A high-speed target time-domain synthetic ultra-wideband imaging method based on phase estimation speed

Abstract

The application discloses a high-speed target time-domain synthetic ultra-wideband imaging method based on phase velocity estimation. First, a high-speed target dechirp echo model based on a frequency modulation stepping signal is established. The model needs to consider the influence of intrapulse Doppler modulation. Then, distance image cross-correlation is performed on the same frequency point sub-pulses of different frames of echoes, and phase velocity estimation is performed, so that high-precision velocity estimation information is obtained, which supports velocity compensation of synthetic ultra-wideband imaging. Finally, time domain shift items, first phase correction items and constant phase correction items of different sub-pulses are derived, and a phase-continuous and longer-duration synthetic pulse is obtained through phase correlation synthesis processing, and then high-quality synthetic ultra-wideband imaging results are obtained.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a high-speed target temporal synthesis ultra-wideband imaging method based on phase inference acceleration in deslant processing mode. Background Technology

[0002] Employing wide-bandwidth signals is beneficial for target perception, yielding richer and more detailed information. Therefore, improving radar resolution has always been a crucial research direction in radar technology development. Ultra-wideband imaging can be achieved by transmitting a series of continuously hopping carrier frequency subpulses, followed by coherent synthesis. This simultaneously addresses the requirements of small instantaneous bandwidth and large synthesized bandwidth, reducing the complexity of radar system implementation. Simple frequency-stepped signals use single-carrier frequency modulation for each subpulse, resulting in very small subpulse bandwidths. Increasing the number of subpulses is necessary to improve the synthesized bandwidth, but this further reduces the signal data rate. Under the same bandwidth conditions, the number of pulses required can be reduced by increasing the bandwidth of each subpulse. Typical signals include frequency-modulated (FM) stepping signals and phase-coded frequency-stepped signals. FM stepping signals, combining the advantages of linear frequency-modulated (LFM) signals and frequency-stepped signals, are also an important type of synthesized ultra-wideband signal.

[0003] Currently, commonly used methods for synthesizing broadband signals include IFFT (Inverse Fast Fourier Transform) coherent pulse compression, frequency domain stitching, and time domain stitching. IFFT coherent pulse compression is simple and efficient, but subsequent decimation and stitching processes during high-resolution range image synthesis can cause truncation and grating lobes, and it is unsuitable for frequency-modulated step signals with few pulses. Frequency domain stitching synthesizes a large-bandwidth signal by stitching the spectra of different signals in the frequency domain. Therefore, it requires direct sampling of the echo signal, meaning the sampling rate needs to be greater than the bandwidth of each sub-pulse, making this method unsuitable for situations where each sub-pulse has a large bandwidth. For time domain stitching, different methods are required for different types of echo signals. For example, direct sampling of the echo requires stitching the baseband signals of each sub-pulse, involving upsampling, spectrum shifting, and other steps, which is quite complex. However, if the echo requires de-skewing, only time-domain shifting and phase correction are needed, making it relatively simple. De-skewing also reduces the sampling rate requirement, thereby reducing the complexity of the radar system and saving costs. In summary, synthetic ultrawideband signals based on deslant processing have broader application prospects; however, existing signal processing models do not consider the impact of high-speed targets on synthetic ultrawideband imaging. Summary of the Invention

[0004] Considering that the number of sub-pulses of frequency-modulated step signals is relatively small, it is not suitable for IFFT coherent synthesis; in addition, the frequency domain synthesis method has certain requirements on the sampling rate when the sub-pulse bandwidth is large. In order to overcome the above-mentioned defects, this invention proposes a time-domain synthesis ultra-wideband imaging method for high-speed moving targets in deslant processing mode.

[0005] The technical solution for implementing the present invention is as follows:

[0006] A high-speed target temporal synthetic ultrawideband imaging method based on phase inference acceleration includes the following steps:

[0007] Step 1: By analyzing the echo delay of high-speed targets, a descrambling echo model considering the Doppler modulation effect is established based on the frequency-modulated step signal, and the second phase term of the echo is compensated.

[0008] Step 2: Perform FFT (Fast Fourier Transform) on the deslanted echo to obtain a one-dimensional range profile of the target. For the one-dimensional range profiles of pulse echoes at the same frequency in adjacent frames, use phase inference acceleration technique based on cross-correlation of range profiles to obtain the target's velocity estimate. Then, further obtain the target's range and acceleration estimates.

[0009] Step 3: For pulses at different frequencies, time-domain shifting is performed on each sub-pulse based on the estimated values ​​of target velocity, distance, and acceleration; and phase correction is performed on each sub-pulse by considering the first phase correction term and the constant phase correction term of the Doppler modulation effect, so as to obtain a synthetic pulse with continuous phase, thereby obtaining high-quality synthetic ultrawideband imaging results.

[0010] Furthermore, the high-speed target echo delay t obtained in step one of this invention... r for:

[0011]

[0012] Where t is the fast time, R i,n v represents the distance of the target during the observation of the i-th sub-pulse in the n-th frame. i,n Let a be the velocity at the corresponding moment. i,n Let be the acceleration at the corresponding moment, and c be the speed of light.

[0013] Furthermore, in step three of this invention, the time-domain shift phase term in the nth frame of the i-th sub-pulse is in frequency domain form as follows:

[0014]

[0015] The above delays satisfy the following conditions:

[0016]

[0017] Where M is the number of sub-pulses, Δf is the frequency step between each sub-pulse, and k is the frequency modulation slope;

[0018]

[0019] Where ΔR M-i,n =R M,n -R i,n The envelope movement relative to the Mth sub-pulse at frame n of the target i-th sub-pulse.

[0020] Furthermore, in step three, the present invention includes a frequency correction term that considers the Doppler modulation effect during the nth frame of the i-th sub-pulse:

[0021]

[0022] Where f M Let ΔR be the initial carrier frequency of the Mth sub-pulse. ref(M-i,n) =R ref(M,n) -R ref(i,n) The amount of movement relative to the Mth subpulse in the nth frame of the i-th subpulse of the reference gate.

[0023] Furthermore, in step three, the present invention includes a constant phase correction term that considers the Doppler modulation effect in the nth frame of the i-th sub-pulse:

[0024] φ com(i,n) =2π(φ com1(i,n) +φ com2(i,n) +φ com3(i,n) )

[0025] in:

[0026]

[0027]

[0028]

[0029] Beneficial effects:

[0030] (1) The present invention obtains a high-precision estimate of the target velocity by using the phase estimation velocities method, and the velocity estimation accuracy meets the velocity compensation accuracy requirements of synthetic ultra-wideband imaging.

[0031] (2) The present invention constructs a high-speed target deslant echo model, which can realize high-quality synthetic ultra-wideband imaging including high-speed moving targets.

[0032] (3) The phase correction term and constant phase correction term proposed in this invention fully consider the effects of intrapulse Doppler modulation, interpulse distance movement and gate movement in the deskewing process, and can effectively correct the phase of each sub-pulse. Attached Figure Description

[0033] Figure 1 This is a flowchart of the synthesis of ultra-wideband imaging.

[0034] Figure 2 This is a schematic diagram of the time-frequency relationship of a frequency-modulated step signal.

[0035] Figure 3 This is the result of envelope velocity measurement.

[0036] Figure 4 This represents the envelope velocity measurement error.

[0037] Figure 5 To predict the speed of the result.

[0038] Figure 6 This is to estimate the velocity error.

[0039] Figure 7 To synthesize ultra-wideband imaging results. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0041] This invention provides a temporal-domain synthetic ultrawideband imaging method for high-speed targets based on phase estimation acceleration, such as... Figure 1 As shown, a high-speed target deslant echo model based on frequency-modulated step signals is first established, which needs to consider the influence of intra-pulse Doppler modulation. Then, by performing range-image cross-correlation on sub-pulses of the same frequency from different frame echoes and performing phase estimation velocity processing, high-precision velocity estimation information is obtained to support velocity compensation in synthetic ultra-wideband imaging. Finally, the time-domain shift term, first-order phase correction term, and constant phase correction term of different sub-pulses are derived, and a synthetic pulse with continuous phase and longer duration is obtained through coherent synthesis, thus obtaining high-quality synthetic ultra-wideband imaging results.

[0042] The method specifically includes the following steps:

[0043] Step 1: High-speed target deslant echo model based on frequency-modulated step signal

[0044] This step analyzes the echo delay of high-speed targets to establish a descrambling echo model based on a frequency-modulated step signal. Subsequent processing is performed based on this model. Here, a negative linear frequency-modulated signal is used as an example. Figure 2 The time-frequency distribution diagram of the frequency-modulated step signal within one frame is given.

[0045] The signal can then be represented as:

[0046]

[0047] Where T r T is the pulse repetition time, k is the linear frequency modulation slope, and T is the pulse repetition time. p Given the pulse width, B = |kT p | is the time-width-bandwidth product, M is the number of pulses in a frame, f i =f1+(i-1)Δf, (i=1,…M), where f1 is the initial carrier frequency of the first pulse, Δf is the frequency step, and the above M sub-pulses will be combined into a composite pulse with a longer duration.

[0048] Without loss of generality, we will take a uniformly accelerated target as an example, and denote the distance of the target at the nth frame of the i-th sub-pulse as R. i,n Speed ​​is denoted as v i,n The acceleration is a i,n The reference distance for the declination during observation is R. ref(i,n) .

[0049] Considering the echo model of intrapulse Doppler modulation, denote the fast time... The echo after deskewing the i-th pulse is s. r(i,n) (t), then the descrambling echo signal is:

[0050]

[0051] in:

[0052]

[0053]

[0054]

[0055]

[0056] Where ο(t) is a higher-order term, its influence can be ignored. The second phase can be compensated by the target coarse velocity measurement results. This phase has low requirements for velocity compensation accuracy and will not affect the synthetic ultra-wideband imaging. Therefore, the subsequent considerations are mainly the first phase term and the constant phase term of different sub-pulses.

[0057] Step 2: Target motion parameter estimation based on phase velocities estimation technique

[0058] The one-dimensional high-resolution distance images after recording pulse pressure are y i,n (l),y i,n+1 (l), then This represents the Fourier transform. Cross-correlation is performed on the two range images. According to reference [1] (GUO L, FAN H, LIU Q, et al. A Novel High-Accuracy Phase-Derived Velocity Measurement Method for Wideband LFM Radar[J].IEEE Geoscience and RemoteSensing Letters, 2019, 16(4): 529-33.), the cross-correlation result of the range images can be expressed as:

[0059]

[0060] remember

[0061] Δf i,n =f i,n+1 -f i,n (8)

[0062] Δφ i,n =φ i,n+1 -φ i,n (9)

[0063] Equation (7) shows that Δf can be estimated by waveform analysis based on the peak information of the range image cross-correlation results. i ' ,n And extract the phase increment Δφ' i,n .

[0064] In practice, radar data rates are high and the duration within adjacent frames is short. It can be assumed that the target undergoes uniform acceleration motion between adjacent frames.

[0065]

[0066] v i,n+1 =v i,n +a i,n (MT r (11)

[0067] In practice, the initial distance estimate of the target can be obtained by tracking the gate.

[0068]

[0069] A coarse estimate of the acceleration can be obtained by least-squares fitting of the initial distance, according to equations (8)(10)(11)(12) regarding the unknown (R). i,n+1 ,R i,n ;v i,n+1 ,v i,n This can yield coarse envelope velocity measurement results. Its analytical expression can be found in reference [1].

[0070] Phase increment Δφ' is extracted based on the cross-correlation results of the range and image. i,n Due to the periodicity of the phase, the phase increment is ambiguous, differing from the true unambiguous phase by an integer multiple of 2π. The phase ambiguity number is denoted as K. Based on the available envelope measurement results, the phase ambiguity number K is resolved using the help of equation (8), and substituted into equation (8) to obtain the reference phase Δφ. ref(i,n) We can obtain:

[0071]

[0072] In this context, [·] represents rounding.

[0073] After obtaining the ambiguity number K, the deambigued phase is:

[0074]

[0075] The phase velocity estimation results can be obtained from equations (9), (10), (11), and (12). Similarly, its analytical expression can be further found in reference [1].

[0076] Acceleration can be estimated based on the phase inference acceleration results:

[0077]

[0078] Based on the phase estimation acceleration results, the distance increment of the target within adjacent frames can be obtained. Combined with the initial distance estimate, the distance estimate of the target in different frames can be obtained:

[0079]

[0080] in:

[0081] Since the time between adjacent frames is extremely short, it can be assumed that the target is undergoing uniform acceleration motion within adjacent frames. The acceleration estimates for frames N-1 and N, and the velocity estimates for frame N, can be predicted through smoothing filtering.

[0082] In summary, based on phase accelerometer technology, motion parameter estimates of N frames of high-speed targets can be obtained. In the next step, synthetic ultra-wideband imaging will be performed based on the estimated motion parameters (acceleration, velocity, and distance) of the target.

[0083] Step 3: High-speed target synthesis ultra-wideband imaging

[0084] The key to high-speed target synthetic ultra-wideband imaging is accurate velocity compensation, which involves time-domain shifting and phase correction of sub-pulses within a frame to obtain a synthetic pulse with continuous phase and longer duration. In subsequent processing, a reference sub-pulse (with zero time shift and phase correction) can be selected, and the remaining sub-pulses need to undergo corresponding time-domain shifting and phase correction based on the reference sub-pulse. Taking a negative linear frequency modulated signal as an example, the reference sub-pulse is typically the Mth pulse.

[0085] (1) Time-domain shift

[0086] The time shift of the i-th sub-pulse consists of the following three parts: the time-domain shift Δτ1 corresponding to the carrier frequency jump variable relative to the reference sub-pulse, and the envelope movement Δτ2 caused by the high-speed target.

[0087] For the delay Δτ1, based on the time-frequency correspondence with the reference sub-pulse, we obtain:

[0088]

[0089] The time shift of the i-th sub-pulse relative to the reference sub-pulse:

[0090]

[0091] Where ΔR M-i,n =R M,n -R i,n Since a frame is extremely short, the target can be approximated as moving with uniform acceleration, i.e., satisfying:

[0092]

[0093] Therefore, based on the motion parameter estimation results in step two, equation (19) can be substituted into equation (18) for compensation.

[0094] Based on the time-shifting property of the Fourier transform, introducing a linear phase term in the frequency domain f can achieve time-domain shifting. Therefore, the linear phase term that needs to be compensated in the frequency domain for the i-th sub-pulse can be expressed as:

[0095]

[0096] (2) First phase correction

[0097] For different sub-pulse first phase term 2πf i,n The correction of t is only related to the frequency f i,n Therefore, frequency correction is the primary consideration here. The frequency that the i-th sub-pulse needs to be corrected relative to the reference sub-pulse is:

[0098] f cmp(i,n) =f M,n -f i,n(twenty one)

[0099] According to expression (4), different sub-pulses, after deskewing, can be regarded as single-frequency signals (the quadratic phase term has been compensated), which satisfies:

[0100]

[0101] Where R i =R i,n ,x i =v i,n / c, frequency term f of different sub-pulses r1(i,n) With target motion parameters (R) i ,x i Related to ), denoted as g1(R) i ,x i );f r2(i,n) It is independent of the target motion parameters, but only related to the gate.

[0102] Suppose that the pulse satisfies R in adjacent time intervals. M,n =R i,n +ΔR M-i,n v M,n =v i,n +Δv M-i,n , where ΔR M-i,n and Δv M-i,n Let be the distance and velocity increments of the target relative to the M-th sub-pulse at the n-th frame of the i-th sub-pulse, respectively. Then:

[0103] f cmp1(i,n) =g1(R i +ΔR M-i,n ,x i +Δx M-i,n )-g1(R i ,x i ) (twenty three)

[0104] The above equation can be further simplified using Taylor expansion, where g1(R) i +ΔR M-i,n ,x i +Δx M-i,n ) in (R i ,x i Perform a Taylor expansion at point ), according to the Taylor expansion formula:

[0105]

[0106] When considering high-speed targets, the target speed is x km / s. i It is usually 10. -5 No, Δv i,n Since the velocity difference has a smaller velocity change, its first-order term can be ignored, resulting in:

[0107]

[0108] Substituting into (23), we get:

[0109]

[0110] Similarly, considering the gate shift, we obtain the phase term that needs to be compensated:

[0111]

[0112] Therefore, we get:

[0113]

[0114] (3) Constant phase correction term

[0115] The phases of the sub-pulse after time-domain shifting and one phase correction, and the reference sub-pulse, respectively satisfy:

[0116]

[0117] The constant phase that needs to be compensated is:

[0118] φ com(i,n) =2π×[φ M,n -φ i,n +f i,n Δτ1+f i,n Δτ2)] (30)

[0119] Based on the derivation in Appendix A, the above phase consists of the following parts:

[0120] φ com(i,n) ≈2π×[φ com1(i,n) +φ com2(i,n) +φ com3(i,n) (31)

[0121] Where φ com1(i,n) Phase compensation required to account for intra-pulse Doppler modulation effect:

[0122]

[0123] φ com2(i,n) Considering the phase that needs to be compensated for due to inter-pulse envelope movement:

[0124]

[0125] φ com3(i,n) Considering the phase that needs to be compensated for when the gate is shifted:

[0126]

[0127] To verify the correctness of the method provided by this invention, simulation verification is given below, and the simulation parameters are shown in Table 1. It is assumed that the target is undergoing uniformly accelerated motion relative to the radar, with an initial distance of 35 km, an initial velocity of 4000 m / s, and an acceleration of 50 m / s². 2 The number of observation frames was 64, and the signal-to-noise ratio after single-pulse compression was 21.7dB.

[0128] The envelope velocity measurement results of the target and its true velocity value and fitted value are as follows: Figure 3 As shown, the envelope velocity measurement error is as follows: Figure 4 As shown, the root mean square error of the envelope velocity measurement is 5.6528 m / s, and the theoretical accuracy of the envelope velocity measurement is 5.6144 m / s. The measured value is basically consistent with the theoretical value. The corresponding velocity estimation results and their true velocity values ​​are as follows: Figure 5 As shown, the relative velocity error is as follows: Figure 6 As shown, the root mean square error of the phase velocity estimation is 0.1141 m / s, and the theoretical accuracy of the phase velocity estimation is 0.1131 m / s. The measured values ​​are basically consistent with the theoretical values. The synthetic range image result of one frame of data is shown below. Figure 7 As shown, the obtained synthetic one-dimensional range image has a resolution of 0.0408m, while the theoretical synthetic resolution is 0.0405m. The simulation results are basically consistent with the theoretical analysis.

[0129] Table 1 Simulation Parameters

[0130] parameter Value Initial carrier frequency 13GHz Single pulse bandwidth 1GHz Sampling frequency 60MHz Single pulse duration 0.1ms Pulse repetition period 1.2ms Frequency step interval 0.9GHz Frequency step count 4

[0131] Appendix A: Derivation of the constant phase correction term

[0132] Based on the expressions for the sub-pulse after time-domain shift and first phase correction, and the reference sub-pulse, the phase term that needs correction is rewritten here:

[0133] φ com(i,n) =2π×(φ M,n -φ i,n +f i,n Δτ1+f i,n Δτ2) (35)

[0134] The simplified phases described above will be derived separately below.

[0135] (1) Phase considering intrapulse Doppler modulation compensation

[0136] Considering the phase that needs to be compensated for during intra-pulse Doppler modulation, then φ M,n -φ i,n +f i,n The phase Δτ1 above can be simplified into two terms: one independent of the gate and one dependent on the gate. The phase term independent of the gate is:

[0137]

[0138] Where, ψ com(i,n) Initial frequency f containing different pulses i That is, the phase of the first three terms in equation (36); and With the initial carrier frequency f i It is irrelevant to the last two terms of equation (36).

[0139] Phase terms related to the gate:

[0140]

[0141] Δφ2 will be further simplified in (3); the simplification of Δφ1 will be analyzed below.

[0142] · Phase term ψ com(i,n) :

[0143] By R i =R i,n ,x i =v i,n / c, ignoring second-order and higher phases with respect to Δv / c, therefore we have

[0144] Substituting (38) into (36), we obtain the compensated phase term:

[0145]

[0146] Phase term Ignore about Δv i,n From the quadratic term of / c, we get:

[0147]

[0148] Therefore, an approximate compensation is obtained:

[0149]

[0150] In summary, the constant phase term for correction is:

[0151]

[0152] (2) Phase considering envelope movement compensation

[0153] This phase term is derived by considering the effect of the envelope movement caused by the high-speed motion of the target.

[0154]

[0155] One of the phases f i,n and target motion increment ΔR M-i,nIt can be estimated based on existing target motion parameters.

[0156] (3) Phase considering gate shift compensation

[0157] Phase Δφ2 is the phase that needs to be compensated for considering gate movement, and the compensation phase is easily obtained:

[0158]

[0159] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A high-speed target temporal synthetic ultrawideband imaging method based on phase inference velocities, characterized in that, Includes the following steps: Step 1: By analyzing the echo delay of high-speed targets, a descrambling echo model considering the Doppler modulation effect is established based on the frequency-modulated step signal, and the second phase term of the echo is compensated. Step 2: Perform FFT on the deslanted echo to obtain a one-dimensional range profile of the target. For the one-dimensional range profiles of pulse echoes at the same frequency in adjacent frames, use phase inference acceleration technique based on cross-correlation of range profiles to obtain the target's velocity estimate. Then, further obtain the target's range and acceleration estimates. Step 3: For pulses at different frequencies, based on the estimated values ​​of target velocity, distance, and acceleration, time-domain shift is performed on each sub-pulse; and phase correction is performed on each sub-pulse by considering the first phase correction term and the constant phase correction term of the Doppler modulation effect, so as to obtain a synthetic pulse with continuous phase, thereby obtaining high-quality synthetic ultrawideband imaging results. The high-speed target echo delay obtained in step one for: in To save time, For the goal of Subpulse number Distance at frame observation time For the velocity at the corresponding moment, For the acceleration at the corresponding moment, The speed of light; In step three, for the first Subpulse number The time-domain shift phase term in the frame is in the frequency domain form as follows: The above delays satisfy the following conditions: in It is the number of sub-pulses. This represents the frequency step size between each sub-pulse. This is the frequency modulation slope; in For the goal of Subpulse number Frame time relative to the first The envelope movement of each sub-pulse; Step 3 Subpulse number Frequency correction term considering Doppler modulation effect at frame time: in For the first The initial carrier frequency of each sub-pulse For reference to Borment Subpulse number Frame time relative to the first The amount of movement of each sub-pulse For the goal of Subpulse number Frame time relative to the first The velocity increment of each sub-pulse; Step 3 Subpulse number The constant phase correction term considering the Doppler modulation effect at frame time: in, To account for the phase compensation required to account for the intrapulse Doppler modulation effect, To account for the phase compensation required for inter-pulse envelope movement, To account for the phase compensation required for gate shift; 。

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