Miniature dechirped millimeter wave radar moving target high order motion parameter estimation method and device

Abstract

The application discloses a kind of micro dechirp millimeter wave radar moving target high-order motion parameter estimation method and device, the method includes: the echo signal of moving target received by SAR platform is dechirped, and distance dimension pulse compression is completed by distance dimension Fourier transform;The QRM of distance dimension is corrected using the second-order Keystone transformation of dechirp;The detection of line segment slope is completed using LSD line segment detection technology, and first-order slant range coefficient is solved;Compensation function is constructed to compensate LRM, so that moving target trajectory focuses on the same distance unit;Extract the target trajectory signal after eliminating distance migration at the same distance unit, estimate the residual slant range expansion coefficient;All motion parameters are obtained to focus on unknown moving target signal, and thus the parameter estimation of moving target detection is completed.The application first proposes the moving target focusing scheme for the complex moving target of micro dechirp system radar, and the slant range parameter of target can be accurately estimated.

Description

Technical Field

[0001] This invention belongs to the field of radar detection technology, specifically relating to a method and apparatus for estimating the parameters of moving targets in a miniature frequency-demodulated millimeter-wave radar. Background Technology

[0002] Matched filtering (MF) and constant false alarm rate (CFAR) receivers are fundamental to radar detection technology. MF is essentially intra-pulse integration, or pulse compression (PC). To further improve radar detection capabilities, inter-pulse integration is required, which can be categorized into incoherent integration, coherent integration, and hybrid integration. Incoherent integration algorithms do not use phase information, only accumulating the amplitude of each pulse. Therefore, the accumulated inter-pulse gain is low, resulting in poor parameter estimation performance. Furthermore, when the signal-to-noise ratio (SNR) is below a certain threshold, incoherent integration offers no integration gain due to the "SNR threshold" phenomenon. Compared to incoherent integration, coherent integration algorithms utilize the magnitude and phase information of each pulse to achieve higher integration gain and overcome the limitation of the "SNR threshold." Coherent integration algorithms can be broadly categorized into two types: Joint Motion Parameter Estimation (JMPE) and Separated Motion Parameter Estimation (SMPE). JMPE simultaneously corrects range cell migration (RCM) and estimates unknown motion parameters, which is statistically optimal but computationally expensive. Compared to JMPE, SMPE separately corrects RCM and estimates unknown motion parameters, reducing computational cost to some extent, but introducing derivative problems such as cross-term interference and loss of noise immunity. Hybrid integration algorithms divide the long integration time into several segments, performing coherent integration within each segment and incoherent integration between segments, representing a trade-off between computational cost and performance loss. Miniature millimeter-wave (MMW) radars employing receiver frequency demodulation (or delinear frequency demodulation, Decirp) technology have attracted widespread attention for short-range target detection and imaging due to their high integration, offering advantages such as light weight, low cost, and low sampling frequency. However, research on moving target indication (MTI) for delinear frequency modulated micro millimeter-wave radar is scarce. Higher resolution and shorter wavelengths require accurate slant range (SR) models, i.e., higher-order slant range expansions, which will present new challenges in terms of computational cost and estimation of unknown motion parameters. Summary of the Invention

[0003] Purpose of the invention: In order to solve the problem of moving target detection in radar based on frequency-demodulated receiver, mainly including range migration correction and high computational complexity motion parameter estimation in frequency-demodulated receiver, this invention proposes a method and device for estimating the parameters of moving targets in a miniature frequency-demodulated millimeter-wave radar.

[0004] Technical solution: The present invention provides a method for estimating the parameters of a moving target in a miniature frequency-demodulated millimeter-wave radar, comprising the following steps:

[0005] (1) The echo signal of the moving target received by the SAR platform is de-frequency modulated to obtain the range de-frequency modulated-slow time domain signal, and the range dimension pulse compression is completed by the range dimension Fourier transform.

[0006] (2) For the range-demodulated-slow-time domain moving target signal obtained in step (1), the second-order Keystone transform of the demodulated frequency is used to correct the QRM of the range dimension.

[0007] (3) For the echo signal after QRM correction, the LSD line segment detection technology is used to detect the line segment slope and solve the first-order slope distance coefficient; then a compensation function is constructed to compensate the LRM so that the trajectory of the moving target is focused at the same distance cell.

[0008] (4) Extract the target trajectory signal after the distance migration was eliminated in step (3) at the same distance cell, which contains the residual unknown slant range coefficient, and estimate the residual slant range expansion coefficient;

[0009] (5) Use all the motion parameters obtained in the above steps to focus on the unknown moving target signal, thus completing the parameter estimation for moving target detection.

[0010] Furthermore, the echo signal in step (1) includes a complex trajectory of a high-order slant range model that couples the range and azimuth dimensions.

[0011] Furthermore, the implementation process of step (1) is as follows:

[0012] The transmitted signal of the nth pulse repetition interval PRI of the millimeter-wave radar is represented as:

[0013]

[0014] Among them, t r Is it fast time or distance time, t a =nT is slow time or azimuth time, T is PRI, t = t a +t r It is absolute time; T p It is the scan duration or pulse width, f c It is the carrier frequency, Kr It is the linear frequency modulation slope, rect(·) is the rectangular window function; distance R(t) r ,t a The echo signal received at point ) is:

[0015] s r (t r ,t a )=w1(t)exp(j2πf c (t-τ)+jπK r (t r -τ) 2 (2)

[0016] in, τ=2R(t r ,t a ) / c; The reference signal used for difference frequency processing is at a distance of R. ref Echo signal at:

[0017] s ref (t r ,t a )=s(t r -τ ref ,t a (3)

[0018] Where, τ ref =2R ref / c; The frequency difference calculation between the echo signal and the reference signal is as follows:

[0019]

[0020] in, w a (t a ) = rect(t a / T a ), T a It is the coherent processing time; the first exponential term in equation (4) is the residual video phase (RVP). Ignoring its influence, after eliminating the RVP term, it becomes:

[0021]

[0022] The specific echo delay is expressed as follows:

[0023] τ=τ a +τ r ,

[0024]

[0025]

[0026] Wherein, R(t) a ) is only related to slow time t a The relevant slow-time slope, R(t) r ) is only related to fast time t r Relevant slant distance; scan duration T p Shorter than T to neglect the effect of intrapulse Doppler, which is related to the fast time t r Relatedly, equation (5) is simplified to:

[0027]

[0028] Rearranging equation (6), we get:

[0029]

[0030] in, Taking the transmitted signal as the reference signal for the difference frequency operation, equation (7) is further simplified to:

[0031] S IF (t r ,t a )=Cexp(-j2π(f c +K r t r )τ a (8)

[0032] Where C = w r (t r )w a (t a ), K r t r It is a range-dimensional delinear frequency modulation; the general slant range model for moving targets by a moving radar platform or a static radar platform is:

[0033]

[0034] Where a1, a2, a3, and a4 represent the equivalent velocity, acceleration, jerk, and more complex motion parameters of the moving target; substituting (9) into (8), the difference frequency signal model for delinearized frequency modulated millimeter-wave radar for different applications is expressed as:

[0035]

[0036] Performing a Fourier transform on the above equation in the distance dimension completes the pulse compression in the distance dimension.

[0037] Furthermore, the implementation process of step (2) is as follows:

[0038] Define the second-order trapezoidal transform (DSOKT) for delinear frequency modulation to correct the QRM in the slow time domain:

[0039]

[0040] Where, η a It is the azimuth slow time of resampling; substituting equation (11) into equation (10) yields:

[0041]

[0042] Equation (12) eliminates the coupling between the second-order slow time and the delinearized frequency range frequency, leaving only the coupling between the first-order slow time and the delinearized frequency range frequency.

[0043] Furthermore, the implementation process of step (3) is as follows:

[0044] For satisfying K r t r <<f c The delinear frequency-modulated millimeter-wave radar system, according to the first-order Taylor series expansion, yields the following approximation:

[0045]

[0046] Substituting equation (13) into equation (12), we get:

[0047]

[0048] Performing a distance-dimensional Fourier transform on equation (14) yields:

[0049]

[0050] As can be seen from equation (15), the energy of the target is concentrated on the line segment where QRM has been eliminated, and its specific form is:

[0051]

[0052] The slope of the line segment is:

[0053]

[0054] Using the LSD segment detection technique to obtain the slope, the compensation term of the LRM is constructed as follows:

[0055] S LRM =exp(j2πK) s η a t r (17)

[0056] Multiplying equation (17) by equation (14), we obtain the distance delinearized slow-time signal of the moving target after LRM correction as follows:

[0057]

[0058] Equation (18) is converted to the range pulse compression domain and expressed as:

[0059]

[0060] Slope estimation of line segment, and K s The relevant information is obtained through the line segment detector LSD. At this point, the RCM, including LRM and QRM, has been calibrated; the target is now focused on the line segment within the distance pulse compression domain-slow time domain: f r =-2K r R0 / c achieves decoupling of the distance and orientation dimensions without requiring any prior knowledge of the target.

[0061] Furthermore, the implementation process of step (4) is as follows:

[0062] Extracting the signal at distance unit R0 and considering the cumulative duration of the azimuth pulse, equation (19) is further expressed as:

[0063]

[0064] Where R0 is known and related to η a Irrelevant, w a (η a ) is the resampling time η a The azimuth rectangular window function; omitting the constant complex amplitude, formula (20) is further simplified to:

[0065]

[0066] Formula (21) contains the slant range coefficient of the target to be estimated. The following compensation function is constructed:

[0067]

[0068] Where, a1 is the known first-order slope distance coefficient obtained from (16), a i,e The unknown higher-order coefficients to be estimated; then, the following objective function is constructed:

[0069]

[0070] when a i =a i,e When equation (23) is coherent, the objective function reaches its maximum value; otherwise, equation (23) is incoherent superposition, leading to a certain degree of intensity cancellation; therefore, the estimated values ​​of a2, a3, and a4 are obtained in the following way:

[0071]

[0072] Equation (24) is solved by exhaustively searching the residual parameters.

[0073] Furthermore, the implementation process of step (5) is as follows:

[0074] Using the estimated a2, a3, a4 and the known a1 and R0, construct the azimuth dimension matched filter function:

[0075]

[0076] By multiplying the above equation with equation (19) and then performing a Fourier transform in the orientation dimension, the moving target can be focused.

[0077] The device according to the present invention includes a memory and a processor, wherein:

[0078] Memory is used to store computer programs that can run on a processor;

[0079] The processor is configured to, while running the computer program, execute the steps of the method for estimating high-order motion parameters of a moving target using a miniature de-frequency-modulated millimeter-wave radar as described above.

[0080] The present invention provides a storage medium storing a computer program, which, when executed by at least one processor, implements the steps of the method for estimating high-order motion parameters of a moving target in a miniature de-modulated millimeter-wave radar as described above.

[0081] Beneficial Effects: Compared with existing technologies, the beneficial effects of this invention are as follows: This invention proposes for the first time a moving target focusing scheme for complex moving targets in micro-miniature de-modulated radar systems; it distinguishes the order of the slant range expansion in the range and azimuth dimensions, greatly reducing the slant range complexity of the moving target to be processed; in the range dimension, DSOKT and LSD techniques are used to solve the coupling problem between the range and azimuth dimensions, focusing the target's trajectory onto a straight line within the scene of interest. This process greatly reduces the amount of data required for subsequent parameter estimation and significantly improves the computational efficiency of moving target detection; in the parameter estimation process, a coherent integral method is used to construct the objective function, which is simple and efficient, requires no complex calculations, and can accurately estimate the target's slant range parameters. Attached Figure Description

[0082] Figure 1 A flowchart of a method for estimating the parameters of moving targets for a miniature frequency-distuned millimeter-wave radar;

[0083] Figure 2 These are two representative moving target scenarios proposed in this invention; where (a) is a stationary radar platform scenario; and (b) is a moving radar platform scenario.

[0084] Figure 3 is the moving target focusing result using the second-order slant range model in the azimuth dimension; where (a) is the two-dimensional point target focusing result diagram; (b) is the contour analysis result of the point target in Figure (a); (c) is the azimuth slice result in Figure (a); (d) is the range dimension slice result of the point target in Figure (a);

[0085] Figure 4 is the moving target focusing result using the fourth-order slant range model in the azimuth dimension; (a): the two-dimensional point target focusing result diagram; (b) is the contour analysis result of the point target in Figure (a); (c) is the azimuth slice result in Figure (a); (d) is the range dimension slice result of the point target in Figure (a);

[0086] Figure 5 is the range correction and focusing result of three point targets at a signal-to-noise ratio of 10 dB; where (a) is the original target trajectory, including linear range migration (LRM) and quadratic range migration (QRM), as well as higher-order range curvature terms; (b) is the moving target trajectory after second-order range migration correction; (c) is the moving target trajectory after linear range migration correction; (d) is the target focusing result after motion parameter estimation. DETAILED DESCRIPTION

[0087] The present invention will be further described in detail below with reference to the accompanying drawings.

[0088] As Figure 1 shown, the present invention proposes a parameter estimation method for moving targets of a miniature de-chirp millimeter wave radar, and the specific implementation process is as follows:

[0089] Step 1: The receiver of the SAR platform receives the echo signal of the moving target, which includes a complex trajectory coupled in the range dimension and the azimuth dimension. De-chirp operation is performed on the echo data, and then Fourier transform in the range dimension is executed to complete range dimension pulse compression.

[0090] The transmitted signal of the nth pulse repetition interval (PRI) of the millimeter wave radar is expressed as:

[0091]

[0092] where, t r is the fast time or range time, t a =nT is the slow time or azimuth time, T is the PRI, t = t a +t r is the absolute time. T p (T p <T) is the scan duration or pulse width, f cIt is the carrier frequency, K r It is the linear frequency modulation frequency, and rect(·) is the rectangular window function. Distance R(t) r ,t a The echo signal received at point ) is:

[0093] s r (t r ,t a )=w1(t)exp(j2πf c (t-τ)+jπK r (t r -τ) 2 (2)

[0094] in, τ=2R(t r ,t a The reference signal used for difference frequency processing is at a distance of R. ref Echo signal at:

[0095] s ref (t r ,t a )=s(t r -τ ref ,t a (3)

[0096] Where, τ ref =2R ref / c. The frequency difference calculation between the echo signal and the reference signal is as follows:

[0097]

[0098] The above formula represents the difference frequency signal; where w a (t a ) = rect(t a / T a ), T a This is the coherent processing interval (CPI). The first exponential term in equation (4) is the residual video phase (RVP), which is unique to the difference frequency processing operation, also known as delinear frequency modulation processing. Generally, when the mapping band width of the area of ​​interest is narrow, the influence of RVP is small and can be ignored. After eliminating the RVP term, equation (4) becomes:

[0099]

[0100] The specific echo delay is expressed as follows:

[0101] τ=τ a +τ r ,

[0102]

[0103]

[0104] Wherein, R(t) a ) is only related to slow time t a The relevant slow-time slope, R(t) r ) is only related to fast time t r The relevant slope distance. Assuming the scan duration T. p Shorter than T to neglect the effect of intrapulse Doppler, which is related to the fast time t r Relatedly, equation (5) is simplified to:

[0105]

[0106] Rearranging equation (6), we can obtain:

[0107]

[0108] in, Taking the transmitted signal as the reference signal for the difference frequency operation, equation (7) is further simplified to:

[0109] S IF (t r ,t a )=Cexp(-j2π(f c +K r t r )τ a (8)

[0110] Where C = w r (t r )w a (t a For convenience, K can be temporarily omitted. r t r It is the distance-dimensional delinear frequency modulation. Performing a distance-dimensional Fourier transform on equation (8) yields the target trajectory after distance-dimensional pulse compression. The signal trajectories of the multiple targets at this time are as follows: Figure 5 As shown in (a), RCM exists. The general slant range model for moving targets by a moving radar platform or a static radar platform can be summarized as follows:

[0111]

[0112] Where a1, a2, a3, and a4 represent the equivalent velocity, acceleration, jerk, and more complex motion parameters of the moving target, which are related to the relative velocity and relative acceleration between the radar and the target, regardless of whether the platform is stationary or moving. Substituting equation (9) into equation (8), the general difference frequency signal model for de-modulated millimeter-wave radar for different applications can be expressed as:

[0113]

[0114] Generally, second- and third-order slant range expansions are applicable to both traditional spaceborne and airborne radar systems. For typical delinearized frequency-modulated millimeter-wave radars, a1 and a2 are sufficient to correct for range migration. However, for miniature millimeter-wave radar systems, due to the very short wavelength, fourth-order slant range signal models are more suitable for estimating unknown motion parameters to correctly focus the azimuth echo signal. The range delinearized frequency K... r t r With a1t a and The combination of these factors results in linear range migration (LRM) and quadratic range migration (QRM), respectively, leading to energy defocusing of the moving target along the range dimension. Phase term 2a1t a / λ causes a Doppler center shift (DCS), resulting in a deviation in azimuth position, where λ = c / f c It refers to wavelength. The terms include Linear Doppler Frequency Migration (LDFM), Quadratic Doppler Frequency Migration (QDFM), and Cubic Doppler Frequency Migration (CDFM). and This causes energy defocusing of the moving target along the azimuth dimension.

[0115] Step 2: For the moving target signal in the range demodulated-slow time domain obtained in Step 1 (8), the QRM of the range dimension is corrected by using the second-order Keystone transform of demodulated frequency, i.e., DSOKT.

[0116] Define a dechirped second-order keystone transform (DSOKT) to correct the QRM in the dechirped frequency modulation-slow time domain:

[0117]

[0118] Where, η a This is the azimuth slow time for resampling. Substituting equation (11) into equation (10), we get:

[0119]

[0120] As can be seen from (12), the coupling between the second-order slow time and the delinearized frequency modulation distance frequency is eliminated, leaving only the coupling between the first-order slow time and the delinearized frequency modulation distance frequency. The multi-target motion trajectory after QRM correction is as follows: Figure 5 As shown in (b), the distance curvature problem (QRM) of the moving target has been solved at this point.

[0121] Step 3: For the echo signal after QRM correction in Step 2, the slope of the line segment is detected using LSD line segment detection technology, and the first-order slope range coefficient is solved. Then, a compensation function is constructed to compensate for LRM. At this point, the coupling problem between the range dimension and the orientation dimension of the moving target has been solved, and the trajectory of the moving target has been focused on the same range cell R0.

[0122] For delinear frequency modulation millimeter-wave radar systems, it typically satisfies K r t r <<f c Based on the first-order Taylor series expansion, we can obtain the following approximation:

[0123]

[0124] Substituting equation (13) into equation (12), we get:

[0125]

[0126] Performing a distance dimension Fourier transform (FT) on equation (14) yields:

[0127]

[0128] As can be seen from equation (15), the energy of the target is concentrated on the line segment that eliminates QRM, and its specific form is:

[0129]

[0130] The slope of the line segment is:

[0131]

[0132] As can be seen from equation (16), the slope of the LRM term after DSOKT is reduced to half of the original slope. If the slope K s The estimate is accurate, and the compensation term for LRM can be constructed as follows:

[0133] S LRM =exp(j2πK) s η a t r (17)

[0134] Multiplying equation (17) by equation (14), we can obtain the distance to the moving target after LRM correction as the linear frequency modulation-slow time signal:

[0135]

[0136] Converting equation (18) to the range pulse compression domain, it can be expressed as:

[0137]

[0138] Slope estimation of line segment, and K s The relevant information can be obtained through a line segment detector (LSD). At this point, the RCM, including LRM and QRM, has been corrected. The target trajectory of the multi-target after range travel correction is shown in Figure (5) (c). The moving target is now focused on the line segment within the range pulse compression domain-slow time domain: f r =-2K r R0 / c achieves decoupling of the distance and orientation dimensions without requiring any prior knowledge of the target.

[0139] Step 4: Extract the target trajectory signal after the distance migration has been eliminated in step 3 at the same distance R0. It contains the residual unknown slant range coefficients. Use equation (24) to estimate the residual slant range expansion coefficients.

[0140] Extracting the signal at distance unit R0 and considering the cumulative duration of the azimuth pulse, equation (19) can be further expressed as:

[0141]

[0142] Where R0 is known and related to η a Irrelevant, w a (η a ) is the resampling time η a The azimuth rectangular window function. Omitting the constant complex amplitude, formula (20) is further simplified to:

[0143]

[0144] Formula (21) contains the slant range coefficient of the target to be estimated. The following compensation function is constructed:

[0145]

[0146] Where a1 is the known first-order slope distance coefficient obtained from equation (17), a i,e These are the unknown higher-order coefficients that need to be estimated.

[0147] Then, construct the following objective function:

[0148]

[0149] when a i =a i,e When the equation is true, equation (23) is a coherent integral, and the objective function reaches its maximum value. Otherwise, equation (23) is an incoherent superposition, leading to a certain degree of intensity cancellation. Therefore, the estimated values ​​of a2, a3, and a4 can be obtained in the following way:

[0150]

[0151] The accurate estimate of equation (24) can be obtained through traditional exhaustive search, which is computationally efficient due to the significant reduction in data size and the number of parameters to be estimated.

[0152] Step 5: Use all the motion parameters obtained in the above steps to focus on the unknown moving target signal. At this point, the detection and parameter estimation of the moving target are completed.

[0153] Using the estimated a2, a3, a4 and the known a1 and R0, a matched filter function in the azimuth dimension can be constructed:

[0154]

[0155] Multiplying the above equation by equation (19) and then performing a Fourier transform in the orientation dimension allows for focusing on the moving target. The focusing result for the moving target considering the fourth-order expansion coefficients in equation (25) is as follows: Figure 4 As shown. The focusing result of a moving target considering only the second-order coefficient expansion is as follows. Figure 3 As shown. (Through) Figure 3 and Figure 4 The comparison of (a), (b), and (c) in this paper verifies the rationality and effectiveness of considering the fourth-order explanatory coefficients in the azimuth direction, which is superior to considering only the second-order slant range model. Figure 3 and Figure 4 The result (d) verifies the rationality of considering the second-order expansion coefficients in the distance dimension, which can be handled separately from the expansion coefficients considered in the azimuth direction.

[0156] For motion radar platforms, such as Figure 2 The front-looking SAR platform shown in (b) has an initial time at (0,0,H) and an azimuth velocity of V. p .

[0157] Assume the moving target is located at (X,Y,0) at the initial moment and has a velocity V in the orientation dimension. a Velocity V in the distance dimension r azimuth acceleration A a and distance acceleration A r The slant range between the moving target and the moving radar platform at this point can be expressed as: in,

[0158]

[0159]

[0160]

[0161] in, This can be considered as the equivalent azimuth velocity between a moving radar and a moving target. m,3 and a m,4 It is a complex function of unknown motion parameters, which is related to V. r , A r and A a The relevant information can be obtained using Taylor series expansion.

[0162] For static radar platforms, such as Figure 2 The surveillance radar shown in (a) is located at (0,0,0). The position of the moving target is adjusted to (X,Y,H). Therefore, with slow time t... a The relevant fourth-order Taylor expansion of the static radar's slant range to the target is:

[0163]

[0164] in,

[0165]

[0166]

[0167] in, This refers to the actual azimuth and velocity of the moving target between the static radar and the moving target. Similarly, a s,3 and a s,4 It is a complex function of unknown motion parameters, such as V. r V a s A r and A a.

[0168] Therefore, the slant range can be expressed as follows, whether for a stationary or moving radar platform:

[0169]

[0170] Where a1, a2, a3, and a4 represent the equivalent velocity, acceleration, jerk, and more complex motion parameters of the moving target, for both moving and static radar platforms with the same array configuration, and the relative velocity between the radar platform and the moving target. ( or V r A a A r Related.

[0171] Table 1. Parameters of Millimeter-Wave Radar System

[0172]

[0173]

[0174] Without loss of generality, this invention considers the detection scenarios of moving micro-millimeter-wave radar platforms, such as... Figure 2 As shown in (b), the corresponding system parameters are shown in Table 1. The carrier frequency of the motion radar system is 77 GHz, the transmission bandwidth is 3 GHz, and the maximum detection range is set to 120 m.

[0175] First, the detection performance of the first-order slant range coefficient of the LSD is verified. Assume the target is located at the center of the scene, with an initial azimuth velocity of 1.2 m / s and an azimuth acceleration of 0.3 m / s². 2 The acceleration due to distance is 0.4 m / s². 2 Furthermore, the changing initial distance velocity is related to the LRM slope. Table 2 shows the statistical analysis results of the estimated a1 value when a1 = 4.8 m / s, where "AD" is the difference between the statistical mean and the theoretical value, "ADR" is the ratio of "AD" to the theoretical value, and "STD" is the standard deviation. It can be seen that when the SNR is higher than -20 dB, LSD can accurately estimate the first-order slope range coefficient. Therefore, LSD is a more accurate, efficient, and robust slope estimate for the LRM trajectory of a moving target, and can accurately solve for the first-order slope range coefficient.

[0176] Table 2 shows the LSD estimation results of the first-order slant range coefficient as a function of signal-to-noise ratio.

[0177] -20 303 630 76.7 -15 23 48.6 6.67 -10 5.33 11.1 4.20 -5 5.50 11.5 2.10 0 2.86 5.96 2.86 5 4.29 8.94 1.62 10 3.71 7.73 1.02 15 1.86 3.88 1.20 20 3.29 6.85 0.79

[0178] Assume a slow-moving target is located at (0.8, 60) m in the observation scene, with an initial azimuth velocity of 1.2 m / s and an azimuth acceleration of 0.3 m / s². 2 The initial distance velocity is 1.6 m / s, and the distance acceleration is 0.4 m / s². 2 The theoretical value of a1 is 1.3492 m / s, obtained using LSD. The theoretical value of a2 is 3.1532 m / s. 2 The search range for a2 is [-4, 4] m / s 2 The search step size is 0.0005 m / s. 2 The theoretical value of a3 is -0.1126 m / s. 3 The search range for a3 is [-0.33, 0.33] m / s 3 The search step size is 0.00033 m / s. 3 The theoretical value of a4 is -0.0798 m / s. 3 The search range for a3 is [-0.25, 0.25] m / s 4 The search step size is 0.00025 m / s. 4 In this simulation, the orientation is analyzed by comparing the second-order and fourth-order expansions. The focusing results of the second-order slant range model of the moving target are as follows: Figure 3 As shown. The focusing results based on the fourth-order expansion model of the slant range of the moving target are as follows. Figure 4 As shown in the figure. The specific parameter estimation comparison results are shown in Table 3.

[0179] Table 3. Estimation comparison results of the second-order and fourth-order slant range models at a signal-to-noise ratio of 10 dB.

[0180]

[0181] Where "Peak" represents the coherent cumulative peak value, Z P Represents Z×10 P Z P Represents Z×10 -P When the absolute deviation is less than 10 -4 The value is represented by "0". As shown in Table 3, the focusing effect of the fourth-order slant range model meets the theoretical requirements, proving the effectiveness of the method proposed in this invention.

[0182] In this simulation, the effectiveness of the proposed method for multiple targets is verified. Three moving targets are considered. Moving target 1 is located at (0, 55) m, with an initial azimuth velocity of 3 m / s, an initial range velocity of 2 m / s, and an azimuth acceleration of 0.5 m / s². 2 The acceleration due to distance is 0.2 m / s². 2The moving target 2 is located at (0.8, 60) m, with an initial azimuth velocity of 1.2 m / s, an initial range velocity of 1.6 m / s, and an azimuth acceleration of 0.3 m / s². 2 The acceleration due to distance is 0.4 m / s². 2 The moving target 3 is located at (-0.8, 66) m, with an initial velocity of 1 m / s in the azimuth dimension, an initial velocity of 4 m / s in the range dimension, and an acceleration of 1 m / s² in the azimuth dimension. 2 The range of acceleration is 1 m / s². 2 . Figure 5 The results of range migration correction and focusing for multiple moving targets are displayed. From Figure 5 It can be seen that the distance migration correction process and slant range coefficient estimation method proposed in this invention are effective for detecting and focusing multiple moving targets.

Claims

1. A method for estimating high-order motion parameters of moving targets in a miniature frequency-demodulated millimeter-wave radar, characterized in that, Includes the following steps: (1) The echo signal of the moving target received by the SAR platform is de-frequency modulated to obtain the range de-frequency modulated-slow time domain signal, and the range dimension pulse compression is completed by the range dimension Fourier transform; (2) For the range-demodulated-slow-time domain moving target signal obtained in step (1), the range dimension QRM is corrected by the second-order Keystone transform of the demodulated signal. (3) For the echo signal after QRM correction, the slope of the line segment is detected by LSD line segment detection technology and the first-order slope distance coefficient is solved; then a compensation function is constructed to compensate LRM so that the trajectory of the moving target is focused at the same distance cell. (4) Extract the target trajectory signal after the distance migration was eliminated in step (3) at the same distance cell, which contains the residual unknown slant range coefficients, and estimate the residual slant range expansion coefficients; (5) Use all the motion parameters obtained in the above steps to focus on the unknown moving target signal, thus completing the parameter estimation for moving target detection; The implementation process of step (1) is as follows: Millimeter-wave radar The transmitted signal with a pulse repetition interval is represented as: （1） in, Is it fast time or distance time? Is it slow time or location time? It is the pulse repetition interval. It is absolute time; It is the scan duration or pulse width. It is the carrier frequency. It is the linear frequency modulation slope. It is a rectangular window function; distance The echo signal received at the location is: （2） in, , The reference signal used for difference frequency processing is a distance of... Echo signal at: （3） in, The frequency difference calculation between the echo signal and the reference signal is as follows: （4） in, , , It is the azimuth coherence processing time; the first exponential term in equation (4) is the residual video phase RVP. Ignoring its influence, after eliminating the RVP term, it becomes: （5） The specific echo delay is expressed as follows: in, It is only with slow time The relevant slow-time slant distance, It is only related to fast time Relevant slant distance; scan duration Shorter than To ignore the effects of intrapulse Doppler, its relationship with fast time Relatedly, equation (5) is simplified to: （6） Rearranging equation (6), we get: （7） in, Let the transmitted signal be used as the reference signal for the difference frequency operation, and equation (7) is further simplified to: （8） in, , It is a range-dimensional delinear frequency modulation; the general slant range model for moving targets by a moving radar platform or a static radar platform is: （9） in and The equivalent velocity, acceleration, jerk, and more complex slant range parameters of the moving target are represented; substituting (9) into (8), the general range-demodulated frequency-slow time domain difference frequency signal model for demodulated frequency-slow time domain millimeter-wave radars for different applications is expressed as: （10） Performing a Fourier transform on the above equation in the distance dimension completes the pulse compression in the distance dimension. The implementation process of step (2) is as follows: Define the second-order trapezoidal transform (DSOKT) for delinear frequency modulation to correct the QRM in the slow time domain: （11） in, It is the azimuth slow time of resampling; substituting equation (11) into equation (10) yields: （12） Equation (12) eliminates the second-order slow time and delinearized frequency modulation distance. The coupling is such that only the coupling between the first-order slow time and the delinear frequency modulation distance frequency exists; The implementation process of step (3) is as follows: For satisfying The delinear frequency-modulated millimeter-wave radar system, according to the first-order Taylor series expansion, yields the following approximation: （13） Substituting equation (13) into equation (12), we get: （14） Performing a distance-dimensional Fourier transform on equation (14) yields: （15） As can be seen from equation (15), the energy of the target is concentrated on the line segment where QRM has been eliminated, and its specific form is: The slope of the line segment is: （16） Using the LSD segment detection technique to obtain the slope, the compensation term of the LRM is constructed as follows: （17） Multiplying equation (17) by equation (14), we obtain the distance delinearized frequency modulation-slow time signal of the moving target after LRM correction as follows: （18） Equation (18) is converted to the range pulse compression domain and expressed as: （19） Slope estimation of a line segment, and The relevant information is obtained through the line segment detector LSD. At this point, the RCM, including LRM and QRM, has been calibrated; the target is now focused on the line segment within the distance pulse compression domain – slow time domain. It achieves decoupling of distance and orientation dimensions without requiring any prior knowledge of the target.

2. The method for estimating high-order motion parameters of moving targets in a miniature de-frequency-modulated millimeter-wave radar according to claim 1, characterized in that, The echo signal in step (1) includes a complex trajectory of a high-order slant range model that couples the range and azimuth dimensions.

3. The method for estimating high-order motion parameters of moving targets in a miniature de-modulated millimeter-wave radar according to claim 2, characterized in that, The implementation process of step (4) is as follows: Extracting distance units Taking into account the cumulative duration of the azimuth pulse at the location, equation (19) is further expressed as: （20） in, It is known and with Irrelevant Resampling time The azimuth rectangular window function; omitting the constant complex amplitude, formula (20) is further simplified to: （21） Formula (21) contains the slant range coefficient of the target to be estimated. The following compensation function is constructed: （22） in, The known first-order slope distance coefficients are obtained from (16). The unknown higher-order coefficients of the residuals to be estimated are then used to construct the following objective function: （23） when When equation (23) is coherent, the objective function reaches its maximum value; otherwise, equation (23) is incoherent superposition, leading to a certain degree of intensity cancellation. Therefore The estimated value was obtained in the following way: （24） Equation (24) is solved by exhaustively searching the residual parameters.

4. The method for estimating high-order motion parameters of moving targets in a miniature de-modulated millimeter-wave radar according to claim 3, characterized in that, The implementation process of step (5) is as follows: Using the estimated and known and Construct a matched filter function for the azimuth dimension: （25） By multiplying the above equation with equation (19) and then performing a Fourier transform in the orientation dimension, the moving target can be focused.

5. A device, characterized in that, Includes memory and processor, wherein: Memory is used to store computer programs that can run on a processor; A processor, configured to, while running the computer program, perform the steps of the method for estimating higher-order motion parameters of a moving target using a miniature de-modulated millimeter-wave radar as described in any one of claims 1 to 4.

6. A storage medium, characterized in that, The storage medium stores a computer program that, when executed by at least one processor, implements the steps of the method for estimating high-order motion parameters of a moving target using a miniature de-modulated millimeter-wave radar as described in any one of claims 1 to 4.

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