Mixed norm time domain broadband beam forming method under planar array projection coordinate system

Abstract

The invention provides a mixed norm time domain broadband beam forming method under a planar array projection coordinate system, which belongs to the technical field of sonar signal processing, and comprises the following steps: calculating the expected frequency response of a finite impulse response filter according to a conventional beam forming weight, and carrying out pre-delay processing on a received signal to obtain a mixed norm time domain broadband beam; a mixed norm constraint criterion is adopted to carry out two-norm constraint on a pass band and infinite norm constraint on a stop band, a finite impulse response filter optimization target and constraint conditions are established, a convex optimization solver is utilized to solve a time domain impulse response of a finite impulse response filter, and after a received echo signal passes through the finite impulse response filter, the finite impulse response is obtained. The problems that when array element time delay is calculated in planar array broadband beam forming, due to the fact that a spherical coordinate system is adopted, an azimuth angle and a pitch angle are in a product relation, time delay calculation complexity is high, and beam forming performance is reduced due to the fact that constraints of a pass band and a stop band are unbalanced in the design of a filter are solved.

Description

Technical Field

[0001] This invention belongs to the field of sonar signal processing technology, and specifically relates to a hybrid norm time-domain broadband beamforming method in a planar array projection coordinate system. Background Technology

[0002] Forward-looking sonar systems for underwater vehicles typically employ planar arrays to receive broadband echo signals. Traditional broadband beamforming methods are based on establishing an array model in spherical coordinates, achieving beam pointing control by calculating the time delay difference of each array element relative to a reference point. In existing technologies, the azimuth and elevation angles in the spherical coordinate system exhibit a trigonometric product relationship in time delay calculations, leading to complex calculations of the time delay for each array element and increasing the computational burden of real-time processing. Furthermore, traditional finite impulse response (FIR) filter designs often employ single-norm constraint criteria. Due to the lack of joint constraint mechanisms for different frequency bands, it is difficult to simultaneously guarantee response accuracy within the passband and noise suppression capability outside the stopband, resulting in insufficient accuracy of the beamforming output within the operating frequency band and poor noise suppression performance outside the operating frequency band. In other words, existing technologies suffer from technical problems: the use of a spherical coordinate system in calculating array element time delays in planar array broadband beamforming leads to a product relationship between azimuth and elevation angles, resulting in high time delay calculation complexity; and the unbalanced passband and stopband constraints in filter design degrade beamforming performance. Summary of the Invention

[0003] In view of this, the present invention provides a hybrid norm time-domain broadband beamforming method in a planar array projection coordinate system, which can solve the technical problems in the prior art where the use of a spherical coordinate system when calculating the time delay of array elements in planar array broadband beamforming results in a product relationship between the azimuth and elevation angles, leading to high time delay calculation complexity, and the imbalance between passband and stopband constraints in filter design, resulting in a decrease in beamforming performance.

[0004] This invention is implemented as follows: It provides a hybrid norm time-domain broadband beamforming method under a planar array projection coordinate system. By establishing a projection coordinate system and projecting the direction vector onto two orthogonal planes, the product relationship between the azimuth and elevation angles of the projection coordinate system in the element delay calculation is transformed from a product relationship in spherical coordinates to a linear additive relationship. Furthermore, a hybrid norm constraint criterion is used to apply a second-norm constraint to the passband discretized frequency and an infinite-norm constraint to the stopband discretized frequency to achieve differentiated error control. The method includes the following steps: establishing a projection coordinate system on the planar array; determining the azimuth and elevation angles of the projection coordinate system, where the azimuth angle is the angle between the direction vector and its projection onto the yoz plane, and the elevation angle is the angle between the direction vector and its projection onto the xoz plane; calculating the delay difference of each element based on the projection coordinate system; and determining the delay difference based on the element coordinates and the projection coordinate system... The azimuth angle and elevation angle in the projected coordinate system are linearly summed to calculate the time delay of each array element. The broadband signal is divided into multiple sub-bands, each of which meets the narrowband condition. The conventional beamforming weights at the center frequency of each sub-band are calculated based on the time delay of each array element. The desired frequency response of the finite impulse response filter is calculated based on the conventional beamforming weights. The received signal is pre-delayed to obtain the pre-delay amount. The finite impulse response filter is designed using the hybrid norm constraint criterion. The passband is constrained by the second norm, and the stopband is constrained by the infinite norm. The optimization objective and constraint conditions of the finite impulse response filter are established. The time-domain impulse response of the finite impulse response filter is solved using a convex optimization solver. The received echo signal is passed through the finite impulse response filter and then summed to obtain the time-domain broadband beamforming output.

[0005] The projected coordinate system refers to a coordinate system established in the direction of the normal to the planar array. The projected coordinate system transforms the product relationship between the azimuth and elevation angles of the projected coordinate system in the calculation of the time delay of each array element from that in the spherical coordinate system into a linear summation relationship.

[0006] The calculation of the array element coordinates is as follows: for the m-th array element, the x-axis coordinate is the array element number minus 1, modulo the number of array elements in the x-axis direction, and then multiplied by the array element spacing in the x-axis direction; the y-axis coordinate is the array element number minus 1, divided by the number of array elements in the x-axis direction, rounded down, and then multiplied by the array element spacing in the y-axis direction.

[0007] The time delay of each array element refers to the delay time of the m-th array element relative to the reference point, which is the product of the x-axis coordinate of the m-th array element and the sine of the azimuth angle of the projected coordinate system pointing to the beam, plus the product of the y-axis coordinate of the m-th array element and the sine of the elevation angle of the projected coordinate system pointing to the beam, divided by the speed of sound.

[0008] The sub-band center frequency refers to the center frequency of each sub-band after the broadband signal is divided into K narrowband signals.

[0009] The conventional beamforming weight refers to the weighting coefficient of the m-th element at the sub-band center frequency, which is a complex exponential function with the negative value of the product of the time delay of each element and the sub-band center frequency as the phase, divided by the total number of elements in the planar array.

[0010] The pre-delay amount refers to the delay time applied to the signal to minimize the design error of the finite impulse response filter. It is calculated by multiplying the delay of each array element by the sampling frequency, adding the negative value of the finite impulse response filter length minus 1, dividing by 2, rounding down, and then dividing by the sampling frequency.

[0011] The desired frequency response of the finite impulse response filter is the product of the conjugate of the conventional beamforming weights and a complex exponential function whose phase is the product of the pre-delay and the sub-band center frequency.

[0012] The hybrid norm constraint criterion refers to an optimization criterion that combines the L2 norm and the infinite norm to constrain the design error of a finite impulse response filter. The L2 norm constraint on the passband discretization frequency ensures the response accuracy within the passband, while the infinite norm constraint on the stopband discretization frequency suppresses noise in the non-operating frequency band.

[0013] The optimization objective of the finite impulse response filter is to minimize the weighted sum of the non-negative error weighting factor at the passband discretization frequency and the square of the second norm of the frequency domain response error.

[0014] The constraint condition is that the maximum value of the non-negative error weighting factor and the infinite norm of the frequency domain response error at the stopband discretization frequency does not exceed the upper bound of the stopband error.

[0015] The passband discretization frequency refers to the set of frequency points obtained by discretizing and sampling within the passband frequency range.

[0016] The stopband discretization frequency refers to the set of frequency points obtained by discretizing and sampling within the stopband frequency range.

[0017] The convex optimization solver refers to a numerical calculation tool used to solve convex optimization problems. The convex optimization solver solves the optimization objective and constraints of the finite impulse response filter to obtain the time-domain impulse response coefficients of each array element.

[0018] The time-domain broadband beamforming output refers to the final output signal obtained by summing the echo signals received by each array element after processing them through the corresponding finite impulse response filter.

[0019] The time-domain broadband beamforming output is used to realize broadband beamforming of the forward-looking sonar of underwater vehicles.

[0020] This invention establishes a planar array projection coordinate system, projecting direction vectors onto two orthogonal planes. This transforms the product relationship between the azimuth and elevation angles of the projection coordinate system in the array element time delay calculation from that in spherical coordinates to a linear summation relationship, simplifying the time delay calculation process and reducing the computational complexity of real-time processing. Simultaneously, this invention employs a hybrid norm constraint criterion to design a finite impulse response filter. A L2 norm constraint on the passband discretization frequency ensures response accuracy within the operating frequency band, while an infinite norm constraint on the stopband discretization frequency effectively suppresses noise in the non-operating frequency band, giving the filter differentiated error control capabilities across different frequency bands. By combining time delay linearization in the projection coordinate system with hybrid norm filter optimization, this invention significantly reduces computational load and improves stopband suppression performance while maintaining beamforming accuracy. In summary, the present invention solves the technical problems mentioned in the background art, such as the high complexity of time delay calculation due to the product relationship between azimuth and elevation angles in the calculation of array element time delay when using a spherical coordinate system for broadband beamforming of planar arrays, and the unbalanced passband and stopband constraints in filter design leading to a decrease in beamforming performance. Attached Figure Description

[0021] Figure 1 This is a schematic diagram illustrating the process of using this method for underwater vehicle target detection.

[0022] Figure 2 The transmitted signal's time-domain and frequency-domain waveforms, including sub-wavelength waveforms. Figure 2 A is the time-domain waveform of the transmitted signal, sub- Figure 2 B is the spectrum of the transmitted signal.

[0023] Figure 3 The time-domain and frequency-domain waveforms of the signal received by array element 2, including sub-arrays. Figure 3 C is the time-domain waveform of the signal received by array element 2. Figure 3 D is the spectrum of the received signal of array element 2.

[0024] Figure 4 This is a schematic diagram of the array elements and a diagram showing the coordinate system relationship.

[0025] Figure 5 Considering the mixing norm of the second-element filter and the desired filter response diagram, including sub-... Figure 5 E is the amplitude-frequency response diagram of the second-element filter considering the mixing norm. Figure 5 F is the phase frequency response diagram of the filter with the second element considering the mixing norm.

[0026] Figure 6 Considering the single-norm amplitude-frequency response and desired filter response diagram for the second-element filter, including sub-... Figure 6 H represents the amplitude-frequency response of the second-element filter considering a single norm. Figure 6 I represents the phase frequency response of the filter with a single mixing norm for element 2.

[0027] Figure 7 Beamform cross-section with a pitch angle of 10°.

[0028] Figure 8 The time-frequency signal diagrams of beamforming output using hybrid norm constraints are shown, including sub-figure J, which is the time-domain signal diagram of beamforming output using hybrid norm constraints, and sub-figure K, which is the frequency-domain signal diagram of beamforming output using hybrid norm constraints.

[0029] Figure 9 The time-frequency signal diagrams of beamforming output using single norm constraints include sub-diagram L, which is the time-domain signal diagram of beamforming output using single norm constraints, and sub-diagram M, which is the frequency-domain signal diagram of beamforming output using single norm constraints. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below.

[0031] like Figure 1 The diagram shown is a flowchart of a hybrid norm time-domain broadband beamforming method in a planar array projection coordinate system provided by the present invention. This method includes the following steps:

[0032] S01. Establish a projection coordinate system on the planar array, and determine the azimuth and elevation angles of the projection coordinate system, where the azimuth angle is the angle between the direction vector and the projection onto the yoz plane, and the elevation angle is the angle between the direction vector and the projection onto the xoz plane.

[0033] S02. Calculate the time delay difference of each array element based on the projection coordinate system. Calculate the time delay of each array element by linearly adding the array element coordinates with the azimuth and elevation angles of the projection coordinate system.

[0034] S03. Divide the broadband signal into multiple sub-bands so that each sub-band meets the narrowband condition, and calculate the conventional beamforming weights at the center frequency of each sub-band based on the time delay of each array element.

[0035] S04. Calculate the desired frequency response of the finite impulse response filter based on the conventional beamforming weights, and perform pre-delay processing on the received signal to obtain the pre-delay amount.

[0036] S05. Design a finite impulse response filter using the hybrid norm constraint criterion. Apply the second norm constraint to the passband and the infinite norm constraint to the stopband. Establish the optimization objective and constraint conditions of the finite impulse response filter.

[0037] S06. Solve the time-domain impulse response of the finite impulse response filter using a convex optimization solver. Then, sum the received echo signals after passing them through the finite impulse response filter to obtain the time-domain broadband beamforming output.

[0038] The projected coordinate system is a coordinate system established along the plane array normal direction. Through the projected coordinate system, the azimuth and elevation angles in the calculation of time delay for each array element are transformed from a product relationship in the spherical coordinate system to a linear additive relationship. The array element coordinate expression for the m-th element is: Where m is the array element number, The number of matrix elements along the x-axis. and These represent the element spacing along the x-axis and the element spacing along the y-axis, respectively. Let be the x-coordinate of the m-th array element. Let y be the y-coordinate of the m-th array element.

[0039] The delay of each array element is the delay time of the m-th array element relative to the reference point, expressed as: ,in For the time delay of each array element, The azimuth angle in the projected coordinate system pointing to the beam. denoted by , where is the pitch angle of the projected coordinate system pointing to the beam, and c is the speed of sound.

[0040] The sub-band center frequency is the center frequency of each sub-band after dividing a broadband signal into K narrowband signals, denoted as . Where k ranges from 1 to K. The conventional beamforming weight is the value of the m-th element at the center frequency of the sub-band. The weighting coefficients are expressed as follows: ,in is the conventional beamforming weight, M is the total number of array elements in the planar array, and j is the imaginary unit.

[0041] The pre-delay is the time delay applied to the signal to minimize the design error of the finite impulse response filter, expressed as: ,in For pre-delay amount, The sampling frequency is L, the length of the finite impulse response filter is L, and int represents the integer operation. The desired frequency response of the finite impulse response filter is... The expression is ,in For the desired frequency response of a finite impulse response filter, This represents the conjugate of conventional beamforming weights.

[0042] The hybrid norm constraint criterion is an optimization criterion that combines the 2-norm and the infinite norm to constrain the design error of finite impulse response (FIR) filters. FIR filters possess a time-domain impulse response... , where h is the time-domain impulse response and l is the filter coefficient index. The non-negative error weighting factor is... The passband discretization frequency is The stopband discretization frequency is , where p ranges from 1 to P.

[0043] The optimization objective of the finite impulse response filter is to minimize The constraints are ,in , This is the upper limit of the stopband error. Let represent the transpose of vector e. The hybrid norm constraint criterion ensures the response accuracy within the passband by applying a second-norm constraint to the passband discretized frequency, and suppresses off-peak frequency noise by applying an infinite-norm constraint to the stopband discretized frequency.

[0044] A convex optimization solver is a numerical computation tool used to solve convex optimization problems. It solves the optimization objective and constraints of the finite impulse response filter to obtain the time-domain impulse response coefficients of each array element. The time-domain broadband beamforming output is obtained by summing the echo signals received by each array element after processing them through the corresponding finite impulse response filters. This final output signal is used to achieve broadband beamforming for the forward-looking sonar of the underwater vehicle.

[0045] The specific implementation methods of the above steps are described in detail below.

[0046] The specific implementation of step S01 is to establish a projection coordinate system in the normal direction of the planar array. First, the geometric center of the planar array is determined as the origin of the coordinate system. The normal direction of the plane where the planar array is located is taken as the positive direction of the z-axis. An x-axis and y-axis are established in the plane where the planar array is located to form a right-handed coordinate system. Then, the azimuth angle of the projection coordinate system is defined as the angle between the projection of the spatial direction vector on the yoz plane and the z-axis, and the pitch angle of the projection coordinate system is defined as the angle between the projection of the spatial direction vector on the xoz plane and the z-axis. The projection coordinate system is different from the definition of the azimuth and pitch angles of the traditional spherical coordinate system. By defining the angles on two orthogonal planes respectively, the angle parameters are decoupled, which lays the foundation for the linearization of the subsequent time delay calculation.

[0047] The specific implementation of step S02 is based on calculating the time delay difference of each array element in the projected coordinate system. First, the array element coordinates of the m-th array element are calculated according to the array element number m. The position number of the array element in the x-axis direction is obtained by subtracting 1 from the array element number and taking the modulo operation of the number of array elements in the x-axis direction. Then, the position number of the array element in the x-axis direction is obtained by multiplying by the array element spacing in the x-axis direction. The position number of the array element in the y-axis direction is obtained by subtracting 1 from the array element number, dividing by the number of array elements in the x-axis direction and rounding down. Then, the position number of the array element in the y-axis direction is obtained by multiplying by the array element spacing in the y-axis direction. Then, using the angle definition of the projected coordinate system, the time delay of each array element is expressed as the product of the x-axis coordinate and the sine of the azimuth angle of the projected coordinate system, plus the product of the y-axis coordinate and the sine of the pitch angle of the projected coordinate system, and then divided by the speed of sound. The calculation method transforms the product relationship of the time delay with respect to the two angles in the spherical coordinate system into a linear summation relationship, which significantly reduces the computational complexity and facilitates subsequent processing.

[0048] The specific implementation of step S03 involves dividing the broadband signal into multiple sub-bands and calculating conventional beamforming weights. First, the number of sub-bands K is determined based on the frequency range of the broadband signal and the required frequency resolution. The entire working frequency band is divided into K sub-bands, either uniformly or non-uniformly. The bandwidth of each sub-band should be narrow enough to meet the narrowband signal processing conditions. Generally, the ratio of the sub-band bandwidth to the sub-band center frequency is required to be less than 0.1. Then, the sub-band center frequency of each sub-band is extracted. The phase delay is calculated based on the time delay of each array element and the sub-band center frequency. The phase delay is then exponentially negative and divided by the total number of array elements in the planar array to obtain the conventional beamforming weights. The conventional beamforming weights are essentially weighting coefficients that enable phase alignment of the received signals of each array element in the beam pointing direction. By calculating the weights for different sub-bands, the frequency domain decomposition processing of the broadband signal is achieved.

[0049] The specific implementation of step S04 is to calculate the desired frequency response of the finite impulse response filter based on the conventional beamforming weights. First, the weights are conjugated to obtain the weight conjugate. Then, the pre-delay of each element is calculated based on the length of the finite impulse response filter and the sampling frequency. The pre-delay is obtained by multiplying the delay of each element by the sampling frequency, adding the length of the finite impulse response filter minus 1, dividing by 2, rounding the result, taking the negative value, and then dividing by the sampling frequency. The pre-delay setting makes the actual compensated delay of the finite impulse response filter close to the inherent group delay of the filter, thereby minimizing the filter design error. Finally, the weight conjugate is multiplied by the phase factor at the frequency corresponding to the pre-delay to obtain the desired frequency response of the finite impulse response filter. The desired frequency response defines the amplitude and phase characteristics that the finite impulse response filter should achieve at the center frequency of each sub-band.

[0050] The specific implementation of step S05 involves designing a finite impulse response (FIR) filter using a hybrid norm constraint criterion. First, the operating frequency band is defined as the set of discretized frequencies in the passband, and the non-operating frequency band is defined as the set of discretized frequencies in the stopband. A non-negative error weighting factor is set to adjust the error weights at different frequency points. Then, an optimization objective for the FIR filter is established, using a L2 norm. This objective measures the error between the actual response of the filter and the expected frequency response of the FIR filter within the passband discretized frequency range. Accurate approximation within the passband is achieved by minimizing the weighted sum of squares of this error. Simultaneously, constraints are established, using an infinite norm, to limit the maximum deviation between the actual response of the filter and the expected frequency response of the FIR filter within the stopband discretized frequency range to no more than the upper limit of the stopband error. The reference value for the upper limit of the stopband error is 0.001 to 0.01. This hybrid norm constraint criterion combines the global optimization characteristics of the L2 norm in the passband with the peak suppression capability of the infinite norm in the stopband, ensuring both beamforming accuracy in the passband and effective suppression of stopband noise.

[0051] The specific implementation of step S06 involves using a convex optimization solver to solve the time-domain impulse response. First, the optimization objective and constraints of the finite impulse response filter are transformed into a standard convex optimization problem. This convex optimization problem has a unique global optimal solution and no local optimal traps. Then, the convex optimization solver is called to solve the convex optimization problem. The convex optimization solver can use the conventional interior-point method or a sequential quadratic programming algorithm to iteratively calculate the optimal time-domain impulse response coefficients that satisfy the constraints. These time-domain impulse response coefficients constitute the tap weights of the finite impulse response filter. Finally, the echo signals received by each array element are input into the corresponding finite impulse response filter for convolution operations. The filtered output signals of all array elements are summed in the time domain to obtain the time-domain broadband beamforming output. The time-domain broadband beamforming output enhances the beam pointing direction signal and suppresses interference noise in other directions, thereby improving the detection performance of the forward-looking sonar system of the underwater vehicle.

[0052] The key technical concepts of this invention include two core aspects: projected coordinate system modeling and hybrid norm filter design. Projected coordinate system modeling, by defining a novel coordinate system on a planar array, decouples the product relationship of array element delay with respect to azimuth and elevation angles in the traditional spherical coordinate system into a linear additive relationship. This fundamentally simplifies the mathematical expression for delay calculation, allowing it to be directly decomposed into two independent one-dimensional calculation processes. The computational complexity is reduced from two-dimensional coupled operations in the spherical coordinate system to the superposition of two independent one-dimensional operations. This not only reduces the number of floating-point operations and trigonometric function calls but also creates conditions for the future use of efficient algorithms such as Fast Fourier Transform and two-dimensional convolution, significantly improving the real-time processing capability of beamforming and meeting the stringent real-time requirements of underwater vehicles for detection systems. The hybrid norm filter design overcomes the limitations of the traditional single norm criterion. By applying a L2 norm constraint to the passband, it achieves the minimum mean square error approximation of the desired frequency response, ensuring high beamforming accuracy within the operating frequency band. At the same time, the infinite norm constraint on the stopband strictly limits the maximum response amplitude in the non-operating frequency band, effectively suppressing out-of-band noise and interference signals. Compared with the traditional single L2 norm criterion, which only focuses on passband performance while neglecting stopband suppression, the hybrid norm criterion significantly improves stopband attenuation capability while maintaining passband accuracy, thereby enhancing the beamforming output signal-to-noise ratio and the system's anti-interference performance. The synergistic effect of these two key technical approaches has produced significant comprehensive results. The reduced computational complexity of the projected coordinate system modeling provides a time margin for real-time optimization of the hybrid norm filter, while the improved output signal-to-noise ratio of the hybrid norm filter design fully leverages the real-time advantage brought by the rapid calculation of the projected coordinate system. Together, they have achieved a dual improvement in the real-time performance and detection accuracy of the forward-looking sonar system for underwater vehicles. Compared with traditional methods, this significantly reduces processing latency while maintaining or even improving detection accuracy, providing reliable technical support for rapid decision-making and maneuvering avoidance of underwater vehicles in complex environments.

[0053] It should be noted that this invention also solves the following technical problem: traditional broadband beamforming methods do not consider pre-delay processing when designing finite impulse response (FIR) filters, leading to large filter design errors. This invention preprocesses the received signal by introducing a pre-delay amount, calculated based on the array element delay, sampling frequency, and filter length. This ensures that the desired frequency response of the FIR filter matches the practically achievable filter characteristics, reducing design errors caused by causal constraints. Pre-delay processing essentially transforms a non-causal system into a causal system through time-shifting. The integer part of the total array element delay is implemented in the time domain, while the fractional part is compensated by introducing a phase compensation term in the frequency domain. This allows the filter coefficients to better approximate the desired response within a finite length, thereby improving the overall accuracy of beamforming, ensuring the coherent superposition effect of the broadband signal at various frequency components, and enhancing the reliability of target detection and localization.

[0054] Specifically, the principle of this invention is as follows: The technical solution of this invention can solve the above-mentioned technical problems because the establishment of the projection coordinate system changes the mathematical form of time delay calculation. In the spherical coordinate system, the array element time delay includes a product of the azimuth and elevation angles as sinusoidal functions. The projection coordinate system projects the direction vectors onto the yoz and xoz planes respectively, making the x-axis coordinate only related to the azimuth angle of the projection coordinate system, and the y-axis coordinate only related to the elevation angle of the projection coordinate system. These two coordinates are linearly added in the time delay expression, eliminating trigonometric function coupling and conforming to the superposition principle of linear systems. The logic of the hybrid norm constraint criterion lies in the different sensitivities of the passband and stopband to errors. In the passband, it is necessary to accurately approximate the desired response; using the L2 norm constraint can minimize the overall error in a mean-square sense. In the stopband, it is necessary to strictly limit the maximum error to suppress noise; using the infinite norm constraint can control the upper bound of the error in the worst case. This differentiated constraint strategy enables the finite impulse response filter to achieve a balance between passband accuracy and stopband suppression under the condition of convex optimization solvability, ensuring the quality of the time-domain broadband beamforming output.

[0055] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0056] The specific implementation of step S01 is to establish a projection coordinate system in the normal direction of the planar array. First, the geometric center of the planar array is determined as the origin of the coordinate system. The normal direction of the plane where the planar array is located is taken as the positive direction of the z-axis. An x-axis and y-axis are established in the plane where the planar array is located to form a right-handed coordinate system. Then, the azimuth angle of the projection coordinate system is defined as the angle between the projection of the spatial direction vector on the yoz plane and the z-axis, and the pitch angle of the projection coordinate system is defined as the angle between the projection of the spatial direction vector on the xoz plane and the z-axis. The projection coordinate system is different from the definition of the azimuth and pitch angles of the traditional spherical coordinate system. By defining the angles on two orthogonal planes respectively, the angle parameters are decoupled, which lays the foundation for the linearization of the subsequent time delay calculation.

[0057] The specific implementation of step S02 is based on calculating the time delay difference of each array element using the projected coordinate system. First, the array element coordinates of the m-th array element are calculated according to the array element number m. The array element coordinate expression is as follows:

[0058] ;

[0059] In the formula, Let x be the x-coordinate of the m-th array element, in meters. Let be the y-coordinate of the m-th array element, in meters; The array element number has a value range from 1 to M; This represents the number of matrix elements along the x-axis, typically set to 8. The x-axis element spacing is measured in meters (m), and is typically taken as 0.025 m. The spacing between array elements along the y-axis is in meters (m), and is typically taken as 0.025m. The standard spacing is 1m. This represents the modulo operation; This indicates the floor function; This represents the total number of elements in the planar array. Then, the time delay of each element is calculated using the angle definition of the projected coordinate system. The expression for the time delay of each element is as follows:

[0060] ;

[0061] In the formula, The delay of each array element is expressed in seconds (s). The azimuth angle of the projected coordinate system pointing to the beam is in degrees. The elevation angle of the projected coordinate system pointing to the beam is expressed in degrees. The speed of sound is measured in m / s, and is typically taken as 1500 m / s. The standard speed of sound is 1 m / s; This represents a sine function. The calculation method transforms the product relationship of time delay with respect to two angles in spherical coordinates into a linear summation relationship, significantly reducing computational complexity.

[0062] The specific implementation of step S03 involves dividing the broadband signal into multiple sub-bands and calculating conventional beamforming weights. First, the number of sub-bands K is determined based on the frequency range of the broadband signal and the required frequency resolution. The entire working frequency band is then divided into K sub-bands, either uniformly or non-uniformly. The bandwidth of each sub-band should be narrow enough to meet the requirements of narrowband signal processing. Typically, the ratio of the sub-band bandwidth to the sub-band center frequency is required to be less than 0.1. Then, the sub-band center frequency of each sub-band is extracted. Where k ranges from 1 to K, the conventional beamforming weights are calculated based on the time delay of each array element and the center frequency of the sub-band. The expression for the conventional beamforming weights is as follows:

[0063] ;

[0064] In the formula, For the m-th array element at frequency Conventional beamforming weights under these conditions; This is the center frequency of the sub-band, in Hz. The sub-band is numbered; The number of sub-bands is typically set to 10 to 100. The imaginary unit satisfies ; Pi, with a value of 3.14159; Represents an exponential function; The standard time is 1 second. The standard number of array elements is 1. The conventional beamforming weights are essentially weighting coefficients that enable phase alignment of the received signals of each array element in the beam pointing direction.

[0065] The specific implementation of step S04 involves calculating the desired frequency response of the finite impulse response filter based on the conventional beamforming weights. First, the conventional beamforming weights are conjugates to obtain the weight conjugates, and the expression for the weight conjugates is as follows:

[0066] ;

[0067] In the formula, This indicates that the m-th array element is at frequency The conjugate of conventional beamforming weights; This represents the conjugate operation. Then, based on the finite impulse response filter length and sampling frequency, the pre-delay of each array element is calculated. The expression for the pre-delay is as follows:

[0068] ;

[0069] In the formula, This is the pre-delay amount, measured in seconds (s). This is the sampling frequency, in Hz, typically 100000Hz. The standard frequency is 1Hz. This is the length of the finite impulse response filter, typically taken as 64; This represents the rounding operation. The pre-delay value is set so that the actual compensated delay of the finite impulse response filter is close to the filter's intrinsic group delay, thereby minimizing the filter design error. Finally, the desired frequency response of the finite impulse response filter is calculated, and the expression for the desired frequency response of the finite impulse response filter is as follows:

[0070] ;

[0071] In the formula, For the m-th array element at frequency The desired frequency response of a finite impulse response (FIR) filter is defined as follows: the amplitude and phase characteristics that the FIR filter should achieve at the center frequencies of each subband.

[0072] The specific implementation of step S05 is to design a finite impulse response filter using the hybrid norm constraint criterion. First, the operating frequency band is defined as the set of passband discretized frequencies. The non-operating frequency band is defined as the set of stopband discretized frequencies. Set non-negative error weighting factors Used to adjust the error weights at different frequency points, where Let be the error weighting factor at the k-th passband frequency point, typically set to 1. Then, establish the optimization objective of the finite impulse response filter. The expression for the optimization objective of the finite impulse response filter is as follows:

[0073] ;

[0074] In the formula, Let m be the time-domain impulse response of the m-th array element; For frequency The corresponding frequency vector; Represents the frequency vector Transpose of; The standard amplitude is 1. This represents the modulo operation; This represents the minimization operation. The optimization objective adopts the L2 norm form to measure the error between the actual response of the filter and the expected frequency response of the finite impulse response filter within the passband discretized frequency range. Accurate approximation within the passband is achieved by minimizing the weighted sum of squares of this error. Simultaneously, constraints are established, expressed as follows:

[0075] ;

[0076] In the formula, The stopband discretization frequency is expressed in Hz. The stopband frequency point number; This represents the total number of stopband frequency points, typically ranging from 50 to 200. This is the error weighting factor for the p-th stopband frequency point, which is usually set to 1. This is the upper limit of the stopband error, with an empirical value of 0.001 to 0.01. Represents the frequency vector Transpose of; This indicates the operation of finding the maximum value. The frequency vector is involved. The expression is as follows:

[0077] ;

[0078] In the formula, For frequency The corresponding frequency vector; The frequency variable is expressed in Hz. Time-domain impulse response. The vector form expression is as follows:

[0079] ;

[0080] In the formula, For the l-th filter coefficient of the m-th array element; The superscript represents the filter coefficient index, ranging from 1 to L. This represents the transpose of a vector.

[0081] The specific implementation of step S06 involves using a convex optimization solver to solve the time-domain impulse response. First, the optimization objective and constraints of the finite impulse response filter are transformed into a standard convex optimization problem. This convex optimization problem has a unique global optimal solution and no local optimal traps. Then, the convex optimization solver is called to solve the convex optimization problem. The convex optimization solver can use the conventional interior-point method or sequential quadratic programming algorithm to iteratively calculate the optimal time-domain impulse response coefficients that satisfy the constraints. These time-domain impulse response coefficients constitute the tap weights of the finite impulse response filter. Finally, the echo signals received by each array element are input into the corresponding finite impulse response filter for convolution operations. The filtered output signals of all array elements are summed in the time domain to obtain the time-domain broadband beamforming output. The time-domain broadband beamforming output enhances the beam pointing direction signal and suppresses interference noise in other directions, thereby improving the detection performance of the forward-looking sonar system of the underwater vehicle.

[0082] It should be noted that the variables involved in this embodiment are explained in detail in Table 1.

[0083] Table 1. Variable Explanation Table

[0084]

[0085] To better understand and implement this invention, a specific application scenario of the invention is provided below as Example 2: To verify the application effect of this invention in the forward-looking sonar detection of actual underwater vehicles, technicians built an underwater target detection test system. Simulation experiments were conducted in a water tank environment to evaluate the performance of the hybrid norm time-domain broadband beamforming method in the planar array projection coordinate system. The test system uses an 8×8 planar array as the receiving array, with a total of 64 array elements. The element spacing is set to 0.025m in both the x-axis and y-axis directions. The geometric center of the planar array is used as the origin of the coordinate system, and the normal direction is the positive z-axis direction.

[0086] The technicians first designed the transmission signal, using a linear frequency modulated (LFM) signal as the active detection signal, with a center frequency set at 15000Hz, a signal bandwidth of 10000Hz, and a pulse width of 16ms. Figure 2 The diagram shows the time-domain and frequency-domain waveforms of the transmitted signal. The transmitted signal is emitted outward through the array element at the center of the planar array, and after illuminating an underwater target 1000m away from the receiving array, it generates an echo signal. To simulate a realistic underwater environment, technicians used a six-point model to simulate the echo characteristics of the target. The elevation and azimuth angles of the echo signal were both set to 10°, the speed of sound was set to 1500m / s, and the sampling frequency was set to 100000Hz.

[0087] Technicians perform beamforming processing according to the method described in this invention. First, a projection coordinate system is established on the planar array. The azimuth angle of the projection coordinate system is defined as the angle between the projection of the direction vector onto the yoz plane and the z-axis, and the elevation angle of the projection coordinate system is defined as the angle between the projection of the direction vector onto the xoz plane and the z-axis. Figure 4 The diagram shows a schematic of the planar array elements and their coordinate system relationship. By establishing a projected coordinate system, the time delay calculation of each element is transformed from a product form in spherical coordinates to a linear summation form, significantly reducing computational complexity. Taking element number 2 as an example, its coordinate position is... m、 With beam pointing angles of 10° elevation and 10° azimuth, the calculated time delay of element 2 relative to the reference element is approximately m. s. For example Figure 3 The figure shows the time-domain and frequency-domain waveforms of the signal received by array element 2. It can be seen from the figure that the received signal contains the characteristic information of the target echo as well as environmental noise.

[0088] Technicians divided the received broadband signal into 100 sub-bands, each with a bandwidth of approximately 500Hz, meeting the narrowband processing requirements. The ratio of the sub-band bandwidth to the minimum sub-band center frequency was approximately 0.047, less than the requirement of 0.1. Conventional beamforming weights were calculated for each sub-band, based on the time delay of each array element and the sub-band center frequency. For element 2, its weighting coefficients were calculated at each sub-band center frequency, with the weight amplitude being the reciprocal of the total number of planar array elements. The phase is related to the product of the time delay and the frequency.

[0089] Technicians designed a finite impulse response (FIR) filter based on conventional beamforming weights, setting the filter length to 64 and the sampling frequency to 100,000 Hz. To minimize filter design errors, the pre-delay of each array element was first calculated, ensuring the actual compensated delay of the filter closely approximates the inherent group delay. Taking element 2 as an example, the calculated pre-delay is approximately... Then, based on the weight conjugate and pre-delay, the desired frequency response of the finite impulse response filter is calculated. For example... Figure 5 The figure shows the amplitude-frequency response of the filter with the mixed norm and the desired filter response. It can be seen from the figure that the designed filter can closely approximate the desired response in the passband and has good attenuation characteristics in the stopband.

[0090] Technicians optimized the filter coefficients using a hybrid norm constraint criterion, defining the operating frequency band from 10000Hz to 20000Hz as the passband and the remaining frequency bands as the stopband. The number of discretized frequency points in the passband was set to 21, and in the stopband to 79. The non-negative error weighting factor was set to 1 in both the passband and stopband, and the upper bound of the stopband error was set to 0.001. By applying a L2 norm constraint to the passband to minimize the mean square error, and applying an infinite norm constraint to the stopband to limit the maximum response amplitude, a convex optimization problem was constructed, and a convex optimization solver was used to obtain the time-domain impulse response coefficients of each array element. To compare and analyze the advantages of the hybrid norm criterion, technicians also designed a comparative filter using the traditional single L2 norm criterion, such as... Figure 6 The figure shows the amplitude-frequency response and the desired filter response of the No. 2 array element filter considering a single norm. It can be clearly seen from the figure that the filter designed by the single norm criterion has a significantly weaker attenuation capability in the stopband than the filter designed by the mixed norm criterion.

[0091] Technicians processed the echo signals received by each array element through corresponding finite impulse response (FIR) filters. These filters performed convolution operations on the input signals to achieve fractional delay compensation and frequency selection. The filtered output signals from all 64 array elements were then summed in the time domain to obtain the final time-domain broadband beamforming output. Figure 7The image shows a beam pattern cross-section at a 10° elevation angle. It can be seen that the beam forms a distinct main lobe at 10° in the pointing direction, while the side lobes are effectively suppressed, resulting in a beam pattern with good directionality. Figure 8 The image shows the time-domain signal output of beamforming using the hybrid norm constraint. The output signal exhibits a significant peak at the arrival time of the target echo, with a low background noise level. Figure 9 The figure shows the time-domain signal output of beamforming using a single norm constraint. In comparison, the background noise level of the output signal is significantly higher than that of the mixed norm method, especially since the noise components in the non-operating frequency band are not effectively suppressed.

[0092] Technicians conducted a statistical analysis of the computation time for beamforming processing. Using a projected coordinate system for modeling significantly reduced the total time spent calculating the delay of each array element compared to the traditional spherical coordinate system method. This is because the delay calculation is simplified from two-dimensional coupled trigonometric function operations to two independent one-dimensional linear operations. This simplification not only reduces the complexity of a single calculation but also makes it possible to use fast algorithms such as two-dimensional convolution, further improving processing efficiency. In underwater vehicle applications with high real-time requirements, the reduction in processing time means the system can complete beamforming output faster, providing more timely information support for obstacle avoidance decisions and target tracking.

[0093] Technicians analyzed the signal-to-noise ratio (SNR) of the beamforming output and found that the hybrid norm filter design method significantly improved the output SNR compared to the traditional single norm method. This improvement mainly stems from the effective suppression of stopband noise by the hybrid norm constraint criterion. The infinite norm constraint strictly limits the maximum response amplitude of the non-operating frequency band, preventing out-of-band noise and interference signals from entering the beamforming output through the filter. In contrast, the traditional single L2 norm criterion only focuses on minimizing the mean square error within the passband, lacking effective constraints on stopband characteristics, resulting in a significant leakage of noise components from the non-operating frequency band into the output signal. The improved SNR directly enhances the underwater vehicle's target detection capability, enabling the system to effectively identify target echoes at greater distances or in noisier environments.

[0094] Technicians also evaluated the spatial resolution capability of the beammap, judging the system's angular resolution performance by observing the main lobe width and side lobe levels. Thanks to precise time delay calculations and optimized filter design, the main lobe width is narrow, effectively distinguishing multiple targets at similar angles. Suppression of side lobe levels is achieved through precise control of the frequency response using a hybrid norm filter design, effectively attenuating interference signals from non-directional directions. The excellent beammap characteristics ensure that the underwater vehicle can accurately locate targets during search missions, avoiding false alarms and missed detections.

[0095] Through the aforementioned tests, technicians verified the effectiveness of the method described in this invention in actual forward-looking sonar detection of underwater vehicles. Compared to traditional methods, this invention achieves decoupling and simplification of time delay calculation through projected coordinate system modeling, fundamentally reducing computational complexity and improving the system's real-time processing capabilities. This improvement enables underwater vehicles to maintain continuous and stable forward-looking detection during rapid maneuvers, meeting the real-time requirements of dynamic obstacle avoidance and target tracking. Simultaneously, the hybrid norm filter design method significantly improves the signal-to-noise ratio and anti-interference capability of beamforming output by jointly optimizing passband accuracy and stopband suppression. This improvement allows the system to more reliably detect and identify targets in complex underwater environments, especially in the presence of multipath interference, reverberation noise, and interference from other vessels, where the hybrid norm method exhibits stronger robustness. From the perspective of signal processing principles, the synergistic effect of projected coordinate system modeling and hybrid norm filter design has produced comprehensive advantages. The former provides a more efficient computational foundation for the latter, while the latter fully leverages the former's potential in real-time performance. Together, they have achieved a comprehensive improvement in both the real-time performance and accuracy of the forward-looking sonar system for underwater vehicles, providing reliable technical support for the safe navigation and efficient operation of underwater vehicles in complex environments.

[0096] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A hybrid norm time-domain broadband beamforming method in a planar array projection coordinate system, characterized in that, By establishing a projection coordinate system, the direction vector is projected onto two orthogonal planes, transforming the product relationship between the azimuth and elevation angles of the projection coordinate system in the array element time delay calculation from that in the spherical coordinate system into a linear summation relationship. Furthermore, a hybrid norm constraint criterion is used to apply a L2 norm constraint to the passband discretized frequency and an infinite norm constraint to the stopband discretized frequency to achieve differentiated error control. This includes the following steps: establishing a projection coordinate system on the planar array, determining the azimuth and elevation angles of the projection coordinate system, where the azimuth angle is the angle between the direction vector and its projection onto the yoz plane, and the elevation angle is the angle between the direction vector and its projection onto the xoz plane; calculating the time delay difference of each array element based on the projection coordinate system, and then calculating the time delay difference based on the array element coordinates and the projection coordinate system... The azimuth angle and elevation angle in the projected coordinate system are linearly summed to calculate the time delay of each array element. The broadband signal is divided into multiple sub-bands, each of which meets the narrowband condition. The conventional beamforming weights at the center frequency of each sub-band are calculated based on the time delay of each array element. The desired frequency response of the finite impulse response filter is calculated based on the conventional beamforming weights. The received signal is pre-delayed to obtain the pre-delay amount. The finite impulse response filter is designed using the hybrid norm constraint criterion. The passband is constrained by the second norm, and the stopband is constrained by the infinite norm. The optimization objective and constraint conditions of the finite impulse response filter are established. The time-domain impulse response of the finite impulse response filter is solved using a convex optimization solver. The received echo signal is passed through the finite impulse response filter and then summed to obtain the time-domain broadband beamforming output.

2. The hybrid norm time-domain broadband beamforming method in the planar array projection coordinate system according to claim 1, characterized in that, The projected coordinate system refers to a coordinate system established in the direction of the normal to the planar array. The projected coordinate system transforms the product relationship between the azimuth and elevation angles of the projected coordinate system in the calculation of the time delay of each array element from that in the spherical coordinate system into a linear summation relationship.

3. The hybrid norm time-domain broadband beamforming method in the planar array projection coordinate system according to claim 2, characterized in that, The calculation of the array element coordinates is as follows: for the m-th array element, the x-axis coordinate is the array element number minus 1, modulo the number of array elements in the x-axis direction, and then multiplied by the array element spacing in the x-axis direction; the y-axis coordinate is the array element number minus 1, divided by the number of array elements in the x-axis direction, rounded down, and then multiplied by the array element spacing in the y-axis direction.

4. The hybrid norm time-domain broadband beamforming method in the planar array projection coordinate system according to claim 3, characterized in that, The time delay of each array element refers to the delay time of the m-th array element relative to the reference point, which is the product of the x-axis coordinate of the m-th array element and the sine of the azimuth angle of the projected coordinate system pointing to the beam, plus the product of the y-axis coordinate of the m-th array element and the sine of the elevation angle of the projected coordinate system pointing to the beam, divided by the speed of sound.

5. The hybrid norm time-domain broadband beamforming method in the planar array projection coordinate system according to claim 4, characterized in that, The sub-band center frequency refers to the center frequency of each sub-band after the broadband signal is divided into K narrowband signals.

6. The hybrid norm time-domain broadband beamforming method in the planar array projection coordinate system according to claim 5, characterized in that, The conventional beamforming weight refers to the weighting coefficient of the m-th element at the sub-band center frequency, which is a complex exponential function with the negative value of the product of the time delay of each element and the sub-band center frequency as the phase, divided by the total number of planar array elements.

7. The hybrid norm time-domain broadband beamforming method in the planar array projection coordinate system according to claim 6, characterized in that, The pre-delay amount refers to the delay time applied to the signal to minimize the design error of the finite impulse response filter. It is calculated by multiplying the delay of each array element by the sampling frequency, adding the negative value of the finite impulse response filter length minus 1 divided by 2, taking the integer part, and then dividing by the sampling frequency.

8. The hybrid norm time-domain broadband beamforming method in the planar array projection coordinate system according to claim 7, characterized in that, The desired frequency response of the finite impulse response filter is the product of the conjugate of the conventional beamforming weights and a complex exponential function whose phase is the product of the pre-delay and the sub-band center frequency.

9. The hybrid norm time-domain broadband beamforming method in the planar array projection coordinate system according to claim 8, characterized in that, The hybrid norm constraint criterion refers to the optimization criterion that combines the L2 norm and the infinite norm to constrain the design error of the finite impulse response filter. The L2 norm constraint on the passband discretization frequency ensures the response accuracy within the passband, while the infinite norm constraint on the stopband discretization frequency suppresses noise in the non-operating frequency band.

10. The hybrid norm time-domain broadband beamforming method in the planar array projection coordinate system according to claim 9, characterized in that, The optimization objective of the finite impulse response filter is to minimize the weighted sum of the non-negative error weighting factor at the passband discretization frequency and the square of the second norm of the frequency domain response error.

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