DOA estimation method based on genetic algorithm combined with molecular array

Abstract

The invention relates to a DOA (direction of arrival) estimation method based on a genetic algorithm combined with a molecular array. The DOA estimation method comprises the following steps: optimizing an array by adopting the genetic algorithm, generating a candidate solution and calculating a target function; calculating a digital beam by using the optimal weight vector, dividing the whole array into four sub-arrays according to the physical layout of the antenna array, improving the channel weighting precision, and reducing the angular resolution to be below # imgabs0 #; a sub-array division method is adopted to suppress a grating lobe effect, and the signal quality of a radar system is optimized; dML angle solution is carried out on each sub-array, a target azimuth angle and a target pitch angle are directly calculated from weighted channel data to adapt to a non-uniform array structure, and a DOA angle is obtained through peak detection; according to the method provided by the invention, the flexibility and the precision of the angulation process are improved, the grating lobe effect is effectively inhibited, and the problems of precision and stability of a traditional method under a non-uniform array condition are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of target tracking, and in particular to a DOA estimation method based on a genetic algorithm combined with a molecular array. Background Art

[0002] As a key device in fields such as autonomous driving, meteorological monitoring, and aviation, one of the core functions of a radar system is to accurately detect and track targets. Accurately estimating the direction of arrival (DOA) of a target is the basis for target positioning, tracking, and recognition. Traditional DOA estimation methods rely on beamforming techniques, such as digital beamforming (DBF) and adaptive beamforming (ABF). These methods usually rely on uniform array technology and require complex mathematical models and calculation processes. For the non-uniform array of 4D radars, traditional DBF generally uses sparse channel compensation to make it a uniform array for angle resolution. This compensation process not only increases the computational burden but also may lead to inaccurate angle resolution results. Especially under non-uniform array conditions, the compensation effect is poor and it cannot effectively process non-uniformly distributed channel data. Moreover, existing grating lobe suppression techniques usually reduce grating lobes by methods such as increasing the number of arrays, adjusting the array structure, or using windowing techniques. However, these methods often bring additional system overheads. For example, increasing the number of arrays will increase the hardware cost of the system, or adjusting the array structure will lead to unstable system performance. And a single grating lobe suppression method usually cannot effectively process complex target scenarios, resulting in large errors in angle resolution results. Summary of the Invention

[0003] In view of this, the present invention provides a DOA estimation method based on a genetic algorithm combined with a molecular array, which can effectively solve the problem of inaccurate angle resolution results in the prior art under non-uniform arrays.

[0004] To achieve the above object, a DOA estimation method based on a genetic algorithm combined with a molecular array of the present invention includes the following steps: S1. Set the basic physical parameters of the vehicle-mounted millimeter-wave radar antenna array and the genetic algorithm parameters; S2. Optimize the array using the genetic algorithm to generate candidate solutions and calculate the objective function; S201. Randomly generate M candidate solutions, that is, the initial population. The M candidate solutions are all N-dimensional weight vectors, and the expression is: ; Each weight is mapped to a predetermined numerical range through 10-bit binary coding; S202. Calculate the array beam response and perform normalization processing, calculate the half-power beam width (HPBW) of the main lobe and the maximum side lobe level (MSLL), and construct the objective function ; S203. Iteratively optimize the objective function through a genetic algorithm to generate an optimal weight vector ; S3. Use the optimal weight vector to calculate a digital beam. According to the physical layout of the antenna array, the entire array is divided into 4 sub-arrays; S4. Perform DML angle solution for each sub-array and obtain the DOA angle through peak detection S401. Construct a sample covariance matrix using the received signals , and construct a steering vector according to the structure of the radar array ; S402. Use DML to calculate the power spectrum at the candidate angle , and the expression is: ; where represents the determinant of the matrix; S403. Normalize the power spectrum and set a peak threshold Thr according to the normalized power spectrum; S404. Perform peak detection on each sub-array and set the power except the peak to zero to obtain a binary power spectrum ; S405. Dot-multiply the binary power spectra of all sub-arrays to obtain a fused power spectrum , and multiply it by the original normalized power spectrum to obtain a final power spectrum ; S406. The direction vector corresponding to the maximum value in the final power spectrum is the angle value of the DOA estimate.

[0005] Preferably, calculate the array beam response for a predetermined scanning angle , and the expression is: ; where represents the position parameter of the th array element, represents the wavelength; Normalize the array beam response and convert it to the dB scale, and the expression is: ; Through the normalized array beam response Calculate the half-power beamwidth HPBW and the maximum sidelobe level MSLL of the main board. The approximate expression for the half-power beamwidth HPBW of the main board is as follows: ; where, represents a constant related to the array weighting method, represents the effective aperture of the array; After removing the main lobe region, the maximum sidelobe level MSLL is the maximum value in the normalized beam response ; Combining the half-power beamwidth HPBW and the maximum sidelobe level MSLL of the main board, a target function is constructed, and the expression is: ; where, , represent preset weight coefficients.

[0006] Preferably, the genetic algorithm iteratively optimizes the target function including the following steps: Calculate the fitness values of the target functions of M candidate solutions respectively to determine the fitness, and use the roulette wheel method to select the individuals with higher fitness as the parents; Perform fixed-point crossover recombination on the selected parents with a crossover probability of 0.7 to generate offspring; Perform random mutation on the offspring with a mutation probability of 0.01; Combine the parents and offspring, and retain the better individuals according to the target function values to form a new generation of population; Repeat the above steps until the convergence condition is met or the preset iteration number threshold is reached; Output the optimal weight vector .

[0007] Preferably, forming a digital beam includes the following steps: S301. Apply the optimal weight vector to the original received signal, and weight the signals of each channel. The expression is: ; where, represents the weighted received signal, represents the original received signal; S302. Calculate the beam pointing using the digital beamforming formula. The expression is: ; where, represents the beam pointing, Denote the conjugate transpose of the steering vector, which is used for phase alignment to ensure that signals in the same direction can be superimposed on each other; S303. Minimize the objective function for phase compensation of each channel , and form a digital beam, with the expression: ; ; where, denotes the calibration factor, denotes the relative position index of the th antenna element, denotes the th element, denotes the physical gap between elements; The expression for the azimuth phase difference is: ; The expression for the elevation phase difference is: ; denotes the phase difference between the th channel and the reference channel, with the expression: ; where, denotes the azimuth distance between the th channel and the reference channel, denotes the elevation distance between the th channel and the reference channel, denotes the wavelength, denotes the azimuth angle, denotes the elevation angle.

[0008] Preferably, the expression for the steering vector is: ; where, denotes the wavelength, denotes the number of elements in the subarray, denotes the positions of each element, with the expression: ; ; where, denotes the element spacing; The expression for the covariance matrix is: ; Among them, represents the received signal after sub-array processing, represents the conjugate transpose of the received signal of sub-array processing.

[0009] Preferably, the expression for normalizing the power spectrum obtained by DML processing is: ; Among them, represents the power spectrum obtained by DML angle solution; the peak threshold Thr is set to half of the highest peak of the power spectrum, and the binary power spectrum has the expression: ; the fused power spectrum has the expression: ; the final power spectrum has the expression: .

[0010] Compared with the prior art, the beneficial effects of the present invention are: The present invention uses a genetic algorithm to optimize the weights of the radar array channels, accurately distributes the weights of each channel, not only greatly improves the weighting accuracy of each channel, but also can more effectively focus the main lobe energy, reduce noise and sidelobe interference, thereby greatly reducing the angle estimation error, giving full play to the role of each channel, improving the overall channel utilization rate, and providing higher-quality input data for subsequent angle solution calculation; The present invention uses a sub-array division method to effectively suppress the grating lobe effect, divides the radar array into multiple sub-arrays, reasonably adjusts the channel spacing and arrangement structure, reduces grating lobe interference, optimizes the signal quality of the radar system, reduces its impact on the angle solution result, and at the same time combines the DML angle solution algorithm to refine the direction vector, realizing the angle resolution improvement to within 1 degree, and significantly improving the angle solution accuracy; The present invention can process the special structure of the non-uniform array, directly uses the non-uniform array data for angle solution, breaks through the bottleneck of limited accuracy and stability under the condition of non-uniform array of traditional methods, and adapts to the common non-uniform array scenarios in high-frequency radar applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] FIG. 1 is a schematic flow chart of the present invention; Figure 2 is a schematic flow chart of the sub-array DML angle solution for channel weighting of the present invention; Figure 3 is the beam pattern optimized by the genetic algorithm in the embodiment; Figure 4Simulation result diagram of DOA of channel weighted molecular array and full channel DML for embodiments; Specific embodiments

[0012] To further elaborate on the technical means and effects adopted by the present invention to achieve the intended invention purpose, the following will, in conjunction with the accompanying drawings and preferred embodiments, detail the specific implementation manners, structures, features, and their effects according to the present invention as follows.

[0013] Embodiment 1 A DOA estimation method based on a genetic algorithm combined with a molecular array, comprising the following steps: S1. Set the basic physical parameters of the vehicle-mounted millimeter-wave radar antenna array and the genetic algorithm parameters; S2. Optimize the array using the genetic algorithm to generate candidate solutions and calculate the objective function; S201. Randomly generate M candidate solutions, that is, the initial population. The M candidate solutions are all N-dimensional weight vectors, and the expression is: ; Each weight Is mapped to a predetermined numerical interval through 10-bit binary coding; S202. Calculate the array beam response and perform normalization processing, calculate the main lobe half-power beam width HPBW and the maximum sidelobe level MSLL, and construct the objective function ; For the predetermined scanning angle Calculate the expression of the array beam response Is: ; Among them, Represents the position parameter of the th array element, Represents the wavelength; Normalize the array beam response And convert it to the dB scale. The expression is: ; Calculate the main board half-power beam width HPBW and the maximum sidelobe level MSLL through the normalized array beam response HPBW represents the angular width corresponding to the left and right boundaries where the power drops to 3 dB of the maximum value within the main lobe of the beam. The approximate expression of the main board half-power beam width HPBW is: ; Among them, Represents the effective aperture of the array, Represents a constant related to the array weighting method. In this embodiment , the optimal weights obtained by the genetic algorithm enable the effective aperture of the array to be fully utilized, thereby narrowing the HPBW. As long as the effective aperture is large enough, it can be ensured that , thus achieving the required high angular resolution; After removing the main lobe region, the maximum sidelobe level MSLL is the maximum value in the normalized beam response and is used to measure the sidelobe interference level. A lower MSLL means less sidelobe interference, which is beneficial to improving the accuracy of target detection; Combining the main board half-power beamwidth HPBW and the maximum sidelobe level MSLL, the objective function is constructed, and the expression is: ; Among them, , represent the preset weight coefficients; S203. Iteratively optimize the objective function through the genetic algorithm to generate the optimal weight vector ; Iteratively optimize the objective function through the genetic algorithm to obtain the optimal weight vector, making the main lobe of the array beam sufficiently concentrated ( ) and effectively suppressing the sidelobe interference, providing a high-quality input signal for subsequent DOA processing; The genetic algorithm iteratively optimizes the objective function including the following steps: Calculate the objective function values of M candidate solutions respectively to determine the fitness, and use the roulette wheel method to select the individuals with higher fitness as the parents; Perform fixed-point crossover recombination on the selected parents with a crossover probability of 0.7 to generate offspring; Perform random mutation on the offspring with a mutation probability of 0.01 to ensure population diversity; Merge the parents and offspring, and retain the better individuals according to the objective function values to form a new generation of population; Repeat the above steps until the convergence condition is met or the preset iteration upper limit is reached; Output the optimal weight vector ; S3. Calculate the digital beam using the optimal weight vector . According to the physical layout of the antenna array, the entire array is divided into 4 sub-arrays to ensure high coherence of the antennas within each sub-array; S301. Apply the optimal weight vector to the original received signal, and weight the signals of each channel. The expression is: ; Among them, represents the weighted received signal, represents the original received signal; S302. Calculate the beam direction using the digital beamforming formula, and the expression is: ; Among them, represents the beam direction, represents the conjugate transpose of the steering vector, which is used for phase alignment to ensure that signals in the same direction can be superimposed on each other; S303. Perform phase compensation on each channel to minimize the objective function , and form a digital beam, and the expression is: ; Among them, represents the calibration factor, represents the relative position index of the th antenna element, represents the th element, represents the physical gap between elements; The expression of the azimuth phase difference is: ; The expression of the elevation phase difference is: ; represents the phase difference between the th channel and the reference channel, and the expression is: ; Among them, represents the azimuth distance between the th channel and the reference channel, represents the elevation distance between the th channel and the reference channel, represents the wavelength, represents the azimuth angle, represents the elevation angle.

[0014] S4. Perform DML angle solution on each subarray, and obtain the DOA angle through peak detection; S401. Construct a sample covariance matrix using the received signal , and construct a steering vector according to the structure of the radar array ; For a non-uniform linear array, the steering vector needs to consider the non-uniform distribution of the actual positions of each channel. Assuming the The position of each array element is , and the first array element is located at the origin , and the spacing between array elements is (i.e., the distance between the -th array element and the -th array element), then the positions of each array element can be calculated according to the following expression: ; ; On this basis, the steering vector of the non-uniform array is expressed as: ; where represents the wavelength, represents the number of array elements in the sub-array, represents the positions of each array element, The covariance matrix is expressed as: ; where represents the received signal after sub-array processing, represents the conjugate transpose of the received signal after sub-array processing; S402. Calculate the power spectrum at the candidate angle using DML, and the expression is: ; where represents the determinant of the matrix; For the DML method in radar DOA estimation, the basic idea is to find the angle that can best match the data with the model, and the cost function expression is: ; where represents the orthogonal projection matrix at the angle , that is: ; To prove that the DML angle solution can achieve an accuracy lower than , near the true DOA, the DML cost function shows a high curvature, that is, its second derivative is large, indicating that the cost value changes rapidly near the optimal angle, which helps to distinguish fine angles; under high signal-to-noise ratio conditions, the Cramér-Rao lower bound CRLB of DOA estimation can be approximately expressed as: ; where represents the noise variance, Indicates the signal power. When d is set to 0.5 , when N takes an appropriate value (for example, there are at least 4 - 8 array elements in the sub - array), and under the condition of a relatively high signal - to - noise ratio (high SNR), the calculated CRLB (i.e., the estimated standard deviation) can usually be lower than 0.0175 rad (about ), thus theoretically ensuring that the estimation accuracy of the DML algorithm can be lower than ; S403. Normalize the power spectrum, and the expression is: ; where represents the power spectrum obtained by the DML angle solution; And set the peak threshold Thr according to the normalized power spectrum, which is set to half of the highest peak of the power spectrum; S404. Perform peak detection on each sub - array, and set the power except the peak to zero to obtain a binary power spectrum , and the expression is: ; S405. Dot - multiply the binary power spectra of all sub - arrays to obtain a fused power spectrum , and the expression is: ; Multiply the original normalized power spectra to obtain the final power spectrum , and the expression is: ; S406. The direction vector corresponding to the maximum value in the final power spectrum is the angle value of the DOA estimation.

[0015] Embodiment 2 As a preferred embodiment of the present invention, a total of 12 array elements are set in this embodiment. The ratio of the sampling interval between array elements to the wavelength is set to 0.5, the number of individuals N is 40, the maximum number of genetic generations is 100 times, each variable is encoded with 10 - bit binary, the generation gap is set to 0.95, the crossover probability is set to 0.7, and the mutation probability is set to 0.01.

[0016] The Field Descriptor (FieldD) is used to specify the coding range and discretization rules of each weight variable, so as to ensure that each weight takes values within a predetermined interval; the iterative optimal result is as Figure 3 shown. The weights optimized by the genetic algorithm significantly improve the array beam characteristics, making the main lobe more concentrated and the side lobes effectively suppressed, providing a high - quality input signal for subsequent DOA estimation; Set the simulation target azimuth angle to 1.5°, and the DOA result is as Figure 4As shown in the DOA estimation of the middle-channel weighted molecular array, compared with the full-channel DML estimation, the angular spectrum only has peaks at the positions of the targets. By multiplying the binary power spectra, the echo power in the grating lobe directions is removed.

[0017] The above are only the preferred embodiments of the present invention and do not impose any formal limitations on the present invention. Although the present invention has been disclosed above with the preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to equivalent embodiments by using the disclosed technical content within the scope of the technical solution of the present invention. However, as long as it does not depart from the content of the technical solution of the present invention, any brief modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A DOA estimation method based on genetic algorithm combined with molecular array, characterized in that It includes the following steps: S1. Set the basic physical parameters of the vehicle-mounted millimeter-wave radar antenna array and the genetic algorithm parameters; S2. Optimize the array using the genetic algorithm to generate candidate solutions and calculate the objective function; S201. Randomly generate M candidate solutions, i.e., the initial population, and the M candidate solutions are all N-dimensional weight vectors, and the expression is: ； Each weight is mapped to a predetermined numerical range through a 10-bit binary code; S202. Calculate the array beam response and perform normalization processing, calculate the half-power beamwidth HPBW of the main lobe and the maximum sidelobe level MSLL, and construct an objective function ; S203. Iteratively optimize the objective function through a genetic algorithm Generate an optimal weight vector ; S3. Utilize the optimal weight vector Calculate the digital beam. According to the physical layout of the antenna array, divide the entire array into 4 sub-arrays; S4. Perform DML angle solution on each sub-array, and obtain the DOA angle through peak detection S401. Construct a sample covariance matrix using the received signal , construct a steering vector according to the structure of the radar array ; S402. Calculate the candidate angle using DML The power spectrum at is expressed as: ； Among them, represents the determinant of the matrix; S403. Normalize the power spectrum, and set the peak threshold Thr according to the normalized power spectrum; S404. Perform peak detection on each sub-array, set the power except for the peak to zero, and obtain a binarized power spectrum ; S405. Dot-multiply the binarized power spectra of all sub-arrays to obtain a fused power spectrum , and multiply it with the original normalized power spectrum to obtain the final power spectrum ; S406. The direction vector corresponding to the maximum value in the final power spectrum is the angle value of the DOA estimation.

2. The DOA estimation method based on the genetic algorithm combined with the molecular array according to claim 1, wherein For a predetermined scanning angle Calculate the array beam response The expression is as follows: ； Among them, represents the position parameter of the nth array element, and represents the wavelength; Normalize the array beam response and convert it to the dB scale. The expression is as follows: ； The array beam response after normalization Calculate the half-power beamwidth HPBW and the maximum sidelobe level MSLL of the main board. The approximate expression for the half-power beamwidth HPBW of the main board is as follows: ； Among them, represents a constant related to the array weighting method, represents the effective aperture of the array; After excluding the main lobe region, the maximum sidelobe level MSLL is the maximum value in the normalized beam response; Construct the objective function by combining the half-power beamwidth (HPBW) and the maximum sidelobe level (MSLL) of the main board , and the expression is as follows: ； Among them, and represent preset weight coefficients.

3. The DOA estimation method based on genetic algorithm combined with molecular array according to claim 2, wherein The genetic algorithm iteratively optimizes the objective function including the following steps: Calculate the objective function values of the M candidate solutions respectively to determine the fitness, and use the roulette wheel method to select the individuals with higher fitness as the parents; Perform fixed-point crossover recombination on the selected parents with a crossover probability of 0.7 to generate offspring; Perform random mutation on the offspring with a mutation probability of 0.01; Combine the parents and offspring, and retain the better individuals according to the objective function values to form a new generation of population; Repeat the above steps until the convergence condition is met or the preset iteration number threshold is reached; Output the optimal weight vector .

4. A DOA estimation method based on a genetic algorithm combined with a molecular array according to claim 1, characterized in that Forming a digital beam includes the following steps: S301. Apply the optimal weight vector to the original received signal to weight each channel signal. The expression is as follows: ； Among them, represents the weighted received signal, represents the original received signal; S302. Calculate the beam pointing using the digital beamforming formula, and the expression is: ； Among them, represents the beam direction, represents the conjugate transpose of the steering vector, which is used for phase alignment to ensure that signals in the same direction can be superimposed on each other; S303. Minimize the objective function for phase compensation of each channel , to form a digital beam, with the expression: ； ； Among them, represents the calibration factor, represents the relative position index of the th antenna array element, represents the th element, represents the physical gap between the elements; Azimuth phase difference The expression is as follows: ； Pitch phase difference The expression is as follows: ； Indicates the phase difference between the th channel and the reference channel, and the expression is: ； Among them, represents the azimuth distance between the th channel and the reference channel, represents the elevation distance between the th channel and the reference channel, represents the wavelength, represents the azimuth angle, represents the elevation angle.

5. A DOA estimation method based on a genetic algorithm combined with a molecular array according to claim 1, characterized in that, The steering vector has the following expression: ； Among them, represents the wavelength, represents the number of array elements in the sub-array, represents the positions of the respective array elements, and the expression is: ； ； Among them, represents the element spacing; The covariance matrix has the following expression: ； Among them, represents the received signal after subarray processing, represents the conjugate transpose of the received signal of subarray processing.

6. The DOA estimation method based on the genetic algorithm combined with the molecular array according to claim 5, wherein The expression for normalizing the power spectrum obtained by DML processing is: ； Among them, represents the power spectrum obtained by DML angle solution; The peak threshold Thr is set to half of the highest peak of the power spectrum, and the binary power spectrum has the following expression: ； The fused power spectrum has the following expression: ； The final power spectrum has the following expression: 。

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