Angle estimation and positioning method based on fundamental waves and higher harmonics of unmanned aerial vehicle

Abstract

The invention discloses an angle estimation and positioning method based on fundamental waves and higher harmonics of an unmanned aerial vehicle. Comprising the steps that a plurality of microphone arrays are used for collecting noise signals emitted by an unmanned aerial vehicle, and a linear frequency modulation signal is emitted at the same time in the collection process; synchronizing noise signals acquired by each microphone array according to the linear frequency modulation signals; for each microphone array, performing fast Fourier transform on the synchronized noise signal acquired by any microphone to obtain a spectrogram, and performing harmonic detection on the spectrogram to obtain a harmonic frequency set; for each microphone array, obtaining a harmonic pseudo spectrum of the microphone array at each frequency point in the harmonic frequency set through angle estimation according to the synchronized noise signal collected by each microphone; carrying out Bayesian multiband uncertainty fusion on harmonic pseudo spectrums of each microphone array at all frequency points to obtain an estimation angle; and calculating the estimated position of the unmanned aerial vehicle according to the estimated angles of all the microphone arrays. According to the method, high-accuracy two-dimensional positioning of the unmanned aerial vehicle can be realized in a non-cooperative mode.

Description

Technical Field

[0001] This invention belongs to the field of indoor positioning technology, specifically relating to an angle estimation and positioning method based on the fundamental wave and higher harmonics of unmanned aerial vehicles (UAVs). Background Technology

[0002] In recent years, the rapid development of lightweight unmanned aerial vehicle (UAV) technology and the decline in hardware costs have driven its widespread deployment in various application areas, including on-demand urban logistics, fire and rescue operations, and entertainment consumption. Reliable real-time location information is crucial for safe autonomous flight and effective mission execution; therefore, these applications place increasingly stringent demands on efficient and high-precision positioning methods. Compared to open outdoor environments, indoor environments typically lack GNSS capabilities and have complex propagation conditions, thus requiring higher positioning accuracy and robustness for UAV operations. Currently, indoor UAV positioning methods being researched by academia and industry include 3D point cloud registration based on lidar, vision-based feature tracking and simultaneous localization and mapping (SLAM), and ultra-wideband (UWB) two-way time-of-flight (ToF) ranging methods.

[0003] Despite their promising prospects, these methods also have some significant limitations. First, lidar sensors are relatively bulky; the increased payload severely limits the mass budget of a small body, and interruptions in the line-of-sight (LoS) or specular reflections from walls, furniture, and other clutter often distort point clouds and reduce pose estimation. Second, vision-based localization relies heavily on stable lighting and sufficient scene texture; weak light, rapid lighting changes, or glare can lead to feature loss, and in extreme cases, even complete tracking failure. Third, while UWB systems can theoretically achieve centimeter-level ranging, signal attenuation and excessive delay spread often result in significant performance degradation in industrial environments rich in metal or with strong multipath propagation.

[0004] Acoustic-based drone positioning methods have become increasingly popular. Existing methods typically require mounting microphone arrays or speakers on the drone body; however, the high-amplitude broadband noise generated by the rotors can severely contaminate the received signal, reduce the signal-to-noise ratio (SNR), and exacerbate latency and multipath errors. Furthermore, the weight, power consumption, and installation limitations of microphone arrays, influenced by payload and airflow, increase system complexity and limit the applicability of such solutions to small or long-endurance drones.

[0005] In conclusion, a non-cooperative acoustic localization technology that does not require additional load is urgently needed. Summary of the Invention

[0006] To address the aforementioned problems in the existing technology, this invention provides an angle estimation and positioning method based on the fundamental wave and higher harmonics of a UAV, which can achieve high-accuracy two-dimensional positioning of UAVs in indoor spaces in non-cooperative mode.

[0007] The present invention adopts the following technical solution:

[0008] I. An Angle Estimation and Positioning Method Based on UAV Fundamental Wave and Higher Harmonic Waves

[0009] The method of the present invention specifically includes the following steps:

[0010] Step S1: Use multiple microphone arrays to collect noise signals emitted by the drone. During the collection process, a linear frequency modulated signal is continuously transmitted simultaneously.

[0011] In step S1, the duration of linear frequency modulation is 10~100ms, the frequency range is 18~22kHz, the sampling frequency is 48kHz, and the signal refresh rate is 2~10Hz.

[0012] In step S1, the microphone arrays are all circular arrays.

[0013] Step S2: Based on the linear frequency modulation signal in the noise signal collected by each microphone array, synchronize the noise signal collected by each microphone array to obtain the synchronized noise signal of each microphone array.

[0014] Step S2 includes: using the noise signal collected by any microphone array as a reference noise signal, calculating the inter-array delay between the noise signal collected by the microphone array and the reference noise signal for each of the other microphone arrays, and aligning the noise signal according to the inter-array delay by integer sample time shifting to obtain the synchronized noise signal.

[0015] Step S3: For each microphone array, perform a Fast Fourier Transform on the synchronized noise signal acquired by any microphone to obtain a spectrum. Perform harmonic detection on the spectrum to obtain a set of harmonic frequencies. The set of harmonic frequencies consists of the frequency points of the fundamental frequency and its higher harmonics.

[0016] In step S3, the harmonic frequency set consists of the fundamental frequency and the frequency points of its fifth and lower harmonics.

[0017] Step S4: For each microphone array, based on the synchronized noise signal collected by each microphone, at each frequency point in the harmonic frequency set, the harmonic pseudo-spectrum of the microphone array at the frequency point is obtained by angle estimation.

[0018] Step S4 includes:

[0019] The synchronized noise signal collected by each microphone is evenly divided into L time-domain snapshots, and a fast Fourier transform is performed on each time-domain snapshot to obtain the complex spectrum.

[0020] At each frequency point in the harmonic frequency set, the spectral value is extracted from the complex spectrum of all microphones to obtain the frequency domain snapshot vector corresponding to the frequency point;

[0021] Based on the frequency domain snapshot vector corresponding to each frequency point, the sample covariance is constructed, the sample covariance is decomposed into features to separate the noise subspace, and then the harmonic pseudospectrum is constructed.

[0022] Step S5: Perform Bayesian multi-band uncertainty fusion on the harmonic pseudospectrum of each microphone array at all frequency points to obtain the estimated angle.

[0023] In step S5, the process of performing Bayesian multi-band uncertainty fusion on each microphone array includes:

[0024] For each frequency point of the microphone array: the harmonic pseudo-spectrum at the frequency point is normalized by the maximum value to obtain the normalized pseudo-spectrum; the total harmonic energy is calculated based on the frequency domain snapshot vector corresponding to the frequency point, and the temperature coefficient is obtained by mapping. The total energy of the frequency domain snapshot vector is used to represent the confidence level; the normalized pseudo-spectrum is shaped using the temperature coefficient and then normalized into a probability map.

[0025] For the probability maps at all frequency points of the microphone array, the operations are performed in the logarithmic domain and accumulated to obtain the fused map;

[0026] Peak picking is performed on the fused image to obtain the estimated angle of the microphone array.

[0027] Step S6: Calculate the estimated position of the UAV based on the estimated angles of all microphone arrays.

[0028] Step S6 includes: obtaining the corresponding unit direction vector based on the estimated angle of each microphone array; inputting the two-dimensional position vector and the corresponding unit direction vector of each microphone array into an overdetermined linear equation to solve for the estimated position of the UAV.

[0029] In step S6, the estimated position of the UAV is obtained by solving the following formula:

[0030]

[0031]

[0032] In the formula, Represents the identity matrix. Indicates the first The unit direction vector corresponding to each microphone array, with the superscript "T" indicating the transpose of the matrix. Indicates the first Two-dimensional position vectors of a microphone array Describes the first matrix. Represents the second matrix, This indicates the location of the drone.

[0033] II. An Angle Estimation and Positioning System Based on UAV Fundamental Wave and Higher Harmonic Waves

[0034] The system is used to implement the above-mentioned angle estimation and positioning method based on UAV fundamental wave and higher harmonics, including:

[0035] A signal generator used to transmit linear frequency modulated signals;

[0036] Multiple microphone arrays are used to collect noise signals and linear frequency modulation signals emitted by the drone;

[0037] The harmonic detection module is used to obtain the set of harmonic frequencies based on the synchronized noise signal;

[0038] The angle estimation module is used to estimate the angle based on the synchronized noise signals collected by all microphones in the microphone array, and to obtain the harmonic pseudo-spectrum of the microphone array at each frequency point in the harmonic frequency set.

[0039] The fusion module is used to perform Bayesian multi-band uncertainty fusion on the harmonic pseudo-spectrum of the microphone array at all frequency points in the harmonic frequency set to obtain the estimated angle.

[0040] The position estimation module is used to calculate the estimated position of the UAV based on the estimated angles of all microphone arrays.

[0041] The beneficial effects of this invention are:

[0042] This invention performs UAV positioning in a completely non-cooperative manner; uses 18-22 kHz linear frequency modulation (Chirps) signals as transmission signals to synchronize multiple microphone arrays; and employs Bayesian multi-band uncertainty fusion to remove interference and multipath effects, achieving high accuracy in real-world environments.

[0043] The angle estimation and positioning method based on UAV fundamental wave and higher harmonics proposed in this invention has good applicability and can be used for non-line-of-sight identification in complex indoor environments. Attached Figure Description

[0044] Figure 1 This is a flowchart of the angle estimation and positioning method based on the fundamental wave and higher harmonics of a UAV provided by the present invention;

[0045] Figure 2 This is a schematic diagram of the microphone equipment layout;

[0046] Figure 3 This is a diagram illustrating the forces acting on a drone during flight.

[0047] Figure 4 This is a diagram illustrating harmonics during the flight of a drone;

[0048] Figure 5 These are test results of the model under different positioning scenarios. Detailed Implementation

[0049] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0050] This invention provides a method for angle estimation and positioning of unmanned aerial vehicles (UAVs) based on their fundamental and higher harmonic frequencies. This method enables UAV positioning in a completely non-cooperative manner. Specifically, it uses a 18-22 kHz linear frequency modulated (Chirps) signal as the transmission signal for synchronization between multiple microphone arrays; it also employs Bayesian multi-band uncertainty fusion to remove interference and multipath effects, achieving high accuracy in real-world environments. Therefore, this method has good applicability and can be used for non-line-of-sight identification in complex indoor environments.

[0051] Furthermore, in the method of this invention, "based on the fundamental frequency and higher harmonics of the UAV" means that the peak structure of the propeller's fundamental frequency and its higher harmonics directly maps to the composite mode of the motor speed. When all four rotors rotate at the same speed (e.g., hovering, vertical ascent / descent, or steady-state lateral translation), each harmonic exhibits a single peak. During roll or pitch maneuvers, the left / right (or forward / rear) rotors are driven at two different speeds, thus producing a pair of distinguishable split peaks at the same harmonic order. During yaw, the co-rotating and counter-rotating rotors also employ two speed levels, but the difference is much smaller than that in the aforementioned attitude maneuvers. Figure 4 The amplitude spectrum of the fundamental frequency and higher harmonics of the drone propeller is shown. In order to more accurately estimate the angle of the drone, it is necessary to correctly identify the frequencies of its fundamental frequency and higher harmonics.

[0052] The method of the present invention specifically includes the following steps:

[0053] Step S1: Use multiple microphone arrays to collect noise signals emitted by the drone. During the collection process, a linear frequency modulation (Chirps) signal is transmitted simultaneously.

[0054] Preferably, the duration of linear frequency modulation is 10~100ms, the frequency is 18~22kHz, the sampling frequency is 48kHz, and the signal refresh rate is 2~10Hz.

[0055] Preferably, the microphone arrays are all circular arrays.

[0056] Preferably, the length of the noise signal is 0.1s.

[0057] Step S2: Synchronize the noise signals collected by each microphone array according to the linear frequency modulation signal to obtain the synchronized noise signals of each microphone array.

[0058] Specifically, this includes: within each synchronization cycle, using the noise signal collected by any microphone array as a reference noise signal, calculating the inter-array delay between the noise signal collected by the microphone array and the reference noise signal for each of the other microphone arrays, and aligning the noise signal based on the inter-array delay through integer sample time shifting to obtain the synchronized noise signal.

[0059] Step S3: For each microphone array, perform a Fast Fourier Transform on the synchronized noise signal acquired by any microphone to obtain a spectrum. Perform harmonic detection on the spectrum to obtain a set of harmonic frequencies. The set of harmonic frequencies consists of the fundamental frequency and the frequency points of its higher harmonics.

[0060] Preferably, the harmonic frequency set consists of the fundamental frequency and the frequency points of its fifth and lower harmonics.

[0061] Step S4: For each microphone array, based on the synchronized noise signal collected by each microphone, at each frequency point where the fundamental and higher harmonics exist in the harmonic frequency set, the angle is estimated by using the Multiple Signal Classification (MUSIC) algorithm to obtain the harmonic pseudo-spectrum of the microphone array at the frequency point.

[0062] Specifically, it includes:

[0063] Step S4.1) Divide the synchronized noise signal collected by each microphone into L time-domain snapshots, and perform a fast Fourier transform on each time-domain snapshot to obtain the complex spectrum;

[0064] Step S4.2) At each frequency point in the harmonic frequency set, extract the spectral value at the frequency point from the complex spectrum of all microphones to obtain the frequency domain snapshot vector corresponding to the frequency point;

[0065] Step S4.3) Based on the frequency domain snapshot vector corresponding to each frequency point, construct the sample covariance, perform feature decomposition on the sample covariance, separate the noise subspace, and then use the noise subspace to construct the harmonic pseudospectrum.

[0066] Step S5: Perform Bayesian multi-band uncertainty fusion on the harmonic pseudospectrum of each microphone array at all frequency points in the harmonic frequency set to obtain the estimated angle of the microphone array.

[0067] Specifically, the process of performing Bayesian multi-band uncertainty fusion on each microphone array includes:

[0068] Step S5.1) For each frequency point of the microphone array: normalize the harmonic pseudo-spectrum at the frequency point by the maximum value to obtain the normalized pseudo-spectrum; calculate the total harmonic energy according to the frequency domain snapshot vector corresponding to the frequency point, and obtain the temperature coefficient by mapping. The total energy of the frequency domain snapshot vector is used to represent the confidence level; after shaping the normalized pseudo-spectrum with the temperature coefficient, it is normalized into a probability map.

[0069] Step S5.2) Perform calculations and summation on the probability maps at all frequency points of the microphone array in the logarithmic domain to obtain a fused map;

[0070] Step S5.3) Peak picking is performed on the fused image to obtain the estimated angle of the microphone array.

[0071] Step S6: Calculate the estimated position of the UAV based on the estimated angles of all microphone arrays.

[0072] Specifically, this includes: obtaining the corresponding unit direction vector based on the estimated angle of each microphone array; and inputting the two-dimensional position vector and the corresponding unit direction vector of each microphone array into an overdetermined linear equation to solve for the estimated position of the UAV.

[0073] Specifically, the estimated position of the UAV is obtained by solving the following formula:

[0074]

[0075]

[0076] In the formula, Represents the identity matrix. Indicates the first The unit direction vector corresponding to each microphone array, with the superscript "T" indicating the transpose of the matrix. Indicates the first Two-dimensional position vectors of a microphone array Describes the first matrix. Represents the second matrix, This indicates the location of the drone.

[0077] In practice, the least squares method can be used to solve the problem.

[0078] This invention also provides an angle estimation and positioning system based on the fundamental and higher harmonic frequencies of an unmanned aerial vehicle (UAV), comprising:

[0079] A signal generator used to transmit linear frequency modulated signals;

[0080] Multiple microphone arrays are used to collect noise signals and linear frequency modulation signals emitted by the drone;

[0081] The harmonic detection module is used to obtain the set of harmonic frequencies based on the synchronized noise signal;

[0082] The angle estimation module is used to estimate the angle based on the synchronized noise signals collected by all microphones in the microphone array, and to obtain the harmonic pseudo-spectrum of the microphone array at each frequency point in the harmonic frequency set.

[0083] The fusion module is used to perform Bayesian multi-band uncertainty fusion on the harmonic pseudo-spectrum of the microphone array at all frequency points in the harmonic frequency set to obtain the estimated angle.

[0084] The position estimation module is used to calculate the estimated position of the UAV based on the estimated angles of all microphone arrays.

[0085] Specific embodiments of the present invention are as follows:

[0086] Example 1

[0087] Reference Figure 1 , Figure 2 , Figure 3 , Figure 4 As shown, this embodiment provides an angle estimation and positioning method based on the fundamental wave and higher harmonics of a UAV.

[0088] This embodiment specifically includes the following steps:

[0089] Step S1: Use multiple microphone arrays to collect noise signals emitted by the drone. During the collection process, a linear frequency modulation (Chirps) signal is transmitted simultaneously.

[0090] In this embodiment, the microphone array is an eight-element circular array with a radius of 7.5 cm. A customized signal has a duration of 10 ms, a frequency of 18~22 kHz, a sampling frequency of 48 kHz, and a signal refresh rate of 2 Hz. In actual implementation, the signal refresh rate can be adjusted based on experience.

[0091] Step S2: Synchronize the noise signals collected by each microphone array according to the linear frequency modulation signal to obtain the synchronized noise signals of each microphone array.

[0092] In this embodiment, the process of using a linear frequency modulated signal to perform soft synchronization between multiple microphone arrays includes:

[0093] microphone array Using the received signal as a reference signal, we calculate the microphone array within each synchronization cycle. Generalized cross-correlation between the received signal and the reference signal And estimate the inter-array delay. :

[0094]

[0095] Then, the microphone array The data stream is aligned using integer sample time shifting to obtain integer sample delay time. :

[0096]

[0097] Thus, microphone array Final synchronization sequence for:

[0098]

[0099] Where n represents the sampling point index.

[0100] Step S3: For each microphone array, perform a Fast Fourier Transform on the synchronized noise signal acquired by any microphone to obtain a spectrum. Then, use a harmonic detection algorithm to detect harmonics in the spectrum, identify the frequency points of the fundamental wave and its higher harmonics, and obtain a set of harmonic frequencies. In this embodiment, the signal length extracted for each detection is 0.1s.

[0101] The specific process is as follows:

[0102] For a given frame of audio signal Its analysis frequency band is Set the sampling rate to The window function is (Generally set to around 200Hz), the goal is to detect and associate the preceding frequencies. The frequency set of first harmonics .

[0103] First, for the input frame Perform a zero-filled Fast Fourier Transform (FFT) to calculate its one-sided amplitude spectrum:

[0104]

[0105] In the formula, Indicates input frame The single-sided amplitude spectrum, Indicates the input frame Perform a Fourier transform, where || represents the modulus of the complex number.

[0106] Optionally, for Smoothing is performed to reduce random fluctuations in spectral estimation.

[0107] Next, in the baseband region The point with the largest amplitude during the internal search is taken as the fundamental frequency:

[0108]

[0109] In the formula, This represents the fundamental frequency, corresponding to the fundamental component of the propeller's rotation. Indicates input frame The single-sided amplitude spectrum.

[0110] Subsequently, for each harmonic According to the frequency of the previous harmonic Prediction is performed to obtain the ideal harmonic frequency:

[0111]

[0112] In the formula, Indicates the first The ideal harmonic frequency of the first harmonic is This indicates the corrected harmonic frequency of the previous harmonic.

[0113] To counteract the effects of offsets or noise in the actual signal, within a window near the ideal harmonic frequency... By performing a local peak search, the corrected harmonic frequencies are obtained:

[0114]

[0115] In the formula, Indicates the first The corrected harmonic frequency of the first harmonic. Indicates input frame The single-sided amplitude spectrum.

[0116] Finally, by combining the fundamental frequency and the corrected harmonic frequencies of each order harmonic, the complete set of harmonic frequencies is obtained. In this embodiment, K is set to 5.

[0117] Step S4: For each microphone array, based on the synchronized noise signal collected by each microphone, at each frequency point where the fundamental and higher harmonics exist in the harmonic frequency set, the angle is estimated by using the Multiple Signal Classification (MUSIC) algorithm to obtain the harmonic pseudo-spectrum of the microphone array at the frequency point.

[0118] To fully utilize the established line spectrum prior in the amplitude spectrum, a narrowband MUSIC subspace method is used for each harmonic frequency point. Perform DoA estimation. The geometry and isotropic nature of the uniform circular array (UCA) make it particularly suitable for UAV acoustic localization tasks that require 360° azimuth coverage.

[0119] Let the radius of UCA be... , This indicates the starting azimuth angle of the microphone array (determined based on the array's placement). Then the... The polar angles of the microphones are:

[0120]

[0121] In the formula, Indicates the first The polar angle of each microphone, The azimuth angle represents the starting angle of the microphone array, m represents the microphone number, and M represents the total number of microphones in the microphone array.

[0122] No. The three-dimensional coordinates corresponding to each microphone are:

[0123]

[0124] In the formula, Indicates the first The three-dimensional coordinates of the microphones, where R represents the radius of the uniform circular array.

[0125] Arrival direction is indicated by azimuth. and elevation angle The incident unit vector is described as follows:

[0126]

[0127] At the speed of sound Under the far-field plane wave assumption, the first The relative time delay of each microphone with respect to the array reference point for:

[0128]

[0129] Among them, the corresponding steering components for:

[0130]

[0131] In the formula, j represents the imaginary unit.

[0132] Among them, array guide vector Represented as:

[0133]

[0134] The length from each microphone is data frames Divide evenly There are M snapshots, with each microphone acting as a channel. The signal length is 0.1 seconds, N=4800, and the number of snapshots L can be set empirically. The segment length L of each snapshot is... s for:

[0135]

[0136] Among them, the snapshot index is For each snapshot of each channel, calculate Point FFT yields the complex spectrum. .

[0137] for First harmonic frequency ,in This represents the sampling rate, and the corresponding frequency binning index. The calculation is as follows:

[0138]

[0139] In the formula, round() represents the floor function. express The frequency response index of the first harmonic frequency response. Indicates the sampling rate. This represents the number of FFT points.

[0140] exist First harmonic frequency point Complex spectral values ​​are extracted from all channels and formed into a frequency domain snapshot vector. :

[0141]

[0142] In the formula, This indicates that the l-th snapshot of the m-th channel is in First harmonic frequency The spectral value at that location.

[0143] Using data frames First harmonic frequency Based on L frequency domain snapshots, the estimated sample covariance is:

[0144]

[0145] In the formula, express First harmonic frequency The sample covariance of the corresponding frequency domain snapshot vector, l represents the snapshot index, L represents the total number of snapshots, and the superscript H represents the conjugate transpose.

[0146] Then, to Perform eigenvalue decomposition (or SVD) and, under the single-source assumption, obtain the noise subspace. .

[0147] On a predefined angle grid, First harmonic frequency MUSIC pseudo-spectrum at the location It is expressed as follows:

[0148]

[0149] In the formula, express First harmonic frequency The array guide vector at that location, The superscript H denotes the noise subspace.

[0150] Step S5: Perform Bayesian multi-band uncertainty fusion on the harmonic pseudospectrum of each microphone array at all frequency points in the harmonic frequency set to obtain the estimated angle of the microphone array.

[0151] Given the fundamental and higher-order harmonics caused by the propellers observed during UAV flight, different harmonics MUSIC pseudo-spectrum at the location Typically, significant differences are observed in SNR, sidelobe structure, and peak sharpness: some harmonics within a frame have high energy and sharp peaks (low variance, reliable), while other harmonics are broadened due to spectral leakage or attitude changes, and may even be dominated by noise. Simply averaging or summing the cross-band spectrum flattens strong bands, while a single anomalous harmonic can introduce spurious peaks. This invention employs Bayesian multi-band uncertainty fusion: first, each harmonic surface is normalized to a common scale; then, the confidence of each band is encoded by an energy-related "temperature / sharpening" coefficient; and each band is interpreted as a probability accumulated in the logarithmic domain (equivalently, multiplied by the probability). This method has three advantages: adaptive weighting—higher energy harmonics have a greater impact, approximating the "low variance, high weight" principle; consistency-based denoising—only angles supported by multiple harmonics can significantly improve the posterior and suppress spurious single-band peaks; and numerical stability—normalization and logarithmic domain accumulation can mitigate cross-band scale mismatch and avoid product underflow, thus contributing to robust implementation. In this embodiment, the final angle search is performed in steps of 0.5 degrees.

[0152] The specific process is as follows:

[0153] To eliminate interband amplitude scale differences, each harmonic pseudospectrum is normalized using its maximum value:

[0154]

[0155] In the formula, express First harmonic frequency The normalized pseudospectral at the given location has a value range of [0,1]. Indicates the harmonic pseudo-spectrum From all possible angles The maximum value on.

[0156] Therefore, subsequent temperature-based shaping only affects the surface shape, not its absolute size. Within the current data frame, the... One harmonic The total energy across all frequency domain snapshots is used as a proxy for the confidence score:

[0157]

[0158] In the formula, express First harmonic frequency place The total energy over a frequency domain snapshot, || ||2 represents the calculation of the L2 norm.

[0159] The first One harmonic Total energy on each frequency domain snapshot Mapping to the temperature coefficient, we obtain the temperature coefficient of the k-th harmonic. :

[0160]

[0161] In the formula, K represents the total energy of all harmonics, where K represents the total number of harmonics. Index representing harmonics.

[0162] make sure .when At that time, surface Sharpening (sharper peaks, lower sidelobes); when At this time, the surface flattens. Therefore, higher-energy harmonics (which are usually associated with higher signal-to-noise ratios and larger peak curvatures) contribute more to the fusion, which is consistent with the principle that low-variance estimates should receive greater weight.

[0163] Then, the surface of each temperature shape is standardized into a probability map:

[0164]

[0165] Assuming that the harmonics are conditionally independent, the frame-level posterior probability is proportional to the product of the likelihoods of each individual frequency band. To ensure numerical stability, we perform calculations and summation in the logarithmic domain to obtain the fused graph. :

[0166]

[0167] in, It is a way to avoid occurrence Small constant (recommended value) (roughly matching the grid resolution). The resulting fused image. It is used as the posterior probability of the fusion angle in the subsequent peak detection step.

[0168] In the fusion diagram Peak picking is performed on the data frame to obtain the final DoA:

[0169]

[0170] Step S6: Calculate the estimated position of the UAV based on the estimated angles of all microphone arrays. The process is as follows:

[0171] Assuming deployment The microphone array group, the first Two-dimensional position of a microphone array for:

[0172]

[0173] After soft synchronization and preprocessing, each array estimates the UAV's direction of arrival (DoA) and generates... Time series of arrival directions , where t is the data frame index.

[0174] To mitigate systematic bias, offsets are calibrated sequentially using array geometry and baseline measurements. For each time frame... drone location Represented as:

[0175]

[0176] in, , These represent the coordinates of the UAV in the x and y directions on the horizontal plane, respectively.

[0177] No. The unit direction vector corresponding to DoA measured by a microphone array for:

[0178]

[0179] In the formula, They represent the first The azimuth angle of the array in the DoA measured in the t-th time frame.

[0180] Using direction vectors and array positions Based on the geometric relationship between them, establish overdetermined linear equations:

[0181]

[0182] In the formula, Represents the identity matrix. Indicates the first The unit direction vector corresponding to the DoA measured by each microphone array. Indicates the first Two-dimensional position of a microphone array The superscript T indicates the location of the drone, and the superscript T indicates the transpose of the matrix.

[0183] All The overdetermined linear equations in the arrays are stacked together to obtain:

[0184]

[0185]

[0186] In the formula, Describes the first matrix. This represents the second matrix.

[0187] The final result can be expressed as:

[0188] q'(t)=(A(t) T A(t)) -1 A(t) T b(t)

[0189] In the formula, q'(t) represents the estimated position of the UAV, A(t) represents the first matrix, the superscript T represents the transpose of the matrix, the superscript "-1" represents the inverse matrix, and b(t) represents the second matrix.

[0190] In this embodiment, the method was tested under both line-of-sight and non-line-of-sight conditions, and the results are as follows. Figure 5 As shown, the root mean square error is 0.188m in a line-of-sight environment and 0.330m in a non-line-of-sight environment.

[0191] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope of the present invention.

Claims

1. A method for angle estimation and positioning based on fundamental and higher harmonic waves of a UAV, characterized in that, Includes the following steps: Step S1: Use multiple microphone arrays to collect noise signals emitted by the drone. During the collection process, a linear frequency modulated signal is transmitted simultaneously. Step S2: Synchronize the noise signals collected by each microphone array according to the linear frequency modulation signal to obtain the synchronized noise signals of each microphone array. Step S3: For each microphone array, perform a fast Fourier transform on the synchronized noise signal collected by any microphone to obtain a spectrum. Perform harmonic detection on the spectrum to obtain a set of harmonic frequencies. The set of harmonic frequencies consists of the frequency points of the fundamental wave and its higher harmonics. Step S4: For each microphone array, based on the synchronized noise signal collected by each microphone, at each frequency point in the harmonic frequency set, the harmonic pseudo-spectrum of the microphone array at the frequency point is obtained by angle estimation. Step S5: Perform Bayesian multi-band uncertainty fusion on the harmonic pseudospectrum of each microphone array at all frequency points to obtain the estimated angle; Step S6: Calculate the estimated position of the UAV based on the estimated angles of all microphone arrays.

2. The angle estimation and positioning method based on UAV fundamental wave and higher harmonics according to claim 1, characterized in that: In step S1, the duration of linear frequency modulation is 10~100ms, the frequency is 18~22kHz, the sampling frequency is 48kHz, and the signal refresh rate is 2~10Hz.

3. The angle estimation and positioning method based on UAV fundamental wave and higher harmonics according to claim 1, characterized in that: Step S2 includes: using the noise signal collected by any microphone array as a reference noise signal, calculating the inter-array delay between the noise signal collected by the microphone array and the reference noise signal for each of the other microphone arrays, and aligning the noise signal according to the inter-array delay by integer sample time shifting to obtain the synchronized noise signal.

4. The angle estimation and positioning method based on UAV fundamental wave and higher harmonics according to claim 1, characterized in that: In step S3, the harmonic frequency set consists of the fundamental frequency and the frequency points of its fifth and lower harmonics.

5. The angle estimation and positioning method based on UAV fundamental wave and higher harmonics according to claim 1, characterized in that: Step S4 includes: The synchronized noise signal collected by each microphone is evenly divided into L time-domain snapshots, and a fast Fourier transform is performed on each time-domain snapshot to obtain the complex spectrum. At each frequency point in the harmonic frequency set, the spectral value is extracted from the complex spectrum of all microphones to obtain the frequency domain snapshot vector corresponding to the frequency point; Based on the frequency domain snapshot vector corresponding to each frequency point, the sample covariance is constructed, the sample covariance is decomposed into features to separate the noise subspace, and then the harmonic pseudospectrum is constructed.

6. The angle estimation and positioning method based on UAV fundamental wave and higher harmonics according to claim 1, characterized in that: In step S5, the process of performing Bayesian multi-band uncertainty fusion on each microphone array includes: For each frequency point of the microphone array: the harmonic pseudo-spectrum at the frequency point is normalized by the maximum value to obtain the normalized pseudo-spectrum; the total harmonic energy is calculated based on the frequency domain snapshot vector corresponding to the frequency point, and the temperature coefficient is obtained by mapping. The total energy of the frequency domain snapshot vector is used to represent the confidence level; the normalized pseudo-spectrum is shaped using the temperature coefficient and then normalized into a probability map. For the probability maps at all frequency points of the microphone array, the operations are performed in the logarithmic domain and accumulated to obtain the fused map; Peak picking is performed on the fused image to obtain the estimated angle of the microphone array.

7. The angle estimation and positioning method based on UAV fundamental wave and higher harmonics according to claim 1, characterized in that: Step S6 includes: obtaining the corresponding unit direction vector based on the estimated angle of each microphone array; inputting the two-dimensional position vector and the corresponding unit direction vector of each microphone array into an overdetermined linear equation to solve for the estimated position of the UAV.

8. The angle estimation and positioning method based on UAV fundamental wave and higher harmonics according to claim 7, characterized in that: In step S6, the estimated position of the UAV is obtained by solving the following formula: In the formula, Represents the identity matrix. Indicates the first The unit direction vectors corresponding to each microphone array, with the superscript "T" indicating the transpose of the matrix. Indicates the first Two-dimensional position vectors of a microphone array Describes the first matrix. Represents the second matrix, This indicates the location of the drone.

9. The angle estimation and positioning method based on UAV fundamental wave and higher harmonics according to claim 1, characterized in that: In step S1, the microphone arrays are all circular arrays.

10. An angle estimation and positioning system based on UAV fundamental wave and higher harmonics, used to implement the angle estimation and positioning method based on UAV fundamental wave and higher harmonics as described in any one of claims 1 to 9, characterized in that, include: A signal generator used to transmit linear frequency modulated signals; Multiple microphone arrays are used to collect noise signals and linear frequency modulation signals emitted by the drone; The harmonic detection module is used to obtain the set of harmonic frequencies based on the synchronized noise signal; The angle estimation module is used to estimate the angle based on the synchronized noise signals collected by all microphones in the microphone array, and to obtain the harmonic pseudo-spectrum of the microphone array at each frequency point in the harmonic frequency set. The fusion module is used to perform Bayesian multi-band uncertainty fusion on the harmonic pseudo-spectrum of the microphone array at all frequency points in the harmonic frequency set to obtain the estimated angle. The position estimation module is used to calculate the estimated position of the UAV based on the estimated angles of all microphone arrays.

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