Frequency steered 3D multibeam sonar

Abstract

An example method includes detecting, by a receiver of an apparatus at a reception time, a sound signal reflected by an object in an environment. The example method further includes determining, by identifying a frequency of the sound signal, a first angle in a first plane at which the object is disposed; determining a distance between the apparatus and the object based on a time delay between a transmission time of the sound signal and the reception time of the sound signal; and determining a second angle in a second plane at which the object is disposed based on a position of the receiver. A position of the object in the environment is determined based on the first angle, the distance between the apparatus and the object, and the second angle.

Description

FREQUENCY STEERED 3D MULTIBEAM SONARCROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to U.S. Provisional App. No. 63 / 525,963, which was filed on July 10, 2023 and is incorporated by reference herein in its entirety.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support under Grant No. N0002421 F8705, awarded by the Office of Naval Research (ONR). The government has certain rights in the inventionBACKGROUND

[0003] Since its invention in the early 1900s, Sonar (SOund NAvigation and Ranging) systems have been finding an increasing number of applications, ranging from simple depth or range measurements to high resolution mapping, underwater communications, and autonomous vehicle navigation. Active sonar systems transmit sound into the water and receive returns from objects located at some range from the system.

[0004] An active sonar system includes, in some cases, transmit electronics, receive electronics, precision timing circuitry and power supplies connected to one or more transducer elements. In an example active sonar imaging system, a transducer optimized for transmitting sonar signals converts electrical energy into mechanical vibrations which project sound into the environment. A separate set of transducers optimized for receiving sound convert the mechanical vibrations from echoes reflected back toward the sonar into electrical signals that are recorded. Because many transducers are "reciprocal” (they can be used as a transmitter or a receiver), some systems use a single transducer to both transmit and receive, in which case the system is called “monostatic.” Active sonars are used for high resolution imaging, and though some monostatic imaging sonars exist, they frequently use distinct transducers for transmitting and receiving. This configuration, in which separate transducers are used for transmitting and receiving, is called a "bistatic” configuration.

[0005] To increase resolution, directionality and Signal-to-Noise ratio (SNR) many sonar systems are composed of arrays of multiple receiver hydrophones (or “elements”), allowing the systems to steer or beamform data on transmit and / or reception. Sonar systems that create multiple beams simultaneously using array processing are often referred to as “multibeam” sonar systems as each of the beams receive echo data from different transmit directions in the water.BRIEF DESCRIPTION OF THE DRAWINGS

[0006] Some of the materials submitted herewith may be better understood in color. Applicant considers the color versions of the disclosure as part of the original submission and reserves the right to present color images of the materials of this disclosure in later proceedings.

[0007] FIGS. 1A and 1 B illustrate an example environment of an underwater vehicle utilizing frequency-steered multibeam sonar in accordance with various examples of the present disclosure. FIG 1A illustrates the environment along an xy plane during a transmission phase. FIG. 1 B illustrates the environment along a xz plane during a reception phase.

[0008] FIG. 2 illustrates example signaling of a transmit phase of a 3D multibeam sonar technique.

[0009] FIG. 3 illustrates example signaling of a reception phase of a 3D multibeam sonar technique.

[0010] FIG. 4 illustrates an example process for determining a position of a surface of an object within 3D space.

[0011] FIG. 5 illustrates an example of a device configured to perform various functions described herein.

[0012] FIG. 6 illustrates an example comparison of an array and 3D beam-configurations for a standard planar array (left) and an example of the new 3D sonar based on frequency dispersion (left).

[0013] FIG. 7 illustrates an angle vs. frequency dispersion curve using the grating equation for m=1, assuming a nearly 1 -octave band spanning 330 to 600 kHz, with a grating spacing of 0.65 centimeters.

[0014] FIG. 8 illustrates an example of blazed array imaging sections for a single element showing the two imaging sectors that can be created using separate ping transmissions with inverted polarity. Color corresponds to the frequency.

[0015] FIG. 9 illustrates an example of a commercial blazed array (The BlueView M450-Mk2), showing the three separate blazed arrays (left, middle), used to populate the six different sectors in the image on the right.

[0016] FIG. 10 illustrates example beam widths and angles associated with 1) mechanical blazed arrays, which are fixed based on hardware design and point off-center from the array normal (left plot), and 2) the new design in which the width and orientation of the imaging sector is definable in software.

[0017] FIG. 11 illustrates instantaneous frequency vs. time for an example signal bank.

[0018] FIG. 12 illustrates an example of a signal envelope as a function of time for the signal bank with the instantaneous frequencies shown in FIG. 9. The color scale is linear.

[0019] FIG. 13 illustrates example magnitudes of the signals shown in FIG. 10 after applying an additional chirp for amplitude regularization.

[0020] FIG. 14 is a flowchart showing an example realization of the 3D volumetric beamforming sonar and post processing algorithms described in this document.DETAILED DESCRIPTION

[0021] Various techniques have been proposed to achieve 3D imaging in an underwater environment. However, existing techniques have various drawbacks. An example multibeam configuration includes a transmitter with a wide across-track spread but a very tight along-track beam pattern used to transmit a signal. A receiver array, composed of a single uniform linear array (ULA) of elements is associated with a fan of receptive fields, from which the ULA elements receive beams from an environment. The ULA has high across-track resolution but poor forward (along-track) resolution. The transmit and the receive beam-patterns combine to form a fan composed of beams that have fineresolution in both the along-track dimension (due to the transmitter beam pattern) and fine across-track resolution (due to the receiver ULA beam pattern), with multiple beams in the across-track dimension created by post processing the signals captured by each of the elements in the ULA.

[0022] The ULA includes N separate transducer elements arranged in a line, such that the transducer elements create an N x 1 array. This array design is relatively simple to create from a mechanical perspective. In general, the ULA can detect N receive beams with statistically independent echo information captured from the environment (subject to various design implementation details). In various cases, the ULA can beamform in the dimension parallel to the array, but cannot beamform in another direction. To achieve high resolution in the dimension perpendicular to the array axis, in some cases, the ULA can be paired with a transmitter that has high directivity in the perpendicular direction but disperses the beam in the axial dimension of the ULA. The result is a set of beams that combine the directivity of the ULA and transmitter in a fan shape.

[0023] In some cases, a ship can generate a depth map using a ULA. Each ping creates a new line of data, and the forward motion of the ship creates a swath that can be projected onto a map. Using such a system, line by line, a 3D terrain map can be built up.

[0024] In some cases, a planar array includes multiple ULAs stacked in the vertical dimension to allow for some elevation angle-of-arrival data to be determined from the system. These systems are called “interferometric” sonar systems because they can compute the angle-of-arrival in the elevation dimension by looking at how the phase characteristics of the echoes interfere with each other. A drawback of interferometric systems is that they make a “sparsity” assumption about the features being observed by the system. In general, they assume that the vertical scattering profile of the environment can be described by the number of elements in the vertical dimension minus one. Using a two-element array, for example, one vertical angle of arrival can be determined, limiting the description of the 3D world to a less than 3D height map. For a multi-element system with 2 < M « N elements in the dimension perpendicular to the ULA, generally M-1 or less statistically independent scatterers in the elevation direction can be used to describe the environment being analyzed (Kraeutner, et al., OCEANS' 99. MTS / IEEE. RIDING THE CREST INTO THE 21 ST CENTURY. CONFERENCE AND EXHIBITION. CONFERENCE PROCEEDINGS, 1 :37-45 (1999)). In complex environments, or environments with a lot of vertical features (e.g., pilings, piers, harbor borders, etc.) this type of 3D imaging requires a much larger number of elements: M x N, and it can still fail when a dense number of points is required to describe an environment. Alternatives for complex environments include mechanically scanning high resolution systems comprised of ULA's oriented vertically, or with a vertical tilt, to create a 3D array using multiple pings. This is often accomplished using multibeam systems or tripod-mounted systems.

[0025] In various implementations of the present disclosure, a traditional Mills Cross design, which includes perpendicularly mounted ULAs, can also be used to create a high resolution 3D image with N x N beams. However, N separate transmit beams are produced to create the volumetric image, which results in a relatively long transmission time, effectively negating any value this approach might otherwise have for autonomy or real-time applications.

[0026] Though the previously described methods for performing high resolution 3D imaging can be used to great effect for detailed harbor surveys or archeological purposes, the necessity of combining multiple pings to create 3D images limits their usefulness for contexts in which real-time 3D information would be beneficial. This has been recognized, and to meet the need for real-time 3D imaging, planar arrays (the 2D analogy to the ULA) have been developed. A planar array, for instance, includes an N x N grid of hydrophone elements in a square array. Fully populating the array in two dimensions allows beamforming in azimuth and elevation, overcoming the primary limitation of the ULA.

[0027] The directivity characteristics for the transmitter are relaxed in this case. Although along-track length was used in the ordinary multibeam or Mills Cross designs to make narrow fans, the planar array creates a densely resolved grid of beams in both azimuth and elevation. In contrast to standard multibeam designs, a planar array utilizes a transmit beam that is broad enough to disperse sufficient energy in each receive-beam direction to create a positive signal-to- noise ratio (SNR). An example of this kind of array is the ECHOSCOPE PIPE™ by Coda Octopus Products, Inc. (of Orlando, FL). Though the theoretical operation of planar arrays is straightforward, there remain some non-trivial drawbacks to this sonar design approach.

[0028] First, the complexity of the mechanical design relates to the square of the size of the array. The 3D equivalent of a 128 beam multibeam system, for example, would utilize 128 x 128 elements or greater than 16,000 individual hydrophones. Electronic complexity increases rapidly with resolution for 2D planar arrays, and the associated data post-processing also becomes more complex and resource intensive. Both of these increases translate to increases in costs and a reduction of viable scenarios in which the technology can be used. For instance, planar arrays are impractical for devices that utilize low power, such as autonomous underwater vehicle (AUV)-oriented operations.

[0029] Second, the 2D planar array format is incompatible with the forward-looking geometry utilized for autonomy on AUV systems due to a lack of streamlining: mounting a planar array on the front of an AUV, such that the surface normal is parallel to the vehicle axis will severely hinder the AUV’s hydrodynamic performance. A hemispherical array could solve this problem, however that would come at a significant cost in terms of mechanical complexity. Such hemispherical array designs, if implemented, would be cost-prohibitive.

[0030] The present disclosure describes various techniques for creating a cost-effective, low complexity truly 3D multibeam sonar system which overcomes the previously described drawbacks of planar arrays. Implementations described herein are simple both mechanically and from a post-processing perspective. Various examples are readily streamlined for use as an AUV forward-looker to benefit autonomy. Various implementations of the 3D multibeam sonar system can be realized using a wide range of electronics and transducer designs. In some implementations, the system can include: 2 or more arrays oriented orthogonally or in some other non-coincidental orientation, a broad-band transmit signal with a bandwidth that is several hundred kilohertz wide, and an appropriate transmit waveform that performs angle-based frequency dispersion on transmit. In contrast to an existing Blazed Array design (Thompson, et al., MTS / IEEE OCEANS 2001. AN OCEAN ODYSSEY. CONFERENCE P OCEEDINGS, 2:985-88 (2001 )), various implementationsof the present disclosure greatly increase the generality and resolution of the image along the dimension in which frequency dispersion is performed.

[0031] Implementations of the present disclosure provide a new type of 3D sonar system. This type of system can be used in many applications including but not limited to: forward looking sonar (FLS); obstacle avoidance systems (OAS), such as forAUV applications; mapping; fisheries biomass estimation; seabed awareness systems; port security; and diver awareness.

[0032] Various implementations of the present disclosure will now be described with reference to the accompanying figures.

[0033] FIGS. 1A and 1 B illustrate an example environment 100 of an underwater vehicle 102 utilizing frequency- steered multibeam sonar in accordance with various examples of the present disclosure. FIG. 1A illustrates the environment 100 along an xy plane during a transmission phase. In various cases, the environment 100 is an aquatic environment. For instance, the underwater vehicle 102 is at least partially disposed underwater. The environment 100, for instance, includes fresh water or saltwater.

[0034] The underwater vehicle 102 includes various components that enable it to operate in the environment 100. In various cases, the underwater vehicle 102 includes a watertight housing configured to enclose various elements of the underwater vehicle 102. For example, the housing includes a metal (e.g., steel, copper, brass, aluminum), glass (e.g., borosilicate glass), a plastic, or any combination thereof. The housing of the underwater vehicle 102 may be sealed in a protective coating, such as a paint including one or more of epoxy polyamide, acrylic, silicone alkyd enamel, urethane, or a siloxane. In various cases, the underwater vehicle 102 includes at least one on-board power source, such as one or more batteries (e.g., lithium-ion batteries), a nuclear reactor, a solar cell, or any combination thereof. The on-board power source(s), for instance, are configured to power one or more active components of the underwater vehicle 102.

[0035] The underwater vehicle 102 may include one or more movement-controlling elements, which include devices configured to control movement of the underwater vehicle 102 in the environment 100. The underwater vehicle 102 may include one or more ballast tanks. The underwater vehicle 102, for instance, can control its vertical movement within the environment 100 by filling or emptying the ballast tank(s) with a fluid (e.g., water). In some examples, the underwater vehicle 102 includes one or more movable fins and / or rudders that enable the underwater vehicle 102 to change direction within the environment 100 during movement. The underwater vehicle 102, in various cases, includes one or more propulsion components that enable to the underwater vehicle 102 to propel itself in a direction in the environment 100. For example, the underwater vehicle 102 includes one or more propellers.

[0036] In various cases, the underwater vehicle 102 is configured to identify objects and / or surfaces within the environment 100. In some examples, the environment 100 is unsuitable for light-based imaging methods. For example, the environment 100 may be deep underwater and may lack ambient lighting. Furthermore, the environment 100 may include particles or other contaminants that prevent the underwater vehicle 102 from imaging the environment 100 using a light-based technique, even if the underwater vehicle 102 includes a light source. For instance, particles withinthe environment 100 may significantly scatter light output by the underwater vehicle 102 itself, such that a light-based field of view (FOV) of the underwater vehicle 102 may be significantly limited. Thus, in some cases, it may be beneficial for the underwater vehicle 102 to utilize sonar-based technologies to ascertain the physical orientation and positions of surfaces within the environment 100. As used herein, the term "sonar,” and its equivalents, may refer to a technique that utilizes sound signals to detect objects within an environment.

[0037] According to various implementations of the present disclosure, the underwater vehicle 102 includes an array of transmitters 104 configured to generate physical signals that are output into the environment 100. For example, the array of transmitters 104 is configured to generate sound signals According to various implementations, the sound signals are in a range of 100 hertz (Hz) to 500 kilohertz (kHz). In various cases, the array of transmitters 104 generates sound pulses within the environment 100.

[0038] In various cases, the array of transmitters 104 include an array of transducers configured to output the physical signals. For example, the array of transmitters 104 includes one or more piezoelectric transducers (e.g. , lead zirconate titanate (PZT), lead magnesium niobate (PMN), Terfenol-D, etc.), one or more magnetostrictive transducers, one or more electrostatic transducers, or any combination thereof. In various cases, an example transmitter among the array of transmitters 104 includes a piezoelectric material disposed between at least two electrodes. When a voltage is applied across the electrodes, the piezoelectric material is configured to mechanically strain and / or deform. In various cases, the piezeoelectric material generates a sound signal in accordance with an electrical signal applied to its electrodes. Thus, the underwater vehicle 102 may cause the array of transmitters 104 to output the physical signals by outputting electrical signals to the electrodes of various transmitters within the array of transmitters 104.

[0039] The array of transmitters 104 may be a one-dimensional (1 D) array. The array of transmitters 104 may extend along a line segment, such as a line segment extending along a y direction. That is, the array of transmitters 104 may be a single stack of transmitters that is aligned in the y direction. Although FIGS. 1A and 1 B illustrate the array of transmitters 104 disposed along a straight line, implementations are not so limited. For example, an FOV of the underwater vehicle 102 may be adjusted by changing a curvature of a line on which the array of transmitters 104 is disposed. In various cases, the array of transmitters 104 is disposed along an arc that is aligned onto an xy plane.

[0040] In some cases, the array of transmitters 104 is mounted on the housing of the of the underwater vehicle 102. For instance, the array of transmitters 104 can be enclosed within the housing, integrated with the housing, or disposed outside of the housing. In various cases, the array of transmitters 104 is disposed on the housing of the underwater vehicle 102 on a leading edge of the underwater vehicle 102 in a direction of movement of the underwater vehicle 102 in the environment 100.

[0041] The array of transmitters 104, for instance, is configured to output a wavefront 106 into the environment 100. The wavefront 106, in various cases, collectively includes the physical signals output by the array of transmitters 104. In various cases, the wavefront 106 collectively includes a pulse (e.g., a ping) output by the array of transmitters 104 within the environment 100. The wavefront 106 is generated by constructive and destructive interference of physicalsignals (e.g., sound pulses) output by respective transmitters among the array of transmitters 104 within the environment 100.

[0042] In various implementations, the underwater vehicle 102 causes the array of transmitters 104 to output the wavefront 106 in an expanding arc as it travels through the environment 100. The arc, for instance, expands along the x direction in an xy plane as the wavefront 106 travels from the array of transmitters 104. A volume of the environment 100 through which the wavefront 106 travels includes the FOV of the underwater vehicle 102.

[0043] The underwater vehicle 102, in various cases, generates the wavefront 106 using frequency steering techniques. The wavefront 106 includes multiple frequency-steered components, such as a first component 108 and a second component 110. In various cases, these components represent respective beams within the wavefront 106.

[0044] In various cases, each component of the wavefront 106 includes one or more distinct frequencies. For example, the first component 108 may include sound having a first frequency, the second component 110 may include sound having a second frequency, and the first frequency may be different than the second frequency. According to some cases, each component of the wavefront 106 includes a distinct frequency range.

[0045] The respective components of the wavefront 106 are transmitted by the array of transmitters 104 along respective elevation angles. For example, the first component 108 is transmitted at a first elevation angle cp1 , and the second component 110 is transmitted at a second elevation angle q>2. Other components of the wavefront 106 may be transmitted along other elevation angles. The total range of elevation angles of the components of the wavefront 106 may represent the transmission field of the array of transmitters 104.

[0046] The underwater vehicle 102 may implement the distinct components of the wavefront 106 using beamforming techniques. For example, the underwater vehicle 102 may cause the transmitters among the array of transmitters 104 to generate physical signals with varying frequencies. However, portions of the physical signals with the same frequency may be selectively generated at different, but coordinated times and / or phases in order to cause those portions to constructively interfere and be transmitted at a consistent elevation angle. According to various cases, the array of transmitters 104 is a phased array that outputs superposing physical signals within the environment 100, such that the physical signals combine to generate the distinct frequency components of the wavefront 106.

[0047] In some cases, the underwater vehicle 102 outputs electrical signals (also referred to as "excitation signals”) to the respective transmitters among the array of transmitters 104 that cause the array of transmitters 104 to collectively generate the wavefront 106, with its distinct frequency components. In various implementations, the electrical signals include chirps. As used herein, the term “chirp,” and its equivalents, may refer to a signal whose frequency increases or decreases over time. For instance, the electrical signals include linear chirps. The length of the chirp in a given excitation signal is dependent on the desired transmission field of the array of transmitters 104 (e.g., the width of the wavefront 106) as well as the position of the transmitter receiving the excitation signal in the array of transmitters 104.

[0048] After transmission, the various components of the wavefront 106 are reflected, or otherwise scattered, from surfaces of various objects within the environment 100. For example, the first component 108 is reflected by a firstobject 112, and the second component 110 is reflected by a second object 114. The first object 112 and the second object 114, for instance, can be any object that distinctly attenuates the physical signals of the wavefront 106 with respect to a bulk transmission medium (e.g., water) within the environment 100. In various cases, the first object 112 and the second object 114 include one or more materials that have a distinct acoustic attenuation to water at the frequencies of sound of the components of the wavefront 106. In some cases, the first object 112 and the second object 114 include rocks, debris, metallic components, other underwater vehicles, animals, or other structures in the environment 100.

[0049] FIG. 1 B illustrates the environment 100 along a xz plane during a reception phase. The underwater vehicle 102 includes an array of receivers 116 configured to detect components of the wavefront 106 that are reflected by surfaces within the environment 100. According to various cases, the array of receivers 116 include an array of sensors. In various examples, the array of receivers 116 includes an array of transducers, such as the types of transducers listed above with respect to the array of transmitters 104. In various cases, piezoelectric crystals in the individual receivers of the array of receivers 116 are configured to generate electrical signals output by their respective electrodes when the piezoelectric crystals receive pressure waves that cause physical distortion of the piezoelectric crystals The electrical signals output by the array of receivers 116, in various cases, are dependent on the characteristics of the received pressure waves.

[0050] Each receiver among the array of receivers 116 is associated with a receptive field (also referred to as a “reception field’’). Each receptive field represents a volume within the environment 100 from which physical signals (e.g., sound signals) can be transmitted or reflected and received by the corresponding receiver. In various cases, the signals received by a given receiver from its receptive field is referred to as a “receive beam."

[0051] In various cases, the array of receivers 116 is distinct from a planar array. For instance, the array of receivers 116 is a 1 D array, rather than a 2D array. Accordingly, the power requirements, electrical and mechanical complexity, as well as size of the array of receivers 116 is improved over previous planar array technologies. In the example of FIGS. 1A and 1 B, the array of receivers 116 are disposed along a line segment that is aligned in a z direction. The array of receivers 116, for instance, are stacked along the z direction. However, implementations are not so limited. In some cases, the array of receivers 116 are disposed along a curved line segment (e.g., an arc) that is aligned on an xz plane. The reception field of the array of receivers 116 can be adjusted based on the curvature of the line segment. Notably, the line segment on which the array of receivers 116 are disposed crosses (e.g., is perpendicular to) the line segment on which the array of transmitters 104 are disposed. Although FIGS. 1A and 1 B illustrate the array of receivers 116 disposed below (e.g., in a negative y direction with respect to) the array of transmitters 104, implementations are not so limited.

[0052] In some cases, the array of receivers 116 is mounted on the housing of the of the underwater vehicle 102. For instance, the array of receivers 116 can be enclosed within the housing, integrated with the housing, or disposed outside of the housing. In various cases, the array of receivers 116 is disposed on the housing of the underwater vehicle102 on a leading edge of the underwater vehicle 102 in a direction of movement of the underwater vehicle 102 in the environment 100.

[0053] The reflection of the first component 108 from the first object 112 is detected by a first receiver 118 among the array of receivers 116. The reflection of the second component 110 from the second object 114 is detected by a second receiver 120 among the array of receivers 116. In various cases, the first object 112 is disposed at a first azimuthal angle A1 with respect to the array of receivers 116. Further, the second object 114 is disposed at a second azimuthal angle A2 with respect to the array of receivers 116. A receptive field of the first receiver 118 includes a volume of the environment that is disposed at the first azimuthal angle A1. A receptive field of the second receiver 120 includes a volume of the environment that is disposed at the second azimuthal angle A2.

[0054] In various implementations of the present disclosure, the underwater vehicle 102 is configured to identify the positions of surfaces of objects within the environment 100 based on the reflected components of the wavefront 106 that are detected by the array of receivers 116. Although FIG. 1 B illustrates only the first component 108 and the second component 110 for ease of explanation, it should be understood that numerous components of the wavefront 106 may be reflected and detected by the array of receivers 116.

[0055] The underwater vehicle 102 may determine the elevation angles of various surfaces in the environment 100 by identifying the frequencies of the components of the wavefront 106 that are reflected from the surfaces in the environment 100. For instance, the underwater vehicle 102 determines that the first object 112 is disposed at the first elevation angle cp1 By determining that the reflected first component 108 of the wavefront 106 has a frequency that corresponds to the first elevation angle q>1. Similarly, the underwater vehicle 102 determines that the second object 114 is disposed at the second elevation angle cp2 by determining that the reflected second component 110 of the wavefront 106 has a frequency that corresponds to the second elevation angle q>2.

[0056] According to some examples, the underwater vehicle 102 identifies the frequencies of the physical signals received by respective receivers among the array of receivers 116 by converting data representative of the physical signals from a time domain to a frequency domain. For example, the underwater vehicle 102 may perform a fast Fourier transform (FFT) or short-time Fourier-transform (STFT) on data representative of the magnitude of the physical signals over time. In the frequency domain, the underwater vehicle 102 may identify whether a received signal is a reflection a given component of the original wavefront 106 by analyzing, in the frequency-domain signal, a frequency band corresponding to that component. For instance, if the magnitude of the portion of the frequency-domain signal corresponding to the component is greater than a threshold, then the underwater vehicle 102 may determine that the received signal is a reflection of the component. In some cases, the underwater vehicle 102 utilizes at least one of the subspace method, the minimum variance method, the compressive sensing method, the parametric method, or the non-parametric method to identify the frequency. Relatedly, the underwater vehicle 102 may also infer that the received signal was reflected from an object located at an elevation angle in which the given component was originally transmitted in the wavefront 106.

[0057] In various cases, the underwater vehicle 102 may determine the azimuthal angles of various surfaces in the environment 100 by based on the positions of the receivers (among the array of receivers 116) that detect the components of the wavefront that are reflected from the surfaces in the environment 100. For example, the underwater vehicle 102 determines that the first object 112 is disposed at the first azimuthal angle A1 because the azimuthal angle A1 is within the receptive field of the first receiver 118, and the first receiver 118 has detected the reflection of the first component 108. In various cases, the underwater vehicle 102 determines that the second object 114 is disposed at the second azimuthal angle A2 because the second azimuthal angle A2 is within the receptive field of the second receiver 120, and the second receiver 120 has detected the reflection of the second component 110.

[0058] Further, the underwater vehicle 102 may determine the distance between the underwater vehicle 102 and various surfaces within the environment 100 based on a time delay between the transmission of the wavefront 106 by the array of transmitters 104 and the reception of various reflections of the components of the wavefront 106 from the surfaces in the environment 100. In various cases, the speed of the components of the wavefront 106 within the environment 100 may be predetermined. For example, in cases in which the wavefront 106 includes a pressure wave (e.g., sound), the speed of the wavefront 106 may be the speed of sound within the environment 100 (e.g., within an aquatic environment). For instance, the distance between the first object 112 and the underwater vehicle 102 may be determined to be equal to half of the product of the speed of the wavefront 106 in the environment and the time delay between transmission of the first component 108 in the wavefront 106 and reception of the first component 108 by the first receiver 118. Similarly, the distance between the second object 114 and the underwater vehicle 102 may be determined to be equal to half of the product of the speed of the wavefront 106 in the environment 100 and the time delay between transmission of the second component 110 in the wavefront 106 and reception of the second component 110 by the second receiver 120.

[0059] By identifying the elevation angles, azimuthal angles, and distances of surfaces in the environment 100 with respect to the underwater vehicle 102, the underwater vehicle 102 can derive positions of the surfaces in a three- dimensional (3D) coordinate space. For example, the underwater vehicle 102 may determine the positions of the first object 112 and / or the second object 114, relative to the position of the underwater vehicle 102, based on the signals detected by the array of receivers 116 In some cases, the underwater vehicle 102 is configured to determine absolute positions of the first object 112 and / or the second object 114 by also determining its own absolute position within the environment 100. Various techniques can be utilized to provide the underwater vehicle 102 with its position in the environment 100. For instance, the underwater vehicle 102 may triangulate its own location with the environment 100 by detecting signals (e.g., wireless signals) from known locations relative to the environment 100. In some cases, the underwater vehicle 102 determines its own position within the environment 100 using Global Positioning System (GPS)- based techniques.

[0060] According to some cases, the underwater vehicle 102 generates a 3D image of the environment 100 based on the determined positions of various surfaces within the environment 100. In some cases, the underwater vehicle102 generates a 3D point cloud that is representative of the surfaces within the environment 100, such as the positions of the surfaces of the first object 112 and the second object 114 In various cases, the underwater vehicle 102 generates a surface image of the environment 100. In some cases, other types of 3D representations of the environment are generated by the underwater vehicle 102. For example, the underwater vehicle 102 may generate a 3D volumetric image including a 3D array of voxels, whose values are indicative of the presence of the surfaces of objects within the environment 100.

[0061] In some cases, the underwater vehicle 102 generates the image of the environment 100 for the purpose of reporting. For example, the underwater vehicle 102 may output (e.g., transmit) data indicative of the image to an external device, such as an external computing device. In some examples, transmission within the environment 100 can be difficult. For instance, the underwater vehicle 102 may transmit data indicative of the image after the underwater vehicle 102 has later emerged from the environment 100.

[0062] In some cases, the underwater vehicle 102 has a pilot that is configured to drive the underwater vehicle 102 throughout the environment 100. For example, the underwater vehicle 102 may display the image of the environment 100 to the pilot, in order to provide the pilot with context to effectively navigate the underwater vehicle 102 throughout the environment 100. The pilot, for instance, may be located within the housing of the underwater vehicle 102. In some cases, the pilot is located remotely from the underwater vehicle 102. For instance, the underwater vehicle 102 may, in some cases, be a remotely operated vehicle (ROV).

[0063] In some examples, the underwater vehicle 102 utilizes the positions of the objects and / or the image of the environment to autonomously navigate itself through the environment 100. For example, the underwater vehicle 102 may execute predetermined methods that cause the underwater vehicle 102 to propel itself between objects in the environment 100 indicated by the image. In some cases, the underwater vehicle 102 is configured to drive itself through a gap between the first object 112 and the second object 114.

[0064] According to some cases, the underwater vehicle 102 repeatedly produces pulses including respective instances of the wavefront 106. For instance, the underwater vehicle 102 outputs the wavefront 106 at a first time and waits for a time period necessary to transmit, reflect, and receive the wavefront 106 from objects disposed at a predetermined distance from the underwater vehicle 102. After the time period expires, the underwater vehicle 102 may identify the positions of surfaces in the environment 100 at a second time by outputting another wavefront 106 at the second time. The process can repeat in order to identify a substantially real-time video of the environment 100 including multiple images of the environment 100 at the different transmit times. In some cases, the underwater vehicle 102 can adjust its movement based on changes within the environment 100 over time.

[0065] FIG. 2 illustrates example signaling 200 of a transmit phase of a 3D multibeam sonar technique. The signaling 200 includes the wavefront 106 described above with reference to FIGS 1 A and 1 B, for instance.

[0066] A signal generator 202 is configured to generate a first electrical signal 204 and a second electrical signal 206. According to various cases, the signal generator 202 includes analog circuitry configured to produce the firstelectrical signal 204 and the second electrical signal 206. In some cases, the signal generator 202 is controlled by one or more processors. For instance, the signal generator 202 includes a digital-to-analog converter (DAC) configured to generate the first electrical signal 204 and the second electrical signal 206.

[0067] Each of the first electrical signal 204 and the second electrical signal 206 may be pulses including multiple frequency components. However, the first electrical signal 204 may be distinct from the second electrical signal 206. For example, a leading edge of the first electrical signal 204 may include a first frequency component, whereas the first frequency component may be at a trailing edge of the second electrical signal 206. In contrast, a trailing edge of the first electrical signal 204 may include a second frequency component, whereas the second frequency component may be at a leading edge of the second electrical signal 206.

[0068] A first transmitter 208 is configured to generate a first portion 210 of the wavefront 106 based on the first electrical signal 204. Similarly, a second transmitter 212 is configured to generate a second portion 214 of the wavefront 106 based on the second electrical signal 206. The first portion 210 and the second portion 214, for example, include sound signals. In various cases, the first transmitter 208 and the second transmitter 212 are piezoelectric transducers. For example, the first transmitter 208 includes a first piezoelectric crystal that generates the first portion 210 when the first electrical signal 204 is output to electrodes coupled with the first piezoelectric crystal. Similarly, the second transmitter 212 includes a second piezoelectric crystal that generates the second portion 214 when the second electrical signal 206 is output to electrodes coupled with the second piezoelectric crystal.

[0069] Because the first electrical signal 204 and the second electrical signal 206 include different frequency components, the first portion 210 and the second portion 214 may also include different frequency components. In some cases, a leading edge of the first portion 210 includes a first frequency component, whereas the first frequency component may be at a trailing edge of the second portion 214. In some examples, a trailing edge of the first portion 210 may include a second frequency component, whereas the second frequency component may be at a leading edge of the second portion 214. The various phases and / or timing of different frequency components of the first portion 210 and the second portion 214, as well as the geometric orientation and positioning of the first transmitter 208 and the second transmitter 212, impacts the directions in which the frequency components are transmitted in the wavefront 106. For example, the first frequency components of the first portion 210 and the second portion 214 may constructively interfere in a first direction (e.g., at a first elevation angle), and the second frequency components of the first portion 210 and the second portion 214 may constructively interfere in a second direction (e.g., at a second elevation angle). In some cases, the first portion 210 and the second portion 214 may include components that combine using destructive interference. In various cases, the portions of the wavefront 106 combine such that distinct frequency components of the wavefront 106 are transmitted along different directions in a first plane.

[0070] Although FIG. 2 illustrates only two electrical signals, transmitters, and portions of the wavefront 106, implementations are not so limited. In various cases, more than two electrical signals, transmitters, portions of the wavefront 106, or any combination thereof, can be utilized to identify positions of surfaces of objects within anenvironment. Further, in some cases, multiple instances of the wavefront 106 can be transmitted in order to sample the positions of the surfaces of objects within the environment at different times.

[0071] FIG. 3 illustrates example signaling 300 of a reception phase of 3D multibeam sonar technique. The signaling 300 includes the first component 108, second component 110, first receiver 118, and second receiver 120 described above with reference to FIGS. 1A and 1 B. In various cases, the first receiver 118 receives a reflection of the first component 108 of a wavefront (e.g., the wavefront 106) from a first surface in an environment, and the second receiver 120 receives a reflection of the second component 110 of the wavefront from a second surface in the environment.

[0072] The first receiver 118 is configured to generate first reception data 302 based on receiving the first component 108. For example, the first receiver 118 includes an analog to digital converter (ADC) configured to convert an electrical signal generated by a piezoelectric crystal of the first receiver 118 into digital data. The second receiver 120 similarly generates second reception data 304 based on receiving the second component 110. For instance, the second receiver 120 includes an ADC configured to convert an electrical signal generated by a piezoelectric crystal of the second receiver 120 into digital data. In some cases, the first reception data 302 is representative of a current or voltage over time generated by the first receiver 118 in response to receiving the first component 108, and the second reception data 304 is representative of a current or voltage over time generated by the second receiver 120 in response to receiving the second component 110.

[0073] An image generator 306 is configured to determine positions of surfaces of objects within the environment based, at least in part, on the first reception data 302 and the second reception data 304. In various cases, the image generator 306 is configured to determine that the surface of a first object is located at a first angle along a first plane by determining that the first component 108 has a first frequency The image generator 306 may further determine that the surface of the first object is located at a first angle along a second plane by determining that the first component 108 is received by the first receiver 118, wherein the receptive field of the first receiver 118 includes the first angle along the second plane. Further, the image generator 306 may determine a distance between the first receiver 118 and the first object by determining a difference between a time at which the first component 108 (e.g., a wavefront including the first component 108) was transmitted and a time at which the first component 108 was received by the first receiver 118. The image generator 306, further, may be configured to determine that the surface of a second object is located at a second angle along the first plane by determining that the second component 110 has a second frequency associated with the second angle. The image generator 306 may further determine that the surface of the second object is located at a second angle along the second plane by determining that second component 110 is received by the second receiver 120, wherein the receptive field of the second receiver 120 includes the second angle along the second plane. Further, the image generator 306 may determine a distance between the second receiver 120 and the second object by determining a difference between a time at which the second component 110 (e.g., a wavefront including the second component 110) was transmitted and a time at which the second component 110 was received by the second receiver 120.

[0074] In various implementations, the image generator 306 is configured to generate an image of the surfaces of the objects (e.g., the first and second objects) within 3D space based on their determined positions. In some cases, the image is a 3D point cloud and / or projection image.

[0075] FIG. 4 illustrates an example process 400 for determining a position of a surface of an object within 3D space. The process 400, for instance, is performed by an entity including at least one of an ultrasound transducer, a computing device, at least one processor, a vehicle (e.g., an underwater vehicle), an apparatus, a system, or any combination thereof.

[0076] At 402, the entity identifies a signal reflected by an object in an environment and detected by a receiver. For instance, the receiver includes at least one transducer. In various cases, the signal is a sound signal. In some examples, the sound signal is in a range of 200 kHz to 900 kHz, 400 kHz to 700 kHz, or the like. In various cases, the environment is an aquatic environment. According to various cases, the signal is reflected from a surface of the object in the environment.

[0077] According to some cases, the signal was transmitted by an array of transmitters disposed along a first line segment, and the receiver is among an array of receivers disposed along a second line segment that crosses the first line segment. In various cases, the array of transmitters and the array of receivers form an inverted “T” shape. In some cases, the first line segment and / or the second line segment are curved. The array of transmitters includes an array of transducers, for instance. According to some examples, the array of transmitters outputs a wavefront including various components, at least one of which corresponds to the signal detected by the receiver. In some examples, each component of the wavefront is associated with a distinct frequency (e.g., frequency range) as well as a distinct angle along the first plane. According to various cases, portions of individual signals output by the respective transmitters among the array of transmitters may constructively interfere to form each distinct component of the wavefront. The signals output by the transmitters can be generated based on electrical signals output to the transmitters, such as by a signal generator. The electrical signals, for instance, include pulses. In various examples, the electrical signals include linear chirps, such as linear frequency modulated chirps.

[0078] At 404, the entity determines, by identifying a frequency of the signal, a first angle at which the object is disposed The first angle is defined in a first plane. For example, the first angle may be an elevation angle. In various cases, the entity determines the frequency of the signal by converting data representative of the received signal into the frequency domain and analyzing a portion of the frequency domain signal corresponding to the frequency. For instance, the entity may perform a Fourier transform (e.g., FFT, STFT, etc.).

[0079] At 406, the entity determines, by identifying a position of the receiver, a second angle at which the object is disposed. The second angle is defined in a second plane. The second plane may be perpendicular to the first plane. For example, the second angle may be an azimuthal angle. For instance, the receiver may be associated with a receptive field that corresponds to the second angle. By determining the position at which the receiver is disposed, the second angle of the object can be derived.

[0080] At 408, the entity identifies a position of the object in the environment based on the first angle and the second angle. In some implementations, the entity generates an image of the environment based on the position of the object. For example, the entity can perform a similar process to determine the locations of surfaces of various objects within FOV of the entity. The FOV, for instance, corresponds to a volume in which the wavefront travels as well as the receptive fields of one or more receivers, including the receivers, of the entity. In some cases, the image is a projection image, a point cloud, or some other 3D representation of the environment. In some examples, the entity outputs an indication of the image, such as to a computing device or display. In some cases, the entity changes a direction, position, velocity, or acceleration of an apparatus based on the position of the object in the environment and / or the image. For instance, the entity may activate one or more devices that can change or initiate movement of the apparatus within the environment.

[0081] FIG. 5 illustrates an example of a device 500 configured to perform various functions described herein. The device 500 may be at least a portion of a platform or system meant to house sonar hardware and software; e.g. an AUV or towfish. The device 500 includes any of memory 504, processor(s) 506, removable storage 508, non-removable storage 510, input device(s) 512, output device(s) 514, and transceiver(s) 516. The device 500 may be configured to perform various methods and functions disclosed herein.

[0082] The memory 504 may include component(s) 518. The component(s) 518 may include at least one of instruction (s), program(s), database(s), software, operating system(s), etc. In some implementations, the component(s) 518 include instructions that are executed by processor(s) 506 and / or other components of the device 500. According to some examples, the component(s) 518 include instructions that, when executed by the processor(s) 506, cause the processor(s) 506 to perform one or more operations. For example, the operations may include generating volumetric data of an underwater environment based on sound signals received by an array of receivers. In various cases, the memory 504 stores instructions for executing the signal generator 202 and / or image generator 306.

[0083] In some embodiments, the processor(s) 506 include a central processing unit (CPU), a graphics processing unit (GPU), or both CPU and GPU, or other processing unit or component known in the art.

[0084] The device 500 may also include additional data storage devices (removable and / or non-removable) such as, for example, magnetic disks, optical disks, or tape. Such additional storage is illustrated in FIG. 5 by removable storage 508 and non-removable storage 510. Tangible computer-readable media can include volatile and non-volatile, removable and non-removable media implemented in any method or technology for storage of information, such as computer readable instructions, data structures, program modules, or other data. The memory 504, the removable storage 508, and the non-removable storage 510 are all examples of computer-readable storage media. Computer- readable storage media include, but are not limited to, Random Access Memory (RAM), Read-Only Memory (ROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), flash memory, or other memory technology, Compact Disk Read-Only Memory (CD-ROM), Digital Versatile Discs (DVDs), Content-Addressable Memory (CAM), or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices,or any other medium which can be used to store the desired information and which can be accessed by the device 500. Any such tangible computer-readable media can be part of the device 500. Various examples of the computer- readable storage media are non-transitory.

[0085] The device 500 may be configured to communicate over a telecommunications network using any common wireless and / or wired network access technology. Moreover, the device 500 may be configured to run any compatible device Operating System (OS), including but not limited to, Microsoft Windows Mobile, Google Android, Apple iOS, Linux Mobile, as well as any other common mobile device OS.

[0086] The device 500 also can include input device(s) 512, such as a keypad, a cursor control, a touch-sensitive display, voice input device, etc., and output device(s) 514 such as a display, speakers, printers, etc. In some implementations, the input device(s) 512 include an array of receivers, as described herein. In various cases, the output device(s) 514 include an array of transmitters, as described herein. According to some cases, the transceivers(s) 516 provide input to a system configured to steer and / or propel an AUV through the water, such as one or more rudders and / or propellers. In various implementations, the input device(s) 512 and / or output device(s) 514 include one or more ADCs, DACs, pulsers, power amplifiers, or drivers.

[0087] As illustrated in FIG. 5, the device 500 also includes one or more wired or wireless transceiver(s) 516. For example, the transceiver(s) 516 can include a network interface card (NIC), a network adapter, a Local Area Network (LAN) adapter, or a physical, virtual, or logical address to connect to various network components, for example. To increase throughput when exchanging wireless data, the transceiver(s) 516 can utilize multiple-input / multiple-output (MIMO) technology. The transceiver(s) 516 can comprise any sort of wireless transceivers capable of engaging in wireless, radio frequency (RF) communication. The transceiver(s) 516 can also include other wireless modems, such as a modem for engaging in Wi-Fi, WiMAX, Bluetooth, infrared communication, and the like. The transceiver(s) 516 may include transmitter(s), receiver(s), or both.

[0088] FIG. 6 illustrates an example comparison of an array and 3D beam-configurations for a standard planar array (left) and an example of a novel 3D sonar system utilizing frequency dispersion (right). In various implementations of the present disclosure, the frequency dispersion system creates a beam in an arbitrary direction within the FOV by performing classical beam-forming on receive to get the azimuth direction, and then frequency sub-banding to get the elevation direction.

[0089] A principle behind examples of the novel design is that beamforming in one dimension is performed upon signal transmission, and beamforming in an orthogonal dimension is performed on receipt. Similar to an optical prism, the beamforming on transmission leveraged by implementations of the present disclosure separates the frequency components of a wide bandwidth signal and transmits each in a distinct elevation direction. Upon receipt, vertical beams are created by selecting frequency band, and horizontal beams are created using classic array processing. A comparison between the planar array concept and the new concept is shown in FIG. 6.

[0090] Superficially, the frequency dispersion leveraged to resolve angles of arrival in elevation as demonstrated in FIG. 8 has some similarities to the principles leveraged by mechanical or digital “blazed array” processing (Thompson, et al., MTS / IEEE OCEANS 2001. AN OCEAN ODYSSEY. CONFERENCE PROCEEDINGS, 2:985-88 (2001); U.S. Patent No. 7,606,114), however, example processing described herein is distinct and overcomes several problems associated with classic blazed array processing. On reception, beamforming in the orthogonal dimension can be performed via classic delay-and-sum processing leveraged by most multibeam sonars. Thus, the number of array elements used for 3D imaging can be reduced from N2(a standard planar array) to 2N. For instance, for a 128 x 128 beam system a planar array would utilize 16,384 elements, whereas implementations of the present disclosure could achieve similar imaging with 256 elements.

[0091] Particular implementations of disclosed 3D multibeam designs leverage two ULAs, which may be arranged in a common plane, mounted perpendicular to each other as shown in FIG. 6. In some cases, one or both arrays could be curved for streamlining. For the purpose of illustration, assume a design like the one in FIG. 6 that looks like an inverted T, (e.g.,“l” where the vertical array is an N x 1 element linear array, and the horizontal element (the bottom of the “I”) is a 1 x N ULA). In various examples, the elements have been designed such that the width of the beam pattern perpendicular to the axis matches the beamwidth of the elements of the complementary array. This could be done mechanically and / or by applying an acoustic lensing to the face of the elements. The vertical array steers beams vertically as a function of frequency, along the vertical axis. For instance, frequency is swept from high-to-low, from +30 to -30 degrees, or vice versa. A fully populated N x M x T (where T is the time (range) dimension) 3D data cube can be generated on receipt by performing time-delay-and-sum beam steering to the data captured by the 1 x N horizontal receive array on the bottom of the 1, computing computationally cheap STFTs in the range dimension to the azimuthally beamformed data, and mapping between Fourier bin and elevation angle.

[0092] Various implementations of the present disclosure provide an improved method for digital frequency- dispersive beamforming, as well as the combination of perpendicularly oriented frequency-dispersive beamforming and classic linear array beamforming to create dense 3D imagery from a single ping. Blazed-array beamforming in the vertical dimension and synthetic aperture processing in the horizontal dimension was demonstrated in Thompson, et al., MTS / IEEE OCEANS 2001. AN OCEAN ODYSSEY. CONFERENCE PROCEEDINGS, 2:985-88 (2001), however this type of processing does not create high resolution 3D imagery from a single ping, is not compatible with forward-looking geometry, and does not contain the benefits of the herein described frequency dispersive beamforming techniques that use ULA arrays to supersede limitations of blazed array beamforming. Thompson et al. also describes various configurations using multiple blazed array or blazed array and real-array combinations that could be used to create volume renderings but, critically, only planar real or synthetic arrays are described as being used in conjunction with blazed arrays to create volume imagery.

[0093] Frequency steered beamforming has nearly exclusively made use of mechanically blazed arrays (Thompson, et al., MTS / IEEE OCEANS 2001. AN OCEAN ODYSSEY. CONFERENCE PROCEEDINGS, 2:985-88 (2001); U.S. Patent No.7,606, 114), which leverage acoustic diffraction gratings to perform frequency dispersion. Acoustic diffraction gratings are analogous to optical prisms: rays passing through them will bend differently depending on wavelength. For an in- phase signal transmitted across the elements of a blazed array the relationship between transmit angle, wavelength, and mode (integer-number of wavelengths across the blazed elements) is governed by the diffraction equation: d sin(0m) = mA (1)

[0094] where d is the blazed element spacing (analogously in optics, the spacing of the grating slits), m is the mode order (the integer number of wavelengths between gratings), / is wavelength, and 0mis the direction of transmission through the grating associated with the mode number m and wavelength A Thus, for a given mode m and set of wavelengths Ao to Ahi (determined by system bandwidth), a unique mapping exists between and 0, as shown by the following equation:

[0095] FIG. 7 illustrates an example angle vs. frequency dispersion curve using the grating equation for m=1 , assuming a nearly 1 -octave band spanning 330 to 600 kHz, with a grating spacing of 0.65 centimeters. In an m=1 mode a 330 to 600k Hz system could map the frequencies to angle as shown in the FIG. 7 using a grating spacing of 0.0065 meters.

[0096] Notably, FIG. 7 shows only the response for m=1. If the bandwidth is extended beyond an octave, then an angular ambiguity exists between frequencies mapped for m=2 and m=1, limiting the bandwidth that can be supported for a blazed-array system.

[0097] In addition, the center of the span of angles is not 0 (i.e., normal to the array) but is offset. This has ramifications for resolution as the maximum resolution at any frequency will be the convolution of the spatial response of the array projected in the direction of the direction of the frequency along with the bandwidth of the filter used to isolate that signal component. The use of an off-axis beam-pattern reduces the effective transmitter aperture length, under-utilizing the physical aperture of the array.

[0098] The angular spread is fairly narrow; however the field of view can be expanded by reversing polarity. This creates a gapped, two-sector coverage from a single blazed array as shown in FIG. 8. Note that though the FOV can be expanded by reversing polarity, to prevent angular ambiguity two separate transmissions are generally used.

[0099] FIG. 8 illustrates an example of blazed array imaging sections for a single element showing the two imaging sectors that can be created using separate ping transmissions with inverted polarity. Note that the frequency dispersion has mirror symmetry.

[0100] As a result of this gapped coverage created by individual arrays, commercial blazed arrays can be designed in sets to fill in the gaps. FIG. 9 illustrates an example of a commercial blazed array, with three separate blazed arrays (left, middle), used to populate the six different sectors in the image on the right. Each array contributes to two sectors; each sector utilizes a separate ping to create an image, thus 6 separate transmissions are used to generate a full image.

[0101] There are several inherent drawbacks of this sectored approach using blazed array designs. First, there is a decrease in the effective system sample rate by a factor of the number of sectors. For instance, rather than imaging the full field of view in a single ping, the sectors must be filled in one at a time, which causes problems if the sonar is rapidly moving. Second, due to the different scattering statistics and resolution characteristics at the sector boundaries, the images tend to be disjoint, even when the sonar is stationary.

[0102] An advantage of the blazed array design relative to ordinary linear arrays, which has contributed to its commercial success, is the massive simplification of the associated electronics and signal-processing utilized to create images, allowing for cost and power reductions for the sonar design.

[0103] As the electronics associated with ULA designs have decreased in price and power consumption the advantages of the blazed-array type imaging systems, namely, cost and simplicity, have steadily decreased.

[0104] Implementations of the present disclosure provide an innovative way to leverage ULA or curvilinear arrays to perform frequency-dispersive beamforming on transmit similar to blazed arrays while overcoming the significant drawbacks of blazed arrays, such as one or more of:• Re-orienting the FOV such that the center of the FOV aligns with the array normal, thereby improving angular resolution;• Arbitrarily steering the beam from broadside by changing the frequency-dispersion beamforming parameters of the transmit array;• Widening or narrowing the FOV by changing transmit frequency-dispersion beamforming parameters;• Widening without sub-sectors for scanning large regions, thereby increasing ping repetition rate;• Linearizing the relationship between angle and frequency; and• Removing the 1 -octave bandwidth limitation imposed by modal ambiguity.

[0105] In FIG. 10 several advantages of various implementations of the present disclosure are graphically depicted to illustrate the advantages of the new approach toward beam steering. Beam widths and angles associated with blazed arrays can be fixed based on hardware design and point off-center from the array normal (left plot). In contrast, in implementations of the present disclosure, the width of the field of view is controlled by the beamforming parameters and may be changed via software. Additionally, the sonar can be steered from broadside and tilted up or down.

[0106] Various implementations of the present disclosure, as well as their associated advantages, will be described with reference to several equations. The equations describing the signals transmitted from each element of the array performing beam steering are designed directly in the frequency domain. For the general case of an arbitrary curvilinear array the frequency domain representation of the transmit signal at the nth element can be defined using the following equation:where Anis the vector from the array centroid to the element, is the unity magnitude vector aligned with transmit angle <p, c is speed of sound in water, a> is angular frequency and cr(co) is a spectral windowing function over the transmit bandwidth, designed to reduce temporal ringing artifacts.

[0107] For a ULA oriented parallel to the vertical axis, Equation 3 can be more directly expressed as:where znis the vertical displacement relative to the center of the ULA. Constraining the mapping between <p and co to be linear, Sn(oo) can be written entirely as a function of to with the exception of tunable beamforming constants as follows:where modifying / ? changes the FOV (i.e., a range of angles over which frequencies are projected), and rj changes the FOV bias direction (i.e., central steering angle). A simple time-domain equivalent is not readily calculable from Equation 5, however, for small values of <p, the phase argument becomes approximately quadratic with respect to co and the signal is similar to a standard linear chirp with length modified by the distance of the current element vs. the centroid of the array. In practice the time domain signals can be reconstructed by calculating Sn(to) for a discrete set of frequencies and performing an inverse DFT to get the sampled time-domain representation.

[0108] FIG. 11 illustrates instantaneous frequency vs. time for an example signal bank. The color bar on the right shows frequency (kHz) vs. lightness. In the time domain, the signals can be viewed a function of instantaneous frequency vs. time and array element; an example is shown in FIG. 9 for a hypothetical system with a bandwidth of 380 to 870 kHz, a field of view of + / - 45 degrees and a 64 element ULA with a total length of 0.08 meters. Note the approximate linearity but changing slope of the instantaneous frequency vs. element number.

[0109] FIG. 12 shows the envelope of the time-domain signal for which the instantaneous frequencies were shown in FIG. 11. FIG. 12 reveals a difficulty associated with implementations of the previously described signal bank. Many transmitters utilize rail-to-rail signals, and cannot faithfully represent the dynamic ranges present in FIG. 12. The compression of the signal bank described by FIGS. 11 and 12, as well as Equation 5, into a binary (e.g. 0 and 1 ) or trilevel (e.g {-1 , 0, 1}) signal could distort the frequency-dispersive characteristics of the signal bank.

[0110] To mitigate this problem, each signal in the signal bank can be convolved in time with a fixed linear chirp having a total chirp length much greater than the longest dispersion prescribed by Equation 5, such that Equation 5 can be converted to:where x is the sweep rate of the extra chirp signal. The result of this dispersion is a bank of signals that are nearly uniform in magnitude and can undergo amplitude bit-reduction without sacrificing frequency dispersion performance. FIG. 13 shows an example of the envelopes of the signals plotted in FIG. 12 but after tuning x to include an extra~600ps chirp term. FIG. 13 illustrates the magnitudes of the signals shown in FIG. 12 after applying an additional chirp for amplitude regularization.

[0111] In various approaches toward 3D beamforming described herein, frequency-dispersive beamforming on transmit provides angular resolution along the dimension of the transmit array (e.g., the elevation dimension), however it provides no azimuthal resolution. Azimuthal resolution, for instance, results from receiving the data via a horizontally oriented ULA and leveraging the horizontal spatial diversity of the ULA elements to perform azimuthal beam steering. An example of a total signal processing chain to arrive at a 3D image cube is shown in the flowchart in the FIG. 14.

[0112] FIG. 14 depicts a flowchart showing an example realization of the 3D volumetric beamforming sonar and post processing steps described in this document. The output is a volume in spherical coordinates having orthogonal dimensions {Range, Azimuth, Elevation}.EXAMPLE CLAUSES

[0113] The following clauses provide various examples of the present disclosure:1 . A frequency-steered sonar apparatus, including: an array of transmitters disposed along a first line segment and configured to transmit, into an environment, a wavefront including a first component and a second component, the first component being transmitted in a first elevation angle and having a first frequency, the second component being transmitted in a second elevation angle and having a second frequency; an array of receivers disposed along a second line segment and including: a first receiver configured to detect a reflection of the first component from a first object in the environment by performing acoustic beamforming; and a second receiver configured to detect a reflection of the second component from a second object in the environment by performing acoustic beamforming; and a processor configured to: determine a position of the first object in the environment by: determining that the first object is disposed at the first elevation angle by determining that the reflection of the first component has the first frequency; determining a distance between the frequency-steered sonar apparatus and the first object based on a time delay between a time at which the array of transmitters transmitted the wavefront of sound and a time at which the first receiver detected the reflection of the first component; and determining that the first object is disposed at a first azimuthal angle based on a position of the first receiver; determine a position of the second object in the environment by: determining that the second object is disposed at the second elevation angle by determining that the reflection of the second component has the second frequency; determining a distance between the frequency-steered sonar apparatus and the second object based on a time delay between a time at which the array of transmitters transmitted the wavefront of sound and a time at which the second receiver detected the reflection of the second component; and determining that the second object is disposed at a second azimuthal angle based on a position of the second receiver; and generate a 3D image of the environment based on the position of the first object and the position of the second object.2. The frequency-steered sonar apparatus of clause 1 , wherein the array of transmitters includes: a first transmitter configured to transmit a first signal including a first portion that includes the first frequency and a second portion that includes the second frequency; and a second transmitter configured to transmit a second signal includinga third portion that includes the first frequency and a fourth portion that includes the second frequency, wherein the first component of the wavefront includes constructive interference of the first portion of the first signal and the third portion of the second signal, and wherein the second component of the wavefront includes constructive interference of the second portion of the first signal and the fourth portion of the second signal.3. The frequency-steered sonar apparatus of clause 2, wherein the first portion is transmitted by the first transmitter at a different time than the second portion, and wherein the third portion is transmitted by the second transmitter at a different time than the fourth portion.4. The frequency-steered sonar apparatus of clause 2 or 3, wherein the first portion is transmitted by the first transmitter at a different time than the second transmitter transmits the third portion, and wherein the second portion is transmitted by the first transmitter at a different time than the second transmitter transmits the fourth portion.5. The frequency-steered sonar apparatus of any of clauses 2 to 4, further including: a signal generator configured to transmit a first electrical signal to the first transmitter and to transmit a second electrical signal to the second transmitter, wherein the first transmitter is configured to transmit the first signal in response to receiving the first electrical signal, and wherein the second transmitter is configured to transmit the second signal in response to receiving the second electrical signal.6. The frequency-steered sonar apparatus of clause 5, wherein the first electrical signal and the second electrical signal include a chirp signal.7. The frequency-steered sonar apparatus of any of clauses 1 to 6, wherein the wavefront includes sound.8. The frequency-steered sonar apparatus of any of clauses 1 to 7, wherein the environment is an aquatic environment.9. The frequency-steered sonar apparatus of any of clauses 1 to 8, wherein the array of transmitters includes an array of transducers.10. The frequency-steered sonar apparatus of any of clauses 1 to 9, wherein the array of receivers includes an array of transducers.11. The frequency-steered sonar apparatus of any of clauses 1 to 10, wherein the first line segment is a curved line segment.12. The frequency-steered sonar apparatus of any of clauses 1 to 11 , wherein the second line segment is a curved line segment.13. The frequency-steered sonar apparatus of any of clauses 1 to 12, wherein the first line segment is perpendicular to the second line segment.14. The frequency-steered sonar apparatus of any of clauses 1 to 13, wherein the 3D image includes a point cloud or a projection image.15. The frequency-steered sonar apparatus of any of clauses 1 to 14, wherein the processor is configured to determine that the reflection of the first component has the first frequency by: identifying a first digital signal indicativeof a first electrical signal generated by the first receiver over time; generating a first frequency domain signal by applying a transform to the first digital signal; and analyzing a portion of the first frequency domain signal corresponding to the first frequency, and wherein the processor is configured to determine that the reflection of the second component has the second frequency by: identifying a second digital signal indicative of a second electrical signal generated by the second receiverover time; generating a second frequency domain signal by applying the transform to the second digital signal; and analyzing a portion of the second frequency domain signal corresponding to the second frequency.16. The frequency-steered sonar apparatus of clause 15, wherein the transform includes a short-time Fourier transform (STFT).17. The frequency-steered sonar apparatus of any of clauses 1 to 16, wherein the processor is configured to determine that the reflection of the first component has the first frequency by: identifying a first digital signal indicative of a first electrical signal generated by the first receiver over time; and analyzing the first digital signal using at least one of a subspace method, a minimum variance method, a compressive sensing method, a parametric method, or a non-parametric method, and wherein the processor is configured to determine that the reflection of the second component has the second frequency by: identifying a second digital signal indicative of a second electrical signal generated by the second receiver over time; and analyzing the second digital signal using at least one of the subspace method, the minimum variance method, the compressive sensing method, the parametric method, or the non- parametric method.18. The frequency-steered sonar apparatus of any of clauses 1 to 17, further including: a propeller configured to move the frequency-steered sonar apparatus in the environment, wherein the processor is further configured to control the propeller based on the 3D image.19. The frequency-steered sonar apparatus of any of clauses 1 to 18, further including: a watertight housing enclosing array of transmitters, the array of receivers, and the processor.20. The frequency-steered sonar apparatus of any of clauses 1 to 19, further including: a transceiver configured to transmit, to an external device, an indication of the 3D image.21 . A method, including: detecting, by a receiver of an apparatus at a reception time, a sound signal reflected by an object in an environment; determining, by identifying a frequency of the sound signal, a first angle at which the object is disposed, the first angle being defined with respect to the apparatus in a first plane; determining a distance between the apparatus and the object based on a time delay between a transmission time of the sound signal and the reception time of the sound signal; determining a second angle at which the object is disposed based on a position of the receiver, the second angle being defined with respect to the apparatus in a second plane; and identifying a position of the object in the environment based on the first angle, the distance between the apparatus and the object, and the second angle22. The method of clause 21, wherein the receiver includes at least one transducer.23. The method of clause 21 or 22, wherein the sound signal has a frequency in a range of about 200 kilohertz (kHz) to about 900 kHz.24. The method of any of clauses 21 to 23, wherein the environment includes an aquatic environment.25. The method of any of clauses 21 to 24, wherein the sound signal is reflected from a surface of the object.26. The method of any of clauses 21 to 25, wherein the first angle is an elevation angle and the second angle is an azimuthal angle, or wherein the first angle is the azimuthal angle and the second angle is the elevation angle.27. The method of any of clauses 21 to 26, wherein the first plane is perpendicular to the second plane.28 The method of any of clauses 21 to 27, wherein identifying the frequency of the sound signal includes: generating a frequency domain signal by applying a transform to a digital signal indicative of an electrical signal output by the receiver in response to receiving the sound signal; and analyzing a portion of the frequency domain signal corresponding to the frequency.29. The method of clause 28, wherein the transform includes a Fourier transform.30. The method of any of clauses 21 to 29, the sound signal being a first sound signal, the method further including: outputting, by an array of transmitters at the transmission time, a wavefront including the first sound signal transmitted at the first angle and a second sound signal transmitted at a third angle, the third angle being defined with respect to the apparatus along the first plane.31. The method of clause 30, wherein outputting, by the array of transmitters, the wavefront including the first sound signal transmitted at the first angle and the second sound signal transmitted at a third angle includes: outputting, by a first transmitter among the array of transmitters, a first component of the wavefront including a first portion of the first sound signal and a first portion of the second sound signal; and outputting, by a second transmitter among the array of transmitters, a second component of the wavefront including a second portion of the first sound signal and a second portion of the second sound signal, wherein the first portion of the first sound signal constructively interferes with the second portion of the second sound signal in the environment, and wherein the first portion of the second sound signal constructively interferes with the second portion of the second sound signal in the environment.32. The method of clause 30 or 31 , wherein the array of transmitters extends along a first line segment, and wherein the receiver is among an array of receivers extending along a second line segment.33. The method of clause 32, wherein the first line segment is curved and / or the second line segment is curved.34. The method of clause 32 or 33, wherein the first line segment is perpendicular to the second line segment.35. The method of any of clauses 21 to 34, further including: generating multiple electrical signals that respectively cause transmitters in an array to output a wavefront including the sound signal.36. The method of clause 35, wherein the multiple electrical signals include pulses.37 The method of clause 35 or 36, wherein the multiple electrical signals include a linear frequency modulated chirp.38. The method of any of clauses 21 to 37, further including: generating an image of the environment based on the position of the object in the environment.39. The method of clause 38, further including: outputting an indication of the image.40. The method of any of clauses 21 to 39, further including: changing a direction, position, velocity, or acceleration of the apparatus based on the position of the object in the environment.41. A system, including; at least one processor; and memory storing instructions that, when executed by the at least one processor, cause the at least one processor to perform operations including the method of any of clauses 21 to 40.42. The system of clause 41, wherein the system includes the apparatus.43. The system of clause 41 or 42, wherein the system includes the receiver.44. The system of any of clauses 41 to 43, wherein the system includes at least one transmitter configured to transmit the sound signal into the environment.45. A non-transitory computer-readable medium storing instructions for performing the method of any of clauses 21 to 40.

[0114] The features disclosed in the foregoing description, or the following claims, or the accompanying drawings, expressed in their specific forms or in terms of a means for performing the disclosed function, or a method or process for attaining the disclosed result, as appropriate, may, separately, or in any combination of such features, be used for realizing implementations of the disclosure in diverse forms thereof.

[0115] This document cites to various printed publications, articles, and other references. Each one of these references is incorporated by reference herein in its entirety

[0116] As will be understood by one of ordinary skill in the art, each implementation disclosed herein can comprise, consist essentially of or consist of its particular stated element, step, or component. Thus, the terms “include” or “including” should be interpreted to recite: “comprise, consist of, or consist essentially of.” The transition term “comprise" or “comprises” means has, but is not limited to, and allows for the inclusion of unspecified elements, steps, ingredients, or components, even in major amounts. The transitional phrase “consisting of’ excludes any element, step, ingredient or component not specified. The transition phrase “consisting essentially of' limits the scope of the implementation to the specified elements, steps, ingredients or components and to those that do not materially affect the implementation. As used herein, the term “based on" is equivalent to “based at least partly on,” unless otherwise specified.

[0117] Unless otherwise indicated, all numbers expressing quantities, properties, conditions, and so forth used in the specification and claims are to be understood as being modified in all instances by the term “about.” Accordingly, unless indicated to the contrary, the numerical parameters set forth in the specification and attached claims are approximations that may vary depending upon the desired properties sought to be obtained by the present disclosure. At the very least, and not as an attempt to limit the application of the doctrine of equivalents to the scope of the claims, each numerical parameter should at least be construed in light of the number of reported significant digits and by applying ordinaryrounding techniques. When further clarity is required, the term ''about” has the meaning reasonably ascribed to it by a person skilled in the art when used in conjunction with a stated numerical value or range, i.e. denoting somewhat more or somewhat less than the stated value or range, to within a range of ±20% of the stated value; ±19% of the stated value; ±18% of the stated value; ±17% of the stated value; ±16% of the stated value; ±15% of the stated value; ±14% of the stated value; ±13% of the stated value; ±12% of the stated value; ±11% of the stated value; ±10% of the stated value; ±9% of the stated value; ±8% of the stated value; ±7% of the stated value; ±6% of the stated value; ±5% of the stated value; ±4% of the stated value; ±3% of the stated value; ±2% of the stated value; or ±1 % of the stated value.

[0118] Notwithstanding that the numerical ranges and parameters setting forth the broad scope of the disclosure are approximations, the numerical values set forth in the specific examples are reported as precisely as possible. Any numerical value, however, inherently contains certain errors necessarily resulting from the standard deviation found in their respective testing measurements.

[0119] The terms “a,” “an,” “the" and similar referents used in the context of describing implementations (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. Recitation of ranges of values herein is merely intended to serve as a shorthand method of referring individually to each separate value falling within the range. Unless otherwise indicated herein, each individual value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein is intended merely to better illuminate implementations of the disclosure and does not pose a limitation on the scope of the disclosure. No language in the specification should be construed as indicating any non-claimed element essential to the practice of implementations of the disclosure.

[0120] Groupings of alternative elements or implementations disclosed herein are not to be construed as limitations. Each group member may be referred to and claimed individually or in any combination with other members of the group or other elements found herein. It is anticipated that one or more members of a group may be included in, or deleted from, a group for reasons of convenience and / or patentability. When any such inclusion or deletion occurs, the specification is deemed to contain the group as modified thus fulfilling the written description of all Markush groups used in the appended claims.

Claims

CLAIMSWhat is claimed is:1 . A frequency-steered sonar apparatus, comprising: an array of transmitters disposed along a first line segment and configured to transmit, into an environment, a wavefront comprising a first component and a second component, the first component being transmitted in a first elevation angle and having a first frequency, the second component being transmitted in a second elevation angle and having a second frequency; an array of receivers disposed along a second line segment and comprising: a first receiver configured to detect a reflection of the first component from a first object in the environment by performing acoustic beamforming; and a second receiver configured to detect a reflection of the second component from a second object in the environment by performing acoustic beamforming; and a processor configured to: determine a position of the first object in the environment by: determining that the first object is disposed at the first elevation angle by determining that the reflection of the first component has the first frequency; determining a distance between the frequency-steered sonar apparatus and the first object based on a time delay between a time at which the array of transmitters transmitted the wavefront of sound and a time at which the first receiver detected the reflection of the first component; and determining that the first object is disposed at a first azimuthal angle based on a position of the first receiver; determine a position of the second object in the environment by: determining that the second object is disposed at the second elevation angle by determining that the reflection of the second component has the second frequency; determining a distance between the frequency-steered sonar apparatus and the second object based on a time delay between a time at which the array of transmitters transmitted the wavefront of sound and a time at which the second receiver detected the reflection of the second component; and determining that the second object is disposed at a second azimuthal angle based on a position of the second receiver; and generate a 3D image of the environment based on the position of the first object and the position of the second object.

2. The frequency-steered sonar apparatus of claim 1 , wherein the array of transmitters comprises:a first transmitter configured to transmit a first signal comprising a first portion that comprises the first frequency and a second portion that comprises the second frequency; and a second transmitter configured to transmit a second signal comprising a third portion that comprises the first frequency and a fourth portion that comprises the second frequency, wherein the first component of the wavefront comprises constructive interference of the first portion of the first signal and the third portion of the second signal, and wherein the second component of the wavefront comprises constructive interference of the second portion of the first signal and the fourth portion of the second signal.

3. The frequency-steered sonar apparatus of claim 2, wherein the first portion is transmitted by the first transmitter at a different time than the second portion, and wherein the third portion is transmitted by the second transmitter at a different time than the fourth portion.

4. The frequency-steered sonar apparatus of claim 2, wherein the first portion is transmitted by the first transmitter at a different time than the second transmitter transmits the third portion, and wherein the second portion is transmitted by the first transmitter at a different time than the second transmitter transmits the fourth portion.

5. The frequency-steered sonar apparatus of claim 2, further comprising: a signal generator configured to transmit a first electrical signal to the first transmitter and to transmit a second electrical signal to the second transmitter, wherein the first transmitter is configured to transmit the first signal in response to receiving the first electrical signal, and wherein the second transmitter is configured to transmit the second signal in response to receiving the second electrical signal.

6. The frequency-steered sonar apparatus of claim 5, wherein the first electrical signal and the second electrical signal comprise a chirp signal.

7. The frequency-steered sonar apparatus of claim 1, wherein the wavefront comprises sound.

8. The frequency-steered sonar apparatus of claim 1 , wherein the environment is an aquatic environment.

9. The frequency-steered sonar apparatus of claim 1, wherein the array of transmitters comprises an array of transducers.

10. The frequency-steered sonar apparatus of claim 1 , wherein the array of receivers comprises an array of transducers.

11. The frequency-steered sonar apparatus of claim 1 , wherein the first line segment is a curved line segment.

12. The frequency-steered sonar apparatus of claim 1 , wherein the second line segment is a curved line segment.

13. The frequency-steered sonar apparatus of claim 1, wherein the first line segment is perpendicular to the second line segment.

14. The frequency-steered sonar apparatus of claim 1 , wherein the 3D image comprises a point cloud or a projection image.

15. The frequency-steered sonar apparatus of claim 1, wherein the processor is configured to determine that the reflection of the first component has the first frequency by: identifying a first digital signal indicative of a first electrical signal generated by the first receiver over time; generating a first frequency domain signal by applying a transform to the first digital signal; and analyzing a portion of the first frequency domain signal corresponding to the first frequency, and wherein the processor is configured to determine that the reflection of the second component has the second frequency by: identifying a second digital signal indicative of a second electrical signal generated by the second receiver over time; generating a second frequency domain signal by applying the transform to the second digital signal; and analyzing a portion of the second frequency domain signal corresponding to the second frequency.

16. The frequency-steered sonar apparatus of claim 15, wherein the transform comprises a short-time Fourier transform (STFT).

17. The frequency-steered sonar apparatus of claim 1, wherein the processor is configured to determine that the reflection of the first component has the first frequency by: identifying a first digital signal indicative of a first electrical signal generated by the first receiver over time; and analyzing the first digital signal using at least one of a subspace method, a minimum variance method, a compressive sensing method, a parametric method, or a non-parametric method, and wherein the processor is configured to determine that the reflection of the second component has the second frequency by: identifying a second digital signal indicative of a second electrical signal generated by the second receiver over time; and analyzing the second digital signal using at least one of the subspace method, the minimum variance method, the compressive sensing method, the parametric method, or the non-parametric method.

18. The frequency-steered sonar apparatus of claim 1 , further comprising: a propeller configured to move the frequency-steered sonar apparatus in the environment, wherein the processor is further configured to control the propeller based on the 3D image.

19. The frequency-steered sonar apparatus of claim 1 , further comprising:a watertight housing enclosing array of transmitters, the array of receivers, and the processor.

20. The frequency-steered sonar apparatus of claim 1 , further comprising: a transceiver configured to transmit, to an external device, an indication of the 3D image.

21. A method, comprising: detecting, by a receiver of an apparatus at a reception time, a sound signal reflected by an object in an environment; determining, by identifying a frequency of the sound signal, a first angle at which the object is disposed, the first angle being defined with respect to the apparatus in a first plane; determining a distance between the apparatus and the object based on a time delay between a transmission time of the sound signal and the reception time of the sound signal; determining a second angle at which the object is disposed based on a position of the receiver, the second angle being defined with respect to the apparatus in a second plane; and identifying a position of the object in the environment based on the first angle, the distance between the apparatus and the object, and the second angle.

22. The method of claim 21, wherein the receiver comprises at least one transducer.

23. The method of claim 21, wherein the sound signal has a frequency in a range of about 200 kilohertz(kHz) to about 900 kHz.

24. The method of claim 21, wherein the environment comprises an aquatic environment.

25. The method of claim 21, wherein the sound signal is reflected from a surface of the object.

26. The method of claim 21, wherein the first angle is an elevation angle and the second angle is an azimuthal angle, or wherein the first angle is the azimuthal angle and the second angle is the elevation angle.

27. The method of claim 21, wherein the first plane is perpendicular to the second plane.

28. The method of claim 21, wherein identifying the frequency of the sound signal comprises: generating a frequency domain signal by applying a transform to a digital signal indicative of an electrical signal output by the receiver in response to receiving the sound signal; and analyzing a portion of the frequency domain signal corresponding to the frequency.

29. The method of claim 28, wherein the transform comprises a Fourier transform.

30. The method of claim 21 , the sound signal being a first sound signal, the method further comprising: outputting, by an array of transmitters at the transmission time, a wavefront comprising the first sound signal transmitted at the first angle and a second sound signal transmitted at a third angle, the third angle being defined with respect to the apparatus along the first plane.

31. The method of claim 30, wherein outputting, by the array of transmitters, the wavefront comprising the first sound signal transmitted at the first angle and the second sound signal transmitted at a third angle comprises:outputting, by a first transmitter among the array of transmitters, a first component of the wavefront comprising a first portion of the first sound signal and a first portion of the second sound signal; and outputting, by a second transmitter among the array of transmitters, a second component of the wavefront comprising a second portion of the first sound signal and a second portion of the second sound signal, wherein the first portion of the first sound signal constructively interferes with the second portion of the second sound signal in the environment, and wherein the first portion of the second sound signal constructively interferes with the second portion of the second sound signal in the environment32. The method of claim 30, wherein the array of transmitters extends along a first line segment, and wherein the receiver is among an array of receivers extending along a second line segment.

33. The method of claim 32, wherein the first line segment is curved and / or the second line segment is curved.

34. The method of claim 32, wherein the first line segment is perpendicular to the second line segment.

35. The method of claim 21 , further comprising: generating multiple electrical signals that respectively cause transmitters in an array to output a wavefront comprising the sound signal.

36. The method of claim 35, wherein the multiple electrical signals comprise pulses.

37. The method of claim 35, wherein the multiple electrical signals comprise a linear frequency modulated chirp.

38. The method of claim 21 , further comprising: generating an image of the environment based on the position of the object in the environment.

39. The method of claim 38, further comprising: outputting an indication of the image.

40. The method of claim 21 , further comprising: changing a direction, position, velocity, or acceleration of the apparatus based on the position of the object in the environment.

41. A system, comprising; at least one processor; and memory storing instructions that, when executed by the at least one processor, cause the at least one processor to perform operations comprising the method of claim 21.

42. The system of claim 41 , wherein the system comprises the apparatus.

43. The system of claim 41 , wherein the system comprises the receiver.

44. The system of claim 41 , wherein the system comprises at least one transmitter configured to transmit the sound signal into the environment.

45. A non-transitory computer-readable medium storing instructions for performing the method of claim

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