System and method for generating a radar image of a scene - Patents.com

Abstract

The present disclosure provides a system and method for generating a radar image of a scene. The method includes receiving radar measurements of the scene collected from a set of antennas, the set of antennas being under uncertainty caused by one or a combination of ambiguity in the position of each of the antennas and clock ambiguity. The method further includes generating a radar image of the scene by solving a sparse reconstruction problem. The sparse reconstruction problem determines a set of image shifts of the radar image corresponding to different uncertainties of the antennas until a termination condition is met, and updates an estimate of the radar image based on the determined set of image shifts of the radar image. The sparse reconstruction problem is solved with a neural network denoiser that removes noise from the filtering of the estimate of the radar image.

Description

[Technical field]

[0001] The present disclosure relates generally to radar systems, and more particularly to a system and method for generating a radar image of a scene. [Background technology]

[0002] High-resolution radar imaging is used in a variety of remote sensing applications, including synthetic aperture radar (SAR) and through-the-wall radar imaging (TWI). The down-range resolution of a radar is controlled by the bandwidth of the transmitted pulse, while the cross-range (azimuth) resolution depends on the aperture of the radar array. Creating a large physical aperture is in practice achieved by deploying several distributed antennas or arrays, each with a relatively small aperture. A distributed setup of antennas allows flexibility in radar platform placement, reduces operational and maintenance costs, and adds robustness against sensor failures. Exploiting prior knowledge of the scene, such as sparsity, precise knowledge of antenna positions, and perfect synchronization of received signals, has been shown to significantly improve radar imaging resolution.

[0003] The main challenge in radar imaging using a distributed setup is being able to identify the antenna position due to inaccurate calibration or various position perturbations. Although modern navigation systems such as the Global Positioning System (GPS) can measure the position, the possibility of position errors due to position perturbations is beyond the scope of high-resolution distributed radar imaging. For example, in the case of vehicle-mounted radar systems, position perturbations are introduced due to uneven road surfaces or varying driving speed and direction when the vehicle is moving along a pre-designed trajectory. These position perturbations can be as large as several wavelengths of the radar center frequency. As a result, applying standard reconstruction techniques without considering the position perturbations produces unfocused radar images.

[0004] There are many solutions that have addressed the radar autofocus problem, especially in SAR settings, by developing tools to compensate for antenna position errors. However, the problem is ill-posed and solving this problem is a computationally demanding process that is difficult to find a solution for. To that end, some methods impose additional constraints on the radar autofocus problem to make it tractable. However, these additional constraints are not always desirable.

[0005] Therefore, what is needed is a radar imaging system and method for autofocusing of an antenna having unknown position perturbations. Summary of the Invention

[0006] It is an objective of some embodiments to provide a radar system and method for generating a radar image of a scene by fusing measurements of various antennas with unknown position perturbations. Specifically, it is an objective of some embodiments to formulate a neural network denoiser-based radar autofocus problem for generating a radar image of a scene.

[0007] Some embodiments are based on the understanding that a fundamental challenge arising in distributed array imaging (i.e., distributed antenna setup) comes from uncertainties caused by one or a combination of the position ambiguity and clock ambiguity of each antenna of a set of antennas. Some embodiments are based on the recognition that the radar autofocus problem of distributed antennas with position ambiguity may be an ill-posed problem with a huge number of unknowns. Specifically, when the radar autofocus problem is formulated as recovering a correct radar image from erroneous measurements caused by an erroneous radar operator that encodes the position ambiguity, each measurement of a region of interest (ROI) contains an error caused by the position ambiguity. Furthermore, due to the nonlinearity of the relationship between the measurement and the error in the position of the antenna, each sample of the measurement from the same antenna may have a different error, thereby increasing the number of unknowns in the model of the radar autofocus problem.

[0008]

number

[0009] Some embodiments are based on the realization that the radar autofocus problem can be reformulated as recovering an inaccurate radar image from correct measurements and a correct radar operator. On the one hand, such a reformulation does not make sense. However, some embodiments are based on the realization that an erroneous radar image determined via such a formulation of the radar autofocus problem can be related to the correct radar image through a linear shift. Due to this linearity, each sample of measurements from the same antenna represents the correct radar image with the same linear shift.

[0010] To that end, the position ambiguity can be modeled as a spatial shift kernel in the domain of the radar image x. Specifically, the new measurement model is given by:

number

[0011] Each antenna measurement is therefore modeled as a product of a radar operator, a radar image and a shift kernel.

[0012] Some embodiments are based on a radar image x and a shift kernel h mThis is based on the further realization that a regularizer can be utilized for both the K and N measurements to reduce the number of measurements M required. One example of a regularizer for a radar image x is the fused lasso regularizer. According to an embodiment, true objects in a radar image x have sparse radar signatures, i.e., most of the radar image x is zero-valued, and the locations of the non-zero entries tend to cluster together. The fused lasso regularizer assigns a small cost to radar images that are sparse and when the locations of the non-zero entries cluster together. As a result, for a radar image x that has K non-zero entries in its spatial gradient region, the number of true unknowns in the radar image x can be represented by Klog(N) unknowns. Similarly, the shift kernel h m is 1-sparse, with the number of true unknowns expressed as log(P). The resulting system of equations therefore contains MF equations with Mlog(P)+Klog(N) unknowns when the fused lasso regularizer is used. Therefore, to be able to solve the radar autofocus problem, it is sufficient that M is larger than log(N) / (F-log(P)).

[0013] As an example, consider a radar autofocus problem with F=100, N=100x100=10000, P=10x10=100, and K=3. There are M=5 measurement vectors y m In this case, the measurement model (1) results in a system with 500 equations with approximately 500+3×log(10000)=528 unknowns. On the other hand, the new measurement model (2) results in a system with 500 equations and approximately 5×log(100)+3×log(10000)=51 unknowns. This reduction in the number of unknowns in the radar autofocus problem allows the radar autofocus problem to be solved efficiently.

[0014] Some embodiments are based on the recognition that the image shift (i.e., the shift kernel) and the radar image may be determined using an alternating optimization. For example, in one embodiment, the radar image is updated while fixing the image shift, and the image shift is updated while fixing the radar image.

[0015] In the alternating optimization, first an estimate of the radar image is generated. Then a set of image shifts corresponding to different uncertainties of the antennas is estimated. The estimate of the radar image is then updated based on the determined set of image shifts, and for each of the antennas, an estimate of the radar image shifted by the corresponding image shift is matched to the antenna measurements. The steps of estimating a set of image shifts followed by updating the estimate of the radar image are performed iteratively until a final condition is met. Once the termination condition is met, a focused radar image is output.

[0016] According to an embodiment, an estimate of the radar image is generated by minimizing the difference between the radar return and the modeled measurements synthesized based on the transmitted pulses and the erroneous antenna position. Furthermore, a regularizer is applied to the estimated radar image to filter noise from the estimated radar image. In an embodiment, the regularizer can be a fused lasso regularizer including a 1-norm regularizer and a total variation (TV) regularizer. The 1-norm regularizer imposes sparsity on the estimated radar image, and the TV regularizer reduces noise in the estimated radar image to generate a filtered radar image. The steps of minimizing the difference between the radar return and the modeled measurements and applying the regularizer are performed iteratively until convergence. Upon convergence, an estimate of the radar image is output.

[0017] Some embodiments are based on the observation that the regularizer (e.g., a fused lasso regularizer) used in the alternating optimization to filter the estimated radar image may not be suitable when the noise in the estimated radar image is large because the noise may introduce image domain artifacts, which also tend to cluster together and thus resemble the shape of the true target. As a result, the alternating optimization may focus on the wrong object, resulting in inaccurate antenna position corrections.

[0018] Some embodiments are based on the recognition that a neural network denoiser can be used instead of a regularizer to mitigate such problems. A neural network denoiser includes a neural network trained to denoise the estimated radar image. In other words, the neural network denoiser filters noise from the estimated radar image. A neural network denoiser has advantages over a regularizer due to the high modeling power of a neural network and its ability to represent signal structures beyond the explicit sparsity in the image domain and its gradients.

[0019] To that end, to estimate the radar image, instead of applying a regularizer to the estimated radar image, a neural network denoiser is applied.

[0020] Some embodiments recognize that artifacts / noise in the estimated radar image are due to iterative update steps that occur during minimization of the difference between the radar return and the modeled measurements. The artifacts / noise due to the iterative update steps are unknown, unpredictable, and may not be the same as the noise on which the neural network is trained. Thus, the estimated radar image may contain noise on which the neural network denoiser is not trained. When such a radar image is applied to the neural network denoiser, the neural network denoiser may inject errors into the output radar image. Thus, simply replacing the normalizer with a neural network denoiser is not sufficient and may cause problems.

[0021] Some embodiments are based on the recognition that, to manage noise for which the neural network denoiser is not trained, the estimated radar image can be filtered by applying a forward radar operator and an adjoint radar operator to the estimated radar image before applying the estimated radar image to the neural network denoiser. The forward and adjoint operators filter noise for which the neural network is not trained from the estimated radar image to generate a filtered radar image. The filtered radar image is then applied to the neural network denoiser. As a result, the neural network denoiser does not inject errors into the output radar image and the reconstruction of the radar image remains stable.

[0022] According to an embodiment, a neural network denoiser for denoising filtering of radar image estimates includes a residual Unet architecture. The residual Unet architecture is symmetric and includes two parts, namely a left part and a right part. The left part is called a contraction path and is composed of a general convolution process. The right part is an expansion path and is composed by a transposed 2d convolution layer. Additionally or alternatively, in some embodiments, the neural network denoiser includes a denoising convolutional neural network architecture.

[0023] Some embodiments are based on the realization that because the forward and adjoint radar operators filter noise from the estimated radar image that the neural network denoiser is not trained on, the neural network denoiser does not need to be trained on a large training data set that includes all possible noise that may be observed in the alternative optimization. Thus, the neural network denoiser may be trained on a simpler training data set. In one embodiment, the simpler training data set is the input / output pair (z m ,x m ), and the training input image z mis the back projection operator A m H Let y be an example radar measurement. m =A m x m +n, and z m =A m H y m and the output image x m where is the ground truth object radar image, and n represents the additive noise. Since the neural network denoiser can be trained with a simple training data set, training the neural network denoiser becomes easier and faster.

[0024] In addition, some embodiments are based on the realization that the neural network denoiser-based radar autofocus problem of the present disclosure is capable of reconstructing an object using fewer measurements. This feature allows embodiments of the present invention to be deployed in object tracking systems where the radar signature of an object is determined at a faster rate than the object's motion. Such processing allows for continuous object detection and object tracking by detection.

[0025] Furthermore, detection of a moving object received from a radar reflection may provide a partial view of the object when the object has a large extension relative to the radar beam width. In such a scenario, the neural network denoiser can be trained to reconstruct the partial shape of the object intended to be tracked instead of reconstructing the point object of the object's strong reflector. The reconstructed partial shape can then be used to facilitate an additional module that determines the current state of the object, which includes information about the size, orientation, and direction of the moving object.

[0026] Thus, one embodiment discloses a system for generating a radar image of a scene. The system includes: A set of antennas,A system for detecting radar images of a scene comprising at least one processor and a memory having instructions stored thereon, the instructions, when executed by the at least one processor, cause the system to receive radar measurements of a scene collected from a set of antennas, the radar measurements being measurements of returns associated with radar pulses transmitted into the scene, the instructions, when executed by the at least one processor, further cause the system to generate a radar image of the scene by solving a sparse reconstruction problem, the sparse reconstruction problem determining a set of image shifts of the radar image corresponding to different uncertainties of the antennas until a termination condition is met. The set of antennas is subject to uncertainty caused by one or a combination of ambiguity in the position of each of the antennas and ambiguity in the clock, and the sparse recovery problem is , configured to update an estimate of the radar image based on a set of determined image shifts of the radar image, and for each of the antennas, an estimate of the radar image shifted by a corresponding shift of the radar image is matched to the radar measurement of the antenna, and the sparse restoration problem is solved with a neural network denoiser that denoises filtering of the estimate of the radar image, and the instructions, when executed by the at least one processor, further cause the system to render a radar image if a termination condition is met. Further, filtering of the radar image estimate is performed by applying a forward radar operator and an adjoint radar operator to the radar image estimate.

[0027] Accordingly, another embodiment discloses a method for generating a radar image of a scene, the method including receiving radar measurements of the scene collected from a set of antennas, the radar measurements being measurements associated with reflections of radar pulses transmitted into the scene, the method further including generating a radar image of the scene by solving a sparse reconstruction problem, the sparse reconstruction problem determining a set of image shifts of the radar image corresponding to different antenna uncertainties until a termination condition is met. The set of antennas is subject to uncertainty caused by one or a combination of ambiguity in the position of each of the antennas and ambiguity in the clock, and the sparse recovery problem is , and is configured to update an estimate of the radar image based on a set of determined image shifts of the radar image, and for each of the antennas, an estimate of the radar image shifted by a corresponding shift of the radar image is matched to the radar measurement of the antenna, and the sparse restoration problem is solved with a neural network denoiser that denoises filtering of the estimate of the radar image, and the method further includes rendering the radar image if a termination condition is met. Further, filtering of the radar image estimate is performed by applying a forward radar operator and an adjoint radar operator to the radar image estimate.

[0028] Accordingly, yet another embodiment discloses a computer-readable storage medium having embodied thereon a program executable by a processor to execute a method for generating a radar image of a scene, the method including receiving radar measurements of the scene collected from a set of antennas, the radar measurements being measurements of returns associated with radar pulses transmitted into the scene, the method further including generating a radar image of the scene by solving a sparse reconstruction problem, the sparse reconstruction problem determining a set of image shifts of the radar image corresponding to different uncertainties of the antennas until a termination condition is met. The set of antennas is subject to uncertainty caused by one or a combination of ambiguity in the position of each of the antennas and ambiguity in the clock, and the sparse recovery problem is , configured to update an estimate of the radar image based on a set of determined image shifts of the radar image, and for each of the antennas, an estimate of the radar image shifted by a corresponding shift of the radar image is matched to the radar measurement of the antenna, and the sparse restoration problem is solved with a neural network denoiser that denoises filtering of the estimate of the radar image, and the method further includes rendering the radar image if a termination condition is met. Further, filtering of the radar image estimate is performed by applying a forward radar operator and an adjoint radar operator to the radar image estimate.

[0029] The present invention will now be described in detail with reference to the accompanying drawings, in which: The drawings shown are not necessarily to scale, with emphasis instead generally being placed upon illustrating the principles of embodiments of the present disclosure. [Brief description of the drawings]

[0030] [Figure 1A] FIG. 1 is a block diagram of a radar system for generating a radar image of a scene, according to one embodiment of the disclosure. [Figure 1B] FIG. 1 is a schematic diagram illustrating a radar system according to an embodiment of the present disclosure. [Figure 1C] 1A-1C are schematic diagrams illustrating, taken together, the distortions affecting the measured time domain signal of each antenna due to antenna position uncertainty when measuring the reflection of a single object, in accordance with an embodiment of the present disclosure. [Figure 1D]1A-1C are schematic diagrams illustrating, taken together, the distortions affecting the measured time domain signal of each antenna due to antenna position uncertainty when measuring the reflection of a single object, in accordance with an embodiment of the present disclosure. [Figure 1E] FIG. 1 is a schematic diagram illustrating a mapping between a set of antennas having perturbed positions and measuring reflections of a single object and a set of antennas having uniform linear positions and measuring shifted versions of the same object, in accordance with an embodiment of the present disclosure. [Figure 1F] FIG. 2 is a schematic diagram illustrating the relationship between a shifted object image and a true object image convolved with a set of shift kernels according to an embodiment of the present disclosure. [Figure 2A] FIG. 1 is a block diagram of an alternating optimization for estimating a set of radar images and image shifts according to one embodiment of the present disclosure. [Figure 2B] 4 is a graph illustrating a transmit pulse according to one embodiment of the present disclosure. [Figure 2C] 1 is a graph illustrating radar reflection according to one embodiment of the present disclosure. [Figure 3A] FIG. 1 is a block diagram of a method for estimating a radar image according to one embodiment of the present disclosure. [Figure 3B] FIG. 1 is a block diagram of a method for estimating a radar image using a neural network denoiser, according to one embodiment of the present disclosure. [Figure 3C] FIG. 1 is a block diagram of a method for estimating a radar image using forward and adjoint radar operators and a neural network denoiser according to one embodiment of the present disclosure. [Figure 3D] 1 is an exemplary radar image according to one embodiment of the present disclosure. [Figure 4A] FIG. 2 is a block diagram of a method for estimating a set of image shifts according to one embodiment of the present disclosure. [Figure 4B] FIG. 2 is a schematic diagram illustrating alignment of a set of estimated image shifts with the average assumed position of the antenna according to one embodiment of the present disclosure. [Figure 5A]FIG. 2 is a block diagram of a method for updating an estimated radar image according to one embodiment of the present disclosure. [Figure 5B] 1 is an exemplary updated radar image according to one embodiment of the present disclosure. [Figure 5C] 1 is an exemplary focused radar image according to one embodiment of the present disclosure. [Figure 6] 1 is a residual Unet architecture of a neural network denoiser according to one embodiment of the present disclosure. [Figure 7A] FIG. 1 is a schematic diagram of a vehicle including a tracker for determining a state of a moving object, according to one embodiment of the present disclosure. [Figure 7B] FIG. 2 is a schematic diagram illustrating control of a vehicle based on a state of a moving object according to one embodiment of the present disclosure. [Figure 8] FIG. 1 is a block diagram of a method for determining a radar image of a scene according to one embodiment of the disclosure. [Figure 9A] 1 is a block coordinate descent algorithm according to some embodiments of the present disclosure. [Figure 9B] 13 is an algorithm of a Fast Iterative Shrinkage / Thresholding Algorithm (FISTA) subroutine for updating the shift kernel hm, according to some embodiments of the present disclosure. [Figure 9C] 1 is an algorithm of a FISTA subroutine for radar image x, according to some embodiments of the present disclosure. [Figure 10] FIG. 1 is a block diagram of a computer system for generating a radar image of a scene according to one embodiment of the disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0031] In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure. However, it will be apparent to those skilled in the art that the present disclosure may be practiced without these specific details. In other instances, the devices and methods are shown only in block diagram form to avoid obscuring the present disclosure.

[0032] As used herein and in the claims, the words "for example," "for example," "e.g.," "etc.," and the verbs "comprise," "have," "include," and other verb forms thereof, when used with a list of one or more components or other items, should each be construed as open-ended, meaning that the list should not be considered to exclude other additional components or items. The wording "based on" means based at least in part on. Furthermore, it should be understood that the phraseology and terminology used herein are for purposes of description and should not be considered limiting. Any headings used within this description are for convenience only and have no legal or limiting effect.

[0033] FIG. 1A illustrates a block diagram of a radar system 100 according to an embodiment of the present disclosure. The radar system 100 includes a set of antennas 101 and a system 103 for generating a radar image of a scene. The scene may be an area of ​​interest that includes one or more objects. The one or more objects may include stationary and / or moving objects. The set of antennas 101 includes M distributed antennas 101a, 101b, ..., 101m that can communicate with each other. The system 103 includes a memory 105, a processor 107, and a user interface 109. The set of antennas 101 is configured to transmit radar pulses into the scene and receive corresponding reflections. The reflections of the radar pulses transmitted into the scene are referred to as radar measurements (hereinafter "measurements"). The measurements may be stored in the memory 105. The processor 107 is configured to solve a sparse reconstruction problem and generate an autofocused high-resolution two-dimensional (2D) radar image of the scene. The user interface 109 is configured to render the generated radar image.

[0034] FIG. 1B is a schematic diagram illustrating a radar system 100 according to an embodiment of the present disclosure. The radar system 100 may be an airborne or vehicle-mounted platform including at least one moving antenna and M distributed mobile receiver platforms or sets of receivers. For example, the set of antennas 101 may move in space along a predefined trajectory. To that end, the set of antennas includes at least one antenna, such as antenna 101a, antenna 101b, antenna 101c, and antenna 101d. Those skilled in the art will understand that four antennas (101a-101d) are shown in FIG. 1B for illustrative purposes. In practice, any number of antennas may be used to achieve the functionality of the radar system 100 described herein without departing from the scope of the present disclosure.

[0035] Radar pulses 111 are transmitted from at least one antenna 101a to illuminate an object 113 located within a region of interest (ROI) 115, and corresponding reflections 117 reflected by the object 113 are recorded by distributed antennas 101a, 101b, 101c, and 101d. The reflections 117 are characterized as a weighted combination of delayed pulses, where the complex weights depend on the particular object reflectivity and antenna pattern. Given the transmitted pulses 111 and the reflections 117, a radar image can be generated in the range-azimuth plane according to the corresponding weights and delays. The azimuth resolution of the radar image depends on the size of the array aperture, and the range resolution depends on the bandwidth of the transmitted pulses 111.

[0036] A fundamental challenge that arises in distributed array imaging (i.e., distributed antenna setup) stems from uncertainties caused by one or a combination of position ambiguity and clock ambiguity of each antenna of the set of antennas 101. As used herein, position ambiguity corresponds to an error or uncertainty in the position of the set of antennas 101. As used herein, clock ambiguity indicates that the clocks of the set of antennas 101 may or may not be synchronized, and the set of antennas 101 may be either synchronous or asynchronous. Although advanced positioning and navigation systems, such as Global Navigation Satellite Systems (GPS / GNSS) and Inertial Navigation Systems (INS), provide somewhat accurate position information, the remaining uncertainty in the antenna positions may span multiple wavelengths. As a result, measurements contain gain and phase ambiguities when imprecise antenna positions are used as a reference. As a result, applying standard reconstruction techniques without considering the antenna position uncertainties produces unfocused radar images.

[0037] 1C and 1D, taken together, are schematic diagrams illustrating the distortions affecting the measured time domain signal of each antenna due to the uncertainties (or errors) in the antenna positions when measuring the reflection of the object 113, according to an embodiment of the present disclosure. Additionally, FIG. 1C and 1D are schematic diagrams illustrating the effect of position perturbations of different antennas on the alignment in time of the reflections.

[0038] Furthermore, some embodiments are based on the recognition that the radar autofocus problem of distributed antennas with position ambiguity may be an ill-posed problem with a huge number of unknowns. Specifically, when the radar autofocus problem is formulated as recovering the correct radar image from erroneous measurements caused by an erroneous radar operator that encodes the position ambiguity, each measurement of the ROI 115 contains an error caused by the position ambiguity. Furthermore, due to the nonlinearity of the relationship between the measurements and the errors in the positions of the antennas (such as antennas 101a-101d), each sample of measurements from the same antenna may have different errors, thereby increasing the number of unknowns in the model of the radar autofocus problem.

[0039]

number

[0040] Some embodiments are based on the realization that the radar autofocus problem can be reformulated as recovering an inaccurate radar image from correct measurements and a correct radar operator. On the one hand, such a reformulation does not make sense. However, some embodiments are based on the realization that an erroneous radar image determined via such a formulation of the radar autofocus problem can be related to the correct radar image through a linear shift. Due to this linearity, each sample of measurements from the same antenna represents the correct radar image with the same linear shift.

[0041] To that end, the position ambiguity can be modeled as a shift kernel in the domain of the radar image x. Specifically, the new measurement model is given by:

number

[0042] Each antenna measurement is therefore modeled as a product of a radar operator, a radar image and a shift kernel.

[0043] Figure 1E is a schematic diagram illustrating a mapping between a set of antennas 101 having perturbed positions and measuring the reflection of a single object and a set of antennas 101 having uniform linear positions and measuring a shifted version of the same object from Figures 1C and 1D according to an embodiment of the present disclosure. Furthermore, Figure 1E is a schematic diagram of a signal model in which the measured reflection of a single object at a perturbed antenna position is equivalent to measuring a shifted version of the same object at a false position of the set of antennas 101.

[0044] FIG. 1F is a schematic diagram illustrating the relationship between the shifted object images 119a, 121a, 123a, 125a and the true object image 127 convolved with the set of shift kernels 119b, 121b, 123b, 125b, according to one embodiment of the present disclosure. The measured reflections 101ax, 101bx, 101cx, 101dx of FIG. 1D correspond to measurements of the true object 113 by the set of antennas 101 located at the perturbed positions of FIG. 1C. These same measured reflections also correspond to radar reflections of the shifted objects 119a, 121a, 123a, 125a by the set of antennas 101 located at the incorrect antenna positions of FIG. 1E, which are shown to be equivalent to the reflections of the true object 113 convolved with the set of shift kernels 119b, 121b, 123b, 125b of FIG. 1F.

[0045] Some embodiments are based on a radar image x and a shift kernel h m This is based on the further realization that a regularizer can be utilized for both the K and N measurements to reduce the number of measurements M required. One example of a regularizer for a radar image x is the fused lasso regularizer. According to an embodiment, true objects in a radar image x have sparse radar signatures, i.e., most of the radar image x is zero-valued, and the locations of the non-zero entries tend to cluster together. The fused lasso regularizer assigns a small cost to radar images that are sparse and when the locations of the non-zero entries cluster together. As a result, for a radar image x that has K non-zero entries in its spatial gradient region, the number of true unknowns in the radar image x can be represented by Klog(N) unknowns. Similarly, the shift kernel h m is 1-sparse, with the number of true unknowns expressed as log(P). The resulting system of equations therefore contains MF equations with Mlog(P)+Klog(N) unknowns when the fused lasso regularizer is used. Therefore, to be able to solve the radar autofocus problem, it is sufficient that M is larger than log(N) / (F-log(P)).

[0046] As an example, consider a radar autofocus problem with F=100, N=100x100=10000, P=10x10=100, and K=3. There are M=5 measurement vectors y m In this case, the measurement model (1) results in a system with 500 equations with approximately 500+3×log(10000)=528 unknowns. On the other hand, the new measurement model (2) results in a system with 500 equations and approximately 5×log(100)+3×log(10000)=51 unknowns. This reduction in the number of unknowns in the radar autofocus problem allows the radar autofocus problem to be solved efficiently.

[0047] Further, some embodiments are based on the recognition that the set of shift kernels (hereinafter the "set of image shifts") and the radar image may be determined using alternating optimization. For example, in one embodiment, the radar image is updated while fixing the set of image shifts, and the set of image shifts is updated while fixing the radar image.

[0048] FIG. 2A shows a block diagram of an alternating optimization for estimating a set of radar images and image shifts according to one embodiment of the present disclosure. The alternating optimization is performed by the processor 107. In block 205, a radar image is estimated based on a transmit pulse 201 and radar returns 203. FIG. 2B shows a graph illustrating a transmit pulse 201 according to one embodiment of the present disclosure. FIG. 2C shows a graph illustrating radar returns 203 according to an embodiment of the present disclosure. The estimation of the radar image is described in more detail below with reference to FIGS. 3A-3D.

[0049] In block 207, a set of image shifts corresponding to different uncertainties of the set of antennas 101 is estimated. The estimation of the set of image shifts is described in detail below with reference to Figures 4A and 4B. Furthermore, in block 209, the estimated radar image is updated based on the set of image shifts. The updating of the estimated radar image 309 is described below with reference to Figure 5A.

[0050] The steps of estimating a set of image shifts and subsequently updating the radar image are performed iteratively 211 until a termination condition is met, at which point a focused radar image 213 is output.

[0051] FIG. 3A illustrates a block diagram of a method for estimating a radar image according to an embodiment of the present disclosure. In an embodiment, the measurements of each antenna are modeled based on the transmitted pulses 201 and the erroneous antenna positions. In block 301, the difference between the radar return 203 and the modeled measurements is minimized to generate an estimate of the radar image 303. Further, in block 305, a regularizer is applied to the estimated radar image 303 to filter noise from the estimated radar image 303. In an embodiment, the regularizer may be a fused lasso regularizer including a 1-norm regularizer and a total variation (TV) regularizer. The 1-norm regularizer imposes sparsity on the estimated radar image 303, and the TV regularizer reduces noise in the estimated radar image 303 to generate a filtered radar image.

[0052] Further, the measurements are modeled using the filtered radar image, the transmitted pulses 201, and the erroneous antenna position. Further, the difference between the radar return 203 and the modeled measurements is minimized to generate an estimate of the radar image, and then a regularizer is applied to the estimated radar image to generate a filtered radar image. The steps of minimizing the difference between the radar return and the modeled measurements and applying the regularizer are performed iteratively until convergence (307). Upon convergence, an estimate of the radar image 309 is output.

[0053] Some embodiments are based on the observation that the regularizer (e.g., a fused lasso regularizer) used in the alternating optimization to filter the estimated radar image (e.g., estimated radar image 121) may not be suitable when noise in the estimated radar image is large because the noise may introduce image domain artifacts, which may also tend to cluster together and thus resemble the shape of true objects. As a result, the alternating optimization may focus on the wrong object, resulting in inaccurate antenna position corrections.

[0054] Some embodiments are based on the recognition that a neural network denoiser can be used instead of a regularizer to mitigate such problems. A neural network denoiser includes a neural network trained to denoise the estimated radar image 303. In other words, the neural network denoiser filters noise from the estimated radar image 303. A neural network denoiser has advantages over a regularizer due to the high modeling power of a neural network and its ability to represent signal structures beyond the explicit sparsity in the image domain and its gradients.

[0055] To that end, instead of applying a regularizer to the estimated radar image 303 to estimate the radar image, a neural network denoiser is applied 311, as shown in FIG. 3B.

[0056] Some embodiments are based on the recognition that artifacts / noise in the estimated radar image 303 result from iterative update steps that occur during minimization of the difference between the radar return and the modeled measurements. The artifacts / noise that result from the iterative update steps are unknown, unpredictable, and may not be the same as the noise that the neural network denoiser is trained on. Thus, the estimated radar image 303 may contain noise on which the neural network denoiser is not trained. When such a radar image is applied to the neural network denoiser, the neural network denoiser may inject errors into the output radar image 309. Thus, simply replacing the normalizer with a neural network denoiser is not sufficient and may cause problems.

[0057] Some embodiments are based on the recognition that, to manage noise for which the neural network denoiser is not trained, the estimated radar image 303 may be filtered by applying (313) a forward radar operator and a companion radar operator to the estimated radar image 303, as shown in FIG. 3C, before applying (311) the neural network denoiser. The forward and companion radar operators filter noise for which the neural network denoiser is not trained from the estimated radar image 303 to generate a filtered radar image 315. Further, the neural network denoiser is applied (311) to the filtered radar image 315. As a result, the neural network denoiser does not inject errors into the output radar image 309, and the reconstruction of the radar image remains stable.

[0058] The steps of minimizing the difference between the radar return and the modeled measurements 301, applying the forward and adjoint radar operators 313, and applying the neural network denoiser 311 are repeated 307 until convergence, at which point an estimate of the radar image 309 is output.

[0059] FIG. 3D illustrates an example estimation of a radar image 309, according to one embodiment of the present disclosure.

[0060] After obtaining an estimate of the radar image 309, a set of image shifts is estimated that correspond to different uncertainties of the set of antennas 101. The estimation of the set of image shifts is described in detail below with reference to Figures 4A and 4B.

[0061] FIG. 4A shows a block diagram of a method for estimating a set of image shifts according to one embodiment of the present disclosure. In an embodiment, measurements are modeled based on the transmitted pulse 201, the initial image shift, and the radar image 309. In block 401, the difference between the radar return 203 and the modeled measurements is minimized. In block 403, a 1-norm regularization is applied to enforce a single non-zero entry in the set of image shifts. The steps of minimizing the difference between the radar return and the modeled measurements 401 and applying the 1-norm regularization 403 are performed iteratively until convergence (405). Upon convergence, an estimate 407 of the set of image shifts is output.

[0062] Further, in block 409, the set of estimated image shifts 407 are aligned according to the average of the true positions of the set of antennas 101 to generate a new estimate of the set of image shifts 411. Figure 4B is a schematic diagram illustrating the alignment of the set of estimated image shifts 407 according to the average 413 of the true positions of the set of antennas 101 according to one embodiment of the present disclosure. The average 413 of the true positions of the set of antennas 101 is known. The set of estimated image shifts 407 are aligned such that the average 415 of the set of estimated image shifts is equal to the average 413 of the true positions of the set of antennas 101.

[0063] Additionally, the estimated radar image 309 is updated based on new estimates 411 of the set of image shifts such that for each of the set of antennas 101, an estimate of the radar image shifted by the corresponding image shift matches the antenna measurements. Updating the estimated radar image 309 is described below with reference to FIG. 5A.

[0064] 5A illustrates a block diagram of a method for updating an estimated radar image 309 according to one embodiment of the present disclosure. In an embodiment, measurements are modeled based on the transmitted pulses 201, a new estimate of a set of image shifts 411, and the radar image 309. In block 501, the difference between the radar return 203 and the modeled measurements is minimized to generate an estimate of the radar image. In block 503, forward and adjoint radar operators are applied to the estimated radar image to generate a filtered radar image. Furthermore, in block 505, a neural network denoiser is applied to the filtered radar image to denoise the filtered radar image.

[0065] The steps of minimizing the difference between the radar return and the modeled measurements 501, applying the forward and adjoint radar operators 503, and applying the neural network denoiser 505 are performed iteratively until convergence 507. Upon convergence, an updated radar image 509 is output.

[0066] FIG. 5B illustrates an example of an updated radar image 509, according to one embodiment of the present disclosure.

[0067] The steps of estimating a set of image shifts and subsequently updating the radar image are performed iteratively until a termination condition is met, at which point a focused radar image 213 is output, which may be a condition in which the updated radar image remains unchanged for a certain number of iterations, or for two consecutive iterations.

[0068] 5C illustrates an example focused radar image 213, according to one embodiment of the present disclosure. The above problem of generating a focused radar image 213 using alternating optimization is called the sparse reconstruction problem.

[0069] In one embodiment, the neural network denoiser for denoising filtering of the radar image estimate comprises a residual Unet architecture. Additionally or alternatively, in an alternative embodiment, the neural network denoiser comprises a denoising convolutional neural network architecture.

[0070] 6 illustrates a residual Unet architecture 600, according to one embodiment of the present disclosure. The residual Unet architecture 600 is symmetric and includes two parts: a left part 601 and a right part 603. The left part 601 is called the contraction path and consists of general convolution operations. The right part 603 is the expansion path and consists of transposed 2d convolution layers.

[0071] Some embodiments are based on the recognition that the forward and adjoint radar operators filter noise from the estimated radar image that the neural network denoiser is not trained on, and therefore the neural network denoiser does not need to be trained on a large training data set that includes all possible noises that may be observed in the alternative optimization. Thus, the neural network denoiser may be trained on a simpler training data set. In one embodiment, the simpler training data set is the input / output pair (z m ,x m ), and the training input image z m is the inverse projection operator A m H Let y be an example radar measurement. m =A m x m +n, and z m =A m H y m and the output image x mwhere is the ground truth object radar image, and n represents the additive noise. Since the neural network denoiser can be trained with a simple training data set, training the neural network denoiser becomes easier and faster.

[0072] In addition, some embodiments are based on the realization that the neural network denoiser-based radar autofocus problem of the present disclosure (illustrated in FIGS. 2A-5C) is capable of reconstructing an object using fewer measurements. This feature allows embodiments of the present invention to be deployed in object tracking systems where the radar signature of an object is determined at a faster rate than the object's motion. Such processing allows for continuous object detection and object tracking by detection.

[0073] Furthermore, detection of a moving object received from a radar reflection may provide a partial view of the object when the object has a large extension relative to the radar beam width. In such a scenario, the neural network denoiser can be trained to reconstruct the partial shape of the object intended to be tracked instead of reconstructing the point object of the object's strong reflector. The reconstructed partial shape can then be used to facilitate an additional module that determines the current state of the object, where the state of the object includes information about the size, orientation, and / or location of the object.

[0074] 7A shows a schematic diagram of a vehicle 701 including a tracker 703 for determining a state of a moving object according to one embodiment of the present disclosure. The tracker 703 is associated with the system 103. The vehicle 701 may be any type of wheeled vehicle, such as a car, a bus, or a rover. The vehicle 701 may also be an autonomous vehicle or a semi-autonomous vehicle. In one embodiment, a steering system 705 of the vehicle 701 is controlled by the tracker 703. Additionally or alternatively, the steering system 705 may be controlled by a driver of the vehicle 701.

[0075] In some embodiments, the vehicle 701 includes an engine 711 that may be controlled by the tracker 703 or other components of the vehicle 701. In some embodiments, the vehicle 701 includes an electric motor instead of the engine 711 that is controlled by the tracker 703 or other components of the vehicle 701. The vehicle 701 may also include one or more sensors 707 for sensing the surrounding environment. Examples of the sensors 707 include a distance range finder such as a radar. In some embodiments, the vehicle 701 includes one or more other sensors 709 for sensing its current motion parameters and internal status. Examples of the one or more other sensors 709 include a global positioning system (GPS), an accelerometer, an inertial measurement unit, a gyroscope, a shaft rotation sensor, a torque sensor, a deflection sensor, a pressure sensor, and a flow sensor. Sensors such as the one or more sensors 707 and the one or more other sensors 709 provide information to the tracker 703. The vehicle 701 may be equipped with a transceiver 713 that enables communication capabilities of the tracker 703 via a wired or wireless communication channel with the system 103. The tracker 703 includes a processor and a memory that stores instructions executable by the processor. The processor may be a single-core processor, a multi-core processor, a computing cluster, or any number of other configurations. The memory may include random access memory (RAM), read-only memory (ROM), flash memory, or any other suitable memory system.

[0076] FIG. 7B is a schematic diagram illustrating the control of a vehicle 701 based on a state of a moving object such as a vehicle 715, according to one embodiment of the present disclosure. The vehicles 701 and 715 are moving along a road 717, with the vehicle 701 behind the vehicle 715. The system 103 associated with the vehicle 701 is communicatively coupled to the set of antennas 101 shown in FIG. 1A. The set of antennas 101 may cover an area of ​​interest including the road 717. The set of antennas 101 may transmit pulses to the area of ​​interest and receive corresponding reflections. Furthermore, the system 103 receives reflections from the set of antennas 101 and generates a radar image by solving the sparse reconstruction problem described in the previous embodiment. The radar image shows the location of point detections in space of the vehicle 701. For example, the radar image provides a set of point detections of the vehicle 715. The radar image has no artifacts, is less noisy, is generated by the computationally efficient technique described in the previous embodiment, and is a better sampling of the distribution of possible detections of the vehicle 715. The radar image is input to the tracker 703. In an embodiment, the tracker 703 determines the state of the vehicle 715 based on the received radar image and a motion model and a composite measurement model of the vehicle 715. The motion model and the composite measurement model may be stored in a memory of the tracker 703. According to an embodiment, the composite measurement model includes multiple probability distributions constrained to lie on the contour of the vehicle 715 with a predetermined relative geometric mapping to the center of the vehicle 715.

[0077] Additionally, in some embodiments, the tracker 703 generates control inputs based on the state of the vehicle 715 to control the vehicle 701. The control inputs include, for example, commands specifying values ​​for the steering angle of the wheels of the vehicle 701, the rotational speed of the wheels, and any or a combination of acceleration of the vehicle 701. The control inputs are intended to keep the vehicle 701 within certain boundaries of the road 717 and to avoid the vehicle 715. For example, the control inputs cause the vehicle 701 to navigate along a trajectory 719 to safely pass the vehicle 715.

[0078] 8 illustrates a block diagram of a method 800 for generating a radar image of a scene, according to one embodiment of the disclosure. At block 801, the method 800 includes receiving radar measurements collected from a set of antennas (such as the set of antennas 101). The radar measurements correspond, for example, to the reflections 117 described in FIG. 1B.

[0079] At block 803, the method 800 includes obtaining an estimate of a radar image. The estimate of the radar image is obtained as described in FIG. 3C.

[0080] At block 805, the method 800 includes determining a set of image shifts of the radar image corresponding to different uncertainties of the set of antennas. The set of image shifts is determined as described in detail in Figures 4A and 4B.

[0081] At block 807, the method 800 includes updating, for each antenna, an estimate of the radar image based on the determined set of image shifts of the radar image such that an estimate of the radar image shifted by a corresponding shift of the radar image matches the measurement of the antenna. The estimate of the radar image is updated as described in detail in FIG. 5A.

[0082] At block 809, the method 800 includes determining whether a termination condition is met. If the termination condition is not met, a new set of image shifts is further determined. The steps of determining a set of image shifts and subsequently updating the estimate of the radar image are performed iteratively until a termination condition is met. The termination condition may be a certain number of iterations or a condition in which the radar image of two consecutive iterations remains unchanged.

[0083] If the termination condition is met, then in block 811, the method 800 includes outputting the radar image.

[0084] The neural network denoiser based radar autofocus problem formulation is mathematically described below. mathematical calculations

[0085]

number

[0086] Under this particular model, the shift kernel is a 1 sparse vector with unknown support locations, thereby reducing the unknown degrees of freedom to Mlog(F)+N. Signal Model

[0087] This disclosure includes considering a two-dimensional radar imaging scenario in which M distributed antennas are used to detect K objects. The objects are located in a lattice Ω ⊂ R. 2 , |Ω|=N, which is located in the region of interest discretized on N=N x ×N y and N x and N y specifies the number of grid points in the horizontal and vertical directions. Let l∈Ω denote the spatial location of the grid points in Ω.

[0088] Γ ⊂ R 2 Let |Γ|=M be the set of all spatial locations of M antennas. Without loss of generality, assume that a subset of antennas act as transmitters / receivers and the remaining antennas are receivers only. A transmitting antenna at location r∈Γ emits a time-domain pulse p(t) with frequency spectrum P(ω), where ω=2πf is the angular frequency and f∈B is the normal frequency in the signal bandwidth B, |B|=F.

[0089]

number

[0090]

number

[0091]

number

[0092]

number

[0093] This disclosure also considers an alternative model of convolution with a shift kernel in the measurement domain by switching the convolution to the image domain.

number

[0094] This disclosure considers an image domain convolution model, which can be expressed in the spatial Fourier domain as follows:

number

[0095] First, the radar image x is sparse and has a shape that can be learned from the training data, and the kernel h m We incorporate the prior information that is a two-dimensional shift operator into the model (4).

[0096] Therefore, a neural network denoising operator is used to refine the estimate of the radar image x, and a regularizer R x (·) is added to x, and the l1-norm regularizer R x (·) is h m The overall optimization problem can be written as:

number

[0097] Neural Network Based Regularizer R x (x) is the input-output pair (z m ,x m ) a neural network denoiser trained using training data examples

number

[0098]

number

[0099] On the other hand, a certain property of the shift kernel is that for all h m We require that h be sparse with one nonzero entry equal to 1. m Since is non-negative with its entries summing to 1, the only regularization required is the l1-norm penalty:

number

[0100] 9A illustrates a block coordinate descent algorithm 900a for solving (5) according to some embodiments of the present disclosure. Problem (5) is non-convex, and at least one objective of the present disclosure in this context is to find a stationary point for problem (5). Thus, the block coordinate descent algorithm 900a finds, for all m, the x and h m FIG. 2A shows a block diagram of the steps involved in the algorithm shown in FIG. 9A. In step 901, the shift kernel h m are all N h ×N h The zero-valued matrix of the unshifted kernel h 0 is initialized to .

[0101]

number

[0102] FIG. 9B illustrates a method for detecting a smeared portion of ... m 9C illustrates an algorithm 900c of a FISTA subroutine for updating x, according to some embodiments of the present disclosure. In general, FISTA can be used to solve convex optimization problems of the form:

number

[0103] Similarly, image x at iteration t t Given the estimate of h m The forward operator for is defined as follows:

number

[0104] Note that the formula for D in (8) is h for all m. mTherefore, for all m, h m The FISTA subroutine for updating the function T is described in FIG. + (z; τ) is a non-negative soft thresholding operator that sets all values ​​of z less than τ to zero. In FIG. 9B, the update procedure is specific to the use of an explicit regularization function such as the 1-norm penalty or the fused lasso penalty. The non-linear thresholding function that is explicit to the penalty function used is T + In FIG. 9C, the update procedure is specific to using a neural network denoiser, which updates T(v t ) A filtering step is performed in step 4 of algorithm 900c to remove noise that the neural network denoiser was not trained on during its training.

[0105] 10 is a block diagram of a computer system 1000 of a radar system contemplated by the present disclosure, according to some embodiments of the present disclosure. The computer system 1000 can communicate with a radar platform or set of antennas 101 and store collected data in memory 1001 that is processed by a processor 1003 of the computer system 1000. The computer system 1000 can include a human machine interface or user interface 1005 that can connect the computer system 1000 to a keyboard 1007 and a display device 1009. The computer system 1000 can be coupled through a bus 1011 to a display interface 1013 adapted to connect the computer system 1000 to a display device 1015, which can include, among others, a computer monitor, a camera, a television, a projector, or a mobile device.

[0106] The computer system 1000 may include a power supply 1017 depending on the application, which may optionally be located external to the computer system 1000. The processor 1003 may be one or more processors that may be configured to execute stored instructions and may be in communication with a memory 1001 that stores instructions executable by the processor 1003. The processor 1003 may be a single-core processor, a multi-core processor, a computing cluster, or any number of other configurations. The processor 1003 is connected to one or more input / output devices via a bus 1011. The memory 1001 may include a random access memory (RAM), a read-only memory (ROM), a flash memory, or any other suitable memory system.

[0107] 10, the computer system 1000 may also include a storage device 1019 adapted to store supplemental data and / or software modules used by the processor 1003. For example, the storage device 1019 may store, among other things, pre-designed radar platform trajectories, radar operating frequency bandwidths, transmit waveforms, estimated signal-to-noise ratios, image data for object recognition, historical data for imaging results using simulated noise data with different methods of addressing position errors. The storage device 1019 may include a hard drive, an optical drive, a thumb drive, an array of drives, or any combination thereof.

[0108] 10, a printer interface 1021 may also be connected to the computer system 1000 through the bus 1011 and adapted to connect the computer system 1000 to a printing device 1023, which may include a liquid inkjet printer, a solid ink printer, a large scale commercial printer, a thermal printer, a UV printer, or a dye sublimation printer, among others. A network interface controller (NIC) 1025 is adapted to connect the computer system 1000 to a network 1027 via the bus 1011. The image data or related image data may be rendered on a display device, an imaging device, and / or a printing device, among others, via the network 1027.

[0109] 10, the image data or associated image data may be transmitted over a communication channel of a network 1027, among other things, and / or stored in a computer storage device 1019 for storage and / or further processing. Additionally, the image data or associated image data may be received wirelessly or wired from a receiver 1029, or transmitted wirelessly or wired via a transmitter 1031, both of which are connected to the computer system 1000 via a bus 1011.

[0110] The computer system 1000 may be connected to external sensors 1033, one or more input devices 1035, other computers 1037, and other devices 1039. The external sensors 1033 may include motion sensors, inertial sensors, some type of measurement sensor, etc. The external sensors 1033 may include sensors for speed, direction, air flow, distance to an object or location, weather conditions, etc. The input devices 1035 may include, for example, a keyboard, a scanner, a microphone, a stylus, a touch-sensitive pad or display.

[0111] The following description provides exemplary embodiments only and is not intended to limit the scope, applicability, or configuration of the present disclosure. Rather, the following description of exemplary embodiments provides those skilled in the art with an enabling description for implementing one or more exemplary embodiments. Contemplated are various changes that may be made in the function and arrangement of elements without departing from the spirit and scope of the disclosed subject matter as set forth in the claims.

[0112] In the following description, specific details are given for a thorough understanding of the embodiments. However, those skilled in the art can understand that the embodiments may be practiced without these specific details. For example, systems, processes, and other elements in the disclosed subject matter may be shown as components in block diagram form so as not to obscure the embodiments in unnecessary detail. In other instances, well-known processes, structures, and techniques may be shown without unnecessary detail so as to avoid obscuring the embodiments. Additionally, like reference numbers and names in the various drawings refer to like elements.

[0113] Also, particular embodiments may be described as a process that is depicted as a flowchart, a flow diagram, a data flow diagram, a structure diagram, or a block diagram. Although a flowchart may describe operations as a sequential process, many of the operations may be performed in parallel or simultaneously. In addition, the order of operations may be rearranged. A process may be terminated when its operations are completed, but may have additional steps not discussed or included in the diagram. Moreover, not all operations in any process specifically described may occur in all embodiments. A process may correspond to a method, a function, a procedure, a subroutine, a subprogram, etc. When a process corresponds to a function, the end of the function may correspond to a return to the calling function or the main function of the function.

[0114] Furthermore, embodiments of the disclosed subject matter may be implemented, at least in part, either manually or automatically. The manual or automatic implementation may be performed or at least assisted through the use of a machine, hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When implemented in software, firmware, middleware, or microcode, the program code or code segments to perform the necessary tasks may be stored in a machine-readable medium. The necessary tasks may be executed by a processor.

[0115] The embodiments of the present disclosure include coherent distributed radar imaging by allowing for position ambiguity and autofocus of a single sensor array with distributed sensing using multiple sensors. In particular, a multistatic radar imaging approach where one transmit / receive radar platform and multiple receive radar platforms are moving towards a region of interest (ROI) with position perturbations. The embodiments of the present disclosure detect objects within the ROI. Due to inaccurate positioning and motion errors, the actual array position is perturbed up to several times the central radar wavelength. Although the image resolution of each sensor array may be low due to its small aperture size, a high-resolution image can be formed by jointly processing the output of all distributed arrays with well-compensated position errors. The embodiments of the present disclosure are iteratively realized by solving a series of optimization problems to assume a sparse scene, compensate for position-induced phase errors, exploit object signatures, and estimate antenna positions.

[0116] Embodiments of the present disclosure also provide autofocus radar imaging using a single moving transmitting radar platform or combined transmitter / receiver in conjunction with multiple spatially distributed moving radar receiving platforms or receivers to generate radar images of objects located within a region of interest, where the moving radar receiver is perturbed with unknown position errors up to several radar wavelengths.

[0117] The various methods or processes outlined herein may be coded as software executable on one or more processors using any one of a variety of operating systems or platforms. In addition, such software may be written using any of a number of suitable programming languages ​​and / or programming or scripting tools, and may be compiled as executable machine language code or intermediate code that runs on a framework or virtual machine. Typically, the functionality of the program modules may be combined or distributed as desired in various embodiments.

[0118] The embodiments of the present disclosure may be embodied as a method, of which an example has been provided. The acts performed as part of the method may be ordered in any suitable manner. Thus, embodiments may be constructed in which acts are performed in an order different from that illustrated, which may include performing simultaneously some acts shown as sequential acts in the exemplary embodiment.

[0119] Although the present disclosure has been described with reference to certain preferred embodiments, it will be understood that various other adaptations and modifications can be made within the spirit and scope of the present disclosure. It is therefore intended by the appended claims to cover all such variations and modifications that fall within the true spirit and scope of the present disclosure.

Claims

1. 1. A system for generating a radar image of a scene, comprising: a set of antennas; at least one processor; and a memory having instructions stored thereon, the instructions, when executed by the at least one processor, causing the system to: and receiving radar measurements of the scene collected from the set of antennas, the radar measurements being measurements associated with reflections of radar pulses transmitted to the scene, the instructions when executed by the at least one processor further causing the system to: generating the radar image of the scene by solving a sparse reconstruction problem, the sparse reconstruction problem being and determining a set of image shifts of the radar image corresponding to different uncertainties of the set of antennas, the set of antennas being under uncertainty caused by one or a combination of ambiguities in the position of each of the antennas and clock ambiguities, the sparse reconstruction problem being solved by: and updating an estimate of the radar image based on a set of determined image shifts of the radar image until a termination condition is met, where for each of the antennas, the estimate of the radar image shifted by a corresponding shift of the radar image matches the radar measurement of the antenna; The sparse reconstruction problem is solved with a neural network denoiser that denoises filtering the estimate of the radar image, and the instructions, when executed by the at least one processor, further provide the system with: rendering the radar image if the termination condition is satisfied; The system, characterized in that the filtering of the estimate of the radar image is performed by applying a forward radar operator and an adjoint radar operator to the estimate of the radar image.

2. The system of claim 1 , wherein the neural network denoiser comprises a residual Unet architecture.

3. 2. The system of claim 1, wherein the neural network denoiser is trained based on a training data set including an input image and an output image, the input image including a backprojected image and the output image including a ground truth radar image of an object.

4. The system of claim 1 , wherein the scene includes at least one moving object.

5. The system of claim 4 , further comprising a tracker, the tracker configured to determine a state of the at least one moving object based at least on the radar image.

6. The system of claim 5 , wherein the state of the at least one moving object comprises one or a combination of a size, an orientation, and a position of the at least one moving object.

7. 1. A method for generating a radar image of a scene, comprising: receiving radar measurements of the scene collected from a set of antennas, the radar measurements being measurements associated with reflections of radar pulses transmitted into the scene, the method further comprising: generating the radar image of the scene by solving a sparse reconstruction problem, the sparse reconstruction problem comprising: and determining a set of image shifts of the radar image corresponding to different uncertainties of the set of antennas, the set of antennas being under uncertainty caused by one or a combination of ambiguities in the position of each of the antennas and clock ambiguities, the sparse reconstruction problem being solved by: and updating an estimate of the radar image based on a set of determined image shifts of the radar image until a termination condition is met, where for each of the antennas, the estimate of the radar image shifted by a corresponding shift of the radar image matches the radar measurement of the antenna; The sparse reconstruction problem is solved with a neural network denoiser that denoises filtering the estimate of the radar image, the method further comprising: rendering the radar image if the termination condition is satisfied; 11. A method, characterized in that the filtering of the estimate of the radar image is performed by applying a forward radar operator and an adjoint radar operator to the estimate of the radar image.

8. The method of claim 7 , wherein the neural network denoiser comprises a residual Unet architecture.

9. 8. The method of claim 7, wherein the neural network denoiser is trained based on a training data set including input images and output images, the input images including backprojected images and the output images including ground truth radar images of objects.

10. The method of claim 7 , wherein the scene includes a moving object.

11. 1. A non-transitory computer readable storage medium having embodied thereon a program executable by a processor to perform a method for generating a radar image of a scene, the method comprising: receiving radar measurements of the scene collected from a set of antennas, the radar measurements being measurements associated with reflections of radar pulses transmitted into the scene, the method further comprising: generating the radar image of the scene by solving a sparse reconstruction problem, the sparse reconstruction problem comprising: and determining a set of image shifts of the radar image corresponding to different uncertainties of the set of antennas, the set of antennas being under uncertainty caused by one or a combination of ambiguities in the position of each of the antennas and clock ambiguities, the sparse reconstruction problem being solved by: and updating an estimate of the radar image based on a set of determined image shifts of the radar image until a termination condition is met, where for each of the antennas, the estimate of the radar image shifted by a corresponding shift of the radar image matches the radar measurement of the antenna; The sparse reconstruction problem is solved with a neural network denoiser that denoises filtering the estimate of the radar image, the method further comprising: rendering the radar image if the termination condition is satisfied; 11. A non-transitory computer-readable storage medium, characterized in that the filtering of the estimate of the radar image is performed by applying a forward radar operator and an adjoint radar operator to the estimate of the radar image.

12. The non-transitory computer-readable storage medium of claim 11 , wherein the neural network denoiser comprises a residual Unet architecture.

13. 12. The non-transitory computer-readable storage medium of claim 11, wherein the neural network denoiser is trained based on a training dataset including an input image and an output image, the input image including a backprojected image and the output image including a ground truth object radar image.

14. The non-transitory computer-readable storage medium of claim 11 , wherein the scene includes a moving object.

Images