include temporarily disregarding each data point that has a magnitude below the threshold for computation of the ℓp norms. Alternatively or additionally, applying the threshold to the weather radar data to suppress noise and precipitation data may include temporarily zeroing out a magnitude of each data point for which the magnitude is below the threshold for computation of the ℓp norms.

As another example, the method <NUM> may further include determining that the given radial includes the RFI radial based on a consensus of first and second data products included in the weather radar data. In this and other embodiments, computing the ℓp norms of the radials of the weather radar data to construct the ℓp norm profile at block <NUM> may include computing first ℓp norms of radials of the first data product to construct a first ℓp norm profile. The method <NUM> may further include: computing second ℓp norms of radials of the second data product to construct a second ℓp norm profile; and averaging the first ℓp norm profile and the second ℓp norm profile to form an average ℓp norm profile. In this and other embodiments, determining that the given radial is the RFI radial based on the consensus of the first and second data products may include determining that the given radial is the RFI radial based on the average ℓp norm profile.

In some examples, determining that the given radial in the weather radar data is the RFI radial based on the ℓp norm profile of the weather radar data at block <NUM> includes determining that a convolution of a derivative of the ℓp norm profile with a RFI kernel exceeds a threshold at an azimuth angle of the given radial. In this and other embodiments, and prior to determining that the convolution exceeds the threshold, the method <NUM> may further include: computing the derivative of the ℓp norm profile with respect to azimuth angle; obtaining the RFI kernel; and computing the convolution. Obtaining the RFI kernel may include one of: computing a template RFI kernel to use as the RFI kernel, the template RFI kernel including an approximation of a typical RFI radial; deriving a wavelet RFI kernel to use as the RFI kernel, the wavelet RFI kernel derived from data that represents an actual RFI radial; or deriving an average wavelet RFI kernel to use as the RFI kernel, the average wavelet RFI kernel derived from data that represents multiple actual RFI radials.

Alternatively or additionally, the method <NUM> may further include, prior to displaying the image of the weather radar data, despeckling and masking the weather radar data to remove noise. In this and other embodiments, displaying the image of the weather radar data may include displaying the image of the despeckled and masked weather radar data.

<FIG> illustrates an example computational system <NUM> to perform one or more operations of the present disclosure, arranged in accordance with at least one embodiment described herein. The computational system <NUM> may include, be included in, or correspond to the computer device <NUM>, computational resources of the radar system <NUM>, <NUM>, and/or client devices of users that access data and/or services available at or provided by the computer device <NUM>.

The computational system <NUM> (or processing unit) illustrated in <FIG> can be used to perform and/or control operation of any of the embodiments described herein. For example, the computational system <NUM> can be used alone or in conjunction with other components. As another example, the computational system <NUM> can be used to perform any calculation, solve any equation, perform any identification, and/or make any determination described here. As another example, the computational system <NUM> may be used to execute all or portions of the method <NUM> of <FIG>.

The computational system <NUM> may include any or all of the hardware elements shown in <FIG> and described herein. The computational system <NUM> may include hardware elements that are electrically coupled via a bus <NUM> (or may otherwise be in communication, as appropriate). The hardware elements may include one or more processors <NUM>, including one or more general-purpose processors and/or one or more special-purpose processors (such as digital signal processing chips, graphics acceleration chips, or other special-purpose processor); one or more input devices <NUM>; and one or more output devices <NUM>. The input devices <NUM> can include a mouse, a keyboard, or other input device. The output devices <NUM> can include a display device, a printer, or other output device.

The computational system <NUM> may further include (and/or be in communication with) one or more storage devices <NUM>. The storage devices <NUM> may include local and/or network-accessible storage, a disk drive, a drive array, an optical storage device, a solid-state storage device, random access memory ("RAM"), and/or read-only memory ("ROM"), which can be programmable, flash-updateable, and/or the like. The computational system <NUM> may also include a communication subsystem <NUM>, which may include a modem, a network card (wireless or wired), an infrared communication device, a wireless communication device, and/or a chipset (such as a Bluetooth® device, a <NUM> device, a WiFi device, a WiMAX device, cellular communication facilities, etc.), and/or the like. The communication subsystem <NUM> may permit data to be exchanged with a network, such as the network <NUM> of <FIG> and/or any other system or device described herein. In some embodiments, the computational system <NUM> may further include a working memory <NUM>, which may include a RAM or ROM device or other memory.

The computational system <NUM> also can include software elements or programs, depicted in <FIG> as being currently located within the working memory <NUM>. Such software elements may include an operating system <NUM> and/or other code, such as one or more application programs <NUM>. The application programs <NUM> may include computer programs executable, e.g. by the processor <NUM>, to perform or control performance of the method <NUM> of <FIG> or other methods or operations described herein. For example, one or more procedures described with respect to the method(s) discussed herein might be implemented as code and/or instructions executable by a computer (and/or a processor within a computer). A set of these instructions and/or codes might be stored on a computer-readable storage medium, such as the storage device(s) <NUM> of <FIG>.

In some cases, the storage medium may be incorporated within the computational system <NUM> or in communication with the computational system <NUM>. In other embodiments, the storage medium may be separate from the computational system <NUM> (e.g., a removable medium, such as a compact disc, etc.), and/or provided in an installation package, such that the storage medium can be used to program a general-purpose computer with the instructions/code stored thereon. These instructions might take the form of executable code, which is executable by the computational system <NUM> and/or might take the form of source and/or installable code, which, upon compilation and/or installation on the computational system <NUM> (e.g., using any of a variety of generally available compilers, installation programs, compression/decompression utilities, etc.), then takes the form of executable code.

Experiments were performed using data from two different radar systems to illustrate and prove the concept of the disclosed method, various results of which are presented herein. The first data set consists of <NUM> hours of data (e.g., <NUM> images with dimensions <NUM> × <NUM>) from <NUM> different waveforms collected by the Vaisala dual-polarization C-band SSPA prototype at Kumpula, Helsinki, Finland, on Mar <NUM>, <NUM>. The <NUM> different waveforms include a <NUM> microsecond (µs) continuous wave (CW) waveform, a linear frequency modulated (LFM) hybrid waveform, and a non LFM (NLFM) hybrid waveform.

As mentioned elsewhere, this first data set is referred to as the Kumpula data set. The Kumpula data set includes <NUM> different Level <NUM> data products: radar echo classification, differential phase, correlation coefficient (ρhv), normalized coherent power/signal quality index, spectrum width, total power, reflectivity, differential reflectivity, specific differential phase, and mean radial velocity. Two distinct weather events were observed within the Kumpula data set with substantial RFI coincident with precipitation.

Table <NUM> provides details of various parameters and values used by an embodiment of the disclosed invention for a first experiment using the Kumpula data set.

One of the objectives of the first experiment was to determine how standard "off-the-shelf" image processing techniques affect desired precipitation data. Any technique to mitigate RFI should preserve desired precipitation data, in the presence or absence of RFI, to be effective. As illustrated in, e.g., <FIG>, embodiments described herein are more effective than standard image processing techniques with respect to preserving desired precipitation data in the presence or absence of RFI and with respect to identifying, and optionally removing, RFI.

In more detail, <FIG> includes various weather radar data images <NUM>, <NUM>, <NUM> that provide a first comparison of performance of the method <NUM> of <FIG> to a standard image processing technique, arranged in accordance with at least one embodiment described herein. The standard image processing technique generally includes filtering the reflectivity data using a normalized coherent power mask threshold of <NUM>, and despeckling with side length <NUM>.

The image <NUM> was generated from unfiltered reflectivity data of the Kumpula data set and lacks RFI. The image <NUM> was generated by application of the standard image processing technique to the unfiltered reflectivity data. The image <NUM> was generated by application of the method <NUM> to the unfiltered reflectivity data.

It can be seen from a comparison of each of the images <NUM> and <NUM> to the image <NUM> and to each other that the standard image processing technique (image <NUM>) removes significant precipitation data from the image <NUM>, while the embodiment of the method <NUM> (image <NUM>) generally does not.

<FIG> includes various weather radar data images <NUM>, <NUM>, <NUM> that provide a second comparison of performance of the method <NUM> of <FIG> to the standard image processing technique, arranged in accordance with at least one embodiment described herein. The image <NUM> was generated from unfiltered reflectivity data of the Kumpula data set and lacks RFI. The image <NUM> was generated by application of the standard image processing technique to the unfiltered reflectivity data. The image <NUM> was generated by application of the method <NUM> to the unfiltered reflectivity data.

<FIG> includes various weather radar data images <NUM>, <NUM>, <NUM> that provide a third comparison of performance of the method <NUM> of <FIG> to the standard image processing technique, arranged in accordance with at least one embodiment described herein. The image <NUM> was generated from unfiltered reflectivity data of the Kumpula data set and includes isolated RFI, e.g., an RFI radial <NUM> at about <NUM> degrees (about <NUM> o'clock). The image <NUM> was generated by application of the standard image processing technique to the unfiltered reflectivity data. The image <NUM> was generated by application of the method <NUM> to the unfiltered reflectivity data.

It can be seen from <FIG> that the method <NUM> (image <NUM>) successfully identifies and eliminates the RFI radial <NUM>, while the standard image processing technique (image <NUM>) does not. Further, it can be seen from a comparison of each of the images <NUM> and <NUM> to the image <NUM> and to each other that the standard image processing technique (image <NUM>) removes more precipitation data from the image <NUM> than the method <NUM> (image <NUM>).

<FIG> generally show that the method <NUM> is superior to the standard image processing technique at least in the senses of preserving desired precipitation data and removing isolated RFI. Identifying and removing RFI that is coincident with precipitation is more challenging than identifying and removing isolated RFI, but the method <NUM> is able to do so. Even so, <FIG> shows an example of the performance of the method <NUM> of <FIG> when the weather radar data includes both isolated RFI and RFI coincident with precipitation in the same image. In <FIG>, the image <NUM> was generated from unfiltered reflectivity data of the Kumpula data set and includes isolated RFI, e.g., the RFI radial <NUM>, as well as RFI that is coincident with precipitation, e.g., the RFI radials <NUM>, <NUM>. As described above, the image <NUM> was generated by application of a method similar or identical to the method <NUM> to the unfiltered reflectivity data. It can be seen from the image <NUM> of <FIG> that the method <NUM> successfully identifies and eliminates the RFI radials <NUM>, <NUM>, <NUM> visible in the image <NUM> while substantially preserving the precipitation data.

In the example of <FIG>, the RFI, e.g., RFI radials <NUM>, <NUM>, <NUM>, is determined/identified and removed, while also imputing replacement data for the data of the RFI radials <NUM>, <NUM>, <NUM> that was removed. Alternatively or additionally, the RFI may be identified to an end user, e.g., by being displayed by itself separate from the precipitation data to the end user.

<FIG> includes a weather radar data image <NUM> with RFI, including both isolated RFI and RFI coincident with precipitation. The image <NUM> was generated from unfiltered reflectivity data of the Kumpula data set. The RFI of the image <NUM> includes an RFI radial <NUM> that is generally isolated from precipitation and RFI radials <NUM>, <NUM>, <NUM> that are coincident with precipitation. At least some of the method <NUM> may be applied to the unfiltered reflectivity data used to generate the image <NUM> to identify the RFI radials <NUM>, <NUM>, <NUM>, <NUM>. One or more images may then be generated and displayed, e.g., by the computer device <NUM> or computational system <NUM>, that include one or more of the RFI radials <NUM>, <NUM>, <NUM>, <NUM> without the precipitation, e.g., by generating the images using only the data points of the RFI radials <NUM>, <NUM>, <NUM>, <NUM>. In the example of <FIG>, two images <NUM>, <NUM> were generated where each includes some of the RFI radials <NUM>, <NUM>, <NUM>, <NUM>. In particular, the image <NUM> includes the RFI radials <NUM>, <NUM> and the image <NUM> includes the RFI radials <NUM>, <NUM>. In this example, the RFI radials <NUM>, <NUM> are weaker than the RFI radials <NUM>, <NUM> which was used as the criteria to determine which RFI radials <NUM>, <NUM>, <NUM>, <NUM> to display in the images <NUM>, <NUM>.

The examples of <FIG> and <FIG> apply the method <NUM> specifically to reflectivity data as the weather radar data. The method <NUM> may be applied to other Level <NUM> or higher data products, two examples of which are described with respect to <FIG>.

<FIG> includes various weather radar data images <NUM>, <NUM>, <NUM>, <NUM> that show example performance of the method <NUM> when applied to mean radial velocity data and correlation coefficient (ρhv) data, arranged in accordance with at least one embodiment described herein.

The image <NUM> was generated from unfiltered mean radial velocity data of the Kumpula data set and includes RFI, specifically RFI radials <NUM>, <NUM>. The image <NUM> was generated by application of the method <NUM> to the unfiltered mean radial velocity data. It can be seen from the image <NUM> of <FIG> that the method <NUM> successfully identifies and eliminates the RFI radials <NUM>, <NUM> visible in the image <NUM> while substantially preserving the precipitation data.

The image <NUM> was generated from unfiltered correlation coefficient (ρhv) data of the Kumpula data set and includes RFI, specifically RFI radials <NUM>, <NUM>, <NUM>, <NUM>. The image <NUM> was generated by application of the method <NUM> to the unfiltered correlation coefficient (ρhv) data. It can be seen from the image <NUM> of <FIG> that the method <NUM> successfully identifies and eliminates the RFI radials <NUM>, <NUM>, <NUM>, <NUM> visible in the image <NUM> while substantially preserving the precipitation data.

The only parameter change when applying the method <NUM> to the unfiltered mean radial velocity data or the unfiltered correlation coefficient (ρhv) data versus the unfiltered reflectivity data was the ℓ<NUM> norm profile convolution threshold to correspond with the values of the different data. This shows that the method <NUM> is relatively insensitive to parameter selection when considering RFI mitigation in different data products from the same radar system. The results of <FIG> also show that the method <NUM> works effectively on phase-based data (e.g., mean radial velocity) and dual-polarization data (e.g., correlation coefficient (ρhv)). The example of <FIG> utilizes the most challenging RFI scenario from the Kumpula data set as being representative. The results utilizing other data from the Kumpula data set were similar.

In the first experiment, RFI mitigation according to the method <NUM> was quantified using the mean radial velocity data for each of the three waveforms used (e.g., <NUM> CW, LFM hybrid, and NLFM hybrid) since the reflectivity data was too contaminated and thus too ambiguous to quantify. Images of unfiltered mean radial velocity data containing RFI visible to the naked eye were manually identified and counted. The method <NUM> was then applied to the unfiltered mean radial velocity data of the images identified in the previous step, e.g., those with RFI, to generate filtered images. The filtered images were then reviewed manually again to count those filtered images still containing visible RFI and those that no longer contain visible RFI. The results are shown in Table <NUM>.

Computational complexity is one characteristic of an RFI filter. An algorithm to mitigate or filter RFI in real time, such as the method <NUM>, must run quickly to be operationally serviceable. Table <NUM> includes average runtimes for each of a thresholding and despeckling step, an RFI identification step, an RFI removal step, and a data imputation step such as may be implemented in the method <NUM> as applied to the Kumpula data set. Table <NUM> also includes a total runtime, e.g., a sum of the foregoing steps.

As set forth in Table <NUM>, the method <NUM> is quite fast, well within the typical time for a radar system (even a phased array radar) to collect data during a full <NUM>-degree azimuthal sweep.

The second experiment used a different data set than the Kumpula data set. In particular, the second experiment used Next-Generation Radar (NEXRAD) reflectivity data collected by the KMHX NEXRAD radar system at Morehead City, North Carolina during a scan at <NUM> UTC on <NUM> June <NUM>. The data used in the second experiment is similar to that analyzed and shown in the Cho paper in <NUM>.

The Cho paper presents three different RFI mitigation techniques: : (<NUM>) the "Vaisala-<NUM>" algorithm, (<NUM>) a 1D median filter, and (<NUM>) a 2D median filter. The Cho paper is considered to present the current state-of-the-art of RFI mitigation techniques for weather radar data.

The data set used in the second experiment consists of two images, one Level <NUM> reflectivity image (with dimensions <NUM> × <NUM>) and one Level <NUM> reflectivity image (with dimensions <NUM> × <NUM>), collected by the KMHX NEXRAD radar system with the radar system at the lowest elevation angle and low-pulse repetition frequency (PRF) mode during a volume coverage pattern (VCP) <NUM> scan at <NUM> UTC on <NUM> June <NUM>. Level <NUM> data is analyzed here because these data are often used by National Weather Service forecasters in the United States. These images present another challenging scenario where strong RFI is coincident with strong precipitation, where both are similarly valued. The second experiment shows the performance of the method <NUM> using data collected by a radar operating at S-band using a klystron transmitter.

An objective of the second experiment was to determine how the method <NUM> compares in terms of RFI mitigation to what can be considered as the current state-of-the-art RFI mitigation technique on nearly common data.

<FIG> includes various weather radar data images <NUM>, <NUM>, <NUM>, <NUM> that provide a comparison of performance of the three techniques described in the Cho paper, all operating on Level <NUM> data. The image <NUM> was generated from unfiltered Level <NUM> reflectivity data generated by the KMHX NEXRAD radar system with the radar system at the lowest elevation angle and PRF mode during a VCP <NUM> scan at <NUM> UTC on <NUM> June <NUM>.

As illustrated, the reflectivity data includes RFI, e.g., an RFI radial <NUM>, at about <NUM> degrees (about <NUM> o'clock). The RFI radial <NUM> is coincident with strong precipitation out to about <NUM> kilometers (km) from a location of the KMHX NEXRAD radar system.

The image <NUM> was generated by application of the Vaisala-<NUM> algorithm. The image <NUM> was generated by application of the 1D median filter. The image <NUM> was generated by application of the 2D median filter. The images <NUM>, <NUM>, <NUM> are presented in the order in which the corresponding RFI filtering techniques performed, from least to most effective.

<FIG> includes detail images <NUM>, <NUM> of portions of the images <NUM> and <NUM> of <FIG> near the strong precipitation. In particular, the detail image <NUM> includes a zoomed in view of the image <NUM> near the strong precipitation and the detail image <NUM> includes a zoomed in view of the image <NUM> near the strong precipitation.

It can be seen from <FIG> that the Vaisala-<NUM> algorithm and the 1D median filter each leaves residual RFI in areas where the RFI is isolated from precipitation. It can be seen from <FIG> and <FIG> that none of the RFI filtering techniques filters the RFI that is coincident with precipitation.

The 2D median filter disclosed by Cho appears to effectively mitigate isolated RFI in the experiment Cho performed. However, the 2D median filter is not operationally viable. According to Cho, "However, as the 2D RFI filter already has an increased computational burden compared to the conventional 1D algorithms, a more efficient solution is desired for real-time implementation.

<FIG> includes weather radar data images <NUM>, <NUM> that show example performance of the method <NUM> when applied to reflectivity data that closely resembles but does not exactly match the Level <NUM> data used by Cho, arranged in accordance with at least one embodiment described herein. Since Cho's method works on Level <NUM> data, the reflectivity images shown in the Cho paper were generated by Cho from the Level <NUM> data whereas the data used in this experiment were acquired from the National Weather Service (NWS) Level <NUM> NEXRAD Amazon Web Services archive. The processing done by Cho and the NWS on the Level <NUM> data to generate their respective Level <NUM> data is likely slightly different.

The image <NUM> was generated from unfiltered Level <NUM> reflectivity data from the NWS and includes RFI, specifically an RFI radial <NUM> at about <NUM> degrees (about <NUM> o'clock). The image <NUM> has the same or similar aspect and graphically represents similar reflectivity data as the image <NUM> of <FIG>. The image <NUM> was generated by application of the method <NUM> to the unfiltered Level <NUM> reflectivity data. It can be seen from the image <NUM> that the method <NUM> successfully identifies and eliminates the RFI radial <NUM> both where the RFI radial <NUM> is coincident with precipitation and where the RFI radial <NUM> is isolated from precipitation.

<FIG> includes detail images <NUM>, <NUM>, <NUM>, <NUM> of portions of the images <NUM>, <NUM> of <FIG> that include the precipitation, arranged in accordance with at least one embodiment described herein.

The detail image <NUM> includes a zoomed in view of the image <NUM> generated from the unfiltered Level <NUM> reflectivity data and shows the RFI radial <NUM> where it is coincident with precipitation.

The detail images <NUM>, <NUM>, <NUM> each includes a zoomed in view of the image <NUM> generated by application of the method <NUM> to the unfiltered Level <NUM> reflectivity data with a different level of data imputation. In the detail image <NUM>, the method <NUM> applied data imputation to generate replacement data for all data of the RFI radial <NUM> that was removed. In the detail image <NUM>, the method <NUM> applied data imputation to generate replacement data for some, but not all, data of the RFI radial <NUM> that was removed. In the detail image <NUM>, the method <NUM> did not apply any data imputation and instead removed all data of the RFI radial <NUM> without replacing any of the removed data with imputed replacement data. Thus, as illustrated in <FIG> and as described above, the method <NUM> may impute replacement data for all, some, or none of the data of each RFI radial that is removed.

<FIG> includes weather radar data images <NUM>, <NUM> that show example performance of the method <NUM> when applied to Level <NUM> reflectivity data from the same radar system and time as the Level <NUM> reflectivity data used in <FIG>, arranged in accordance with at least one embodiment described herein. The image <NUM> was generated from unfiltered Level <NUM> reflectivity data from the NWS and includes RFI, specifically an RFI radial <NUM> at about <NUM> degrees (about <NUM> o'clock). The image <NUM> has the same or similar aspect and graphically represents the same or similar reflectivity data as the image <NUM> of <FIG> or the image <NUM> of <FIG>. The image <NUM> was generated by application of the method <NUM> to the unfiltered Level <NUM> reflectivity data. It can be seen from <FIG> that the method <NUM> is effective at filtering RFI from both the isolated and overlaid areas of Level <NUM> data, similar to the results using Level <NUM> data.

The second experiment using the NEXRAD data demonstrates the effective applicability of the method <NUM> to a different radar and different data than used in the first experiment. RFI mitigation effectiveness of the method <NUM> was directly compared to what can be considered the current state-of-the-art method (See <FIG> and associated description) and illustrates some of the data imputation options (see <FIG> and associated description) afforded by the method <NUM>. Note that the data imputation shown in <FIG> is a simple first-order (linear) method. More elaborate, higher-order mathematical methods such as polynomial, cubic spline, Piecewise Cubic Hermite Interpolator (PCHIP), or computer vision-based methods such as exemplar-, hybrid diffusion and exemplar-, or deep learning-based inpainting can be used in the data imputation of the method <NUM>, which may give better results.

Table <NUM> includes average runtimes for each of a thresholding and despeckling step, an RFI identification step, an RFI removal step, and a data imputation step such as may be implemented in the method <NUM> as applied to the NEXRAD Level <NUM> data and the NEXRAD Level <NUM> data. Table <NUM> also includes a total runtime, e.g., a sum of the foregoing steps.

As Table <NUM> shows, the disclosed invention is quite fast, well within the typical time for a radar (even a phased array radar) to collect data during a full <NUM>-degree azimuthal sweep. In some embodiments, the method <NUM> may be performed on data of a full <NUM>-degree azimuthal sweep in less time than it takes to complete a subsequent full <NUM>-degree azimuthal sweep.

The second experiment demonstrates that the method <NUM> is relatively insensitive to parameter tuning, as the only changes from the Kumpula dataset (e.g., Vaisala SSPA C-band data) to the NEXRAD Level <NUM> data were changing the size of the despeckling filter from <NUM> to <NUM> and the RFI filter width from <NUM> to <NUM> degrees. The only additional change to the parameters when moving from NEXRAD Level <NUM> to Level <NUM> data was changing the ℓ<NUM> norm threshold from <NUM>,<NUM> to <NUM>,<NUM>.

The second experiment also shows how the method <NUM> performs in a scenario where returns from RFI coincident with precipitation are similarly valued to those returns from surrounding precipitation. The RFI filtering techniques presented by Cho leave RFI overlaid with precipitation data (see <FIG>) while the method <NUM> removes both RFI and precipitation data. The method <NUM> may then impute data at various levels (e.g., none, some, or all), while introducing some artifacts directly proportional to the azimuthal extent of the RFI removed.

Some embodiments described herein, including the experiments, show several differences and benefits over other RFI filtering techniques. These may include:.

Unless specific arrangements described herein are mutually exclusive with one another, the various implementations described herein can be combined in whole or in part to enhance system functionality or to produce complementary functions. Likewise, aspects of the implementations may be implemented in standalone arrangements. Thus, the above description has been given by way of example only and modification in detail may be made within the scope of the present invention.

With respect to the use of substantially any plural or singular terms herein, those having skill in the art can translate from the plural to the singular or from the singular to the plural as is appropriate to the context or application. A reference to an element in the singular is not intended to mean "one and only one" unless specifically stated, but rather "one or more. " Moreover, nothing disclosed herein is intended to be dedicated to the public regardless of whether such disclosure is explicitly recited in the above description.

Claim 1:
A method to mitigate radio frequency interference, RFI, in weather radar data, comprising:
computing (<NUM>) ℓp norms of radials of weather radar data to construct an ℓp norm profile of the weather radar data as a function of azimuth angle, the weather radar data comprising Level <NUM> or higher weather radar data in polar format, wherein each ℓp norm comprises an ℓ<NUM> norm, a Manhattan Distance, or a Euclidian Norm;
determining (<NUM>) that a given radial in the weather radar data is an RFI radial based on the ℓp norm profile of the weather radar data, wherein determining that the given radial in the weather radar data is the RFI radial based on the ℓp norm profile of the weather radar data includes determining that a convolution of a derivative of the ℓp norm profile with a RFI kernel exceeds a threshold at an azimuth angle of the given radial, wherein the RFI kernel is a kernel that is associated with or indicative of RFI; and
displaying (<NUM>) an image from the weather radar data in which at least one of:
the RFI radial is identified in the image as including RFI; or
the RFI radial is omitted from the image,
wherein Level <NUM> weather radar data refers to and includes data resulting from processing and creating data from Level <NUM> weather radar data and wherein Level <NUM> weather radar data refers to and includes time series of complex voltage samples of radar returns generated by a radar system.