CN113900088A - Long-time coherent accumulation method and system for uniform acceleration maneuvering target - Google Patents

Abstract

The invention belongs to the technical field of radar signal processing, and particularly relates to a long-time coherent accumulation method and a long-time coherent accumulation system for a uniform acceleration maneuvering target, wherein the method comprises the following steps: performing pulse compression processing on the target echo signal to obtain a pulse-compressed signal; performing second-order Keystone conversion on the pulse-compressed signal to obtain a second-order Keystone converted signal; determining the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of the search parameter according to the preset search parameter range, traversing the combination of the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of each search parameter, and performing two-dimensional search and coherent accumulation on the signal after the second-order Keystone conversion in the search distance-search speed domain to obtain coherent accumulation results of all targets; and carrying out target detection on the coherent accumulation result, and carrying out motion parameter estimation on the detected target.

Description

Long-time coherent accumulation method and system for uniform acceleration maneuvering target

Technical Field

The invention belongs to the technical field of radar signal processing and radar maneuvering target detection, and particularly relates to a long-time coherent accumulation method and system for a uniform acceleration maneuvering target.

Background

With the continuous development of aerospace technology and the increasingly mature modern stealth technology, how to accurately and effectively realize the detection of weak maneuvering targets becomes a difficult problem in the field of radar signal processing. On the premise of not changing radar hardware and basic parameters as much as possible, long-time coherent accumulation is a technology capable of effectively improving radar weak target detection. Even acceleration motion is a common motion pattern for maneuvering targets. When the maneuvering target in the uniform acceleration motion state is observed by the radar for a long time, the speed of the maneuvering target can cause the first-order range migration of the echo, and the acceleration of the maneuvering target can cause the second-order range migration and Doppler spread of the echo. When the coherent accumulation is carried out on the radar echo of the maneuvering target, the main lobe is widened and the accumulated peak value is reduced, so that the detection performance of the radar on the maneuvering target is influenced. Therefore, range and doppler shifts must be eliminated before radar coherent accumulation detection.

For resolving first order range migration caused by the velocity of a maneuvering target, the Keystone transform and Radon-Fourier transform are typical algorithms. Keystone transformation generally adopts interpolation operation to realize scale transformation of a two-dimensional data plane, so as to effectively correct first-order distance migration (reference [1 ]: R.P. Perry, et al, "SAR imaging of moving targets," IEEE Transactions on Aerospace and Electronic Systems, vol.35, No.1, pp.188-200,1999). Radon-Fourier Transform (reference [2 ]: J.Xu, et al, "Radon-Fourier Transform for Radar Target Detection, I: Generalized Doppler Filter Bank," IEEE Transactions on Aerospace and Electronic Systems, vol.47, No.2, pp.1186-1202,2011) performs coherent accumulation of maneuvering Target energy by two-dimensional joint search of distance and velocity. The two methods can only correct first-order range walk, and when a maneuvering target does uniform acceleration movement and second-order range migration and Doppler walk occur, the coherent accumulation effect is obviously poor.

Aiming at the problems of second-order range migration and Doppler spread of uniform acceleration Maneuvering Target echoes, a Generalized Radon-Fourier Transform (reference [3 ]: J.xu, et al, "Radon Maneuvering Target Motion estimated on Generalized Radon-Fourier Transform," IEEE Transactions on Signal Processing, vol.60, No.12, pp.6190-6201,2012 ") is proposed by the application and the like, is a Generalized definition of the existing Radon-Fourier Transform, and performs coherent accumulation on Maneuvering Target energy through three-dimensional combined search of distance, speed and acceleration. In addition, RFRFT, RLVD, RLCT, etc. algorithms are successively proposed to solve the above problems (reference [4 ]: X.L.Chen, et al, ' Manual Target Detection radio-frame transfer-Based Long-Time coding introduction, ' IEEE Transactions on Signal Processing, vol.62, No.4, pp.939-953,2014, reference [5 ]: X.L.Li, et al, ' human Integration for Manual Target Detection radio-transmission-L's Distribution, ' IEEE Signal Processing Letters, vol.22, No.9, pp.1467-1471,2015, reference [6 ]: X.L.Chen, chemistry, ' parameter of radio-transmission, and [5] ' IEEE 1] noise-sensor, see [5 ]. Microreceiver, volume, see [5 ]. 3, see [6 ]. X.L.Chen, R, RLVD, RLCT, etc.). However, the existing methods jointly search in three dimensions of distance, speed and acceleration, and finally accumulate the energy of the maneuvering target in a three-dimensional or even four-dimensional space, so that target detection needs to be performed in the three-dimensional or even four-dimensional space, which causes higher computational complexity and affects the real-time performance of radar signal processing. The existing method has the problem of high computational complexity.

Disclosure of Invention

In order to overcome the defects in the prior art, the invention provides a long-time coherent accumulation method for a uniform acceleration maneuvering target, and particularly relates to a convenient long-time coherent accumulation method with low calculation complexity.

The invention provides a long-time coherent accumulation method for a uniform acceleration maneuvering target, which comprises the following steps:

the radar adopts a linear frequency modulation signal as a transmitting signal, a radar receiver receives a target echo signal, and pulse compression processing is carried out on the target echo signal to obtain a signal after pulse compression;

performing second-order Keystone conversion on the pulse-compressed signal to obtain a second-order Keystone converted signal;

determining the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of the search parameter according to the preset search parameter range, traversing the combination of the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of each search parameter, and performing two-dimensional search and coherent accumulation on the signal after the second-order Keystone conversion in the search distance-search speed domain to obtain a coherent accumulation result;

and carrying out target detection on the coherent accumulation result, and carrying out motion parameter estimation on the detected target.

As one improvement of the above technical solution, the radar uses a chirp signal as a transmission signal, and the radar receiver receives a target echo signal and performs pulse compression processing on the target echo signal to obtain a pulse-compressed signal; the specific implementation process is as follows:

the radar adopts a linear frequency modulation signal as a transmitting signal, and the radar receiver receives a target echo signal s_raw(t_r,t_m)：

Wherein A is_rIs the amplitude of the echo signal; t is t_rThe time is fast;

represents the unit imaginary number; c is the speed of light; exp (·) represents an exponential function based on the natural logarithm e; f. of_cIs the center frequency of the transmitted signal; t is_pIs the duration of the transmitted signal; k_rA frequency modulation rate for transmitting a chirp signal; t is t_mIs a slow time, t_m＝mT_r(ii) a Wherein M is 0,1,2,. M; t is_rFor the pulse repetition interval, M represents the coherent accumulated total number of pulses;

R_t(t_m) For the target and radar at t_mInstantaneous distance of time:

wherein R is₀Is the initial distance of the target relative to the radar; a is_rRepresents the acceleration of the target; v. of_rRepresents the radial velocity of the target relative to the radar:

v_r＝v_b+M_amb·v_prf (3)

wherein v is_bTo search for base-band unambiguous velocity, v_b∈[-v_prf/2,v_prf/2]；M_ambSearching fuzzy speed multiple; v. of_prfλ × PRF/2 is the blur speed; wherein PRF is pulse repetition frequency of radar, and PRF is 1/T_r(ii) a λ is the wavelength of the transmitted signal, λ is c/f_c；

For target echo signal s_raw(t_r,t_m) Performing pulse compression to obtain a pulse-compressed signal s_rc(t_r,t_m)：

Wherein A is_rcThe amplitude of the signal after pulse compression; b is_rFor transmitting signal bandwidth, B_r＝K_rT_p。

As one improvement of the above technical solution, the second-order Keystone transform is performed on the pulse-compressed signal to obtain a second-order Keystone-transformed signal; the specific implementation process is as follows:

for the pulse-compressed signal s_rc(t_r,t_m) Fast edge time t_rFourier transform is carried out to obtain a fast time frequency-slow time domain signal S_rm(f_r,t_m)：

Wherein f is_rIs a fast time t_rCorresponding fast time frequency, A_rmIs the signal amplitude;

to S_rm(f_r,t_m) T in (1)_mThe following variable substitutions were made:

wherein, t_nA new slow time variable after variable substitution;

after the variable substitution, the signal becomes:

to S_rm(f_r,t_n) Fast edge time t_rPerforming inverse Fourier transform, and making r equal to ct_rAnd/2, obtaining a second-order Keystone converted signal s_sokt(r,t_n)：

Wherein v is_r1＝v_hb+M_ambv_prf(ii) a Wherein the content of the first and second substances,

v_hb∈[-v_prf/4,v_prf/4]。

as one improvement of the above technical solution, the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of the search parameter are determined according to the range of the preset search parameter, the combination of the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of each search parameter is traversed, and two-dimensional search and coherent accumulation are performed in the search distance-search speed domain according to the obtained second-order Keystone transformed signal to obtain a coherent accumulation result; the specific implementation process is as follows:

suppose a search distance r_scSearching for base band unambiguous velocity v_{hb_sc}And searching for a fuzzy velocity multiple m_{amb_sc}；

Setting a search distance r_scHas a search range of [ r_min,r_max]If the corresponding search step is Δ r, the number of search distances is determined

Further obtaining:

r_sc＝n_rΔr+r_min (9)

wherein n is_r＝0,1,2,…,N_r-1，n_rNumber of search distance; r is_minFor searching for a distance r_scMinimum value of (d); r is_maxFor searching for a distance r_scMaximum value of (d);

setting search speed v_sc：

v_sc＝v_{hb_sc}+m_{amb_sc}v_prf；

It should be noted that v is_scCorresponds to v_r1Rather than the true velocity v of the target_r；

Wherein v is_{hb_sc}For searching the base-band unambiguous velocity, the search range is [ -v ]_prf/4,v_prf/4]If the corresponding search step is Δ v, the base band unambiguous velocity search number is N_v，

Further obtaining:

m_{amb_sc}for searching fuzzy speed multiple, its search range is [ M_{amb_min},M_{amb_max}]And the corresponding search step length is 1, and then:

m_{amb_sc}＝M_{amb_min},M_{amb_min}+1,M_{amb_min}+2,…,M_{amb_max}-1,M_{amb_max}；

wherein M is_{amb_min}Searching the minimum value of the fuzzy speed multiple; m_{amb_max}Searching the maximum value of the fuzzy speed multiple;

according to the set search distance r_scAnd a search velocity v_scExtracting a signal s after second-order Keystone transformation_sokt(r,t_n) Signal s in_sokt(r_sc+v_sct_n,t_n) Discrete chirp-Fourier transform is carried out, and then the quadratic term coefficient is estimated to be a according to the peak position of the obtained transform result_{r_est}；

According to a_{r_est}And v_{hb_sc}Constructing phase compensation equation H_{v_a}(t_n)：

Equation of phase compensation H to be constructed_{v_a}(t_n) Substituting the following Radon-Fourier transform algorithm formula into the search distance-search speed domain (r)_sc,v_sc) Carrying out phase-coherent accumulation to obtain a phase-coherent accumulation result R_rv(r_sc,v_sc)：

Wherein, T_CPIThe coherent accumulation time; t is_CPI＝MT_r。

As one improvement of the above technical solution, the target detection is performed on the coherent accumulation result, and the motion parameter estimation is performed on the detected target; the specific process comprises the following steps:

coherent accumulation result R_rv(r_sc,v_sc) Carrying out target detection;

if coherent accumulation results R_rv(r_sc,v_sc) If the accumulated peak value is smaller than a preset threshold value, judging that the target is not detected;

if coherent accumulation results R_rv(r_sc,v_sc) If the accumulated peak value is greater than or equal to a preset threshold value, judging that the target is detected, and performing motion parameter estimation on the detected target;

according to R_rv(r_sc,v_sc) R corresponding to peak point position_scObtaining the distance R between the target and the radar_{0_est}；

According to R_rv(r_sc,v_sc) V corresponding to peak point position_scCorresponding v_{hb_sc}And m_{amb_sc}Calculating the radial velocity v of the target relative to the radar_{r_est}：

v_{r_est}＝2v_{hb_sc}+m_{amb_sc}·v_prf (13)

According to the pair s_sokt(r_sc+v_sct_n,t_n) Performing discrete chirp-Fourier transform to obtain the acceleration a of the target_{r_est}。

The invention also provides a long-time coherent accumulation system for the uniform acceleration maneuvering target, which comprises the following components:

the pulse compression module is used for performing pulse compression processing on the echo signal to obtain a pulse-compressed signal;

the second-order Keystone conversion module is used for carrying out second-order Keystone conversion on the signals after pulse compression to obtain second-order Keystone converted signals;

the coherent accumulation module is used for determining the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of the search parameter according to the preset search parameter range, traversing the combination of the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of each search parameter, and performing two-dimensional search and coherent accumulation in the search distance-search speed range according to the obtained second-order Keystone converted signal to obtain a coherent accumulation result;

and the target detection module is used for carrying out target detection on the coherent accumulation result and carrying out motion parameter estimation on the detected target.

As an improvement of the above technical solution, the specific implementation process of the pulse compression module is as follows:

the radar adopts a linear frequency modulation signal as a transmitting signal, and the radar receiver receives a target echo signal s_raw(t_r,t_m)：

Wherein A is_rIs the amplitude of the echo signal; t is t_rThe time is fast;

represents the unit imaginary number; c is the speed of light; exp (·) represents an exponential function based on the natural logarithm e; f. of_cIs the center frequency of the transmitted signal; t is_pIs the duration of the transmitted signal; k_rA frequency modulation rate for transmitting a chirp signal; t is t_mIs a slow time, t_m＝mT_r(ii) a Wherein M is 0,1,2,. M; t is_rFor the pulse repetition interval, M represents the coherent accumulated total number of pulses;

R_t(t_m) For the target and radar at t_mInstantaneous distance of time:

wherein R is₀Is the initial distance of the target relative to the radar; a is_rRepresents the acceleration of the target; v. of_rRepresents the radial velocity of the target relative to the radar:

v_r＝v_b+M_amb·v_prf (16)

wherein v is_bTo search for base-band unambiguous velocity, v_b∈[-v_prf/2,v_prf/2]；M_ambSearching fuzzy speed multiple; v. of_prfλ × PRF/2 is the blur speed; wherein PRF is pulse repetition frequency of radar, and PRF is 1/T_r(ii) a λ is the wavelength of the transmitted signal, λ is c/f_c；

For echo signal s_raw(t_r,t_m) Performing pulse compression to obtain a pulse-compressed signal s_rc(t_r,t_m)：

Wherein A is_rcThe amplitude of the signal after pulse compression; b is_rFor transmitting signal bandwidth, B_r＝K_rT_p。

As one of the improvements of the above technical solution, a specific implementation process of the second-order Keystone transformation module is as follows:

for the pulse-compressed signal s_rc(t_r,t_m) Fast edge time t_rFourier transform is carried out to obtain a fast time frequency-slow time domain signal S_rm(f_r,t_m)：

Wherein f is_rIs a fast time t_rCorresponding fast time frequency, A_rmIs the signal amplitude.

To S_rm(f_r,t_m) T in (1)_mThe following variable substitutions were made:

wherein, t_nA new slow time variable after variable substitution;

after the variable substitution, the signal becomes:

to S_rm(f_r,t_n) Fast edge time t_rPerforming inverse Fourier transform, and making r equal to ct_rAnd/2, obtaining a second-order Keystone converted signal s_sokt(r,t_n)：

Wherein v is_r1＝v_hb+M_ambv_prf(ii) a Wherein the content of the first and second substances,

v_hb∈[-v_prf/4,v_prf/4]。

as one of the improvements of the above technical solution, the implementation process of the coherent accumulation module is as follows:

suppose a search distance r_scSearching for base band unambiguous velocity v_{hb_sc}And searching for a fuzzy velocity multiple m_{amb_sc}；

Setting a search distance r_scHas a search range of [ r_min,r_max]If the corresponding search step is Δ r, the number of search distances is determined

Further obtaining:

r_sc＝n_rΔr+r_min (22)

wherein n is_r＝0,1,2,…,N_r-1, the number of search distances; r is_minFor searching for a distance r_scMinimum value of (d); r is_maxFor searching for a distance r_scMaximum value of (d);

setting search speed v_sc：

v_sc＝v_{hb_sc}+m_{amb_sc}v_prf；

It should be noted that v is_scCorresponds to v_r1Rather than the true velocity v of the target_r；

Wherein v is_{hb_sc}For searching the base-band unambiguous velocity, the search range is [ -v ]_prf/4,v_prf/4]If the corresponding search step is Δ v, the base band unambiguous velocity search number is N_v，

Further obtaining:

m_{amb_sc}for searching fuzzy speed multiple, its search range is [ M_{amb_min},M_{amb_max}]And the corresponding search step length is 1, and then:

m_{amb_sc}＝M_{amb_min},M_{amb_min}+1,M_{amb_min}+2,…,M_{amb_max}-1,M_{amb_max}；

wherein M is_{amb_min}Searching the minimum value of the fuzzy speed multiple; m_{amb_max}Searching the maximum value of the fuzzy speed multiple;

according to the set search distance r_scAnd a search velocity v_scExtracting a signal s after second-order Keystone transformation_sokt(r,t_n) Signal s in_sokt(r_sc+v_sct_n,t_n) Discrete chirp-Fourier transform is carried out, and then the quadratic term coefficient is estimated to be a according to the peak position of the obtained transform result_{r_est}；

According to a_{r_est}And v_{hb_sc}Constructing phase compensation equation H_{v_a}(t_n)：

Equation of phase compensation H to be constructed_{v_a}(t_n) Substituting the following Radon-Fourier transform algorithm formula into the search distance-search speed domain (r)_sc,v_sc) Carrying out phase-coherent accumulation to obtain a phase-coherent accumulation result R_rv(r_sc,v_sc)：

Wherein, T_CPIThe coherent accumulation time; t is_CPI＝MT_r。

As an improvement of the above technical solution, the specific implementation process of the target detection module is as follows:

coherent accumulation result R_rv(r_sc,v_sc) Carrying out target detection;

if coherent accumulation results R_rv(r_sc,v_sc) If the accumulated peak value is smaller than a preset threshold value, judging that the target is not detected;

if coherent accumulation results R_rv(r_sc,v_sc) If the accumulated peak value is greater than or equal to a preset threshold value, judging that the target is detected, and performing motion parameter estimation on the detected target;

according to R_rv(r_sc,v_sc) R corresponding to peak point position_scObtaining the distance R between the target and the radar_{0_est}；

According to R_rv(r_sc,v_sc) V corresponding to peak point position_scCorresponding v_{hb_sc}And m_{amb_sc}Calculating the radial velocity v of the target relative to the radar_{r_est}：

v_{r_est}＝2v_{hb_sc}+m_{amb_sc}·v_prf (26)

According to the pair s_sokt(r_sc+v_sct_n,t_n) Performing discrete chirp-Fourier transform to obtain the acceleration a of the target_{r_est}。

Compared with the prior art, the invention has the beneficial effects that:

the method of the invention simultaneously utilizes the amplitude and phase information in the radar echo of the maneuvering target to carry out long-time coherent accumulation, and can effectively improve the signal-to-noise ratio of the radar echo, thereby improving the detection performance of the radar to the target; in addition, the method only carries out two-dimensional search of distance and speed, the target echo energy is accumulated in a two-dimensional distance-speed space, the target detection is also only carried out in the two-dimensional distance-speed space, the calculation complexity is low, the real-time processing of radar signals is facilitated, the method is beneficial to engineering realization, and the method has popularization and application values.

Drawings

FIG. 1 is a flow chart of a long-time coherent accumulation method for a uniform acceleration maneuvering target provided by the invention;

FIG. 2 is a diagram illustrating the result of compression of echo pulses received by a radar;

FIG. 3 is a schematic diagram of coherent accumulation results in a long-time coherent accumulation method for a uniform acceleration maneuvering target provided by the invention;

fig. 4 is a schematic diagram of a result of discrete chirp-Fourier transform of a signal extracted when a search distance and a search speed correspond to a target in the long-time coherent accumulation method for a uniform acceleration maneuvering target provided by the invention;

FIG. 5 is a graph showing the results of prior art Moving Target Detection (MTD);

FIG. 6 is a diagram illustrating the result of a Radon-Fourier transform of the prior art;

FIG. 7 is a diagram illustrating the result of a prior art generalized Radon-Fourier transform.

Detailed Description

The invention will now be further described with reference to the accompanying drawings and examples.

The invention provides a long-time coherent accumulation method and a long-time coherent accumulation system for a uniform acceleration maneuvering target, and particularly relates to a long-time coherent accumulation method and a long-time coherent accumulation system for radar echoes of the uniform acceleration maneuvering target based on second-order Keystone and Radon-Fourier transformation;

the method comprises the following steps: pulse compression is carried out on a radar receiving target echo signal, second-order distance migration is corrected through second-order Keystone transformation, then coherent accumulation of target energy is achieved through distance and speed combined search, and finally target detection and parameter estimation are carried out on coherent accumulation results. The invention solves the problems of range migration and Doppler walk in the echo when the radar observes a uniform acceleration target for a long time, and effectively improves the signal-to-noise ratio of the radar echo, thereby improving the detection performance of the target. In addition, the invention only carries out two-dimensional search of distance and speed, accumulates target echo energy in a two-dimensional distance-speed space, and only needs to carry out target detection in the two-dimensional distance-speed space, so that the calculation complexity is low, the radar signal real-time processing is convenient, the engineering realization is facilitated, and the method has popularization and application values.

As shown in fig. 1, the method specifically includes:

step S1) target echo distance to pulse compression

The radar adopts a linear frequency modulation signal as a transmitting signal, a radar receiver receives a target echo signal, and pulse compression processing is carried out on the target echo signal to obtain a signal after pulse compression;

specifically, the radar adopts a linear frequency modulation signal as a transmitting signal, and the radar receiver receives a target echo signal s_raw(t_r,t_m)：

Wherein A is_rIs the amplitude of the echo signal; t is t_rThe time is fast;

represents the unit imaginary number; c is the speed of light; exp (·) represents an exponential function based on the natural logarithm e; f. of_cTo transmit signalsThe center frequency of (d); t is_pIs the duration of the transmitted signal; (ii) a K_rA frequency modulation rate for transmitting a chirp signal; t is t_mIs a slow time, t_m＝mT_r(ii) a Wherein M is 0,1,2,. M; t is_rFor the pulse repetition interval, M represents the coherent accumulated total number of pulses;

R_t(t_m) For the target and radar at t_mInstantaneous distance of time:

wherein R is₀Is the initial distance of the target relative to the radar; a is_rRepresents the acceleration of the target; v. of_rRepresents the radial velocity of the target relative to the radar:

v_r＝v_b+M_amb·v_prf (29)

wherein v is_bTo search for base-band unambiguous velocity, v_b∈[-v_prf/2,v_prf/2]；M_ambSearching fuzzy speed multiple; v. of_prfλ × PRF/2 is the blur speed; wherein PRF is pulse repetition frequency of radar, and PRF is 1/T_r；λ＝c/f_cIs the transmit signal wavelength;

for echo signal s_raw(t_r,t_m) Performing pulse compression processing to obtain a pulse compressed signal:

wherein A is_rcThe amplitude of the signal after pulse compression; b is_rFor transmitting signal bandwidth, B_r＝K_rT_p；

Step S2) second order Keystone transformation

For the pulse-compressed signal s_rc(t_r,t_m) Fast edge time t_rFourier transform is carried out to obtain a fast time frequency-slow time domain signal S_rm(f_r,t_m)：

Wherein f is_rIs a fast time t_rCorresponding fast time frequency, A_rmIs the signal amplitude.

To S_rm(f_r,t_m) T in (1)_mThe following variable substitutions were made:

wherein, t_nA new slow time variable after variable substitution;

after the variable substitution, the signal becomes:

to S_rm(f_r,t_n) Fast edge time t_rPerforming inverse Fourier transform, and making r equal to ct_rAnd/2, obtaining a second-order Keystone converted signal s_sokt(r,t_n)：

In the above formula, v_r1＝v_hb+M_ambv_prf(ii) a Wherein the content of the first and second substances,

v_hb∈[-v_prf/4,v_prf/4]。

after second-order Keystone conversion, the base band does not blur the speed v_hbHas become half of the original.

Step S3) distance-speed two-dimensional search for realizing coherent accumulation

Determining the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of the search parameter according to the preset search parameter range, traversing the combination of the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of each search parameter, and performing two-dimensional search and coherent accumulation in a search distance-search speed domain according to the obtained second-order Keystone converted signal to obtain a coherent accumulation result;

specifically, assume that the search distance r_scSearching for base band unambiguous velocity v_{hb_sc}And searching for a fuzzy velocity multiple m_{amb_sc}；

Setting a search distance r_scHas a search range of [ r_min,r_max]If the corresponding search step is Δ r, the number of search distances is determined

Further obtaining:

r_sc＝n_rΔr+r_min (35)

wherein n is_r＝0,1,2,…,N_r-1，n_rNumber of search distance; r is_minFor searching for a distance r_scMinimum value of (d); r is_maxFor searching for a distance r_scMaximum value of (d);

setting search speed v_sc：

v_sc＝v_{hb_sc}+m_{amb_sc}v_prf；

It should be noted that v is_scCorresponds to v_r1Rather than the true velocity v of the target_r；

Wherein v is_{hb_sc}For searching the base-band unambiguous velocity, the search range is [ -v ]_prf/4,v_prf/4]If the corresponding search step is Δ v, the base band unambiguous velocity search number is N_v，

Further obtaining:

m_{amb_sc}for searching fuzzy speed multiple, its search range is [ M_{amb_min},M_{amb_max}]And the corresponding search step length is 1, and then:

m_{amb_sc}＝M_{amb_min},M_{amb_min}+1,M_{amb_min}+2,…,M_{amb_max}-1,M_{amb_max}；

wherein M is_{amb_min}Searching the minimum value of the fuzzy speed multiple; m_{amb_max}Searching the maximum value of the fuzzy speed multiple;

according to the set search distance r_scAnd a search velocity v_scExtracting a signal s after second-order Keystone transformation_sokt(r,t_n) Signal s in_sokt(r_sc+v_sct_n,t_n) Discrete chirp-Fourier transform is carried out, and then the quadratic term coefficient is estimated to be a according to the peak position of the obtained transform result_{r_est}；

According to a_{r_est}And v_{hb_sc}Constructing phase compensation equation H_{v_a}(t_n)：

Equation of phase compensation H to be constructed_{v_a}(t_n) Substituted into the following Radon-Fourier transform algorithm formula, in the search distance-search speed domain (r)_sc,v_sc) Carrying out phase-coherent accumulation to obtain a phase-coherent accumulation result R_rv(r_sc,v_sc)：

Wherein, T_CPIThe coherent accumulation time; t is_CPI＝MT_r。

Step S4) object detection and motion parameter estimation

And carrying out target detection on the coherent accumulation result, and carrying out motion parameter estimation on the detected target.

Specifically, the coherent integration result R_rv(r_sc,v_sc) Carrying out target detection;

if coherent accumulation results R_rv(r_sc,v_sc) If the accumulated peak value is smaller than a preset threshold value, judging that the target is not detected;

if coherent accumulation results R_rv(r_sc,v_sc) If the accumulated peak value is greater than or equal to a preset threshold value, judging that the target is detected, and performing motion parameter estimation on the detected target;

according to R_rv(r_sc,v_sc) R corresponding to peak point position_scObtaining the distance R between the target and the radar_{0_est}；

According to R_rv(r_sc,v_sc) V corresponding to peak point position_scCorresponding v_{hb_sc}And m_{amb_sc}Calculating the radial velocity v of the target relative to the radar_{r_est}：

v_{r_est}＝2v_{hb_sc}+m_{amb_sc}·v_prf (39)

According to the pair s_sokt(r_sc+v_sct_n,t_n) Performing discrete chirp-Fourier transform to obtain the acceleration a of the target_{r_est}。

The invention also provides a long-time coherent accumulation system for the uniform acceleration maneuvering target, which comprises the following components:

the pulse compression module is used for performing pulse compression processing on the echo signal to obtain a pulse-compressed signal;

specifically, the radar adopts a linear frequency modulation signal as a transmitting signal, and the radar receiver receives a target echo signal s_raw(t_r,t_m)：

Wherein A is_rIs the amplitude of the echo signal; t is t_rThe time is fast;

represents the unit imaginary number; c is the speed of light; exp (·) represents an exponential function based on the natural logarithm e; f. of_cIs the center frequency of the transmitted signal; t is_pIs the duration of the transmitted signal; k_rA frequency modulation rate for transmitting a chirp signal; t is t_mIs a slow time, t_m＝mT_r(ii) a Wherein M is 0,1,2,. M; t is_rFor the pulse repetition interval, M represents the coherent accumulated total number of pulses;

R_t(t_m) For the target and radar at t_mInstantaneous distance of time:

wherein R is₀Is the initial distance of the target relative to the radar; a is_rRepresents the acceleration of the target; v. of_rRepresents the radial velocity of the target relative to the radar:

v_r＝v_b+M_amb·v_prf (42)

wherein v is_bTo search for base-band unambiguous velocity, v_b∈[-v_prf/2,v_prf/2]；M_ambSearching fuzzy speed multiple; v. of_prfλ × PRF/2 is the blur speed; wherein PRF is pulse repetition frequency of radar, and PRF is 1/T_r(ii) a λ is the wavelength of the transmitted signal, λ is c/f_c；

For echo signal s_raw(t_r,t_m) Performing pulse compression processing to obtain a pulse compressed signal:

wherein A is_rcThe amplitude of the signal after pulse compression; b is_rTo launchSignal bandwidth, B_r＝K_rT_p；

The second-order Keystone conversion module is used for carrying out second-order Keystone conversion on the signals after pulse compression to obtain second-order Keystone converted signals;

for the pulse-compressed signal s_rc(t_r,t_m) Fast edge time t_rFourier transform is carried out to obtain a fast time frequency-slow time domain signal S_rm(f_r,t_m)：

Wherein f is_rIs a fast time t_rCorresponding distance frequency, A_rmIs the signal amplitude.

To S_rm(f_r,t_m) T in (1)_mThe following variable substitutions were made:

wherein, t_nA new slow time variable after variable substitution;

after the variable substitution, the signal becomes:

to S_rm(f_r,t_n) Fast edge time t_rPerforming inverse Fourier transform, and making r equal to ct_rAnd/2, obtaining a second-order Keystone converted signal s_sokt(r,t_n)：

In the above formula, v_r1＝v_hb+M_ambv_prf(ii) a Wherein the content of the first and second substances,

v_hb∈[-v_prf/4,v_prf/4]。

the coherent accumulation module is used for determining the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of the search parameter according to the preset search parameter range, traversing the combination of the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of each search parameter, and performing two-dimensional search and coherent accumulation in the search distance-search speed range according to the obtained second-order Keystone converted signal to obtain a coherent accumulation result;

specifically, assume that the search distance r_scSearching for base band unambiguous velocity v_{hb_sc}And searching for a fuzzy velocity multiple m_{amb_sc}；

Setting a search distance r_scHas a search range of [ r_min,r_max]If the corresponding search step is Δ r, the number of search distances is determined

Further obtaining:

r_sc＝n_rΔr+r_min (48)

wherein n is_r＝0,1,2,…,N_r-1，n_rNumber of search distance; r is_minFor searching for a distance r_scMinimum value of (d); r is_maxFor searching for a distance r_scMaximum value of (d);

setting search speed v_sc：

v_sc＝v_{hb_sc}+m_{amb_sc}v_prf；

It should be noted that v is_scCorresponds to v_r1Rather than the true velocity v of the target_r；

Wherein v is_{hb_sc}For searching the base-band unambiguous velocity, the search range is [ -v ]_prf/4,v_prf/4]If the corresponding search step is Δ v, the base band unambiguous velocity search number is N_v，

Further obtaining:

m_{amb_sc}for searching fuzzy speed multiple, its search range is [ M_{amb_min},M_{amb_max}]And the corresponding search step length is 1, and then:

m_{amb_sc}＝M_{amb_min},M_{amb_min}+1,M_{amb_min}+2,…,M_{amb_max}-1,M_{amb_max}；

wherein M is_{amb_min}Searching the minimum value of the fuzzy speed multiple; m_{amb_max}Searching the maximum value of the fuzzy speed multiple;

according to the set search distance r_scAnd a search velocity v_scExtracting a signal s after second-order Keystone transformation_sokt(r,t_n) Signal s in_sokt(r_sc+v_sct_n,t_n) Discrete chirp-Fourier transform is carried out, and then the quadratic term coefficient is estimated to be a according to the peak position of the obtained transform result_{r_est}；

According to a_{r_est}And v_{hb_sc}Constructing phase compensation equation H_{v_a}(t_n)：

Equation of phase compensation H to be constructed_{v_a}(t_n) Substituting the following Radon-Fourier transform algorithm formula into the search distance-search speed domain (r)_sc,v_sc) Carrying out phase-coherent accumulation to obtain a phase-coherent accumulation result R_rv(r_sc,v_sc)：

Wherein, T_CPIThe coherent accumulation time; t is_CPI＝MT_r。

And the target detection module is used for carrying out target detection on the coherent accumulation result and carrying out motion parameter estimation on the detected target.

Specifically, the coherent integration result R_rv(r_sc,v_sc) Carrying out target detection;

if coherent accumulation results R_rv(r_sc,v_sc) If the accumulated peak value is smaller than a preset threshold value, judging that the target is not detected;

if coherent accumulation results R_rv(r_sc,v_sc) If the accumulated peak value is greater than or equal to a preset threshold value, judging that the target is detected, and performing motion parameter estimation on the detected target;

according to R_rv(r_sc,v_sc) R corresponding to peak point position_scObtaining the distance R between the target and the radar_{0_est}；

According to R_rv(r_sc,v_sc) V corresponding to peak point position_scCorresponding v_{hb_sc}And m_{amb_sc}Calculating the radial velocity v of the target relative to the radar_{r_est}：

v_{r_est}＝2v_{hb_sc}+m_{amb_sc}·v_prf (52)

According to the pair s_sokt(r_sc+v_sct_n,t_n) Performing discrete chirp-Fourier transform to obtain the acceleration a of the target_{r_est}。

As shown in fig. 2-7, the method of the present invention combines with simulation tests to verify the long-time coherent accumulation method for radar echoes of a uniform acceleration maneuvering target provided by the present invention.

Center frequency f of signal emitted by radar system_c1.25GHz, transmission signal bandwidth B_r40MHz, transmission duration T_p5us, pulse repetition frequency PRF 1000, coherent accumulation pulse number M1000, coherent accumulation time T_CPI＝1s。Corresponding fuzzy speed v of the system_prf120 m/s. The initial distance of the simulation target relative to the radar is R₀100km, radial velocity v_r340m/s with a radial acceleration of a_r＝30m/s². The target corresponds to a base band unambiguous velocity v_b-20M/s, a multiple of the blur speed M_amb＝3。

FIG. 2 shows the result of the echo pulse compression received by the radar, the signal-to-noise ratio after the pulse compression is 3dB, and the visible target signal envelope generates range migration. Fig. 3 is a coherent accumulation result of the method, and it can be seen that a target signal is accumulated into a peak, and fig. 4 is a result of discrete chirp-Fourier transform of a signal extracted when the search distance and speed of the method correspond to a target. The distance R of the target can be estimated from the peak point position in FIG. 3_{0_est}99.99km, velocity v_{r_est}340 m/s; the target acceleration a can be estimated from the peak position in fig. 4_{r_est}＝29.98m/s²。

To illustrate the effectiveness of the present method, fig. 5, 6, and 7 show coherent accumulation results of 3 prior art exemplary methods. Fig. 5 and 6 are results of Moving Target Detection (MTD) and Radon-Fourier transform, respectively, and it can be seen that, due to the influence of target echo distance and doppler migration, coherent accumulation performance of conventional Moving Target Detection (MTD) and Radon-Fourier transform algorithms is significantly degraded, and a target accumulation peak cannot appear in both graphs. FIG. 7 shows a generalized Radon-Fourier transform at a search acceleration value of 30m/s²The obtained distance-speed section can see that the target signal is accumulated into a peak with the amplitude equivalent to that of the method, but the calculation amount of the algorithm is obviously higher than that of the method.

Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and are not limited. Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (10)

1. A long-time coherent accumulation method for a uniform acceleration maneuvering target, characterized by comprising:

the radar adopts a linear frequency modulation signal as a transmitting signal, a radar receiver receives a target echo signal, and pulse compression processing is carried out on the echo signal to obtain a signal after pulse compression;

performing second-order Keystone conversion on the pulse-compressed signal to obtain a second-order Keystone converted signal;

determining the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of the search parameter according to the preset search parameter range, traversing the combination of the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of each search parameter, and performing two-dimensional search and coherent accumulation on the signal after the second-order Keystone conversion in the search distance-search speed domain to obtain a coherent accumulation result;

and carrying out target detection on the coherent accumulation result, and carrying out motion parameter estimation on the detected target.

2. The long-time coherent accumulation method for the uniform acceleration maneuvering target according to claim 1, characterized in that the radar adopts a chirp signal as a transmission signal, a radar receiver receives a target echo signal, and pulse compression processing is performed on the echo signal to obtain a pulse-compressed signal; the specific implementation process is as follows:

the radar adopts a linear frequency modulation signal as a transmitting signal, and the radar receiver receives a target echo signal s_raw(t_r,t_m)：

Wherein A is_rIs the amplitude of the echo signal; t is t_rThe time is fast;

representing unit imaginary number(ii) a c is the speed of light; exp (·) represents an exponential function based on the natural logarithm e; f. of_cIs the center frequency of the transmitted signal; t is_pIs the duration of the transmitted signal; k_rA frequency modulation rate for transmitting a chirp signal; t is t_mIs a slow time, t_m＝mT_r(ii) a Wherein M is 0,1,2,. M; t is_rFor the pulse repetition interval, M represents the coherent accumulated total number of pulses;

R_t(t_m) For the target and radar at t_mInstantaneous distance of time:

wherein R is₀Is the initial distance of the target relative to the radar; a is_rRepresents the acceleration of the target; v. of_rRepresents the radial velocity of the target relative to the radar:

v_r＝v_b+M_amb·v_prf (3)

wherein v is_bTo search for base-band unambiguous velocity, v_b∈[-v_prf/2,v_prf/2]；M_ambSearching fuzzy speed multiple; v. of_prfλ × PRF/2 is the blur speed; wherein PRF is pulse repetition frequency of radar, and PRF is 1/T_r(ii) a λ is the wavelength of the transmitted signal, λ is c/f_c；

For target echo signal s_raw(t_r,t_m) Performing pulse compression to obtain a pulse-compressed signal s_rc(t_r,t_m)：

Wherein A is_rcThe amplitude of the signal after pulse compression; b is_rFor transmitting signal bandwidth, B_r＝K_rT_p。

3. The long-time coherent accumulation method for the uniform acceleration maneuvering target according to claim 1, characterized in that the second-order Keystone transform is performed on the pulse-compressed signal to obtain a second-order Keystone transformed signal; the specific implementation process is as follows:

for the pulse-compressed signal s_rc(t_r,t_m) Fast edge time t_rFourier transform is carried out to obtain a fast time frequency-slow time domain signal S_rm(f_r,t_m)：

Wherein f is_rIs a fast time t_rCorresponding fast time frequency, A_rmIs the signal amplitude;

to S_rm(f_r,t_m) T in (1)_mThe following variable substitutions were made:

wherein, t_nA new slow time variable after variable substitution;

after the variable substitution, the signal becomes:

to S_rm(f_r,t_n) Fast edge time t_rPerforming inverse Fourier transform, and making r equal to ct_rAnd/2, obtaining a second-order Keystone converted signal s_sokt(r,t_n)：

In the above formula, v_r1＝v_hb+M_ambv_prf(ii) a Wherein the content of the first and second substances,

v_hb∈[-v_prf/4,v_prf/4]。

4. the long-time coherent accumulation method for the uniform acceleration maneuvering target according to claim 1, characterized in that the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of the search parameter are determined according to a preset search parameter range, a combination of the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of each search parameter is traversed, and two-dimensional search and coherent accumulation are performed in a search distance-search speed domain according to the obtained second-order Keystone converted signal to obtain a coherent accumulation result; the specific implementation process is as follows:

suppose a search distance r_scSearching for base band unambiguous velocity v_{hb_sc}And searching for a fuzzy velocity multiple m_{amb_sc}；

Setting a search distance r_scHas a search range of [ r_min,r_max]If the corresponding search step is Δ r, the number of search distances is determined

Further obtaining:

r_sc＝n_rΔr+r_min (9)

wherein n is_r＝0,1,2,…,N_r-1 is the number of search distances; r is_minFor searching for a distance r_scMinimum value of (d); r is_maxFor searching for a distance r_scMaximum value of (d);

setting search speed v_sc：

v_sc＝v_{hb_sc}+m_{amb_sc}v_prf；

It should be noted that v is_scCorresponds to v_r1Rather than the true velocity v of the target_r；

Wherein v is_{hb_sc}For searching basebandUnambiguous velocity, with a search range of [ -v ]_prf/4,v_prf/4]If the corresponding search step is Δ v, the base band unambiguous velocity search number is N_v，

Further obtaining:

m_{amb_sc}for searching fuzzy speed multiple, its search range is [ M_{amb_min},M_{amb_max}]And the corresponding search step is 1, and then:

m_{amb_sc}＝M_{amb_min},M_{amb_min}+1,M_{amb_min}+2,…,M_{amb_max}-1,M_{amb_max}；

wherein M is_{amb_min}Searching the minimum value of the fuzzy speed multiple; m_{amb_max}Searching the maximum value of the fuzzy speed multiple;

according to the set search distance r_scAnd a search velocity v_scExtracting a signal s after second-order Keystone transformation_sokt(r,t_n) Signal s in_sokt(r_sc+v_sct_n,t_n) Discrete chirp-Fourier transform is carried out, and then the quadratic term coefficient is estimated to be a according to the peak position of the obtained transform result_{r_est}；

According to a_{r_est}And v_{hb_sc}Constructing phase compensation equation H_{v_a}(t_n)：

Equation of phase compensation H to be constructed_{v_a}(t_n) Substituting the following Radon-Fourier transform algorithm formula into the search distance-search speed domain (r)_sc,v_sc) Carrying out phase-coherent accumulation to obtain a phase-coherent accumulation result R_rv(r_sc,v_sc)：

Wherein, T_CPIThe coherent accumulation time; t is_CPI＝MT_r。

5. The method for accumulating the coherent integration result for the uniform acceleration maneuvering target for the long time according to the claim 1, characterized in that the coherent integration result is subjected to target detection, and the detected target is subjected to motion parameter estimation; the specific process comprises the following steps:

coherent accumulation result R_rv(r_sc,v_sc) Carrying out target detection;

if coherent accumulation results R_rv(r_sc,v_sc) If the accumulated peak value is smaller than a preset threshold value, judging that the target is not detected;

if coherent accumulation results R_rv(r_sc,v_sc) If the accumulated peak value is greater than or equal to a preset threshold value, judging that the target is detected, and performing motion parameter estimation on the detected target;

according to R_rv(r_sc,v_sc) R corresponding to peak point position_scObtaining the distance R between the target and the radar_{0_est}；

According to R_rv(r_sc,v_sc) V corresponding to peak point position_scCorresponding v_{hb_sc}And m_{amb_sc}Calculating the radial velocity v of the target relative to the radar_{r_est}：

v_{r_est}＝2v_{hb_sc}+m_{amb_sc}·v_prf (13)

According to the pair s_sokt(r_sc+v_sct_n,t_n) Performing discrete chirp-Fourier transform to obtain the acceleration a of the target_{r_est}。

6. A long-term coherent accumulation system for a uniform acceleration maneuver target, the system comprising:

the pulse compression module is used for performing pulse compression processing on the echo signal to obtain a pulse compressed signal;

the second-order Keystone conversion module is used for carrying out second-order Keystone conversion on the signals after pulse compression to obtain second-order Keystone converted signals;

the coherent accumulation module is used for determining the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of the search parameter according to the preset search parameter range, traversing the combination of the search distance, the search baseband unambiguous speed and the search ambiguous speed multiple of each search parameter, and performing two-dimensional search and coherent accumulation in the search distance-search speed range according to the obtained second-order Keystone converted signal to obtain a coherent accumulation result;

and the target detection module is used for carrying out target detection on the coherent accumulation result and carrying out motion parameter estimation on the detected target.

7. The long-time coherent accumulation system for the uniform acceleration maneuvering target according to claim 6, characterized in that the pulse compression module is realized by the following specific processes:

the radar adopts a linear frequency modulation signal as a transmitting signal, and the radar receiver receives a target echo signal s_raw(t_r,t_m)：

Wherein A is_rIs the amplitude of the echo signal; t is t_rThe time is fast;

represents the unit imaginary number; c is the speed of light; exp (·) represents an exponential function based on the natural logarithm e; f. of_cIs the center frequency of the transmitted signal; t is_pIs the duration of the transmitted signal; k_rTo transmit linearlyThe frequency modulation rate of the frequency modulated signal; t is t_mIs a slow time, t_m＝mT_r(ii) a Wherein M is 0,1,2,. M; t is_rFor the pulse repetition interval, M represents the coherent accumulated total number of pulses;

R_t(t_m) For the target and radar at t_mInstantaneous distance of time:

wherein R is₀Is the initial distance of the target relative to the radar; a is_rRepresents the acceleration of the target; v. of_rRepresents the radial velocity of the target relative to the radar:

v_r＝v_b+M_amb·v_prf (16)

wherein v is_bTo search for base-band unambiguous velocity, v_b∈[-v_prf/2,v_prf/2]；M_ambSearching fuzzy speed multiple; v. of_prfλ × PRF/2 is the blur speed; wherein PRF is pulse repetition frequency of radar, and PRF is 1/T_r(ii) a λ is the wavelength of the transmitted signal, λ is c/f_c；

For echo signal s_raw(t_r,t_m) Performing pulse compression to obtain a pulse-compressed signal s_rc(t_r,t_m)：

Wherein A is_rcThe amplitude of the signal after pulse compression; b is_rFor transmitting signal bandwidth, B_r＝K_rT_p。

8. The long-time coherent accumulation system for the uniform acceleration maneuvering target according to claim 6, characterized in that the second-order Keystone transformation module is realized by the following specific processes:

to pulse pressureReduced signal s_rc(t_r,t_m) Fast edge time t_rFourier transform is carried out to obtain a fast time frequency-slow time domain signal S_rm(f_r,t_m)：

Wherein f is_rIs a fast time t_rCorresponding fast time frequency, A_rmIs the signal amplitude;

to S_rm(f_r,t_m) T in (1)_mThe following variable substitutions were made:

wherein, t_nA new slow time variable after variable substitution;

after the variable substitution, the signal becomes:

to S_rm(f_r,t_n) Fast edge time t_rPerforming inverse Fourier transform, and making r equal to ct_rAnd/2, obtaining a second-order Keystone converted signal s_sokt(r,t_n)：

Wherein v is_r1＝v_hb+M_ambv_prf(ii) a Wherein the content of the first and second substances,

v_hb∈[-v_prf/4,v_prf/4]。

9. the long-time coherent accumulation system for the uniform acceleration maneuvering target according to claim 6, characterized in that the coherent accumulation module is realized by the following specific processes:

suppose a search distance r_scSearching for base band unambiguous velocity v_{hb_sc}And searching for a fuzzy velocity multiple m_{amb_sc}；

Setting a search distance r_scHas a search range of [ r_min,r_max]If the corresponding search step is Δ r, the number of search distances is determined

Further obtaining:

r_sc＝n_rΔr+r_min (22)

wherein n is_r＝0,1,2,…,N_r-1，n_rNumber of search distance; r is_minFor searching for a distance r_scMinimum value of (d); r is_maxFor searching for a distance r_scMaximum value of (d);

setting search speed v_sc：

v_sc＝v_{hb_sc}+m_{amb_sc}v_prf；

It should be noted that v is_scCorresponds to v_r1Rather than the true velocity v of the target_r；

Wherein v is_{hb_sc}For searching the base-band unambiguous velocity, the search range is [ -v ]_prf/4,v_prf/4]If the corresponding search step is Δ v, the base band unambiguous velocity search number is N_v，

Further obtaining:

m_{amb_sc}to search for a fuzzy speed multiple, the search thereofIn the range of [ M_{amb_min},M_{amb_max}]And the corresponding search step length is 1, and then:

m_{amb_sc}＝M_{amb_min},M_{amb_min}+1,M_{amb_min}+2,…,M_{amb_max}-1,M_{amb_max}；

wherein M is_{amb_min}Searching the minimum value of the fuzzy speed multiple; m_{amb_max}Searching the maximum value of the fuzzy speed multiple;

according to the set search distance r_scAnd a search velocity v_scExtracting a signal s after second-order Keystone transformation_sokt(r,t_n) Signal s in_sokt(r_sc+v_sct_n,t_n) Discrete chirp-Fourier transform is carried out, and then the quadratic term coefficient is estimated to be a according to the peak position of the obtained transform result_{r_est}；

According to a_{r_est}And v_{hb_sc}Constructing phase compensation equation H_{v_a}(t_n)：

Equation of phase compensation H to be constructed_{v_a}(t_n) Substituting the following Radon-Fourier transform algorithm formula into the search distance-search speed domain (r)_sc,v_sc) Carrying out phase-coherent accumulation to obtain a phase-coherent accumulation result R_rv(r_sc,v_sc)：

Wherein, T_CPIThe coherent accumulation time; t is_CPI＝MT_r。

10. The long-time coherent accumulation system for the uniform acceleration maneuvering target according to claim 6, characterized in that the target detection module is realized by the following specific processes:

coherent accumulation result R_rv(r_sc,v_sc) Carrying out target detection;

if coherent accumulation results R_rv(r_sc,v_sc) If the accumulated peak value is smaller than a preset threshold value, judging that the target is not detected;

if coherent accumulation results R_rv(r_sc,v_sc) If the accumulated peak value is greater than or equal to a preset threshold value, judging that the target is detected, and performing motion parameter estimation on the detected target;

according to R_rv(r_sc,v_sc) R corresponding to peak point position_scObtaining the distance R between the target and the radar_{0_est}；

According to R_rv(r_sc,v_sc) V corresponding to peak point position_scCorresponding v_{hb_sc}And m_{amb_sc}Calculating the radial velocity v of the target relative to the radar_{r_est}：

v_{r_est}＝2v_{hb_sc}+m_{amb_sc}·v_prf (26)

According to the pair s_sokt(r_sc+v_sct_n,t_n) Performing discrete chirp-Fourier transform to obtain the acceleration a of the target_{r_est}。

Images