Radar echo signal amplitude fourier transform method under staggered pulse repetition intervals

Abstract

This invention relates to the field of radar signal processing technology, and provides a method for Fourier transform of radar echo signal amplitude under staggered pulse repetition intervals, including: signal reconstruction: confirming the staggered pulse repetition interval, understanding the formation mechanism of the staggered pulse repetition interval through time-domain multiplication, and reconstructing the signal column vector to obtain a uniform sampling interval; Fourier transform under the uniform sampling interval: performing Fourier transforms of the staggered pulse repetition interval column vector and the reconstructed signal column vector, and calculating the amplitude spectral density; matrix generation and obtaining the amplitude spectral density of the real radar echo signal: reconstructing the staggered pulse repetition interval amplitude spectral density column vector and the reconstructed signal column vector amplitude spectral density column vector into a matrix, obtaining the amplitude spectral density matrix of the deconstructed signal based on frequency domain deconvolution of the amplitude spectral density, converting the matrix into a vector, and removing ground clutter and image frequency components to extract the effective amplitude spectral density. This invention solves the problem of converting radar signals with staggered pulse repetition intervals from the time domain to the frequency domain.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing technology, and in particular to a method for Fourier transform of radar echo signal amplitude under staggered pulse repetition intervals. Background Technology

[0002] The general method for frequency-domain radar signal processing is to perform a Discrete Fourier Transform (DFT) on the time-domain signal under a single pulse repetition interval (also known as a period). This method can only process uniformly sampled signals. Specifically, the signal is processed by arranging a certain number of pulse echo signals at the same range gate into a column vector, which is the time-domain sequence. To reduce frequency leakage, this time-domain sequence can also be processed by windowing similar to Von Hann. Then, a normal DFT is performed to obtain the echo signal sequence in the frequency domain. This processing method is mainly used for frequency-domain processing of radar echo signals using a single pulse repetition interval.

[0003] To improve radar performance and resolve the dilemma of range and velocity ambiguity, ensuring both unambiguous range and velocity meet requirements, staggered pulse repetition intervals are typically used in radar operating mode design. However, since the pulse repetition interval is not uniform, the corresponding sampling frequency is naturally non-uniform. Normal Discrete Fourier Transform (DFT) requires uniform sampling frequency, making this transformation impossible.

[0004] In many applications, radar detection signals can achieve better results if frequency domain processing is used, such as eliminating ground objects and co-channel interference clutter, and extracting multi-peak characteristics of signal velocity.

[0005] Clearly, Fourier transform techniques under staggered pulse repetition intervals become necessary. Summary of the Invention

[0006] This invention provides a method for Fourier transform of radar echo signal amplitude under staggered pulse repetition intervals, which solves the problem of converting radar signals with staggered pulse repetition intervals from the time domain to the frequency domain, and provides a foundation for high-performance frequency domain processing of radar echo signals.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] The Fourier transform method for radar echo signal amplitude under staggered pulse repetition intervals includes:

[0009] Signal reconstruction: confirming the staggered pulse repetition interval T 1 and T 2, of which T 1= n 1T u , T 2= n 2 T u , n 2= n 1+1, T u This is the virtual sampling time interval. n 1 is a natural number from 2 to 10; obtain the total number of staggered pulses of gates at the same distance. M , M If the number is even, calculate the minimum period. p =( n 1+ n 2); For T 1 corresponds to pulse complement ( n 1-1) zero-value samples, for T 2 corresponds to pulse complement ( n 2-1) zero-value samples, resulting in a length of N = pM / 2 uniform sampling sequence v i ;

[0010] Fourier transform under uniform sampling interval: for uniform sampling sequence v i After windowing, a discrete Fourier transform is performed to obtain the amplitude spectral density of the reconstructed signal column vector.

[0011] Calculation of matrix generation and acquisition of amplitude spectral density of real radar echo signal: Constructing coded sequence c i Its length is N Used to label uniformly sampled sequences v i The actual sample location in the encoded sequence; c i Perform a discrete Fourier transform to obtain the convolution matrix, and then simplify based on the periodicity of this convolution matrix to obtain... p*p The amplitude deconvolution inverse matrix is ​​obtained; the amplitude spectral density column vectors corresponding to the staggered pulse repetition interval and the amplitude spectral density column vectors of the reconstructed signal are reconstructed into a matrix, and the matrix is ​​deconvolved in the frequency domain by the amplitude deconvolution inverse matrix to obtain the amplitude spectral density matrix of the deconstructed signal. The matrix is ​​converted into column vectors, and ground clutter elimination and image frequency component elimination are performed in sequence to obtain the effective amplitude spectral density.

[0012] In this specification, the total number of zeros padded in the signal reconstruction is ( p -2) M / 2.

[0013] In this specification, the windowing process used in the Fourier transform under uniform sampling interval is the von Hanning window, and the discrete Fourier transform is performed on the windowed sequence. w n * v i The transformation is performed, where n is the time series index. w n These are the coefficients of the nth window function.

[0014] In this specification, the encoded sequence c i The construction method is as follows: in a uniformly sampled sequence v i In this process, the actual sample positions are marked as 1, and the zero-filled positions are marked as 0, forming a periodic sequence with a period of . p .

[0015] In this specification, the method for obtaining the magnitude deconvolution inverse matrix is ​​as follows: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] c i The amplitude of the discrete Fourier transform result is used to obtain the amplitude convolution matrix abs{ C}, for abs{ C Inverse the matrix to obtain the magnitude deconvolution inverse matrix [abs{ C}] -1 .

[0016] In this specification, the steps for eliminating ground clutter are as follows: determining the zero velocity and image frequency. q At each ground clutter location, with each ground clutter location as the center, the ground clutter velocity spectrum width... W gnd Within the specified range, the spectral density values ​​within that range are set to the noise power spectral density values.

[0017] In this specification, the steps for eliminating image frequency components are as follows: by searching for the maximum value at each range gate, continuous sliding median filtering is performed on the position of the maximum value in the velocity-range two-dimensional space to determine the center position of the main frequency domain interval; with this center position as the center, in The spectral density is retained within a certain range, and the remaining part is set as the noise power spectral density value.

[0018] This specification includes a precipitation echo compensation step before obtaining the effective amplitude spectral density: using a velocity spectral width greater than that of ground clutter. W gnd speed value Taking the left side of the reference as the benchmark, we take the left side of the reference as... The right side is The interval is defined, and linear interpolation is performed within this interval, where the preset compensation range parameter is used. .

[0019] In this specification, the length of the amplitude spectral density column vector of the staggered pulse repetition interval is... N Its positive and negative boundary frequencies are The corresponding conversion speed is ,in, This refers to the operating wavelength of the radar.

[0020] In this specification, when the ratio of the staggered pulse repetition interval is 2:3 to 8:9, the amplitude deconvolution inverse matrix is ​​a matrix of 5×5 to 15×15.

[0021] In summary, the present invention has at least the following beneficial effects:

[0022] Solving core technical challenges: Breaking through the limitation that the traditional Discrete Fourier Transform is only applicable to uniformly sampled signals, it has for the first time realized the amplitude conversion of radar echo signals from the time domain to the frequency domain under staggered pulse repetition intervals, providing a feasible solution for the frequency domain processing of non-uniformly sampled signals.

[0023] Improving the accuracy of amplitude spectral density estimation: through signal reconstruction (zero-padding to form uniform sampling) and deconvolution of periodic matrices (using the amplitude inverse matrix [abs{ C}] -1 These steps effectively eliminate the inherent frequency leakage caused by zero-padding, accurately restore the amplitude spectral density of the real radar echo, and avoid errors caused by direct transformation.

[0024] Extending Radar Performance Boundaries: Through Virtual Sampling Intervals T u The design extends the unambiguous speed of the radar to... λ / ( 4T u Compared to the traditional single-pulse repetition interval scheme, it significantly improves the unambiguous velocity range and can better adapt to the detection needs of high-speed targets (such as UAVs) or wide velocity spectrum signals.

[0025] Enhanced anti-interference capability: Elimination through ground clutter (based on ground clutter velocity spectrum) W gnd Zeroing, image frequency component elimination (identifying the main frequency range and retaining the effective signal), and rain echo compensation (linear interpolation to repair the effective signal in the ground clutter area) significantly reduce the impact of ground object interference, image frequency leakage, and meteorological clutter on the effective signal, making the frequency domain characteristics of radar echoes clearer.

[0026] Improved processing efficiency and practicality: For common stagger ratios from 2:3 to 8:9, amplitude inversion matrices of 5×5 to 15×15 are preset, which can be directly obtained by looking up the table, reducing the amount of real-time calculation and facilitating engineering applications; at the same time, the design of discarding phase information simplifies the processing flow while meeting the needs of most scenarios (such as ground clutter elimination and velocity feature extraction).

[0027] Expanding application scenarios: It can be directly applied to equipment such as dual-polarization Doppler weather radar, effectively supporting tasks such as severe weather monitoring, insect and bird migration tracking, and forest fire detection. It performs particularly well in the detection of meteorological echoes (with rapidly changing amplitude) and high-speed moving targets (such as drones), improving the radar's detection accuracy in complex scenarios. Attached Figure Description

[0028] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a schematic diagram of the uneven pulse repetition interval sampling uniformization process involved in this invention.

[0030] Figure 2 The Feng involved in this invention A schematic diagram of the Hanning window.

[0031] Figure 3 This is a schematic diagram of the power spectrum of the image frequency without ground objects over a distance of 15km involved in this invention.

[0032] Figure 4 This is a schematic diagram of the power spectrum of the image frequency and ground objects over a distance of 8km involved in this invention.

[0033] Figure 5 This is a schematic diagram of the distance-power spectrum distribution of the discrete Fourier transform of the 4:5 staggered pulse repetition period involved in this invention, including the image frequency and ground clutter.

[0034] Figure 6 This is a schematic diagram of the distance-power spectrum distribution of the discrete Fourier transform of the 4:5 staggered pulse repetition period involving image frequency ground clutter, which is involved in this invention.

[0035] Figure 7 This is a schematic diagram of the distance-power spectrum distribution of the discrete Fourier transform for image frequency and ground clutter removal using a 4:5 staggered pulse repetition period involved in this invention.

[0036] Figure 8-aThis is a schematic diagram of the target rapidly changing complex signal involved in this invention (solid lines represent in-phase - real part I signals, and dashed lines represent orthogonal - imaginary part Q signals, such as meteorological echo signals).

[0037] Figure 8-b This is a schematic diagram of the target fast-moving complex signal involved in this invention (solid lines represent in-phase - real part I signals, and dashed lines represent orthogonal - imaginary part Q signals, such as UAV echo signals).

[0038] Figure 9 This is a schematic diagram of the uneven pulse repetition interval UAV echo sampling homogenization processing involved in this invention.

[0039] Figure 10 This is a schematic diagram of a 5×5 inverse matrix of staggered pulse repetition intervals with a staggered ratio of 2:3 involved in this invention.

[0040] Figure 11 This is a schematic diagram of a 7×7 inverse matrix of staggered pulse repetition intervals with a staggered ratio of 3:4 involved in this invention.

[0041] Figure 12 This is a schematic diagram of a 9×9 inverse matrix with a staggered pulse repetition interval of 4:5 involved in the present invention.

[0042] Figure 13 This is a schematic diagram of an 11×11 inverse matrix of staggered pulse repetition intervals with a staggered ratio of 5:6 involved in this invention.

[0043] Figure 14 This is a schematic diagram of a 12×12 inverse matrix of staggered pulse repetition intervals with a staggered ratio of 6:7 involved in this invention.

[0044] Figure 15 This is a schematic diagram of a 13×13 inverse matrix with a staggered pulse repetition interval of 7:8 involved in this invention.

[0045] Figure 16 This is a schematic diagram of a 15×15 inverse matrix of staggered pulse repetition intervals with a staggered ratio of 8:9 involved in this invention. Detailed Implementation

[0046] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the embodiments of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0047] The following disclosure provides many different implementations or examples for carrying out different structures of the embodiments of the present invention. To simplify the disclosure of the embodiments of the present invention, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the embodiments of the present invention. Furthermore, reference numerals and / or reference letters may be repeated in different examples of the embodiments of the present invention; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various implementations and / or arrangements discussed.

[0048] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0049] like Figure 1 As shown, this embodiment provides a method for Fourier transform of radar echo signal amplitude under staggered pulse repetition intervals, including:

[0050] Signal reconstruction: confirming the staggered pulse repetition interval T 1 and T 2, of which T 1= n 1 T u , T 2= n 2 T u , n 2= n 1+1, T u This is the virtual sampling time interval. n 1 is a natural number from 2 to 10; obtain the total number of staggered pulses of gates at the same distance. M , M If the number is even, calculate the minimum period. p =( n 1+ n 2); For T 1 corresponds to pulse complement ( n 1-1) zero-value samples, for T 2 corresponds to pulse complement ( n 2-1) zero-value samples, resulting in a length of N = pM / 2 uniform sampling sequence v i ;

[0051] Fourier transform under uniform sampling interval: for uniform sampling sequence v i After windowing, a discrete Fourier transform is performed to obtain the amplitude spectral density of the reconstructed signal column vector.

[0052] Calculation of matrix generation and acquisition of amplitude spectral density of real radar echo signal: Constructing coded sequence ci Its length is N Used to label uniformly sampled sequences v i The actual sample location in the encoded sequence; c i Perform a discrete Fourier transform to obtain the convolution matrix, and then simplify based on the periodicity of this convolution matrix to obtain... p*p The amplitude deconvolution inverse matrix is ​​obtained; the amplitude spectral density column vectors corresponding to the staggered pulse repetition interval and the amplitude spectral density column vectors of the reconstructed signal are reconstructed into a matrix, and the matrix is ​​deconvolved in the frequency domain by the amplitude deconvolution inverse matrix to obtain the amplitude spectral density matrix of the deconstructed signal. The matrix is ​​converted into column vectors, and ground clutter elimination and image frequency component elimination are performed in sequence to obtain the effective amplitude spectral density.

[0053] In some embodiments, the total number of zeros padded in the signal reconstruction is ( p -2) M / 2.

[0054] In some embodiments, in the Fourier transform under the uniform sampling interval, the windowing process uses the von Hanning window, and the discrete Fourier transform is performed on the windowed sequence. w n * v i The transformation performed.

[0055] In some embodiments, the encoded sequence c i The construction method is as follows: in a uniformly sampled sequence v i In this process, the actual sample positions are marked as 1, and the zero-filled positions are marked as 0, forming a periodic sequence with a period of . p .

[0056] In some embodiments, the magnitude deconvolution inverse matrix is ​​obtained by: processing the encoded sequence. c i The amplitude of the discrete Fourier transform result is used to obtain the amplitude convolution matrix abs{ C}, for abs{ C Inverse the matrix to obtain the magnitude deconvolution inverse matrix [abs{ C}] -1 .

[0057] In some embodiments, the ground clutter cancellation step includes: determining the zero velocity and image frequency. q At each ground clutter location, with each ground clutter location as the center, the ground clutter velocity spectrum width... W gnd Within the specified range, the spectral density values ​​within that range are set to the noise power spectral density values.

[0058] In some embodiments, the image frequency component elimination step comprises: determining the center position of the main frequency domain interval by searching for the maximum value at each range gate and performing continuous sliding median filtering on the position of the maximum value in the velocity-range two-dimensional space; using this center position as the center, in The spectral density is retained within a certain range, and the remaining part is set as the noise power spectral density value.

[0059] In some embodiments, before obtaining the effective amplitude spectral density, a precipitation echo compensation step is included: with a velocity spectral width greater than that of ground clutter. W gnd speed value Taking the left side of the reference as the benchmark, we take the left side of the reference as... The right side is The interval is defined, and linear interpolation is performed within this interval, where the preset compensation range parameter is used. .

[0060] In some embodiments, the length of the amplitude spectral density column vector of the staggered pulse repetition interval is N Its positive and negative boundary frequencies are The corresponding conversion speed is .

[0061] In some embodiments, when the ratio of the staggered pulse repetition interval is 2:3 to 8:9, the amplitude deconvolution inverse matrix is ​​a matrix of 5×5 to 15×15.

[0062] The technical concept of this invention is as follows:

[0063] The Fourier transform method for radar echo signal amplitude under staggered pulse repetition intervals includes:

[0064] Signal reconstruction: confirmation of staggered pulse repetition interval, formation mechanism of staggered pulse repetition interval by time-domain multiplication, and signal column vector reconstruction to obtain uniform sampling interval.

[0065] Staggered repeat interval T 1 and T 2. Launch, must meet the following requirements T 1= n 1 T u， T 2= n 2 T u ,and n 2= n A strict 1+1 relationship. Among them, T u = T 2- T 1 represents the virtual sampling time interval.n 1 = The natural numbers 2, 3, 4, ..., 10.

[0066] The total number of pulses with the same distance gate staggered pulse repetition interval is M (Even number). At this time, according to n 1 and n The value of 2 is used to calculate the minimum period for the subsequent Fourier transform. p =( n 1+ n 2). Using virtual sampling time intervals T u Based on this, it can be considered that the original M If a sequence of points with uneven repeating time intervals is considered as having uniform repeating time intervals, then... T Part 1 needs to be supplemented ( n 1-1) zero-value samples, while T Part 2 needs to be supplemented ( n 2-1) Zero-value samples, the total number of pulses with the same pulse repetition interval at the same distance gate becomes N = pM / 2, of course the actual number of zeros padded is ( p -2) M / 2. It should be noted here that pulse repetition interval and sampling pulse interval have the same meaning, but are referred to differently in radar signals and frequency domains.

[0067] As a result, after zero-padding, the time-domain sequence became a sequence of length [length missing]. N The uniform sampling sequence is denoted as v i ,like Figure 1 As shown.

[0068] Calculation matrix generation and acquisition of amplitude spectral density of real radar echo signal: The amplitude spectral density column vector of staggered pulse repetition interval and the amplitude spectral density column vector of reconstructed signal are reconstructed into a matrix. The amplitude spectral density matrix of the deconstructed signal is obtained by frequency domain deconvolution based on the amplitude spectral density. The matrix is ​​converted into a vector, and the effective amplitude spectral density is extracted by removing ground clutter and image frequency components.

[0069] set up c i For length is N The encoded sequence is used to convert the original staggered samples. g i Mapping to uniform sampling sequence v i During the process, v i The zero-padding positions in the data are marked as 0, and the corresponding samples are... g i The position is marked as 1.

[0070] For pulse repetition interval variance ratio is K = T 1 / T 2= n 1 / n 2. At this time,

[0071] ;

[0072] set up e i The signal is delivered at uniform time intervals. T u The sampled sequence, of course, is unknown, and e i = g i Then it can be used. e i and c i Product representation v i ,Right now:

[0073] ;

[0074] Taking the discrete Fourier transform, we obtain the spectrum:

[0075] ;

[0076] symbol DFT Represents the Discrete Fourier Transform, symbol This represents convolution.

[0077] Obviously, to make the above expression computable, it needs to be transformed into matrix form.

[0078] The formation of the deconvolution inverse matrix from the encoded vector. First, we study the pulse repetition interval stagger ratio. K Encoding sequence c i The discrete Fourier transform, i.e. DFT ( c i ). c i For p As a periodic sequence, based on the properties of "discrete-periodic" signals in the time domain, its frequency domain also exhibits "discrete-periodic" characteristics. If the phase variation is ignored, its amplitude spectrum is completely periodic.

[0079] Therefore, C k = DFT ( c iOne period of a vector can represent the entire amplitude spectrum of its length N. If the column vector... C k Performing a circular shift can create a N * N convolution matrix C total Based on its periodicity, it can actually be simplified to a... p*p The deconvolution inverse matrix C In the formulas that follow, use subscripts. r It is represented as a rearranged matrix.

[0080] ;

[0081] ;

[0082] Similarly, E k = DFT ( e i ), V k = DFT ( v i ).because C Periodicity, column vector E k It can be decomposed into p*M matrix E express:

[0083] ;

[0084] column vector V k It can also be broken down into p*M matrix V express:

[0085] ;

[0086] Therefore, the deconvolution inverse matrix is ​​used to replace the encoding sequence. c i Yes, the relationship in the frequency domain has become multiplication. Removing the rearranged indices, we get:

[0087] ;

[0088] Obviously, if the convolution matrix C If it is inverseable, then multiply the left side by a... C By reversing the matrix, we can obtain the desired result. E Formation.

[0089] To calculate power from the spectrum, the convolution matrix... CWe need to normalize it so that each column vector is a unit vector. At the same time, the row vectors are also normalized.

[0090] However, the rank of the convolution matrix, which equals the number of stochastic samples M, is singular and cannot be inverted; therefore, its inverse cannot be used to calculate... E k If the phase information of each element in the convolution matrix is ​​discarded, the matrix becomes non-singular. Thus, the amplitude spectral density abs{ can be successfully calculated. E At this point, the simplified convolution matrix abs{ C} is reversible. Therefore, it can be used to invert abs{ E k}

[0091] ;

[0092] Where, abs{ V} and abs{ E}for p*M The matrix is ​​represented by column vectors abs{ V k} and abs{ E k The matrix representation of} contains completely identical content. This enables the estimation of the amplitude spectral density of staggered pulse repetition intervals.

[0093] To accurately represent the amplitude spectral density, the matrix abs{ E} Restore to N *1 column vector abs{ E k}

[0094] The column vector abs{ for estimating the amplitude spectral density of staggered pulse repetition intervals E k} length is N The positive and negative boundary frequencies are Converted to speed, it is Clearly, the speed of achieving unambiguity has been greatly improved at this point.

[0095] The above calculation process does not mention amplitude weighting. In fact, for time-domain column vector sequences... v i Perform Discrete Fourier Transform DFT ( v i Before performing a discrete Fourier transform (DFT), windowing is required to prevent frequency leakage. The windowing process involves... Figure 2 The Feng shown The von Hann window, whose window function is expressed as follows, where,D = N +1 represents the window length. n =0,1, 2, …, N The Discrete Fourier Transform becomes DFT ( w n * v i ).

[0096] ;

[0097] As mentioned above, [abs{ C}] -1 It is an inverse amplitude deconvolution matrix, and it expresses all repeating periods using one period. Clearly, the amplitude spectral density estimated from this also has the same periodicity. In fact, in the frequency domain, this will appear... p The strongest amplitude spectral density range is outside the main amplitude spectral density range, while the weaker ranges are the image frequencies. This is a fundamental leakage caused by a small amount of valid data and a large number of zero values.

[0098] If the radar signal is narrowband, or in other words, considering the velocity spectrum width, if the velocity spectrum width is less than... If the effective amplitude spectral density does not alias at the image frequency, then this is a necessary condition for the feasibility of this method. In fact, in the vast majority of observations, no individual case has been found where this condition does not hold.

[0099] Figure 3 This represents the power spectral density at a distance of 30m with weak image frequencies and no ground clutter at a distance of 15km. The square of the amplitude is the power, so it is a typical frequency domain result.

[0100] Due to the imperfections of the radar lobe, the extended portion of the antenna main lobe, as well as the side lobe components near the ground end, especially in the close-range area, will eliminate severe ground clutter interference. Figure 4 The image shows a typical power spectrum at a distance of 8km, including image frequencies and ground features at a distance of 30m resolution.

[0101] The signal's behavior is not easily discernible from this spectral density. However, by connecting more range gates, a two-dimensional image of the spectral density distribution over distance can be obtained, such as... Figure 5 The figure shows the distance-power spectrum distribution of the discrete Fourier transform of a 4:5 staggered pulse repetition period, including image frequencies and ground clutter. The main amplitude spectral density range and the weaker image frequency range are clearly visible in the figure; of course, there is also the ground clutter frequency band near zero velocity and above the image frequency.

[0102] Because ground clutter can be stronger than normal signals, eliminating ground feature components is a necessary task.

[0103] Zero speed and its mirror frequency q The location of local clutter can be represented as follows: ,in, .

[0104] Due to factors such as wind and grass movement, the frequency or velocity of ground clutter is not always zero. By observation, the velocity spectral width (which is essentially the standard deviation) of ground clutter can be obtained, denoted as [missing information]. W gnd Based on the location of ground clutter Centered on, with W gnd For the speed range, i.e. Then, all spectral density values ​​within it are set to the noise power spectral density values. Scanning across all distances yields the amplitude power spectral density distribution after eliminating ground clutter. For example... Figure 6 It is the distance-power spectrum distribution of the discrete Fourier transform of a 4:5 staggered pulse repetition period, including the image frequency but with ground clutter removed.

[0105] Considering the continuity of radar signals, by searching for the maximum value at each range gate and realizing the maximum value in the velocity-range two-dimensional space, and by performing continuous sliding median filtering on the range for the location of the maximum intensity value (i.e., the velocity value), the center position of the main frequency domain interval can be determined. Using this center position as the center, and with... The region is defined as the dominant frequency domain interval; the other parts are replaced with noise power spectral density values, thus eliminating the image frequency component. This can be easily achieved using distance scanning in two dimensions. This process is called dominant frequency domain interval identification and image frequency component elimination.

[0106] At this point, only the compensation for precipitation echoes remains. Because precipitation signals may exist in the ground clutter region (zero-velocity region), this is caused by stationary weather processes. A velocity value slightly larger than the ground clutter velocity spectrum will be used. (here, Based on ), its left side is The right side is Based on the principle that precipitation targets follow a Gaussian distribution, linear interpolation within this interval achieves lossless compensation for precipitation echoes. Similarly, two-dimensional results can be easily obtained through distance scanning. The final results are shown below. Figure 7 The display shows the 4:5 staggered pulse repetition interval discrete Fourier transform distribution with image frequency removed and ground object distance-power spectrum distribution removed.

[0107] In one specific embodiment, the amplitude spectrum estimation of the echo signal from a dual-polarization Doppler weather radar under staggered pulse repetition intervals is as follows:

[0108] Dual-polarization Doppler weather radar plays a significant role in detecting and monitoring severe weather events, bird and insect migrations, and forest fires. This method can greatly improve the estimation of radar detection variables.

[0109] The weather radar digital receiver can directly output a baseband complex signal carrying all the detection information, such as... Figure 8-a and Figure 8-b As shown. Figure 8-a The complex signal output of the meteorological echo is shown, which belongs to the type of rapidly changing amplitude signal; Figure 8-b This indicates that the drone's echo signal output is complex and belongs to the high-speed moving target type.

[0110] First, reassemble the echo signal as follows: Figure 9 In the form that each pulse receives the echo complex baseband signal, with distance increments as the distance dimension, and the length denoted as . N R The pulse dimension is defined as the increment of the pulse, and its length is denoted as . N P This yields uneven pulses. P1 , P2 Alternating increments in pairs, until... M = N P / 2 pairs of pulses. This forms a pulse number minus distance composition. M N R Two-dimensional matrix [ MN R ].

[0111] Note that at this point, the time intervals vary unevenly along the pulse dimension. In other words, when performing a Discrete Fourier Transform on a certain distance gate, because the sampling intervals are inconsistent, or non-uniform, this transformation does not conform to the principles of the Discrete Fourier Transform, and a direct transformation will lead to incorrect results.

[0112] Then, in the pulse dimension, based on the staggered characteristics of the pulse repetition interval, i.e., the time ratio is... n 1 :n 2 =n 1 :(n 1 + 1 ) ,exist P1 Insertion after ( n 1-1) The echo complex baseband value is 0 (i.e. I(n) =0 and Q(n) Pulse data with =0), while P2 Insertion after ( n 2-1) = n One echo baseband value is 0 (i.e.) I(n)=0 and Q(n) Pulse data with =0). Based on the foregoing, staggered and... p = n 1+ n 2. Obviously, the above pulse number-distance matrix becomes ( M p ) N R (Here, the two multiplications use different symbols to indicate the difference in their relationship) a two-dimensional matrix [( M p ) N R ].

[0113] At this point, although there are many echo pulses with a sample value of 0, the sampling interval becomes consistent, that is... T 2- T 1= T u .like Figure 9 The figure shows a typical representation of UAV echo sampling homogenization processing with a staggered pulse repetition interval of 3:4 stagger ratio. In the figure, v i The sequence is transformed into a uniformly sampled signal by inserting zero values ​​at a certain distance gate.

[0114] Of course, at this time v i The signal has changed from the original signal; that is, it now contains some zero values. To maintain a certain relationship with the original signal, we can make the following assumptions:

[0115] Assuming the original radar was based on pulse repetition intervals of... T u The signal output by the digital intermediate frequency receiver used for this purpose is... e i Theoretically, it is with v i Similar signals, but v i The signals at those positions where the value is 0 are real.

[0116] Now construct a periodic vector c i The first element is 1, followed by ( n 1-1) zeros, then a 1, followed by ( n 2-1) = n One zero; this constitutes one cycle, repeating. M = N PIt consists of two cycles. Clearly, it exists. v i = c i e i Relationship. This is the initial intention of this method. Let... e i The length is N Therefore, N = M p = N P p / 2.

[0117] As mentioned above, DFT(c i ) Two-dimensional matrix can be formed C p p Furthermore, its amplitude inverse matrix is ​​obtained. abs { C}] -1 ; v i Discrete Fourier Transform V k =DFT(v i ) , can be represented as p M Two-dimensional matrix V r Furthermore, its amplitude Fourier transform matrix is ​​obtained. abs { V};and e i Fourier transform E k =DFT(e i ) Also changed to p M Two-dimensional matrix E r This indicates that... Then use... The relationship can be used to calculate e i Amplitude Fourier Transform Matrix abs { E}, which can be further replaced by the vector abs{ E k}

[0118] For cases with staggered pulse repetition intervals of staggered ratios from 2:3 to 8:9, see attached... Figures 10 to 16 Give its 5 5 to 15 15 amplitude reverse matrix [ abs { C}] -1 This allows users to directly use table lookup instead of calculation, saving computation time.

[0119] In the processing of actual observation data from weather radar with a 4:5 stagger ratio and an actual pulse interval of 574µs:717.5µs, for horizontally polarized echoes, Figure 5 The distance-power spectrum distribution of the discrete Fourier transform including mirror frequencies and ground clutter is shown; Figure 6 This shows the range-power spectrum distribution including mirror frequencies but with ground clutter removed; Figure 7 This is the distance-power spectrum distribution of the true meteorological echo, which completely removes the image frequency and ground clutter.

[0120] The embodiments described above are for illustrative purposes only and are not intended to limit the invention. Therefore, any changes in numerical values ​​or substitutions of equivalent elements should still fall within the scope of this invention.

[0121] The above detailed description will enable those skilled in the art to understand that the present invention can indeed achieve the aforementioned objectives and has complied with the provisions of the Patent Law.

[0122] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention. The above descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. It should be noted that any modifications, equivalent substitutions, and improvements made within the spirit and principles of the invention should be included within the scope of protection of the invention.

[0123] It should be noted that the above description of the process is for illustrative purposes only and does not limit the scope of this specification. Those skilled in the art can make various modifications and changes to the process under the guidance of this specification. However, these modifications and changes remain within the scope of this specification.

[0124] The basic concepts have been described above. Obviously, for those skilled in the art who have read this application, the above disclosure is merely illustrative and does not constitute a limitation of this application. Although not explicitly stated herein, those skilled in the art may make various modifications, improvements, and corrections to this application. Such modifications, improvements, and corrections are suggested in this application, and therefore, such modifications, improvements, and corrections still fall within the spirit and scope of the exemplary embodiments of this application.

[0125] Furthermore, this application uses specific terms to describe its embodiments. For example, "an embodiment," "one embodiment," and / or "some embodiments" refer to a particular feature, structure, or characteristic related to at least one embodiment of this application. Therefore, it should be emphasized and noted that "an embodiment," "one embodiment," or "an alternative embodiment" mentioned twice or more in different positions in this specification do not necessarily refer to the same embodiment. In addition, certain features, structures, or characteristics in one or more embodiments of this application can be appropriately combined.

[0126] Furthermore, those skilled in the art will understand that aspects of this application can be described and illustrated through several patentable types or situations, including any new and useful combination of processes, machines, products, or substances, or any new and useful improvements thereof. Therefore, aspects of this application can be implemented entirely in hardware, entirely in software (including firmware, resident software, microcode, etc.), or a combination of hardware and software. All of the above hardware or software can be referred to as a “unit,” “module,” or “system.” Furthermore, aspects of this application can take the form of a computer program product embodied in one or more computer-readable media, wherein computer-readable program code is contained therein.

[0127] Furthermore, unless expressly stated in the claims, the order of processing elements and sequences, the use of numbers and letters, or other names described in this application are not intended to limit the order of the processes and methods of this application. Although some currently considered useful embodiments of the invention have been discussed in the foregoing disclosure by way of various examples, it should be understood that such details are for illustrative purposes only, and the appended claims are not limited to the disclosed embodiments; rather, the claims are intended to cover all modifications and equivalent combinations that conform to the substance and scope of the embodiments of this application. For example, although the implementation of the various components described above can be embodied in a hardware device, it can also be implemented as a purely software solution, such as an installation on an existing server or mobile device.

[0128] Similarly, it should be noted that, in order to simplify the description of the present application and thus aid in the understanding of one or more embodiments of the invention, the foregoing description of the embodiments of the present application sometimes combines multiple features into a single embodiment, drawing, or description thereof. However, this approach of the present application should not be construed as reflecting an intention that the claimed subject matter requires more features than expressly recited in each claim. Rather, the subject of the invention should possess fewer features than in any single embodiment described above.

Claims

1. A method for Fourier transform of radar echo signal amplitude under staggered pulse repetition intervals, characterized in that, include: Signal reconstruction: confirming the staggered pulse repetition interval T 1 and T 2, of which T 1= n 1 T u , T 2= n 2 T u , n 2= n 1+1, T u For virtual sampling time interval, n 1 is a natural number from 2 to 10; Obtain the total number of staggered pulses for gates at the same distance. M , M If the number is even, calculate the minimum period. p =( n 1+ n 2); For T 1 corresponds to pulse complement ( n 1-1) zero-value samples, for T 2 corresponds to pulse complement ( n 2-1) zero-value samples, resulting in a length of N = pM / 2 uniform sampling sequence v i ; Fourier transform under uniform sampling interval: for uniform sampling sequence v i After windowing, a discrete Fourier transform is performed to obtain the amplitude spectral density of the reconstructed signal column vector. Calculation of matrix generation and acquisition of amplitude spectral density of real radar echo signal: Constructing coded sequence c i Its length is N Used to label uniformly sampled sequences v i The actual sample location in the encoded sequence; c i Perform a discrete Fourier transform to obtain the convolution matrix, and then simplify based on the periodicity of this convolution matrix to obtain... p*p The amplitude deconvolution inverse matrix is ​​obtained; the amplitude spectral density column vectors corresponding to the staggered pulse repetition interval and the amplitude spectral density column vectors of the reconstructed signal are reconstructed into a matrix, and the matrix is ​​deconvolved in the frequency domain by the amplitude deconvolution inverse matrix to obtain the amplitude spectral density matrix of the deconstructed signal. The matrix is ​​converted into column vectors, and ground clutter elimination and image frequency component elimination are performed in sequence to obtain the effective amplitude spectral density.

2. The method for Fourier transform of radar echo signal amplitude under staggered pulse repetition intervals according to claim 1, characterized in that, In the signal reconstruction, the total number of zeros padded is ( p -2) M / 2.

3. The method for Fourier transform of radar echo signal amplitude under staggered pulse repetition intervals according to claim 1, characterized in that, In the Fourier transform under the uniform sampling interval, the windowing process uses the von Hanning window, and the discrete Fourier transform is performed on the windowed sequence. w n * v i The transformation is performed, where n is the time series index. w n These are the coefficients of the nth window function.

4. The method for Fourier transform of radar echo signal amplitude under staggered pulse repetition intervals according to claim 1, characterized in that, The encoded sequence c i The construction method is as follows: in a uniformly sampled sequence v i In this process, the actual sample positions are marked as 1, and the zero-filled positions are marked as 0, forming a periodic sequence with a period of . p .

5. The method for Fourier transform of radar echo signal amplitude under staggered pulse repetition intervals according to claim 1, characterized in that, The method for obtaining the magnitude deconvolution inverse matrix is ​​as follows: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] c i The amplitude of the discrete Fourier transform result is used to obtain the amplitude convolution matrix abs{ C }, for abs{ C Inverse the matrix to obtain the magnitude deconvolution inverse matrix [abs{ C }] -1 .

6. The method for Fourier transform of radar echo signal amplitude under staggered pulse repetition intervals according to claim 1, characterized in that, The steps for eliminating ground clutter are as follows: determining the zero velocity and image frequency. q At each ground clutter location, with each ground clutter location as the center, the ground clutter velocity spectrum width... W gnd Within the specified range, the spectral density values ​​within that range are set to the noise power spectral density values.

7. The method for Fourier transform of radar echo signal amplitude under staggered pulse repetition intervals according to claim 1, characterized in that, The steps for eliminating image frequency components are as follows: By searching for the maximum value at each range gate, continuous sliding median filtering is performed on the position of the maximum value in the velocity-range two-dimensional space to determine the center position of the main frequency domain interval; with this center position as the center, in... Within a certain range, the spectral density is retained, and the remaining portion is set as the noise power spectral density value, where, To achieve the maximum unambiguous speed, This refers to the operating wavelength of the radar.

8. The method for Fourier transform of radar echo signal amplitude under staggered pulse repetition intervals according to claim 1, characterized in that, Before obtaining the effective amplitude spectral density, a precipitation echo compensation step is also included: with a velocity spectral width greater than that of ground clutter. W gnd speed value Taking the left side of the reference as the benchmark, we take the left side of the reference as... The right side is The interval is defined, and linear interpolation is performed within this interval, where the preset compensation range parameter is used. .

9. The method for Fourier transform of radar echo signal amplitude under staggered pulse repetition intervals according to claim 1, characterized in that, The length of the amplitude spectral density column vector of the staggered pulse repetition interval is N Its positive and negative boundary frequencies are The corresponding conversion speed is ,in This refers to the operating wavelength of the radar.

10. The method for Fourier transform of radar echo signal amplitude under staggered pulse repetition intervals according to claim 1, characterized in that, When the ratio of the staggered pulse repetition interval is 2:3 to 8:9, the amplitude deconvolution inverse matrix is ​​a matrix of 5×5 to 15×15.

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