Method for estimating angle and frequency of radar target based on space-time maximum likelihood

Abstract

The application discloses a method for estimating target angle and frequency of a mechanical phase scanning radar based on space-time maximum likelihood, and the implementation steps are as follows: a two-dimensional absolute coordinate system is established; target echo signals received by an antenna array of the mechanical phase scanning radar in the two-dimensional absolute coordinate system are synthesized into space-time joint data; a space-time joint matrix is constructed according to the form of the space-time joint data; and space-time maximum likelihood estimation is performed on the space-time joint data by using the space-time joint matrix, so that the estimated values of the target angle and the Doppler frequency are obtained. The method for estimating the target angle and the frequency designed by the application can estimate the Doppler frequency of the target while estimating the target angle, can greatly improve the accuracy and reliability of the estimation of the target angle, and can obtain stable performance.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and more specifically relates to a method for estimating the target angle and frequency of mechanically scanned radar based on space-time maximum likelihood in the field of radar signal processing technology. This invention can be applied to mechanically scanned radar systems, using a maximum likelihood algorithm on joint space-time data to estimate the angle and frequency of radar echo signals. Background Technology

[0002] Unlike phased array radars with fixed antenna arrays, mechanically scanned phased array radars achieve full airspace coverage through the mechanical rotation of the array, while also being able to manipulate the radar beam to track targets. Therefore, mechanically scanned phased array radars can detect targets in any direction using the array's normal beam, without the antenna gain and detection accuracy losses caused by beam broadening. By reducing the number of antenna elements, mechanically scanned phased array radars significantly reduce system costs, overcome the limitation of mechanically scanned radars having only one channel, and expand the scanning angle range of phased array radars. In recent years, this type of radar has received widespread attention.

[0003] In their paper "A Method for Estimating the Azimuth Angle of Key Targets Based on Mechanically Scanned Phased Array Radar" (Shipborne Electronic Countermeasures, 2021, 8, 44-4), Wan Cheng et al. proposed a method for estimating the azimuth angle of key targets using mechanically scanned phased array radar. The method involves employing a one-dimensional phased array system with simultaneous mechanical and electronic azimuth scanning. Utilizing digital multi-beam technology, multiple receiving beams can be formed in different azimuth ranges to satisfy a larger surveillance area. In full-array operation mode, the radar can perform sliding window processing of target azimuth solely through mechanical scanning. Once a target is found, it is tracked as a key target. The radar operates in a mode of simultaneous surveillance and tracking of key targets. The array can be divided into two subarrays: one for surveillance and search, and the other for tracking the key target. Accurate tracking of key targets requires consideration not only of the radar's rotational characteristics but also of the fact that the beam shape of the array radar is different in each azimuth. Therefore, firstly, a polynomial fitting method is used to accurately model each beam in different azimuths. Then, for cases where the radar array rotates, an amplitude comparison method is applied to estimate the azimuth angle of key targets. Although this method can estimate the angle of key targets, it still has the following two shortcomings: First, when estimating the target angle, it only focuses on the spatial structure of the signal and ignores the temporal structure, and cannot simultaneously estimate the Doppler frequency of the signal. Second, when tracking key targets, multiple accumulation detections can only improve the estimation accuracy of the azimuth angle of key targets. If there are multiple targets in the monitored area and the included angles of the targets are small, the angle measurement accuracy of multiple targets is poor. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the existing technologies by proposing a target angle and frequency estimation method for mechanically scanned radar based on space-time maximum likelihood. This method solves the problems in the existing technologies, such as the inability to estimate the Doppler frequency of the signal, the limitation to tracking only key targets, and the poor angle measurement accuracy when the angle interval between multiple targets is small.

[0005] To achieve the above objectives, the present invention constructs a space-time joint matrix for an optically scanned radar. In direction-of-arrival estimation, it utilizes the temporal and spatial structure information of the target echo from the optically scanned radar, transforming the one-dimensional spatial estimation into a two-dimensional space-time plane parameter estimation. This solves the problem of existing technologies being unable to estimate the target Doppler frequency. The present invention employs the space-time maximum likelihood method, using the space-time joint matrix to perform maximum likelihood estimation on the space-time joint data vector received by the optically scanned radar. This simplifies the estimation of the complex envelope of each pulse echo signal to the estimation of the initial complex amplitude of the echo signal, reducing the number of parameters that need to be estimated. Furthermore, the space-time maximum likelihood method requires the received data to be projected into the time domain before estimating the direction of arrival, which reduces the coupling between signals and between signals and noise, thus solving the problem of poor angular resolution in existing technologies when the angular intervals between multiple targets are small.

[0006] To achieve the above objectives, the technical solution adopted by the invention includes the following steps:

[0007] Step 1: Establish a two-dimensional absolute coordinate system;

[0008] Step 2: Combine the target echo signals received by the phase-scanning radar antenna array in the two-dimensional absolute coordinate system into space-time joint data.

[0009] Step 3: Construct the space-time joint matrix based on the model of the space-time joint data;

[0010] Step 4: Use the spatiotemporal joint matrix to perform spatiotemporal maximum likelihood estimation on the spatiotemporal joint data to obtain the estimated values ​​of the target angle and Doppler frequency.

[0011] Compared with the prior art, the present invention has the following advantages:

[0012] First, because the present invention transforms the one-dimensional spatial estimation into the parameter estimation of the two-dimensional spatial-temporal plane by constructing the space-time joint matrix of the phase-scanning radar when estimating the direction of arrival, it overcomes the shortcomings of the prior art that it cannot estimate the Doppler frequency of the signal, and enables the present invention to estimate the Doppler frequency of the target while estimating the target angle.

[0013] Second, since the present invention uses the space-time maximum likelihood method, the received data needs to be projected into the time domain first, which reduces the coupling between signals and between signals and noise, reduces the number of parameters that need to be estimated, and overcomes the shortcomings of poor angular resolution when the angle interval of multiple targets is small in the prior art. Attached Figure Description

[0014] Figure 1 This is a flowchart of the present invention;

[0015] Figure 2 This is a schematic diagram of the operation of a phase-scanning radar in an embodiment of the present invention, wherein, Figure 2 (a) is a simplified diagram of the operation of an mechanically scanned radar. Figure 2 (b) represents the state of the l-th pulse of the mechanically scanned radar. Figure 2 (c)

[0016] This is the final operating state of the mechanically scanned radar;

[0017] Figure 3 This is a simulation diagram of the present invention, wherein, Figure 3 (a) is a trend graph showing the root mean square error of single target angle estimation as a function of the detection signal-to-noise ratio in the simulation experiment of this invention. Figure 3 (b) is a trend graph of the root mean square error of Doppler frequency estimation of a single target as a function of the detection signal-to-noise ratio in the simulation experiment of the present invention; 3(c) is a trend graph of the root mean square error of angle estimation of two targets with the same Doppler frequency but different angles as a function of the detection signal-to-noise ratio in the simulation experiment of the present invention; 3(d) is a trend graph of the root mean square error of Doppler frequency estimation of two targets with the same Doppler frequency but different angles as a function of the detection signal-to-noise ratio in the simulation experiment of the present invention; 3(e) is a trend graph of the root mean square error of angle estimation of two targets with different Doppler frequencies and different angles as a function of the detection signal-to-noise ratio in the simulation experiment of the present invention; 3(f) is a trend graph of the root mean square error of Doppler frequency estimation of two targets with different Doppler frequencies and different angles as a function of the detection signal-to-noise ratio in the simulation experiment of the present invention. Detailed Implementation

[0018] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0019] Reference Figure 1 The implementation steps of the embodiments of the present invention will be described in further detail below.

[0020] Step 1, establish a two-dimensional absolute coordinate system as follows:

[0021] The first step is to establish a two-dimensional absolute coordinate system XOY, where X represents the horizontal axis of the absolute coordinate system, Y represents the vertical axis of the absolute coordinate system, and O represents the origin of the absolute coordinate system.

[0022] The second step involves rotating the mechanically scanned radar antenna array clockwise at a constant speed θ around the origin of the absolute coordinate system, using the origin as the fulcrum. BW Angle, θ BW The value of is equal to the beamwidth in the normal direction of the mechanically scanned radar antenna array.

[0023] The phase-scanning radar antenna array of the present invention can be selected with any array structure.

[0024] In this embodiment of the invention, the array structure selected is an equidistant linear array. (Refer to...) Figure 2 (a) Further description is given of the process of receiving array space signals by the mechanically scanned radar with an equidistant linear array structure according to an embodiment of the present invention.

[0025] The center point of the equidistant linear array structure of the mechanically scanned radar antenna array in this embodiment of the invention coincides with the origin of its corresponding absolute coordinate system. The mechanically scanned radar antenna array along... Figure 2 The arrow in (a) rotates clockwise around the origin at a constant speed θ. BW angle. Figure 2 In (a), dashed lines 2, 3, and the dashed circle represent the absolute coordinate system. Figure 2 The dashed line in (a) represents the initial state of operation of an equidistant linear array radar. The dashed line 1 in 2(a) represents the direction of the normal of the equidistant linear array antenna array in the absolute coordinate system in the initial state of operation of the equidistant linear array radar. The θ0 in 2(a) represents the angle value of the normal of the equidistant linear array antenna array in the absolute coordinate system in the initial state of operation of the equidistant linear array radar. Figure 2 (a) The dotted line 1 represents the direction of the i-th target in the absolute coordinate system. Figure 2 (a) The angle value of the i-th target relative to the normal direction of the mechanical phase-scanning radar antenna array in the initial state of operation represents the initial state of the radar's operation. Figure 2 The solid line in (a) represents the final operating state of a mechanically scanned phased array radar antenna array with an equidistant linear array structure. The solid line 1 in 2(a) represents the direction of the normal to the mechanically scanned radar antenna array in the absolute coordinate system during the final operating state. Figure 2 θ0-θ in (a) BW This represents the angle value of the normal direction of the mechanically scanned radar antenna array in the absolute coordinate system in the final state of operation. In the initial state of operation, all targets are located near the normal direction of the mechanically scanned radar antenna array, the number of array elements is 14, and the element spacing is 0.57 times the carrier wavelength, receiving the target echo signal.

[0026] Step 2: Combine the target echo signals received by the phase-scanning radar antenna array in the two-dimensional absolute coordinate system into space-time joint data.

[0027] The target echo signal is as follows:

[0028] X(l)=A s (θ l S(l)+n(l)

[0029] Where X(l) represents the M×1 dimensional echo signal composed of all targets received by the mechanically scanned radar antenna array in the l-th snapshot, M represents the number of rows of vector X(l), the value of which is equal to the total number of array elements of the mechanically scanned radar antenna array, l=1,2,…,L, and L represents the clockwise rotation θ of the mechanically scanned radar antenna array around the mechanically scanned radar pivot. BW The total number of pulses for the angle, where L is a value that approximates θ. BW / Δθ is an integer value, where Δθ represents the angle of clockwise rotation of the mechanically scanned radar antenna array around the radar pivot point within two adjacent pulses. A s (θ l θ represents the guidance matrix composed of the guidance vectors of all targets at the l-th snapshot. l This represents the vector consisting of the angles between all targets and the normal to the machine-type phase-scanned radar array at the time of the l-th snapshot. Let represent the angle between the i-th target in the echo signal during the l-th snapshot and the normal direction of the mechanically scanned radar array, where i = 1, 2, ..., P, and P represents the total number of targets in the echo signal received by the mechanically scanned radar antenna array during the l-th snapshot. This represents the angle between the P-th target in the echo signal during the l-th snapshot and the normal direction of the mechanically scanned radar array. θ i θi represents the angle value of the i-th target in the echo signal during the l-th snapshot in the absolute coordinate system, and θ0 represents the angle value of the normal direction of the phase-scanned radar antenna array during the first snapshot in the absolute coordinate system. The angle between the i-th target and the normal direction of the machine-scanned radar array during the l-th snapshot in the echo signal is denoted as . The guiding vector, S(l), represents the vector composed of the complex envelopes of all targets in the l-th snapshot, S(l) = [s1(l), s2(l), ..., s i (l),…,s P (l)] T s i (l) represents the complex envelope of the i-th target during the l-th snapshot, s i (l)=s i exp(j2πf di Tr(l-1)), s i Let s represent the initial complex amplitude of the i-th target. i =ρ i exp(jζ i ), ρ i ζ represents the initial complex amplitude of the i-th target. i The phase of the initial complex amplitude of the i-th target is represented by exp, which represents the exponential operation with the natural constant e as the base, j represents the imaginary unit sign, π represents pi, and f diLet represent the Doppler frequency of the i-th target, and Tr represent the pulse repetition period of the mechanically scanned radar. T This represents the transpose operation, and n(l) represents the variance of the M×1 dimension of the l-th snapshot, which is σ. 2 The zero-mean Gaussian white noise is uncorrelated with the signal source.

[0030] Reference Figure 2 (b) A further detailed description is given of the target echo signal received from the mechanically scanned radar antenna array in a two-dimensional absolute coordinate system. Figure 2 In (b), the solid line 1 represents the position of a mechanically scanned radar antenna array with an equidistant linear array structure during the l-th pulse. Figure 2 In (b), the dashed line 5 represents the position of a mechanically scanned radar antenna array with an equidistant linear array structure in the initial state of operation of the mechanically scanned radar. Figure 2 In (b), the dashed line 1 represents the direction of the normal to the phase-scanned radar antenna array during the l-th pulse in the absolute coordinate system. Figure 2 In (b), θ0+(l-1)Δθ represents the angle value of the normal direction of the phase-scanned radar antenna array in the absolute coordinate system during the l-th pulse. Figure 2 (b) The dashed line 4 represents the direction of the i-th target in the absolute coordinate system. Figure 2 θ in (b) i This represents the angle value of the i-th target in the absolute coordinate system. Figure 2 (b) This represents the angle value of the i-th target relative to the normal direction of the machine-scanned radar antenna array during the l-th pulse. Figure 2 (b) The angle of the i-th target relative to the array normal direction during the l-th pulse is . The guide vector. Figure 2 In (b), (l-1)Δθ represents the angle value that the mechanically scanned radar rotates around the origin after l pulses.

[0031] Reference Figure 2 (c) A further detailed description is given of the target echo signal received from the mechanically scanned radar antenna array in a two-dimensional absolute coordinate system. Figure 2 In (c), the solid line 1 represents the position of a mechanically scanned radar antenna array with an equidistant linear array structure in its final operational state. Figure 2 In (c), the dashed line 4 represents the position of a mechanically scanned radar antenna array with an equidistant linear array structure in the initial state of operation of the mechanically scanned radar. Figure 2 In (c), the dashed line 1 represents the direction of the normal to the phase-scanned radar antenna array in the absolute coordinate system when the array is in its final operating state. Figure 2In (c), θ0+(L-1)Δθ represents the angle value of the normal direction of the phase-scanned radar antenna array in the absolute coordinate system when the phase-scanned radar antenna array is in its final working state. Figure 2 (c) The dashed line 5 at the midpoint represents the direction of the i-th target in the absolute coordinate system. Figure 2 θ in (c) i This represents the angle value of the i-th target in the absolute coordinate system. Figure 2 (c) This represents the angle value of the i-th target relative to the normal direction of the mechanically scanned radar antenna array in the final operating state. Figure 2 In (c), (L-1)Δθ represents the angle through which the phase-scanning radar antenna array rotates around the origin from the initial state of the phase-scanning radar to the final state of the phase-scanning radar. Figure 2 (c) The angle of the i-th target relative to the normal direction of the phase-scanned radar antenna array in the final operating state is denoted as . The guide vector.

[0032] The spatiotemporal joint data is as follows:

[0033] Y = [X] T (1),X T (2),…,X T (l),…,X T (L)] T

[0034] Where Y represents the ML×1-dimensional spatiotemporal joint data synthesized in time order from the echo signals received by the mechanically scanned radar array antenna in a total of L snapshots, and X(L) represents the M×1-dimensional echo signal composed of all targets received by the mechanically scanned radar array in the Lth snapshot.

[0035] Step 3: Construct the space-time joint matrix based on the model of the space-time joint data as follows:

[0036]

[0037] Among them, A st (Ω) represents the ML×P-dimensional space-time joint matrix of P arbitrary angles and P arbitrary Doppler frequencies in the absolute coordinate system, and Ω represents the universal parameter vector of P arbitrary angles and P arbitrary Doppler frequencies in the absolute coordinate system. This represents the i-th arbitrary angle value in the absolute coordinate system. f represents the P-th arbitrary angle value in the absolute coordinate system. i f represents the i-th arbitrary Doppler frequency value. P Represents the P-th arbitrary Doppler frequency value. This indicates that the angle value in the absolute coordinate system is... The Doppler frequency is f i The ML×1 dimensional space-time joint vector,

[0038]

[0039] In the absolute coordinate system The angle between the direction and the direction of the array normal during the lth snapshot In the absolute coordinate system The angle between the direction and the direction of the array normal at the Lth snapshot.

[0040] Step 4: Use the spatiotemporal joint matrix to perform spatiotemporal maximum likelihood estimation on the spatiotemporal joint data to obtain the estimated values ​​of the target angle and Doppler frequency.

[0041] The space-time maximum likelihood estimate is obtained by the following equation:

[0042]

[0043] in, This represents a vector consisting of the angle and Doppler frequency estimates of all targets received by the mechanically scanned radar array, obtained from the space-time maximum likelihood estimation. θ represents the angle value of the i-th target in the absolute coordinate system. i The estimated value, θ represents the angle value of the P-th target in the absolute coordinate system. P The estimated value, f represents the Doppler frequency of the i-th target. di The estimated value, f represents the Doppler frequency of the P-th target. dP The estimated value, This operation represents the search for the maximum value of Ω within a certain range and returns the corresponding angle and Doppler frequency estimation vector. The search range of Ω is... f i ∈[f iLOW ,f iHIGH ], This represents the lower limit of the search range for the i-th target angle. θ represents the upper limit of the search range for the i-th target angle. i exist Search scope Inside, f iLOW f represents the lower bound of the Doppler frequency search range for the i-th target. iHIGH f represents the upper limit of the Doppler frequency search range for the i-th target. di In fi Search range [f iLOW ,f iHIGH ]Inside.

[0044] The invention will be further explained below with reference to simulation diagrams:

[0045] 1. Simulation conditions:

[0046] The simulation experiment of this invention was conducted with an Intel(R) Core(TM) i9-13900HX CPU@5.40GHz and 64G of memory.

[0047] The software platform for the simulation experiment of this invention is: Windows 11 operating system and MATLAB R2023a.

[0048] 2. Simulation Content and Result Analysis

[0049] The simulation experiments of this invention were conducted using the method of this invention, and three simulation experiments were carried out in a Gaussian white noise environment.

[0050] Simulation Experiment 1 simulates the root mean square error (RMSE) of angle and Doppler frequency estimation for a single target. Specifically, it shows the trend of the RMS error of angle estimation for a single target with a signal-to-noise ratio (SNR) ranging from [20, 45] dB under Gaussian white noise conditions, using the method of this invention. The results are as follows: Figure 3 The curve shown in (a) is a trend graph of the root mean square error of Doppler frequency estimation as a function of the detection signal-to-noise ratio. The results are as follows: Figure 3 The curve shown in (b).

[0051] The mechanically scanned radar antenna array used in simulation experiment 1 of this invention is an equidistant linear array with the phase reference point at the array center. The total number of elements in the mechanically scanned radar antenna array is 14, and the beamwidth in the normal direction of the mechanically scanned radar antenna array is θ. BW =6.35°, the angle by which the mechanically scanned radar antenna array rotates clockwise around the radar pivot point within two adjacent pulses is Δθ = 0.072°, and the pulse repetition period T of the mechanically scanned radar is... r =2ms, mechanically scanned radar pulse repetition frequency F r =500Hz, carrier wavelength λ=3m, element spacing is 0.57 times the carrier wavelength, the angle and Doppler frequency of a single target in the absolute coordinate system are (θ1, f d1 ) = (45°, 20Hz), the target's complex amplitude is 1, and the mechanically scanned radar antenna array rotates clockwise by θ around the radar pivot point. BW The total number of pulses is 89, and the detection signal-to-noise ratio range is SNR∈[20,45]dB.

[0052] Simulation Experiment 2 simulates the root mean square error (RMSE) of angle and Doppler frequency estimation for two targets with the same Doppler frequency but different angles under a Gaussian white noise environment. Specifically, it simulates the trend of the RMS error of angle estimation as a function of the detection SNR (signal-to-noise ratio) for two targets with the same Doppler frequency but different angles under a Gaussian white noise environment, using the method of this invention. The results are shown in the figure. Figure 3 The curve shown in (c) is a trend graph of the root mean square error of Doppler frequency estimation as a function of the detection signal-to-noise ratio. The results are as follows: Figure 3 The curve shown in (d).

[0053] The parameters used in simulation experiment 2 are (θ1,f1)=(45°,20Hz) and (θ2,f2)=(48°,20Hz) for the two targets in the absolute coordinate system, respectively. The complex amplitude of both targets is 1, and other parameters are the same as those in simulation experiment 1.

[0054] Simulation Experiment 3 simulates the root mean square error (RMSE) of angle and Doppler frequency estimation for two targets with different Doppler frequencies and angles under a Gaussian white noise environment. Specifically, it simulates the trend of the RMS error of angle estimation as a function of the detection SNR in a Gaussian white noise environment using the method of this invention. The results are shown in the figure. Figure 3 The curve shown in (e) is a trend graph of the root mean square error of Doppler frequency estimation as a function of the detection signal-to-noise ratio. The results are as follows: Figure 3 The curve shown in (f).

[0055] The parameters used in simulation experiment 3 are (θ1,f1)=(45°,15Hz) and (θ2,f2)=(48°,20Hz) for the two targets in the absolute coordinate system. The complex amplitude of both targets is 1, and other parameters are the same as those in simulation experiment 1.

[0056] The following is combined with Figure 3 The simulation diagrams further illustrate the effects of the present invention.

[0057] Figure 3 (a) The x-axis represents the detection signal-to-noise ratio range in dB, and the y-axis represents the root mean square error of the target angle estimation in °. Figure 3 The curve in (a) shows the root mean square error of the target angle estimation obtained by the method proposed in this invention as a function of the detection signal-to-noise ratio. Figure 3 (a) It can be seen that the root mean square error of the target angle estimation is small. As the signal-to-noise ratio increases, the root mean square error of the angle measurement tends to zero, indicating that the angle estimation performance of the present invention is stable when dealing with a single target.

[0058] Figure 3(b) The horizontal axis represents the detection signal-to-noise ratio range in dB, and the vertical axis represents the root mean square error of the target Doppler frequency estimation in Hz. Figure 3 The curve in (b) represents the root mean square error of the target Doppler frequency estimation as a function of the detection signal-to-noise ratio. Figure 3 (b) It can be seen that the root mean square error of the Doppler frequency estimation is small. As the signal-to-noise ratio increases, the root mean square error of the Doppler frequency estimation tends to zero, indicating that the Doppler frequency estimation performance of the present invention is stable in single-target scenarios.

[0059] Figure 3 (c) The x-axis represents the detection signal-to-noise ratio range in dB, and the y-axis represents the root mean square error of the target angle estimation in °. Figure 3 The curve in (c) represents the root mean square error of the target angle estimation as a function of the detection signal-to-noise ratio. From Figure 3 (c) It can be seen that as the signal-to-noise ratio increases, the root mean square error of angle measurement tends to zero, but the root mean square error is large when the signal-to-noise ratio is small, indicating that the angle estimation performance of the method of the present invention is poor when the two targets have the same Doppler frequency but different angles.

[0060] Figure 3 (d) The horizontal axis represents the detection signal-to-noise ratio range in dB, and the vertical axis represents the root mean square error of the target Doppler frequency estimation in Hz. Figure 3 The curve in (d) represents the root mean square error of the target Doppler frequency estimation as a function of the detection signal-to-noise ratio. Figure 3 (d) It can be seen that the root mean square error of Doppler frequency estimation is small. As the signal-to-noise ratio increases, the root mean square error of Doppler frequency estimation tends to zero, indicating that the Doppler frequency estimation performance of this method is stable when the two targets have the same Doppler frequency but different angles.

[0061] Figure 3 (e) The x-axis represents the detection signal-to-noise ratio range in dB, and the y-axis represents the root mean square error of the target angle estimation in °. Figure 3 The curve in (e) represents the root mean square error of the target angle estimation as a function of the detection signal-to-noise ratio. From Figure 3 (e) It can be seen that the root mean square error of the target angle estimation is small. As the signal-to-noise ratio increases, the root mean square error of the angle measurement tends to zero. The small root mean square error with a small signal-to-noise ratio indicates that the angle estimation performance of the method of the present invention is stable when the two targets have different Doppler frequencies and different angles.

[0062] Figure 3 (f) The x-axis represents the detection signal-to-noise ratio range in dB, and the y-axis represents the root mean square error of the target Doppler frequency estimation in Hz. Figure 3 The curve in (f) represents the root mean square error of the target Doppler frequency estimation as a function of the detection signal-to-noise ratio. From Figure 3 (f) It can be seen that the root mean square error of Doppler frequency estimation is small. As the signal-to-noise ratio increases, the root mean square error of Doppler frequency estimation tends to zero, indicating that the Doppler frequency estimation performance of this method is stable when the two targets have different Doppler frequencies and different angles.

Claims

1. A method for estimating the target angle and frequency of mechanically scanned radar based on space-time maximum likelihood, characterized in that, The space-time joint matrix of a phase-scanning radar is constructed, and the target angle and Doppler frequency are estimated using the space-time maximum likelihood method. The steps of this estimation method include the following: Step 1: Establish a two-dimensional absolute coordinate system; Step 2: Combine the target echo signals received by the phase-scanning radar antenna array in the two-dimensional absolute coordinate system into space-time joint data. Step 3: Construct the space-time joint matrix based on the model of the space-time joint data as follows: ， in, Represents P arbitrary angles and P arbitrary Doppler frequencies in an absolute coordinate system. A dimensional space-time joint matrix, Let P be a universal parameter vector representing P arbitrary angles and P arbitrary Doppler frequencies in an absolute coordinate system. , This represents the i-th arbitrary angle value in the absolute coordinate system. This represents the P-th arbitrary angle value in the absolute coordinate system. Represents the i-th arbitrary Doppler frequency value. Represents the P-th arbitrary Doppler frequency value. This indicates that the angle value in the absolute coordinate system is... Doppler frequency is of A spacetime joint vector of dimension 1. , In the absolute coordinate system The angle between the direction and the direction of the array normal during the lth snapshot , In the absolute coordinate system The angle between the direction and the direction of the array normal at the Lth snapshot; Step 4: Use the spatiotemporal joint matrix to perform spatiotemporal maximum likelihood estimation on the spatiotemporal joint data to obtain the estimated values ​​of the target angle and Doppler frequency.

2. The method for estimating the target angle and frequency of mechanically scanned radar based on space-time maximum likelihood as described in claim 1, characterized in that, The steps for establishing a two-dimensional absolute coordinate system described in step 1 are as follows: The first step is to establish a two-dimensional absolute coordinate system. , The horizontal axis represents the absolute coordinate system. The vertical axis represents the absolute coordinate system. Represents the origin of the absolute coordinate system; The second step involves using the origin of the absolute coordinate system as the fulcrum for the mechanically scanned radar, and rotating the radar antenna array clockwise at a uniform speed around the origin. angle, The value of is equal to the beamwidth in the normal direction of the mechanically scanned radar antenna array.

3. The method for estimating the target angle and frequency of mechanically scanned radar based on space-time maximum likelihood as described in claim 1, characterized in that, The target echo signal mentioned in step 2 is as follows: ， in, This represents the composition of all targets received by the phase-scanned radar antenna array in the lth snapshot. dimensional echo signal, Representing vectors The number of rows is equal to the total number of elements in the mechanically scanned radar antenna array. , This indicates that the mechanically scanned radar antenna array rotates clockwise around the radar fulcrum. The total number of pulses at the angle, The value of approximation integer values, This indicates the angle by which the phase-scanning radar antenna array rotates clockwise around the radar pivot point within two adjacent pulses. This represents the guidance matrix composed of the guidance vectors of all targets at the l-th snapshot. This represents the vector consisting of the angles between all targets and the normal to the machine-type phase-scanned radar array at the time of the l-th snapshot. , This represents the angle between the i-th target in the echo signal during the l-th snapshot and the normal direction of the mechanically scanned radar array. P represents the total number of targets in the echo signal received by the phase-scanned radar antenna array in the lth snapshot. This represents the angle between the P-th target in the echo signal during the l-th snapshot and the normal direction of the mechanically scanned radar array. , This represents the angle value of the i-th target in the absolute coordinate system in the echo signal during the l-th snapshot. This represents the angle value in the absolute coordinate system corresponding to the normal direction of the phase-scanning radar antenna array during the first snapshot. , The angle between the i-th target and the normal direction of the machine-scanned radar array during the l-th snapshot in the echo signal is denoted as . The guide vector, This represents the vector consisting of the complex envelopes of all targets in the l-th snapshot. , This represents the complex envelope of the i-th target during the l-th snapshot. , This represents the initial complex amplitude of the i-th target. , This represents the amplitude of the initial complex amplitude of the i-th target. Let represent the phase of the initial complex amplitude of the i-th target, and exp represent the exponential operation with the natural constant e as the base. The symbol representing the imaginary unit. Represents pi (π). Let represent the Doppler frequency of the i-th target. Indicates the pulse repetition period of an mechanically scanned radar. This indicates the transpose operation. Indicates the lth snapshot The variance of dimension is The zero-mean Gaussian white noise is uncorrelated with the signal source.

4. The method for estimating the target angle and frequency of mechanically scanned radar based on space-time maximum likelihood according to claim 3, characterized in that, The space-time joint data mentioned in step 2 is as follows: ， in, This indicates that the mechanically scanned radar array antenna has a total of The echo signals received by the next snapshot are synthesized in time sequence. Dimensional spatiotemporal joint data, This represents the combination of all targets received by the phase-scanned radar antenna array in the Lth snapshot. The echo signal of the dimension.

5. The method for estimating the target angle and frequency of mechanically scanned radar based on space-time maximum likelihood according to claim 4, characterized in that, The space-time maximum likelihood estimation described in step 4 is obtained by the following equation: ， in, This represents a vector composed of the angle and Doppler frequency estimates of all targets received by the mechanically scanned radar array, obtained through space-time maximum likelihood estimation. , This represents the angle value of the i-th target in the absolute coordinate system. The estimated value, This represents the angle value of the P-th target in the absolute coordinate system. The estimated value, Represents the Doppler frequency of the i-th target. The estimated value, Represents the Doppler frequency of the P-th target. The estimated value, Indicates to The operation involves searching for the maximum value within a certain range and returning the corresponding angle and Doppler frequency estimation vector. The search scope is , , This represents the lower bound of the search range for the i-th target angle. This represents the upper limit of the search range for the i-th target angle. exist Search scope Inside, This represents the lower limit of the Doppler frequency search range for the i-th target. This represents the upper limit of the Doppler frequency search range for the i-th target. exist Search scope Inside.

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