CN116660886A - Broadband speed measuring method for linear frequency modulation-frequency stepping signal - Google Patents
Broadband speed measuring method for linear frequency modulation-frequency stepping signal Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 38
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- 238000007476 Maximum Likelihood Methods 0.000 claims abstract description 13
- 238000003384 imaging method Methods 0.000 claims abstract description 12
- 238000012545 processing Methods 0.000 claims abstract description 10
- 238000005259 measurement Methods 0.000 claims abstract description 8
- 230000015572 biosynthetic process Effects 0.000 claims description 8
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Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/50—Systems of measurement based on relative movement of target
- G01S13/58—Velocity or trajectory determination systems; Sense-of-movement determination systems
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
- G01S7/418—Theoretical aspects
Abstract
The invention discloses a broadband speed measuring method for a linear frequency modulation-frequency stepping signal. The invention is developed based on a maximum likelihood estimation method, firstly, a probability density distribution function of a sub-pulse deskewing echo sample is obtained, then a likelihood function related to the speed is constructed based on the probability density distribution, further, the target speed estimation can be completed by obtaining the maximum value of the likelihood function, the robustness is high, the precision is high, the imaging stability can be ensured in actual measurement data processing, and in addition, the invention can complete the target speed estimation only by a smaller sampling rate based on a deskewing system.
Description
Technical Field
The invention relates to the technical field of radar signal processing, in particular to a wideband speed measuring method for a linear frequency modulation-frequency stepping signal.
Background
Modern radars need to be visible and accurate, namely, when measuring and obtaining the position information of a target, various information such as the structure, the size, the shape and the like of the target are acquired so as to accurately identify the target. The basis for improving the target recognition performance is to use a transmission signal with a large bandwidth or even an ultra-wideband (the bandwidth reaches GHz).
Among wideband transmission signals, the chirp signal is the most widely used pulse compression signal. However, chirps typically require a higher sampling rate, which is detrimental to back-end signal processing. Considering the front-end intermediate frequency sampling rate limitation, a wideband signal may be synthesized using a plurality of narrowband sub-pulses using a chirped-frequency stepped signal. The large bandwidth imaging effect is realized while the sub-pulse sampling rate is reduced.
However, for ultra wideband signals, there is a great difficulty in directly transmitting an ultra wideband chirp signal; the adoption of the linear frequency modulation-frequency step signal requires tens or even hundreds of pulses to synthesize an ultra-large bandwidth signal, and brings great difficulty to speed estimation and compensation. Thus, jiang Bitao et al (Jiang Bitao, zhang Yunhua, jiang Jingshan. Full declining method for wideband frequency modulated stepped signals [ J ]. Test technical school, 2008 (03): 225-230.) proposed a synthetic ultra wideband signal based on previous studies in which the pulses were modulated with wideband chirp and steps in frequency between pulses. The signal sub-pulse adopts broadband declivity processing, so that the requirement of the sub-pulse sampling rate can be reduced, the number of sub-pulses synthesized by frequency stepping can be effectively reduced, and the imaging effect and high data rate of the broadband are ensured.
However, the wideband/ultra wideband declivity signal has higher accuracy requirement on the target speed compensation, and if the speed estimation accuracy is poor, the main lobe of the target echo will be distorted, which greatly affects the imaging, measuring and identifying effects of the target. The method based on the minimum entropy in the reference carries out speed estimation and step frequency synthesis on the target, however, the method has higher requirements on the signal-to-noise ratio and the sampling rate of the system, and the speed measurement precision is not ideal under certain conditions, and in addition, the method based on the phase-push speed measurement has higher time complexity and poorer real-time performance. Therefore, how to perform real-time high-precision speed estimation and compensation becomes a challenge in step-frequency synthesis broadband.
Disclosure of Invention
In view of the above, the invention provides a wideband speed measurement method for a linear frequency modulation-frequency stepping signal, which realizes accurate estimation of target speed by constructing likelihood functions on sub-pulse echoes and is suitable for wideband and ultra-wideband stepping frequency echoes.
The invention relates to a linear frequency modulation-frequency stepping signal broadband speed measurement method, which comprises the following steps:
step 1, declassifying a sub-pulse echo signal based on a reference signal; the pulse width of the reference signal is larger than that of the echo signal;
step 2, sampling the sub-pulse echo signals after the declassification processing to obtain echo signal samples; the sampling frequency is larger than twice of the highest frequency of the signal after declivity; calculating probability density distribution of all sub-pulse echo signal samples, and constructing a log likelihood function of the probability density distribution;
and step 3, obtaining the maximum value of the log-likelihood function in the speed reference range, wherein the speed corresponding to the maximum value of the log-likelihood function is the estimated target speed.
Preferably, in the step 3, a speed corresponding to the maximum log likelihood function is obtained in a speed reference range based on a bisection method.
Preferably, the radar emission signal is:
wherein ,t is the sampling time, T p Is pulse width; k is the frequency modulation slope of the signal, k=b/T p B is the signal bandwidth; f (f) n F for the nth sub-pulse n ＝f 0 +(n-1)Δf,n＝1,2,…N，N,f 0 Δf represents the number of sub-pulses, the start frequency, and the frequency step amount, respectively;
the target echo signal with the distance R is:
wherein ,τn The expression of the time delay of the nth sub-pulse is: τ n ＝2(R+v(n-1)T r ) V is the target speed, T r For pulse duration, c is the speed of light;
the reference signals are:
wherein ,τ0 For delay of reference signal relative to transmitted signal, τ 0 ＝2R ref /c，R ref For reference distance, T 0 Is the pulse width of the reference signal;
and carrying out conjugate multiplication on different sub-pulse echo signals and a reference signal in a time domain to finish the declassification processing of the sub-pulse echo signals.
Preferably, the probability density distribution is:
the log likelihood function is:
wherein M is a sampling point, and N is the number of sub-pulses;
the maximum likelihood of the velocity is estimated as
The invention also provides a synthetic broadband imaging method, which adopts the linear frequency modulation-frequency stepping signal broadband speed measuring method to estimate the target speed, constructs an error compensation function according to the estimated target speed, and carries out speed error compensation on the sub-pulse echo signals after declassification processing; and step frequency synthesis is carried out on the sub-pulse echo after the speed error compensation, so that imaging is completed.
Preferably, the specific mode of step frequency synthesis is as follows:
firstly, obtaining an error function by comparing different sub-pulse deskew echo phase differences, wherein the expression is as follows:
then, an error compensation function is obtained according to the estimated speed, and the expression is that
Phase compensating the sub-pulses by using the obtained error compensation function, and then according to f s And (B-delta f)/k is used for calculating the length of the declinized sub-pulse signal corresponding to the time-frequency overlapping part of the adjacent sub-pulses, any sub-pulse echo of the overlapping part is reserved for splicing, and the synthesized high-resolution range profile of the target can be obtained after the declivity splicing.
The beneficial effects are that:
(1) The maximum likelihood estimation is unbiased estimation, and the estimation effect is more accurate than other methods, so the invention is developed based on the maximum likelihood estimation method, firstly, the probability density distribution function of the sub-pulse deskew echo sample is calculated, then the likelihood function related to the speed is constructed based on the probability density distribution, further, the maximum value of the likelihood function is calculated to complete the target speed estimation, the robustness is high, the accuracy is high, the imaging stability can be ensured in the actual measurement data processing, and in addition, the invention is based on the deskewing system, and can complete the target speed estimation only with a smaller sampling rate.
(2) Compared with a traversing searching method, the method for estimating the speed value by utilizing the bisection method has the advantages that the calculation amount is greatly reduced while the estimation accuracy is ensured, and the requirement of the system on real-time performance can be met on the premise of ensuring the accuracy.
Drawings
FIG. 1 is a schematic diagram of a wideband synthesis of a declinized FM stepper signal with pulse overlap;
FIG. 2 is a flow chart of a process for synthesizing a high-resolution range profile from a declivity frequency modulated step signal;
FIG. 3 is a flow chart of a process for synthesizing a high-resolution range profile from a declivity frequency modulated step signal based on a bisection method;
FIG. 4 is a graph comparing the results of two speed measuring methods;
FIG. 5 is a graph showing the one-dimensional distance profile of the composite pulse and sub-pulse after the actual velocity compensation.
Detailed Description
The invention will now be described in detail by way of example with reference to the accompanying drawings.
The invention provides a wideband speed measuring method for a linear frequency modulation-frequency stepping signal.
Let radar transmit signal be:
wherein ,t is the sampling time, T p Is pulse width; k is the frequency modulation slope of the signal, k=b/T p B is the signal bandwidth; f (f) n For the nth sub-pulseThe number of sub-pulses, the starting frequency and the frequency step amount are indicated, respectively.
The target echo signal with the distance R is:
where τ is the signal transmission delay, and τ=2r/c, c is the speed of light.
Let the reference signal be:
τ 0 for delay of reference signal relative to transmitted signal, τ 0 ＝2R ref /c，R ref For reference distance, T 0 Is the pulse width of the reference signal, where T 0 And needs to be larger than the echo signal pulse width to satisfy the process of deskewing for all possible echo signals.
The deskewing process is that the echo signal is multiplied by the conjugate of the reference signal in the time domain, and the echo signal after the frequency modulation is removed can be expressed as:
from equation (4), it can be seen that the different deskew sub-pulse echo phase differences are determined by Δf/k, which is theoretically determined by selecting a reasonable frequency interval Δf and sampling frequency f s Make it satisfy f s And delta f/k is an integer, so that all the declivity sub-pulses are completely connected in the time domain, the observation time equivalent to one target point is longer, the bandwidth is wider, and the resolution of the range profile is improved.
For step frequency systems, Δf+.B should generally be guaranteed in order to avoid grating lobes, where Δf+.B is mainly discussed.
When Δf < B, pulse aliasing occurs, when it is necessary to follow f s And (B-delta f)/k calculates the length of the declivity signal corresponding to the time-frequency overlapping part of the adjacent pulses, and then any sub-pulse echo of the overlapping part is reserved for splicing. Fig. 1 illustrates a flow of the method, the flow includes two sub-pulses, in which the pulse overlapping part represents the region where the frequency spectrums intersect, and a de-overlapping operation is required during signal splicing, and a synthetic high-resolution range profile of the target can be obtained after the de-overlapping splicing.
From equation (4), the above-mentioned synthetic bandwidth algorithm is based on the premise that the target is stationary to ensure that the uniform scattering point is kept consistent in the different sub-pulse deskewing echoes, and when the target moves, the delays τ of the different sub-pulses are no longer the same, but become
τ n ＝2(R+v(n-1)T r )/c (5)
Wherein v is the target speed, T r For the pulse duration.
Substituting equation (5) into equation (4) shows that the phase error due to velocity is
wherein RΔ ＝v(n-1)T r . It is worth noting that the form of equation (6) is more complex when the different sub-pulse reference distances are different.
According to the analysis, the premise of synthesizing the broadband signal by the sub-pulse without distortion is how to obtain the speed estimation value with high precision and strong real-time performance, so the invention provides the ultra-broadband step frequency speed measurement and imaging algorithm based on the bisection method and the maximum likelihood estimation. The flow chart of the algorithm of the invention is shown in fig. 2, and the specific steps are as follows:
step one: substituting the formula (5) into the formula (4), and performing quadratic term compensation to obtain the deghosting echo expressions of the compensated different sub-pulses:
wherein DeltaR is the difference between the distance between the target and the radar and the reference distance; u (t) is Gaussian white noise, and the variance is sigma 2 。
Step two: solving maximum likelihood function for velocity
Because different sampling points of the echo signal all meet the average valueVariance is sigma 2 And thus can obtain a probability density distribution of
Since the different samples are independent of each other, the likelihood function is obtained for all samples
Wherein m represents the mth sampling point, and further obtaining the log-likelihood function as
Wherein M is the total sampling point number.
The maximum likelihood estimate for the motion parameter obtained by solving the maximum value of equation (10) is:
assuming that the target distance is known, the maximum likelihood estimate of the velocity can be obtained as
Step three: and (3) constructing an error compensation function according to the solved speed to compensate the sub-pulse echo, wherein the form is as follows:
wherein
Step four: and step frequency synthesis is carried out on the compensated subpulse deskew echo to obtain a synthesized broadband high-resolution one-dimensional range profile.
It should be noted that, since there is only one extreme point in the main lobe of the speed likelihood function, the objective speed corresponding to the maximum likelihood function can be sought by using the bisection method, the basic flow of the bisection method is that the speed estimation boundary is determined first, then the likelihood function value of the intermediate node and the size of the likelihood function value of the boundary node are judged, then the two nodes with the maximum likelihood function value are reserved as new boundary nodes, and the above operation is repeated until the objective speed estimation value within the error allowable range is obtained. Compared with the traversal searching method, the contrast method has the advantages that the calculation amount is greatly reduced while the estimation precision is ensured, and the requirement of the system on real-time performance can be met on the premise of ensuring the precision. The flow of maximum likelihood velocity estimation in combination with the dichotomy is shown in figure 3.
The following description is made in connection with specific examples:
the radar parameters are as follows: the pulse width is 100us, the pulse duration is 6ms, the sub-pulse bandwidth is 2GHz, the carrier frequency Ka wave band, the number of sub-pulses is 2, the sub-pulse frequency interval is 1.8GHz, the declining sampling frequency is 30MHz, the signal is a negative frequency modulation signal, and the working mode of the radar is to alternately transmit the sub-pulses under different carrier frequencies.
The target speed is estimated by the maximum likelihood method of the present invention and the minimum entropy method of the reference, respectively, and the result is shown in fig. 4. As can be seen from fig. 4, in this scenario, the result obtained by using the minimum entropy speed measurement has larger fluctuation and low stability, while the present invention has higher estimation accuracy and smaller fluctuation, so as to ensure imaging stability.
Fig. 5 shows the composite distance image of sub-pulses before and after speed compensation by the speed measuring method of the present invention, and it can be seen that the resolution of the composite one-dimensional distance image after speed measurement compensation is higher.
In summary, the above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A method for wideband speed measurement of a chirp-frequency stepped signal, comprising:
step 1, declassifying a sub-pulse echo signal based on a reference signal; the pulse width of the reference signal is larger than that of the echo signal;
step 2, sampling the sub-pulse echo signals after the declassification processing to obtain echo signal samples; the sampling frequency is larger than twice of the highest frequency of the signal after declivity; calculating probability density distribution of all sub-pulse echo signal samples, and constructing a log likelihood function of the probability density distribution;
and step 3, obtaining the maximum value of the log-likelihood function in the speed reference range, wherein the speed corresponding to the maximum value of the log-likelihood function is the estimated target speed.
2. The method according to claim 1, wherein in the step 3, a speed corresponding to the maximum log likelihood function is obtained in a speed reference range based on a bisection method.
3. The method of claim 1 or 2, wherein,
the radar emission signal is:
wherein ,t is the sampling time, T p Is pulse width; k is the frequency modulation slope of the signal, k=b/T p B is the signal bandwidth; f (f) n F for the nth sub-pulse n ＝f 0 +(n-1)Δf,n＝1,2,…N，N,f 0 Δf represents the number of sub-pulses, the start frequency, and the frequency step amount, respectively;
the target echo signal with the distance R is:
wherein ,τn The expression of the time delay of the nth sub-pulse is: τ n ＝2(R+v(n-1)T r ) V is the target speed, T r For pulse duration, c is the speed of light;
the reference signals are:
wherein ,τ0 For delay of reference signal relative to transmitted signal, τ 0 ＝2R ref /c，R ref For reference distance, T 0 Is the pulse width of the reference signal;
and carrying out conjugate multiplication on different sub-pulse echo signals and a reference signal in a time domain to finish the declassification processing of the sub-pulse echo signals.
4. A method according to claim 3, wherein the probability density distribution is:
the log likelihood function is:
wherein M is a sampling point, and N is the number of sub-pulses;
the maximum likelihood of the velocity is estimated as
5. A synthetic broadband imaging method, characterized in that a target speed is estimated by adopting the broadband speed measuring method of linear frequency modulation-frequency stepping signals according to any one of claims 1-4, an error compensation function is constructed according to the estimated target speed, and speed error compensation is carried out on sub-pulse echo signals after declassification; and step frequency synthesis is carried out on the sub-pulse echo after the speed error compensation, so that imaging is completed.
6. The imaging method of claim 5, wherein the step frequency synthesis is performed in the following manner:
firstly, obtaining an error function by comparing different sub-pulse deskew echo phase differences, wherein the expression is as follows:
then, an error compensation function is obtained according to the estimated speed, and the expression is that
Phase compensating the sub-pulses by using the obtained error compensation function, and then according to f s And (B-delta f)/k is used for calculating the length of the declinized sub-pulse signal corresponding to the time-frequency overlapping part of the adjacent sub-pulses, any sub-pulse echo of the overlapping part is reserved for splicing, and the synthesized high-resolution range profile of the target can be obtained after the declivity splicing.
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