Improved non-linear imaging radar CS imaging method

Abstract

The invention provides an improved non-linear imaging radar CS imaging method, which comprises the following steps of: firstly, deducing an echo model of a signal from the basic principle of a non-linear radar, improving a CS algorithm by combining the echo characteristics of the non-linear radar on the basis of the echo model, giving the flow of the algorithm, comparing the improved Chirp Scaling scaling factor, and obtaining the CS imaging result of the non-linear radar. And distance modulation after scaling and other imaging steps different from the conventional CS algorithm are carried out, and simulation is carried out by using a point target, so that the effectiveness of the algorithm is verified.

Description

Technical Field

[0001] The invention belongs to the technical field of synthetic aperture radar imaging and relates to an improved nonlinear imaging radar CS imaging algorithm. Background Art

[0002] The proposal of nonlinear radar originated in the 1970s. In the following decades, the relevant theoretical research and practical application of nonlinear radar have been developing continuously. In the 1970s and 1980s, in the early stage of nonlinear radar research, Patterson, Powers, Hong and others conducted research on nonlinear modeling of nonlinear transfer functions, cross-sectional area and radar equation of nonlinear scatterers, and secondary nonlinear wave synthetic aperture radar. In the 1990s, Chen Rushan and others proposed dual-frequency nonlinear radar, which avoided adding a 100dB band-stop filter in front of the transmitter, bringing great convenience to the implementation of the project. Kyle A. Gallagher and others compared linear radar and nonlinear radar and gave synthetic aperture radar images of linear and nonlinear targets. Studies have shown that nonlinear synthetic aperture radar has a good ability to detect small targets.

[0003] Gregory J.Mazzaro and others from the U.S. Army Research Laboratory (ARL) studied nonlinear short-range airborne nonlinear radars, obtained the frequency response of nonlinear radars through experiments, and gave the applicable scope of nonlinear radars to detect nonlinear targets in complex environments. Kyle A.Gallagher studied nonlinear radar imaging of stationary and moving objects, and reconstructed them using the FFTs algorithm. The experiment found that the radar system can detect nonlinear targets at least 7.9 meters away and has strong anti-interference ability. The results confirmed that the clutter suppression ability of nonlinear radars is stronger than that of fundamental linear radars. In 2018, Riccardo Maggiora developed a new type of nonlinear radar that can track insects within a range of 500 meters. In 2019, Bischeltsrieder expanded the application of nonlinear radars in the field of security inspection, using the nonlinear effects of circuit elements and major semiconductor elements to generate location maps of electronic devices, and gave solutions for detecting and locating electronic devices within the measurement range. In 2021, Tanisha G et al. proposed an improved nonlinear radar architecture for distinguishing cooperative targets from non-cooperative targets, verifying the target recognition capability of nonlinear radars. Bischeltsrieder F et al. studied the impact of nonlinear radar multipath on imaging in 2021, revealed the difference between nonlinear radar and classical radar imaging, and proposed a new nonlinear radar imaging algorithm. Lima RA et al. discussed the use of high-order nonlinear filters to replace traditional cascade filters in 2022, making nonlinear radar systems more portable and easier to operate.

[0004] It can be seen from the previous research that simple algorithms such as FFT and BP were used in the early stage of nonlinear radar imaging, and there was a lack of research and derivation of algorithms in the frequency domain. Summary of the invention

[0005] The purpose of the present invention is to overcome the deficiencies of the prior art and to propose an improved nonlinear imaging radar CS imaging method suitable for data processing of nonlinear imaging radar.

[0006] The technical solution of the present invention is:

[0007] An improved nonlinear imaging radar CS imaging method, the steps are as follows:

[0008] Step 1: Acquire echo data and derive the nonlinear imaging radar echo model;

[0009] Step 2: Transform the echo data into the range Doppler domain through azimuth FFT;

[0010] Step 3: Implement Chirp Scaling operation through phase multiplication to make the range migration trajectory of all targets consistent;

[0011] Step 4: Convert the data to two-dimensional frequency domain through distance FFT;

[0012] Step 5: By phase multiplication with the reference function, range compression, SRC and consistent RCMC are completed simultaneously;

[0013] Step 6: Convert the data back to the range Doppler domain through range IFFT;

[0014] Step 7: By performing phase multiplication with the reference function, azimuth compression and additional phase correction are completed simultaneously;

[0015] Step 8: Convert the data back to the two-dimensional time domain through azimuth IFFT to obtain the SAR image.

[0016] Furthermore, the acquisition of echo data and derivation of a nonlinear imaging radar echo model are specifically as follows:

[0017] (1.1) The radar transmission signal is in the form of a pulse with linear frequency modulation characteristics:

[0018] S pul (τ) = w r (τ)cos(2πf 0 τ+πK r τ 2 )

[0019] Among them, τ is the distance time, with the pulse center as the reference origin, f0 is the carrier frequency, K r is the range pulse modulation frequency, w r (τ) is the pulse envelope in the range direction;

[0020] (1.2) Assuming that the pulse beam illuminates a point target at a distance R(η), the radar signal reaching the point target is

[0021]

[0022] Among them, w a (η) is the azimuth pulse envelope, η a is the beam center moment, c is the speed of light, and η is the azimuth time;

[0023] (1.3) Assuming that the transmitting and receiving antennas are close to each other and share the equivalent antenna phase center, the radar signal reaching the receiver is expressed as

[0024]

[0025] Among them, k n It is the amplitude coefficient of the fundamental wave and harmonics scattered after the linear frequency modulation signal acts on the scatterer, which is related to the nonlinear characteristics of the irradiated target;

[0026] (1.4) According to Taylor series expansion and double angle formula, only considering the third order series expansion, we get the following formula

[0027]

[0028] Among them, a 1 、a 2 、a 3 are the 1st, 2nd and 3rd order signal amplitudes, V 0 is the amplitude of the part that changes with the order, ω 0 is the signal frequency;

[0029] Refer to the above formula for the radar signal S reaching the receiver r (τ,η) is expanded by Taylor series to obtain:

[0030]

[0031] in

[0032]

[0033] Among them, k 0 ′ is a DC signal, k 1 ′, k 2 ′ and k 3 ′ is S r (τ,η) The Doppler expansion coefficient of the corresponding order;

[0034] (1.5) When the echo signal is filtered out by cos(2πN har f 0 τ) of N har Subharmonic, get N har Point target signal model in subharmonic imaging mode, that is, nonlinear imaging radar echo model:

[0035]

[0036] in, is the slant distance between the radar and the target in the case of direct side view, R 0 is the shortest slope distance, V r is the platform movement speed, η is the azimuth time relative to the nearest point position; k N ′ is N har Sub-Doppler expansion coefficient.

[0037] Furthermore, the echo data is transformed into the range Doppler domain by azimuth FFT, specifically:

[0038] For the echo signal S N (τ,η) is transformed into the range-Doppler domain by performing FFT along the azimuth direction;

[0039]

[0040] Among them, f η is the distance frequency, A 1 is the echo signal amplitude, migration parameter W a is the azimuthal envelope, f η is the azimuth frequency, f ηc is the azimuth center frequency, K m is the range modulation frequency in the range Doppler domain.

[0041] Furthermore, the Chirp Scaling operation is implemented by phase multiplication to make the distance migration trajectories of all targets consistent, specifically:

[0042] The chirp scaling function is shown below:

[0043]

[0044] in, is the reference center frequency, is the reference rate, R ref is the reference distance.

[0045] Furthermore, the echo data is transformed into a two-dimensional frequency domain by using the range-direction FFT, specifically:

[0046] For S 1 (τ,f η ) and S scN (τ,f η ) is transformed into the distance Fourier transform, written as

[0047] S 2 (f τ ,f η )=∫S 1 (τ,f η )S scN (τ,f η )exp(-j2πf τ τ)dτ

[0048] Among them, f τ is the distance frequency;

[0049] According to the stationary phase principle, the phase derivative is taken to find the distance time where the derivative is zero.

[0050]

[0051] make get

[0052]

[0053] It can be seen from the above formula that the change of the nonlinear radar two-dimensional spectrum is caused by the last sub-term; the Fourier transform result of the distance is written as

[0054]

[0055] Among them, A 2 is the amplitude of the two-dimensional frequency domain signal after scaling.

[0056] Furthermore, the first reference function is as follows:

[0057]

[0058] Furthermore, the data is converted back to the range Doppler domain by using the range IFFT, specifically:

[0059] For S 2 (f τ ,f η ) and H r (f τ ,f η ) and perform inverse Fourier transform of the distance to obtain

[0060]

[0061] Among them, A 3 is the signal amplitude after distance compression.

[0062] Furthermore, the second reference function is as follows:

[0063]

[0064] Furthermore, the data is converted back to the two-dimensional time domain through the azimuth IFFT to obtain the SAR image, specifically:

[0065] For S 3 (τ,f η ) and H a (τ,f η ) and perform inverse Fourier transform on the azimuth direction to obtain

[0066]

[0067] Among them, θ(τ,η) is the target phase, A 4 is the signal amplitude after two-dimensional pulse compression, p r is the distance envelope, which is ω r (f τ ), p a is the distance envelope, which is W a (f η ), θ(τ,η) is the point target phase, η c is the zero Doppler time.

[0068] The beneficial effects of the present invention compared with the prior art are:

[0069] Traditional imaging algorithms are derived based on fundamental wave echo models. Nonlinear radar echoes are secondary or tertiary nonlinear echoes excited by the receiving target, which makes traditional imaging algorithms unsuitable for nonlinear radars. Although there are nonlinear radar imaging processing algorithms in the public literature, they all use simple algorithms such as FFT and BP, which have low computational efficiency, and there is a lack of research and derivation of algorithms in the frequency domain. This patent proposes an improved nonlinear imaging radar CS imaging algorithm, derives the echo model of nonlinear radar signals, improves the CS algorithm on this basis, and gives the algorithm flow. The point target is used for simulation to verify the effectiveness of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 This is a flow chart of an improved nonlinear imaging radar CS imaging algorithm;

[0071] Figure 2This is a schematic diagram of the compression result of the fundamental radar point target;

[0072] Figure 3 This is a schematic diagram of the compression results of the second harmonic radar point target;

[0073] Figure 4 This is a schematic diagram of the compression results of third harmonic radar point targets. DETAILED DESCRIPTION

[0074] The present invention provides an improved nonlinear imaging radar CS imaging method. During the research process, it was found that the nonlinear imaging radar technology uses the nonlinear characteristics of the detection target to receive the nonlinear component scattered by the target to detect the target. Unlike the fundamental wave radar that only receives the reflected signal of the fundamental wave, the nonlinear radar receives the secondary or tertiary nonlinear echo excited by the target. This causes the echo model of the nonlinear imaging radar to be inconsistent with that of the traditional SAR imaging radar. The traditional CS imaging algorithm is derived based on the echo model. Therefore, the traditional CS imaging algorithm is not suitable for nonlinear imaging radar. It is necessary to develop an improved CS imaging algorithm to be suitable for the data processing of nonlinear imaging radar.

[0075] like Figure 1 As shown, the present invention proposes an improved nonlinear imaging radar CS imaging method, the main steps of which are as follows:

[0076] Step 1: Obtain echo data and derive the nonlinear imaging radar echo model.

[0077] The radar transmission signal can be simplified as a pulse with linear frequency modulation characteristics:

[0078] S pul (τ) = w r (τ)cos(2πf 0 τ+πK r τ 2 )

[0079] Among them, τ is the distance time, with the pulse center as the reference origin, f 0 is the carrier frequency, K r is the range pulse modulation frequency, w r (τ) is the pulse envelope in the range direction.

[0080] Assuming that the beam illuminates a point target at a distance R(η), the radar signal reaching the point target is

[0081]

[0082] Among them, w a (η) is the azimuth pulse envelope, η a is the beam center moment, c is the speed of light, and η is the azimuth time;

[0083] Under the irradiation of the external excitation field, the nonlinear target will not only generate the fundamental wave, but also radiate harmonics. If the transmitting and receiving antennas are close to each other and share the equivalent antenna phase center, the radar signal reaching the receiver can be expressed as

[0084]

[0085] Among them, k n It is the amplitude coefficient of the fundamental wave and each harmonic scattered after the linear frequency modulation signal acts on the scatterer, and is related to the nonlinear characteristics of the irradiated target.

[0086] According to Taylor series expansion and double angle formula, only considering the third order series expansion, we get the following formula

[0087]

[0088] Among them, a 1 、a 2 、a 3 are the 1st, 2nd and 3rd order signal amplitudes, V 0 is the amplitude of the part that changes with the order, ω 0 is the signal frequency;

[0089] Refer to the above formula for the radar signal S reaching the receiver r (τ,η) is expanded by Taylor series to obtain:

[0090]

[0091] in

[0092]

[0093] Among them, k 0 ′ is a DC signal, k 1 ′, k 2 ′ and k 3 ′ is S r (τ,η) The Doppler expansion coefficient of the corresponding order;

[0094] When the echo signal is filtered out by cos(2πN har f 0 τ) of N har Subharmonic radar receiver, get N har Point target signal model in subharmonic imaging mode

[0095]

[0096] in, is the slant distance between the radar and the target in the case of direct side view, R 0is the shortest slope distance, V r is the platform movement speed, and η is the azimuth time relative to the nearest point position. N ′ is N har Sub-Doppler expansion coefficient.

[0097] Step 2: Transform the echo data into the range Doppler domain through azimuth FFT.

[0098] The CS algorithm first performs an N (τ,η) is transformed into the range-Doppler domain S(τ,f η ).

[0099]

[0100] Among them, f η is the distance frequency, A 1 is the echo signal amplitude, migration parameter W a is the azimuthal envelope, f η is the azimuth frequency, f ηc is the azimuth center frequency, K m is the range modulation frequency in the range Doppler domain.

[0101] Step 3: Implement Chirp Scaling operation by phase multiplication to make the range migration trajectory of all targets consistent. The scaling function is shown as follows

[0102]

[0103] is the reference center frequency, is the reference rate, R ref is the reference distance. The scaling function is used to multiply the signal phase, thereby realizing the Chirp Scaling operation.

[0104] Step 4: Convert the data to two-dimensional frequency domain through distance FFT.

[0105] For S(τ,f η ) and S scN (τ,f η ) can be written as

[0106] S 2 (f τ ,f η )=∫S 1 (τ,f η )S scN (τ,f η )exp(-j2πf τ τ)dτ

[0107] Among them, f τ is the distance frequency.

[0108] According to the stationary phase principle (POSP), the phase derivative is found to be zero distance time

[0109]

[0110] make get

[0111]

[0112] From the above formula, we can see that the change of the nonlinear radar two-dimensional spectrum is caused by the last sub-term. The Fourier transform result of the distance can be written as

[0113]

[0114] Among them, A 2 is the amplitude of the two-dimensional frequency domain signal after scaling.

[0115] From the perspective of signal processing, nonlinear radar causes changes in azimuth modulation and scaled range modulation, and the position of the point target R 0 / D(f ηref ,V rref )’s linear phase and range migration cancel each other out, and their influence can be ignored.

[0116] Step 5: By phase multiplication with the reference function, range compression, SRC and consistent RCMC are completed simultaneously. The reference function is shown as follows

[0117]

[0118] Step 6: Convert the data back to the range-Doppler domain through range-direction IFFT.

[0119] For S 2 (f τ ,f η ) and H r (f τ ,f η ) and perform inverse Fourier transform of the distance to obtain

[0120]

[0121] Step 7: By multiplying the phase with the reference function, azimuth compression and additional phase correction are completed at the same time. The reference function is shown as follows

[0122]

[0123] Among them, A 3 is the signal amplitude after distance compression.

[0124] Step 8: Convert the data back to the two-dimensional time domain through azimuth IFFT to obtain the SAR image.

[0125] For S 3 (τ,f η ) and H a (τ,f η ) and perform inverse Fourier transform on the azimuth direction to obtain

[0126]

[0127] Among them, θ(τ,η) is the target phase, θ(τ,η) is the target phase, A 4 is the signal amplitude after two-dimensional pulse compression, p r is the distance envelope, which is ω r (f τ ), p a is the distance envelope, which is W a (f η ), θ(τ,η) is the point target phase, η c is the zero Doppler time.

[0128] Example:

[0129] Table 1 compares the core processing flow of the traditional CS algorithm and the improved CS algorithm for nonlinear radar.

[0130] Table 1 Processing flow of traditional CS and improved nonlinear radar CS algorithm

[0131]

[0132]

[0133] In order to verify the effectiveness of the proposed method, the following parameters are selected for simulation verification.

[0134] The flight mode of the positive side-view airborne SAR is adopted. The parameters of the simulation system are shown in Table 2. The simulation analysis is performed on the fundamental wave, second harmonic wave and third harmonic wave imaging modes respectively. The radar range resolution ρ under the fundamental wave is r =0.5m, azimuth resolution ρ a =0.5m.

[0135] Table 2 Computer simulation parameters

[0136] Imaging area center distance 500m Platform operation speed 10m / s Bottom View 60° Pulse Width 5us Center frequency 1.2GHz Pulse repetition frequency 1000Hz bandwidth 300MHz Antenna azimuth aperture 1m

[0137] The simulation results of point targets in fundamental wave, second harmonic and third harmonic imaging modes are shown in Figure 2. Figures 2 to 4 As shown in Table 3, it can be seen from Table 3 that the nonlinear radar has no effect on the azimuth resolution, and the range resolution is improved by the corresponding order times.

[0138] Table 3 Point target compression results based on CS algorithm

[0139]

[0140] The effectiveness of the method of the present invention can be seen from the above examples.

[0141] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. An improved nonlinear imaging radar CS imaging method, characterized in that include: (1) Acquire echo data and derive a nonlinear imaging radar echo model; (2) Transform the echo data into the range Doppler domain through azimuth FFT; (3) Chirp Scaling operation is implemented through phase multiplication to make the range migration trajectories of all targets consistent; (4) Transform the echo data into the two-dimensional frequency domain through range-direction FFT; (5) By transforming to the two-dimensional frequency domain and performing phase multiplication with the first reference function, range compression, SRC, and consistent RCMC are completed simultaneously; (6) Convert the data back to the range Doppler domain through range IFFT; (7) by converting back to the range Doppler domain and performing phase multiplication with the second reference function, azimuth compression and additional phase correction are simultaneously completed; (8) The data is transformed back to the two-dimensional time domain through azimuth IFFT to obtain the SAR image.

2. The improved nonlinear imaging radar CS imaging method according to claim 1, characterized in that: The acquisition of echo data and derivation of a nonlinear imaging radar echo model are specifically as follows: (1.1) The radar transmission signal is in the form of a pulse with linear frequency modulation characteristics: S pul (τ)=w r (τ)cos(2πf0τ+πK r t 2 ) Among them, τ is the distance time, the pulse center is the reference origin, f0 is the carrier frequency, K r is the range pulse modulation frequency, w r (τ) is the pulse envelope in the range direction; (1.2) Assuming that the pulse beam illuminates a point target at a distance R(η), the radar signal reaching the point target is Where wa(η) is the azimuth pulse envelope, η a is the beam center moment, c is the speed of light, and η is the azimuth time; (1.3) Assuming that the transmitting and receiving antennas are close to each other and share the equivalent antenna phase center, the radar signal reaching the receiver is expressed as Among them, k n It is the amplitude coefficient of the fundamental wave and harmonics scattered after the linear frequency modulation signal acts on the scatterer, which is related to the nonlinear characteristics of the irradiated target; (1.4) According to Taylor series expansion and double angle formula, only considering the third order series expansion, we get the following formula Among them, a1, a2, a3 are the amplitudes of 1st, 2nd and 3rd order signals respectively, V0 is the amplitude of the part that changes with the order, and ω0 is the signal frequency; Refer to the above formula for the radar signal S reaching the receiver r (τ,η) is expanded by Taylor series to obtain: in Among them, k0′ is the DC signal, k1′, k2′ and k3′ are S r (τ,η) The Doppler expansion coefficient of the corresponding order; (1.5) When the echo signal is filtered by cos(2πNharf0τ) har Subharmonic, get N har Point target signal model in subharmonic imaging mode, that is, nonlinear imaging radar echo model: in, is the slant distance between the radar and the target in the case of positive side view, R0 is the shortest slant distance, V r is the platform movement speed, η is the azimuth time relative to the nearest point position; k N ′ is N har Sub-Doppler expansion coefficient.

3. The improved nonlinear imaging radar CS imaging method according to claim 2, characterized in that: The echo data is transformed into the range Doppler domain by azimuth FFT, specifically: For the echo signal S N (τ,η) is transformed into the range-Doppler domain by performing FFT along the azimuth direction; Among them, f η is the range frequency, A1 is the echo signal amplitude, and migration parameter W a is the azimuthal envelope, f η is the azimuth frequency, f ηc is the azimuth center frequency, K m is the range modulation frequency in the range Doppler domain.

4. The improved nonlinear imaging radar CS imaging method according to claim 3, characterized in that: The Chirp Scaling operation is implemented by phase multiplication to make the distance migration trajectory of all targets consistent, specifically: The chirp scaling function is shown below: in, is the reference center frequency, is the reference rate, R ref is the reference distance.

5. The improved nonlinear imaging radar CS imaging method according to claim 4, characterized in that: The echo data is transformed into the two-dimensional frequency domain by using the distance FFT, specifically: For S1(τ,f η ) and S scN (τ,f η ) is transformed into the distance Fourier transform, written as S2(f τ ,f η )=∫S1(τ,f η )S scN (t,f η )exp(-j2πf τ t)dt Among them, f τ is the distance frequency; According to the stationary phase principle, the phase derivative is taken to find the distance time where the derivative is zero. make get It can be seen from the above formula that the change of the nonlinear radar two-dimensional spectrum is caused by the last sub-term; the Fourier transform result of the distance is written as Among them, A2 is the amplitude of the two-dimensional frequency domain signal after scaling.

6. The improved nonlinear imaging radar CS imaging method according to claim 5, characterized in that: The first reference function is shown as follows 7. The improved nonlinear imaging radar CS imaging method according to claim 6, characterized in that: The data is converted back to the range Doppler domain by using the range IFFT, specifically: For S2(f τ ,f η ) and H r (f τ ,f η ) and perform inverse Fourier transform of the distance to obtain Among them, A3 is the signal amplitude after distance compression.

8. The improved nonlinear imaging radar CS imaging method according to claim 7, characterized in that: The second reference function is as follows 9. The improved nonlinear imaging radar CS imaging method according to claim 8, characterized in that: The azimuth IFFT is used to transform the data back to the two-dimensional time domain to obtain the SAR image, specifically: For S3(τ,f η ) and H a (τ,f η ) and perform inverse Fourier transform on the azimuth direction to obtain Among them, θ(τ,η) is the target phase, A4 is the signal amplitude after two-dimensional pulse compression, and p r is the distance envelope, which is ω r (f τ ), p a is the distance envelope, which is W a (f η ), θ(τ,η) is the point target phase, η c is the zero Doppler time.

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