Array element segmentation space-time adaptive processing method of airborne sparse array radar

Abstract

The invention discloses an array element segmentation space-time adaptive processing method for an airborne sparse array radar, and the method comprises the steps: carrying out the segmentation processing of array elements of three-dimensional echo data of the sparse array radar, and obtaining a plurality of sub-arrays; calculating a target space-time steering vector of each sub-array; on the basis of the target space-time steering vector, the optimal weight of each subarray is calculated, and an output result is obtained through space-time adaptive processing; splicing the output results to obtain spliced data, and performing signal recovery according to the data; and performing target detection on the data. According to the method, envelope walking of the sparse array radar can be overcome, the clutter suppression effect is good, and target detection can be carried out on the obtained data after clutter suppression.

Description

Technical Field

[0001] The invention belongs to the technical field of radars and relates to a segmented space-time adaptive processing method for array elements of an airborne sparse array radar. Background Art

[0002] In actual engineering applications, clutter is always everywhere. If the clutter in the airborne sparse array radar echo data cannot be effectively suppressed, it will have a great impact on subsequent target detection.

[0003] Because radar clutter exhibits space-time coupling, airborne radars typically employ Space-Time Adaptive Processing (STAP) technology. This technology leverages array elements and pulse multi-channel echo data to effectively suppress clutter through space-time two-dimensional adaptive filtering. However, due to the large spacing between array elements in sparse array radars, the array's aperture length approaches or exceeds the radar's range resolution, resulting in range-dependent clutter. Traditional space-time processing methods are unable to effectively suppress clutter, thus hindering subsequent target detection.

[0004] Therefore, it is very necessary to study the segmented space-time adaptive processing method of array elements of airborne sparse array radar under clutter background. Summary of the Invention

[0005] The present invention aims to solve the technical problem that existing space-time processing methods cannot effectively suppress clutter, thereby affecting subsequent target detection. The present invention provides an element segmented space-time adaptive processing method for airborne sparse array radar, and the technical solution adopted is:

[0006] The invention discloses a segmented space-time adaptive processing method for array elements of an airborne sparse array radar, comprising the steps of:

[0007] S1. Segment processing is performed on the array elements of the three-dimensional echo data of the sparse array radar to obtain several sub-arrays;

[0008] S2. Calculate the target space-time steering vector of each sub-array;

[0009] S3. Based on the target space-time steering vector, respectively calculate the optimal weight of each sub-array, and perform space-time adaptive processing to obtain an output result;

[0010] S4. Splicing the output results to obtain spliced ​​data, and performing signal recovery based on the data.

[0011] In one embodiment of the present invention, step S1 includes:

[0012] Assuming that the clutter data is segmented by array elements, the echo signal of the mth pulse of the 1st array element in the i-th subarray is expressed as:

[0013]

[0014] In formula (1), ξ represents the amplitude, B represents the bandwidth, and t i,m represents the time delay of the mth pulse of the first array element in the i-th subarray, f c is the carrier frequency;

[0015] The echo signal of the mth pulse of the Qth array element in the i-th sub-array is expressed as:

[0016]

[0017] In formula (2), ξ represents the amplitude, B is the bandwidth, and t i+Q-1,m represents the time delay of the mth pulse of the Qth array element in the i-th sub-array, f c is the carrier frequency;

[0018] After the array element segmentation, the starting array element of the i-th sub-array starts from i, and the data in each sub-array meets the conditions of the narrow-band radar.

[0019] In one embodiment of the present invention, the time delay of the m-th pulse of the first array element in the i-th sub-array is expressed as:

[0020]

[0021] The time delay of the m-th pulse of the Q-th array element in the i-th sub-array is expressed as:

[0022]

[0023] In formula (3) and formula (4), d = 2.5λ, d is the array element spacing, λ is the wavelength, T r Represents the pulse repetition period, V t represents the relative radial velocity between the target and the carrier, ψ represents the incident cone angle, R0 represents the distance at which the target is located, and c represents the speed of light.

[0024] In one embodiment of the present invention, step S2 includes:

[0025] Assume that the target's incident cone angle relative to the antenna axis is ψ, and the relative radial velocity between the target and the carrier is V t , the number of array elements in each sub-array is Q, the number of pulses is M, and the spatial steering vector of the i-th sub-array is expressed as:

[0026]

[0027] The time domain steering vector of the i-th sub-array is expressed as:

[0028]

[0029] In formula (5) and formula (6), d is the array element spacing, λ is the wavelength, and T r Represents the pulse repetition period, V t represents the relative radial velocity between the target and the carrier, ψ represents the incident cone angle, θ i represents the spatial frequency, M represents the Mth pulse, represents the normalized Doppler frequency;

[0030] The target space-time steering vector is expressed as:

[0031]

[0032] In formula (7), represents the Kronecker product, represents the time domain steering vector, a(θ i ) represents the spatial steering vector.

[0033] In one embodiment of the present invention, step S2 further includes:

[0034] The target signal of the lth range unit of the i-th subarray Expressed as:

[0035]

[0036] In formula (8), is a QM×1-dimensional column vector, η l is the target signal amplitude of the current range unit, s i represents the target space-time steering vector of the i-th sub-array.

[0037] In one embodiment of the present invention, step S3 includes:

[0038] Assume that the corresponding noise covariance matrix and adaptive weight vector are calculated independently in each sub-matrix;

[0039] The data of each range gate of the i-th sub-array is expressed as:

[0040]

[0041] In formula (9), x i,1 represents the data received by the first pulse of the first element of the i-th sub-array, x i+Q-1,M It represents the data received by the Mth pulse of the Qth array element in the i-th sub-array. It is the data of the lth range gate of the i-th sub-array;

[0042] The optimization equation of each sub-matrix is ​​obtained by using the linear constrained minimum variance criterion, which is expressed as:

[0043]

[0044] The optimal solution of formula (10) is the adaptive weight vector, which is expressed as:

[0045]

[0046] In formula (10) and formula (11), w i represents the optimal weight of the sub-matrix, s i is the space-time steering vector of the target, represents the noise covariance matrix after sub-matrix dimensionality reduction, and H represents the conjugate transpose.

[0047] In one embodiment of the present invention, step S3 further includes:

[0048] The noise covariance matrix after the sub-matrix dimension reduction is expressed as:

[0049]

[0050] In formula (12), L is the number of range gates, represents the lth training sample of the i-th sub-matrix after dimensionality reduction, T is a QM×D dimensionality reduction matrix;

[0051] The output result of the i-th sub-matrix after space-time adaptive processing is expressed as:

[0052]

[0053] In formula (13), Z i,l represents the output result of the i-th sub-matrix, represents the optimal weight of the i-th sub-matrix.

[0054] In one embodiment of the present invention, step S4 includes:

[0055] The range-Doppler two-dimensional planes after space-time processing of each sub-array are spliced ​​to form a three-dimensional cube composed of K array elements, and the range-Doppler two-dimensional plane under each array element is the two-dimensional output of each sub-array.

[0056] In one embodiment of the present invention, the method for segmented space-time adaptive processing of array elements of an airborne sparse array radar further includes: step S5, performing target detection on the data.

[0057] In one embodiment of the present invention, step S5 includes:

[0058] S51, selecting a Doppler channel, aligning and accumulating data in the Doppler channel according to five grating lobe angles, and obtaining accumulated data;

[0059] S52, sorting the accumulated data, and performing amplitude and phase estimation based on the point with the largest sorting;

[0060] S53, removing the three-dimensional element-pulse-range data from the three-dimensional echo data of the sparse array radar and recording the data;

[0061] S54. Repeat steps S51-S53 until the remaining energy in the last two-dimensional plane is minimized or approaches the noise energy, and draw all recorded target information into a three-dimensional cube of angle-distance-speed to complete target detection.

[0062] Beneficial effects of the present invention:

[0063] The present invention's segmented space-time adaptive processing method for airborne sparse array radars performs segmented processing on the element domain of echo data, ensuring that the data within each subarray meets the requirements of narrowband radar. Conventional space-time adaptive processing also operates on the clutter data of each subarray. The outputs of each subarray are then combined to perform signal recovery. This method overcomes envelope movement in sparse array radars, effectively suppressing clutter. Furthermore, the method utilizes the varying movement of targets in different directions to perform target detection on the resulting clutter-suppressed data. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 This is a flow chart of a method for segmented space-time adaptive processing of array elements of an airborne sparse array radar provided by an embodiment of the present invention;

[0065] Figure 2 Schematic diagram of sparse array signal recovery after element segmented STAP processing provided by an embodiment of the present invention;

[0066] Figure 3 This is a schematic diagram of data slicing of a Doppler channel provided by an embodiment of the present invention;

[0067] Figure 4 is a range Doppler map obtained by performing PD processing on the echo data of the sparse array radar according to an embodiment of the present invention;

[0068] Figure 5 This is a range Doppler map obtained by performing traditional EFA processing on the echo data of the sparse array radar in the first experiment of the embodiment of the present invention;

[0069] Figure 6This is a range Doppler map obtained by processing the echo data of a sparse array radar using an array element segmentation method in the first experiment of an embodiment of the present invention;

[0070] Figure 7 This is a range Doppler map obtained by performing PD processing on the echo data of the sparse array radar in the second experiment of the embodiment of the present invention;

[0071] Figure 8 This is a range Doppler map obtained by performing traditional EFA processing on the echo data of the sparse array radar in the second experiment of the embodiment of the present invention;

[0072] Figure 9 This is a range Doppler map obtained by processing the echo data of a sparse array radar using an array element segmentation method in a second experiment of an embodiment of the present invention. DETAILED DESCRIPTION

[0073] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0074] The present invention provides an array element segmented space-time adaptive processing method for airborne sparse array radar, aiming at the range movement of airborne sparse array radar clutter and the subsequent detection of multiple direction targets. Figure 1 The array element segmented space-time adaptive processing method of the airborne sparse array radar includes the following steps:

[0075] S1. Segment processing is performed on the array elements of the three-dimensional echo data of the sparse array radar to obtain several sub-arrays;

[0076] S2. Calculate the target space-time steering vector for each sub-array;

[0077] S3. Based on the target space-time steering vector, the optimal weight of each sub-array is calculated respectively, and the output result is obtained after space-time adaptive processing;

[0078] S4. Splice the output results to obtain spliced ​​data, and perform signal recovery based on the data.

[0079] Because the spacing between array elements in a sparse array radar is too large, the aperture length of the array approaches or exceeds the radar's range resolution, resulting in range wander in the clutter echo data. This paper proposes segmenting the multiple array elements of a sparse array radar to overcome envelope wander. By dividing a large array into multiple small sub-arrays, the starting and ending elements of each sub-array need to be recalculated.

[0080] In an optional embodiment of the present application, it is assumed that the number of array elements on the airborne distributed radar antenna is N, the spacing between each array element is d=2.5λ, the number of pulses transmitted in one coherent accumulation period is M, and the pulse repetition period is T rThe echo signal is discretely sampled with L sampling points, and finally a three-dimensional echo data cube of N×M×L is obtained. The three-dimensional echo data of the sparse array radar is segmented into the array element domain so that the data in each sub-array meets the conditions of the narrowband radar. Specifically, step S1 includes:

[0081] Assuming that the clutter data is segmented by array elements, the echo signal of the mth pulse of the 1st array element in the i-th subarray is expressed as:

[0082]

[0083] In formula (1), ξ represents the amplitude, B represents the bandwidth, and t i,m represents the time delay of the mth pulse of the first array element in the i-th subarray, f c is the carrier frequency.

[0084] The echo signal of the mth pulse of the Qth array element in the i-th sub-array is expressed as:

[0085]

[0086] In formula (2), ξ represents the amplitude, B is the bandwidth, and t i+Q-1,m represents the time delay of the mth pulse of the Qth array element in the i-th sub-array, f c is the carrier frequency.

[0087] The time delay of the mth pulse of the first array element in the i-th sub-array is expressed as:

[0088]

[0089] The time delay of the mth pulse of the Qth element in the i-th sub-array is expressed as:

[0090]

[0091] In formula (3) and formula (4), d = 2.5λ, d is the array element spacing, λ is the wavelength, T r Represents the pulse repetition period, V t represents the relative radial velocity between the target and the carrier, ψ represents the incident cone angle, R0 represents the distance at which the target is located, and c represents the speed of light.

[0092] It can be seen that after the array elements are segmented, the starting array element of the i-th sub-array no longer starts from 1, but starts from i. In addition, due to the segmentation of the array elements, the envelope movement of the data in the same sub-array between the array elements can be ignored.

[0093] After the array elements are segmented, the envelope movement between the elements of each sub-array can be ignored, so the clutter suppression processing can be performed on the data of each sub-array separately. However, the processing of sub-array STAP and narrow-band STAP is slightly different. The original spatial guidance vector of the target in the narrow-band STAP is from the first element to the last element of the entire array, but after the array elements are segmented, the target guidance vector of each sub-array is from the first element to the last element of the sub-array, and the data between sub-arrays are independent of each other, and they all have their own weight vectors.

[0094] Then the first step of the sub-array STAP is to calculate the space-time steering vector of each sub-array separately. In an optional embodiment of the present application, step S2 includes:

[0095] Assume that the target's incident cone angle relative to the antenna axis is ψ, and the relative radial velocity between the target and the carrier is V t , the number of array elements in each sub-array is Q, the number of pulses is M, and the spatial steering vector of the i-th sub-array is expressed as:

[0096]

[0097] The time domain steering vector of the i-th sub-array is expressed as:

[0098]

[0099] In formula (5) and formula (6), d is the array element spacing, λ is the wavelength, and T r Represents the pulse repetition period, V t represents the relative radial velocity between the target and the carrier, ψ represents the incident cone angle, θ i represents the spatial frequency, M represents the Mth pulse, represents the normalized Doppler frequency.

[0100] The target space-time steering vector is expressed as:

[0101]

[0102] In formula (7), represents the Kronecker product, represents the time domain steering vector, a(θ i ) represents the spatial steering vector.

[0103] The target signal of the lth range unit of the i-th subarray Expressed as:

[0104]

[0105] In formula (8), is a QM×1-dimensional column vector, ηl is the target signal amplitude of the current range unit, s i represents the target space-time steering vector of the i-th sub-array.

[0106] Based on the target space-time steering vector obtained in the previous step, the optimal weight of each sub-array is calculated and the output result after space-time adaptive processing is obtained. Step S3 includes:

[0107] It is assumed that the corresponding noise covariance matrix and adaptive weight vector are calculated independently in each sub-matrix.

[0108] The data of each range gate of the i-th sub-array is expressed as:

[0109]

[0110] In formula (9), x i,1 represents the data received by the first pulse of the first element of the i-th sub-array, x i+Q-1,M It represents the data received by the Mth pulse of the Qth array element in the i-th sub-array. It is the data of the lth range gate of the i-th sub-array.

[0111] While maintaining the target signal gain, the energy of the clutter is minimized. The optimization equation for each subarray can be obtained using the linear constrained minimum variance criterion (LCMV), which is expressed as:

[0112]

[0113] The optimal solution of formula (10) is the adaptive weight vector, which is expressed as:

[0114]

[0115] In formula (10) and formula (11), w i represents the optimal weight of the sub-matrix, s i is the space-time steering vector of the target, represents the noise covariance matrix after sub-matrix dimensionality reduction, and H represents the conjugate transpose.

[0116] The linear constrained minimum variance criterion is an adaptive beamforming algorithm that minimizes interference and noise while ensuring that the desired signal gain remains unchanged by adding absorptive constraints.

[0117] The noise covariance matrix after sub-matrix dimensionality reduction is expressed as:

[0118]

[0119] In formula (12), L is the number of range gates, represents the lth training sample of the i-th sub-matrix after dimensionality reduction, T is a QM×D dimensionality reduction matrix.

[0120] The output result of the i-th sub-matrix after space-time adaptive processing is expressed as:

[0121]

[0122] In formula (13), Z i,l represents the output result of the i-th sub-matrix, represents the optimal weight of the i-th sub-matrix.

[0123] According to the previous derivation, the array elements of the entire array are segmented, and the original sparse array echo data is divided into K echo data close to the narrowband array. Since the number of array elements is reduced by 1 / Q, the resolution is also reduced by 1 / Q, and the number of array elements is reduced from the original N to Q. After clutter suppression, in order to restore the high resolution of the target, that is, to distinguish targets with different grating lobes, it is necessary to merge the outputs of these K sub-arrays and finally use the merged data for signal recovery.

[0124] Sparse array signal recovery after element segmented STAP processing is shown in the attached Figure 2 Attached Figure 2 The upper part is the output result after the data of each sub-array is processed by EFA (Extended Factor Approach), and the attached Figure 2 The lower half is a schematic diagram of splicing the outputs of all sub-arrays together. Due to the low resolution of each sub-array, there is no range movement, and the target peak energy only appears at a certain range gate. However, if the segmented data are merged again, it can be seen that since the resolution is improved after the merger, if the data of a certain Doppler channel is taken, the envelope movement of the target can be observed, and the different target incident directions can be judged based on the different movement amounts.

[0125] By merging the segmented data together, we can see that since the resolution is improved after merging, if we take the data of a certain Doppler channel, we can observe the envelope movement of the target and judge the different incident directions of the target based on the different movement amounts.

[0126] To intercept the data slice of a Doppler channel, refer to the attached Figure 3 Attached Figure 3 Represents the data information of a Doppler channel after data splicing.

[0127] After obtaining the spliced ​​data, taking the data plane of the yth Doppler channel, it can be observed that targets of different speeds are in different Doppler channels, and targets in the same Doppler channel have different directions, resulting in different movement amounts and directions of the echo data. This is the result of improving the resolution after merging the data after the array elements are segmented.

[0128] In an optional embodiment of the present application, step S4 includes:

[0129] The range-Doppler two-dimensional planes after space-time processing of each sub-array are spliced ​​to form a three-dimensional cube composed of K array elements, and the range-Doppler two-dimensional plane under each array element is the two-dimensional output of each sub-array.

[0130] Because the data is segmented for clutter suppression, the target's energy is dispersed in multiple sub-arrays. After space-time processing of each sub-array, the data needs to be spliced. After splicing, the target information will be automatically restored.

[0131] In one embodiment of the present invention, the method further includes step S5 of performing target detection on the data.

[0132] In an optional embodiment of the present application, step S5 includes:

[0133] S51, selecting a Doppler channel, aligning and accumulating data in the Doppler channel according to five grating lobe angles, and obtaining accumulated data;

[0134] S52, sorting the accumulated data, and performing amplitude and phase estimation based on the point with the largest sorting;

[0135] S53, removing the three-dimensional element-pulse-range data from the three-dimensional echo data of the sparse array radar and recording the data;

[0136] S54. Repeat steps S51-S53 until the remaining energy in the last two-dimensional plane is minimized or approaches the noise energy, and draw all recorded target information into a three-dimensional cube of angle-distance-speed to complete target detection.

[0137] Since there are multiple grating lobes in the sparse array radar, the target has angle ambiguity. After the target is recovered, direct detection will have angle ambiguity. Therefore, it is necessary to use the different envelope movement of targets entering from different grating lobe directions to align and then eliminate the targets separately. This is equivalent to taking out high-energy targets one by one from a large amount of data.

[0138] In the two optional embodiments of this application, the first experiment is mainly for the front-side array structure, with the main beam and the array axis at an angle of 90 degrees. The platform height is 8000m, the number of array elements is 16, the number of pulses is 32, the pulse repetition frequency is 400Hz, the array element spacing is 10m, the carrier frequency is 75MHz, and the system bandwidth is 5MHz. Please refer to the attached Figure 4 ~Attached Figure 6 .

[0139] Attachment Figure 4 This is a range-Doppler plot obtained by performing PD (Pulse Doppler) processing on the echo data of a sparse array radar. Since a sparse array radar has five grating lobes with the same gain, the PD plot shows that clutter is primarily distributed in five channels: the 9th, 13th, 17th, 21st, and 25th. Furthermore, the channels near these five Doppler channels also have high clutter energy, ultimately occupying the vast majority of the Doppler channels. This shows that this method is less effective at suppressing clutter; if a target falls within the majority of the central channels, target detection is impossible.

[0140] Attachment Figure 5 This is the range-Doppler diagram obtained by performing traditional EFA processing on the echo data of the sparse array radar. It can also be observed that the clutter is mainly concentrated in the five Doppler channels. However, since the main beam of this group of experiments points in the normal direction, for the middle main lobe, the target does not experience range movement between the array elements. The clutter in the middle channel can be well suppressed by the EFA method to only one Doppler channel. However, the clutter in the other four grating lobes will experience range movement between the array elements. The effect obtained by directly using EFA processing cannot suppress the clutter to only one Doppler channel. Several surrounding Doppler channels will also be affected. However, since this method is adaptive, the overall effect is still better than PD processing.

[0141] Attachment Figure 6 This is the range Doppler map obtained by processing the echo data of the sparse array radar using the array element segmentation method. It can be seen that compared with traditional EFA processing, since the data is first segmented and then processed by EFA, the data in each subarray approximately meets the conditions of a narrowband radar. Therefore, this method has a better clutter suppression effect. The clutter energy in the five Doppler channels and their nearby channels is somewhat weakened compared with the previous figure.

[0142] The second experiment is mainly for the front-side array structure, with the main beam and the array axis angle of 60 degrees. The platform height is 8000m, the number of array elements is 16, the number of pulses is 32, the pulse repetition frequency is 400Hz, the array element spacing is 10m, the carrier frequency is 75MHz, and the system bandwidth is 5MHz. Please refer to the attached Figure 7 ~Attached Figure 9 .

[0143] Attachment Figure 7 This is the range-Doppler plot obtained by performing PD processing on the echo data of a sparse array radar. Since a sparse array radar has five grating lobes with the same gain, the PD plot shows that clutter is primarily distributed in five channels: the 10th, 14th, 18th, 22nd, and 26th channels. Furthermore, the channels near these five Doppler channels also have high clutter energy, ultimately occupying the vast majority of the Doppler channels. This shows that this method has a poor clutter suppression effect. If a target falls within the majority of the middle channels, target detection is impossible.

[0144] Attachment Figure 8 This is the range-Doppler plot obtained by applying traditional EFA processing to the echo data of a sparse array radar. It can also be observed that the clutter is mainly concentrated in five Doppler channels. Because the main beam pointing in this experiment deviates from the normal direction, the clutter in the five grating lobes will vary in range between array elements. Direct EFA processing cannot suppress the clutter to only one Doppler channel, and several surrounding Doppler channels will also be affected. However, because this method is adaptive, the overall effect is still better than PD processing.

[0145] Attachment Figure 9 This is the range Doppler map obtained by processing the echo data of the sparse array radar using the array element segmentation method. It can be seen that compared with traditional EFA processing, since the data is first segmented and then processed by EFA, the data in each subarray approximately meets the conditions of a narrowband radar. Therefore, this method has a better clutter suppression effect. The clutter energy in the five Doppler channels and their nearby channels is somewhat weakened compared with the previous figure.

[0146] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A method for segmented space-time adaptive processing of array elements of an airborne sparse array radar, characterized in that: Including steps: S1. Segment processing is performed on the array elements of the three-dimensional echo data of the sparse array radar to obtain several sub-arrays; S2. Calculate the target space-time steering vector of each sub-array; S3. Based on the target space-time steering vector, respectively calculate the optimal weight of each sub-array, and perform space-time adaptive processing to obtain an output result; S4. Splicing the output results to obtain spliced ​​data, and performing signal recovery based on the data.

2. The method for segmented space-time adaptive processing of array elements of an airborne sparse array radar according to claim 1, characterized in that: Step S1 includes: Assuming that the clutter data is segmented by array elements, the echo signal of the mth pulse of the 1st array element in the i-th subarray is expressed as: In formula (1), ξ represents the amplitude, B represents the bandwidth, and t i,m represents the time delay of the mth pulse of the first array element in the i-th subarray, f c is the carrier frequency; The echo signal of the mth pulse of the Qth array element in the i-th sub-array is expressed as: In formula (2), ξ represents the amplitude, B is the bandwidth, and t i+Q-1,m represents the time delay of the mth pulse of the Qth array element in the i-th sub-array, f c is the carrier frequency; After the array element segmentation, the starting array element of the i-th sub-array starts from i, and the data in each sub-array meets the conditions of the narrow-band radar.

3. The method for segmented space-time adaptive processing of array elements of an airborne sparse array radar according to claim 2, characterized in that: The time delay of the mth pulse of the first array element in the i-th sub-array is expressed as: The time delay of the m-th pulse of the Q-th array element in the i-th sub-array is expressed as: In formula (3) and formula (4), d = 2.5λ, d is the array element spacing, λ is the wavelength, T r Represents the pulse repetition period, V t represents the relative radial velocity between the target and the carrier, ψ represents the incident cone angle, R0 represents the distance at which the target is located, and c represents the speed of light.

4. The method for segmented space-time adaptive processing of array elements of an airborne sparse array radar according to claim 1, characterized in that: Step S2 includes: Assume that the target's incident cone angle relative to the antenna axis is ψ, and the relative radial velocity between the target and the carrier is V t , the number of array elements in each sub-array is Q, the number of pulses is M, and the spatial steering vector of the i-th sub-array is expressed as: The time domain steering vector of the i-th sub-array is expressed as: In formula (5) and formula (6), d is the array element spacing, λ is the wavelength, and T r Represents the pulse repetition period, V t represents the relative radial velocity between the target and the carrier, ψ represents the incident cone angle, θ i represents the spatial frequency, M represents the Mth pulse, represents the normalized Doppler frequency; The target space-time steering vector is expressed as: In formula (7), represents the Kronecker product, represents the time domain steering vector, a(θ i ) represents the spatial steering vector.

5. The method for segmented space-time adaptive processing of array elements of an airborne sparse array radar according to claim 4, characterized in that: Step S2 further includes: The target signal of the lth range unit of the i-th subarray Expressed as: In formula (8), is a QM×1-dimensional column vector, η l is the target signal amplitude of the current range unit, s i represents the target space-time steering vector of the i-th sub-array.

6. The method for segmented space-time adaptive processing of array elements of an airborne sparse array radar according to claim 1, characterized in that: Step S3 includes: Assume that the corresponding noise covariance matrix and adaptive weight vector are calculated independently in each sub-matrix; The data of each range gate of the i-th sub-array is expressed as: In formula (9), x i,1 represents the data received by the first pulse of the first element of the i-th sub-array, x i+Q-1,M It represents the data received by the Mth pulse of the Qth array element in the i-th sub-array. It is the data of the lth range gate of the i-th sub-array; The optimization equation of each sub-matrix is ​​obtained by using the linear constrained minimum variance criterion, which is expressed as: The optimal solution of formula (10) is the adaptive weight vector, which is expressed as: In formula (10) and formula (11), w i represents the optimal weight of the sub-matrix, s i is the space-time steering vector of the target, represents the noise covariance matrix after sub-matrix dimensionality reduction, and H represents the conjugate transpose.

7. The method for segmented space-time adaptive processing of array elements of an airborne sparse array radar according to claim 6, characterized in that: Step S3 further includes: The noise covariance matrix after the sub-matrix dimension reduction is expressed as: In formula (12), L is the number of range gates, represents the lth training sample of the i-th sub-matrix after dimensionality reduction, T is a QM×D dimensionality reduction matrix; The output result of the i-th sub-matrix after space-time adaptive processing is expressed as: In formula (13), Z i,l represents the output result of the i-th sub-matrix, represents the optimal weight of the i-th sub-matrix.

8. The method for segmented space-time adaptive processing of array elements of an airborne sparse array radar according to claim 1, characterized in that: Step S4 includes: The range-Doppler two-dimensional planes after space-time processing of each sub-array are spliced ​​to form a three-dimensional cube composed of K array elements, and the range-Doppler two-dimensional plane under each array element is the two-dimensional output of each sub-array.

9. The method for segmented space-time adaptive processing of array elements of an airborne sparse array radar according to claim 1, characterized in that: The method further includes: step S5, performing target detection on the data.

10. The method for segmented space-time adaptive processing of array elements of an airborne sparse array radar according to claim 9, characterized in that: Step S5 includes: S51, selecting a Doppler channel, aligning and accumulating data in the Doppler channel according to five grating lobe angles, and obtaining accumulated data; S52, sorting the accumulated data, and performing amplitude and phase estimation based on the point with the largest sorting; S53, removing the three-dimensional element-pulse-range data from the three-dimensional echo data of the sparse array radar and recording the data; S54. Repeat steps S51-S53 until the remaining energy in the last two-dimensional plane is minimized or approaches the noise energy, and draw all recorded target information into a three-dimensional cube of angle-distance-speed to complete target detection.

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