Motion Error Estimation Method Based on Transform Difference of Adjacent FMCW Pulses

Abstract

The present invention provides a motion error estimation method based on the differential transformation of adjacent pulses of frequency modulated continuous wave, which belongs to the field of frequency modulated continuous wave radar imaging technology. The method includes: dividing the echo signal into two groups of data according to odd and even order; processing the even-order group data to obtain a transformation signal; conjugate multiplying the transformation signals of the odd-order group and the even-order group to obtain a differential signal; and extracting the motion error from the differential signal, integrating it into the imaging process and performing error compensation before frequency domain operation. The present invention does not require cross-correlation operations and upsampling interpolation, and can obtain higher motion parameter estimation accuracy without increasing the amount of calculation; and under high resolution conditions, it can handle the two-dimensional defocus phenomenon caused by large motion errors, and finally obtain higher imaging quality.

Description

Technical Field

[0001] The invention relates to the technical field of frequency modulated continuous wave radar imaging, and in particular to a motion error estimation method based on differential transformation of adjacent frequency modulated continuous wave pulses. Background Art

[0002] As an active microwave remote sensing method, Synthetic Aperture Radar (SAR) is not affected by cloud obstruction or dim light during its working process. It can perform long-distance detection all day and with high efficiency. It has great application value in civilian fields such as geological surveying and vegetation estimation, as well as military fields such as early warning reconnaissance, positioning and tracking.

[0003] Nowadays, on the one hand, due to the limitations of the application environment and available funds, light and small unmanned aerial platforms have low requirements for landing sites and flight space due to their small size and weight, flexible equipment, short equipment development and production cycle, mass production, and low economic cost. More importantly, wartime operations can avoid personnel injuries and improve automated combat capabilities. On the other hand, with the expansion of application fields, the requirements for imaging accuracy are further improved. The use of large-bandwidth signals is the basis for achieving high-resolution imaging, and the development of high-frequency microwave electronic devices also provides favorable conditions for this. Therefore, the combination of light and small airborne platforms and high-resolution SAR provides a powerful way to obtain information and has received widespread attention.

[0004] However, due to the small size and low weight of drones, firstly, their flight state is very susceptible to motion errors caused by airflow disturbances; secondly, their load capacity and power support are limited, and the motion sensors they are equipped with have low measurement accuracy. Large motion errors remain in the echo signals, which ultimately lead to reduced imaging quality and increased difficulty in interpretation. Therefore, for drone SAR imaging, the motion compensation process is essential, and motion estimation based on echo signals is the key and difficulty. The applicant of the present invention found that the prior art has the following technical defects:

[0005] High-frequency SAR is sensitive to motion errors, and high-resolution imaging requires very high precision of motion parameters. In actual situations, motion errors can easily cause the cross-range gate phenomenon of the same target energy, and cause two-dimensional defocusing in the range and azimuth directions. The widely used Phase Gradient Autofocus (PGA) cannot be used directly; and when using a high-efficiency frequency domain imaging algorithm, the frequency domain operation will change the linear relationship between the range migration error and the azimuth phase error in the signal, further increasing the difficulty of estimating and compensating motion errors. At present, there are two types of conventional schemes in the existing algorithms: one is to downsample the signal in the range direction and then perform PGA; the other is to first use a correlation algorithm for envelope correction and then perform PGA. In addition, there are many improvement methods based on the above ideas, but their inherent defects still exist. For example, the downsampling operation in the first type of algorithm will reduce the imaging resolution, and for larger flight trajectory errors, the energy of the same target is severely dispersed, and small multiples of downsampling are difficult to ensure that it is confined to a range gate; in the second type of algorithm, the estimation accuracy of the cross-correlation method based on amplitude grayscale information is only at the pixel level. In order to obtain higher estimation accuracy, upsampling interpolation is required, which increases the amount of calculation, reduces the accuracy in complex low signal-to-noise ratio scenarios, and there is also a risk of error accumulation.

[0006] In addition, the common frequency modulated continuous wave waveforms are mainly sawtooth waves and triangle waves. Among them, the triangle wave can be regarded as a waveform obtained by alternating the emission of sawtooth waves with opposite frequency modulation. According to the fuzzy function of the triangle wave, it has better target resolution ability than the sawtooth wave, and can eliminate the speed-distance coupling phenomenon in the multi-target environment. It is a waveform commonly used in the field of moving target detection. According to this theory, for static target imaging, it can be inverted into an estimation of the flight platform error. There are now works proving that the triangle wave signal can bypass the residual range migration across units and obtain high-precision motion error parameters from the phase. However, it should also be noted that according to the SAR imaging model, it is usually necessary to split it into positive and negative frequency modulated signals and then image them separately. Then the reduction of signal-to-noise is bound to affect the final imaging quality. Therefore, considering the use of sawtooth wave signals, using the dechirp reception characteristics of the frequency modulated continuous wave, according to the corresponding relationship between the sawtooth wave and the triangle wave, and drawing on the application ideas of the triangle wave signal in imaging, the motion error estimation and compensation based on the sawtooth wave is finally realized. Summary of the invention

[0007] In view of this, the main purpose of the present invention is to provide a motion error estimation method based on adjacent pulse transformation difference of frequency modulated continuous wave, in order to solve the above technical problems.

[0008] In order to achieve the above object, the technical solution adopted by the present invention is:

[0009] A motion error estimation method based on adjacent pulse transformation difference of frequency modulated continuous wave comprises the following steps:

[0010] (1) The frequency modulated continuous wave signal is received using the Dechirp method. The expression of the echo signal after removing the residual video phase is as follows:

[0011] S(t r ,t a )=exp{-i2π(γt r +f c )[τ+δτ(t a )]}

[0012] Where, γ represents the modulation frequency of the transmitted signal; f c Indicates the center frequency of the signal; t r Indicates the distance to fast time; t a represents the azimuth slow time; τ is the time delay of the echo; δτ represents the time delay caused by the motion error, which is a function with the slow time as the independent variable. Assuming the motion error is δr, the relationship between the two is approximately δτ=2δrc;

[0013] For a continuous wave signal with a duty cycle of 100%, assuming the pulse width is T r , the slow time is denoted as t a =nT r , and n = 1, 2, 3, ..., N is the sequence number of the pulse, N is the total number of pulses, let it be an even number;

[0014] According to the odd-even sequence, the signals are divided into two groups. Let m represent the new pulse index number of the odd / even signal. The two groups of signals after division are expressed as follows:

[0015]

[0016] Wherein, m=1,2,...,N / 2; Since the motion of the flight platform is continuous and slowly varying, the motion errors of adjacent pulses are considered to be the same;

[0017] (2) Perform distance Fourier transform on the dual sequence data to obtain the distance compression signal:

[0018]

[0019] Among them, f r represents the distance frequency;

[0020] (3) Yes The phase of is conjugated, and the transformed signal is expressed as:

[0021]

[0022] (4) Yes Perform inverse Fourier transform in the distance direction, and the transformed time domain signal is expressed as:

[0023]

[0024] (5) The transformed even sequence S′ e (t r ,m) and the original odd sequence S o (t r ,m) and perform conjugate multiplication to obtain the differential signal:

[0025]

[0026] The differential phase is:

[0027] At this point, the differential signal no longer contains distance dimension information, and all the energy of the target is concentrated in a single range gate at the center of the scene;

[0028] (6) Obtain the phase of the center of the scene, i.e., the differential phase And extract the motion error from it.

[0029] Furthermore, the specific method of step (6) is:

[0030] For any stationary target in the scene, assume that the shortest slant distance between its location and the flight trajectory is r 0 , then when there is no error in the flight platform, the time delay caused by the ideal uniform linear motion is expressed as follows:

[0031]

[0032] Where v is the forward velocity of the flight platform;

[0033] The inherent component introduced by the ideal flight trajectory is eliminated from the differential phase, thereby obtaining the additional phase caused by the motion error; the time delay error caused by non-ideal motion is expressed as follows:

[0034]

[0035] At this point, the estimation of motion error is completed.

[0036] The beneficial effects of the present invention are:

[0037] 1. The present invention provides a motion error estimation and compensation method based on the difference of adjacent odd-even sequences of sawtooth frequency modulated continuous waves. The method does not require prior knowledge related to the error structure and form, is not restricted by the imaging algorithm, and estimates high-order motion errors.

[0038] 2. The estimation process of the present invention is based on phase information, has low computational complexity, can meet the requirements of accuracy and efficiency without the need for upsampling, and has significant advantages such as simplicity, ease of implementation, and high robustness.

[0039] 3. The present invention provides a method of converting a sawtooth wave into a triangular wave, which can give full play to the capabilities of the triangular wave, avoid wasting echo spectrum energy during the imaging process, and maintain the signal-to-noise ratio.

[0040] 4. For SAR high-resolution imaging installed on a small UAV platform, this method does not rely on the measurement of external hardware motion sensors. It can accurately estimate the motion error during flight and integrate error compensation into the imaging process. It can also complete the residual range migration and azimuth phase error. This is of great significance for further reducing the size and weight of the system and reducing economic production costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 An overall flow chart for integrating motion estimation and compensation methods into the imaging process is given.

[0042] Figure 2 The transformation process of even-sequence data and the acquisition process of differential signals are given.

[0043] Figure 3 The corresponding schematic diagram of the range compression image during the differential signal acquisition process is given. DETAILED DESCRIPTION

[0044] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0045] A motion error estimation method based on adjacent pulse transformation difference of frequency modulated continuous wave mainly includes the following steps:

[0046] (1) Assume that the echo signal after Dechirp reception is expressed as follows. Since the influence of the residual video phase is small, it is no longer considered in the analysis process:

[0047] S(t r ,t a )=exp{-i2π(γt r +f c )[τ+δτ(t a )]}

[0048] Among them, t r Indicates the distance to fast time, t a represents the azimuth slow time, γ is the modulation frequency, f cis the center frequency of the signal, τ is the time delay of the echo, δτ represents the motion error, which is a function with slow time as the independent variable. For a frequency modulated continuous wave signal with a duty cycle of 100%, let the pulse width be T r , the slow time can be expressed as t a =nT r , and n = 1, 2, 3, ..., N is the pulse sequence number. Therefore, the motion error can be understood as a function of the pulse sequence number.

[0049] According to the odd and even sequence, the signals are divided into two groups, and they are set as S o (t r ,m) and S e (t r ,m). Let m represent the new pulse index of the odd / even signal, then it can be expressed as:

[0050]

[0051] Wherein, m=1, 2, ..., N / 2; according to the continuity of the flight platform motion, it can be considered that the motion errors of adjacent pulses are the same, that is, the motion error parameters contained in the odd and even sequences are the same.

[0052] (2) Perform distance Fourier transform on the dual sequence data to obtain:

[0053] S E (f r ,m)=sinc[πf r +πγ(τ+δτ)]exp[-i2πf c (τ+δτ)]

[0054] (3) Taking the conjugate of the above distance compressed data, we get:

[0055] S E (t r ,m)=sinc[πf r +πγ(τ+δτ)]exp[i2πf c (τ+δτ)]

[0056] (4) Perform distance inverse Fourier transform on the dual sequence data to obtain:

[0057] S e '(t r ,m)=exp{i2π(-γt r +f c )[τ+δτ(m)]}

[0058] (5) Interfere the processed even sequence with the odd sequence to obtain a differential signal:

[0059]

[0060] in,

[0061] It should be noted that the differential signal no longer has range information, so all energy will be concentrated in a range gate at the center of the scene. The differential phase can be obtained by calculating the phase at the energy location.

[0062] (6) Extract motion error from the above differential signal.

[0063] For a stationary target at a fixed position, let the minimum slant distance be r 0 , whose motion trajectory is fixed and known, and the corresponding time delay can be expressed as follows:

[0064]

[0065] Then, by eliminating the inherent component introduced by the ideal flight trajectory from the phase of the differential signal, the additional phase caused by the motion error can be obtained, and then the time delay error caused by the motion error of the flight platform can be extracted:

[0066]

[0067] Motion error compensation is performed before frequency domain operation, and the compensation function can be expressed as:

[0068] H c (t r ,m)=exp[i2π(γt r +f c )δτ(m)]

[0069] The following uses the range Doppler algorithm as an example to further illustrate this method:

[0070] like Figures 1 to 3 As shown, the method comprises the following steps:

[0071] 1. First, obtain the echo data after de-slanting reception and remove the residual video phase.

[0072] 2. Enter the motion estimation and compensation module, which includes:

[0073] (1) Divide and combine the data according to the odd-even sequence to form two groups of data, odd-order and even-order, and obtain the differential signal. The specific process is:

[0074] a. Compress the echo data in the range direction, select the range gate with high signal-to-noise ratio according to the energy, contrast and other indicators, and perform window selection;

[0075] b. Perform inverse Fourier transform on the windowed data;

[0076] c. Divide the data into two groups according to the odd-even order;

[0077] d. Perform the following operations on the dual sequence group data: perform Fourier transform in the distance direction, take the conjugate, perform inverse Fourier transform in the distance direction, and obtain the transformed signal;

[0078] e. conjugate multiplying the odd-order group and the transformed even-order group data to obtain a differential signal;

[0079] (2) Performing Fourier transform on the differential signal and obtaining the phase of the compression position;

[0080] (3) Eliminate the fixed phase caused by the ideal trajectory and solve for the motion error.

[0081] (4) Construct a matching function based on the motion error and perform motion error compensation on the echo data.

[0082] 3. Perform distance Fourier transform to achieve distance compression.

[0083] 4. Perform secondary phase compensation and range migration correction.

[0084] 5. Perform azimuth matching filtering to achieve two-dimensional compression.

[0085] In summary, the present invention does not require cross-correlation operations and upsampling interpolation, and can obtain higher motion parameter estimation accuracy without increasing the amount of calculation; and under high resolution conditions, it can handle the two-dimensional defocusing phenomenon caused by large motion errors, and ultimately obtain higher imaging quality.

Claims

1. A motion error estimation method based on adjacent pulse transformation difference of frequency modulated continuous wave, characterized in that: The following steps are involved: (1) The frequency modulated continuous wave signal is received using the Dechirp method. The expression of the echo signal after removing the residual video phase is as follows: S(t r ,t a )=exp{-i2π(γt r +f c )[τ+δτ(t a )]} Where, γ represents the modulation frequency of the transmitted signal; f c Indicates the center frequency of the signal; t r Indicates the distance to fast time; t a represents the azimuth slow time; τ is the time delay of the echo; δτ represents the time delay caused by the motion error, which is a function with the slow time as the independent variable. Assuming the motion error is δr, the relationship between the two is approximately δτ=2δr / c; For a continuous wave signal with a duty cycle of 100%, assuming the pulse width is T r , the slow time is denoted as t a =nT r , and n = 1, 2, 3, ..., N is the sequence number of the pulse, N is the total number of pulses, let it be an even number; According to the odd-even sequence, the signals are divided into two groups. Let m represent the new pulse index number of the odd / even signal. The two groups of signals after division are expressed as follows: Wherein, m=1,2,...,N / 2; Since the motion of the flight platform is continuous and slowly varying, the motion errors of adjacent pulses are considered to be the same; (2) Perform distance Fourier transform on the dual sequence data to obtain the distance compression signal: S E (f r ,m)=sinc[πf r +π(τ+δτ)]exp[-i2πf c (t+dt)] Among them, f r represents the distance frequency; (3) For S E (f r ,m) takes the conjugate phase, and the transformed signal is expressed as: S E (f r ,m)=sinc[πf r +π(τ+δτ)]exp[i2πf c (t+dt)] (4) For S E (f r ,m) performs inverse Fourier transform in the distance direction, and the transformed time domain signal is expressed as: S e '(t r ,m)=exp{i2π(-γt r +f c )[τ+δτ(m)]} (5) The transformed even sequence S e '(t r ,m) and the original odd sequence S o (t r ,m) and perform conjugate multiplication to obtain the differential signal: The differential phase is: At this point, the differential signal no longer contains distance dimension information, and all the energy of the target is concentrated in a single range gate at the center of the scene; (6) Obtain the phase of the center of the scene, i.e., the differential phase And extract the motion error from it.

2. The motion error estimation method based on adjacent pulse transformation difference of frequency modulated continuous wave according to claim 1, characterized in that: The specific method of step (6) is: For any stationary target in the scene, assuming that the closest slant distance between its position and the flight trajectory is r0, then when there is no error in the flight platform, the time delay caused by the ideal uniform linear motion is expressed as follows: Where v is the forward velocity of the flight platform; The inherent component introduced by the ideal flight trajectory is eliminated from the differential phase to obtain the additional phase caused by the motion error; the time delay error caused by non-ideal motion is expressed as follows: At this point, the estimation of motion error is completed.

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