CN109655802B

CN109655802B - Multi-target particle swarm long-time accumulation detection method based on CLEAN algorithm

Info

Publication number: CN109655802B
Application number: CN201811398217.7A
Authority: CN
Inventors: 董千里; 杜科; 马宪超; 朱炳祺; 王鹤雷; 李森; 祝伟才
Original assignee: Shanghai Radio Equipment Research Institute
Current assignee: Shanghai Radio Equipment Research Institute
Priority date: 2018-11-22
Filing date: 2018-11-22
Publication date: 2020-09-04
Anticipated expiration: 2038-11-22
Also published as: CN109655802A

Abstract

The invention provides a multi-target particle swarm long-time accumulation detection method based on a CLEAN algorithm, which comprises the steps of segmenting a target echo after a target radar echo is obtained, and ensuring that the motion of a target does not exceed a range Doppler unit within each segmentation time; respectively carrying out coherent accumulation on each section of echo data by utilizing segmented Fourier transform to obtain a plurality of sections of echo coherent accumulation data; carrying out target detection by utilizing a particle swarm algorithm to obtain single target information; eliminating the response of the target in each section of echo coherent accumulation data by using a CLEAN algorithm; carrying out target detection by using the particle swarm algorithm again; the above process is repeated until all targets have been successfully detected. The method can obtain the coherent accumulation data of the multi-segment echoes by utilizing segmented Fourier transform, detect the target in the coherent accumulation data of the multi-segment echoes by utilizing a particle swarm algorithm, and detect a plurality of targets by utilizing a CLEAN algorithm.

Description

Multi-target particle swarm long-time accumulation detection method based on CLEAN algorithm

Technical Field

The invention relates to the field of missile-borne pulse Doppler radars, in particular to a multi-target particle swarm long-time accumulation detection method based on a CLEAN algorithm.

Background

The weak target detection usually adopts long-time accumulation, and the signal-to-noise ratio is improved by increasing the target irradiation time, so that the detection performance is improved. However, when the target has high speed and high maneuvering characteristics, a target Range Unit (ARU) and a cross-frequency Unit (ADU) may occur in the whole accumulation time, which may cause the accumulation performance of the simple accumulation method to be degraded, and the signal-to-noise ratio of the target to be reduced, which may seriously affect the detection performance. Meanwhile, the target often has high-order motion characteristics, such as acceleration and jerk, which increases the difficulty and the calculation amount of parameter compensation. Particle Swarm Optimization (PSO) can be used for radar target detection, but the common particle swarm Optimization can only converge on a global optimum value and cannot realize multi-target detection. For radar, detection of weak, high-speed and high-mobility multiple targets is a key problem.

Patent CN105116395A ("a moving-target long-time coherent accumulation method for space-based bistatic radar") describes a moving-target long-time coherent accumulation method for space-based bistatic radar, which performs pulse compression and Keystone processing by using distance delay and doppler phase information in a pulse compression reference signal, and performs FFT in the azimuth direction of an echo signal to obtain azimuth coherent accumulation data. The method can reduce Doppler phase change caused by the motion of the radar platform. However, the method can only extract the range delay and the Doppler phase information by using a bistatic radar, and cannot be applied to a transmitting-receiving integrated monostatic radar.

Patent CN103323829A ("Radon-fractional order fuzzy function-based radar moving target long-time coherent accumulation detection method") describes a radar moving target long-time coherent accumulation detection method using RFRAF. The method comprises the steps of carrying out intra-pulse accumulation on received echoes, initializing detection parameters according to radar system parameters and motion characteristics of a target, completing coherent accumulation by using RFRAF compensation distance and Doppler walking, and extracting target information after constant false alarm detection. The method can match the phase change generated by the target in the motion process and compensate the phase change to acquire the motion information of the target, but the method has huge calculation amount and can realize real-time processing only under the condition that the motion parameters are accurately pre-installed.

Patent CN104574442A ("adaptive particle swarm optimization particle filter moving target tracking method") introduces an adaptive particle swarm optimization particle filter moving target tracking method, which uses a particle swarm algorithm to perform filter tracking on a target. And in the iterative process, the quantity of the particles is adjusted in real time by using the global optimal value, and the particle swarm algorithm is used for updating the state of the particles. The method has low algorithm complexity and small calculation amount, but can only realize the filtering tracking of a single target.

In 2011, a document published by the royal silk of the journal of the aviation weapons of 5 th phase improves a Keystone transformation method, namely, the Keystone transformation algorithm and the application thereof in weak signal detection. The method combines Chirp-Z transformation and Keystone methods aiming at the distance walking phenomenon generated in the long-time accumulation process of the weak target, can overcome the distance walking phenomenon, and simultaneously reduces the calculation complexity. However, the method is only suitable for targets moving at a constant speed, and the accumulation performance of the method is reduced when the targets have high-order motion parameters to cause range migration and Doppler migration.

A method for combining Keystone transformation and Wigner-Hough transformation is proposed by a novel airborne radar high-speed aerial maneuvering target detection method disclosed by Wuren Biao in journal of electronic bulletin 1 of 2013 aiming at the problems of distance walking and Doppler walking of a high-speed maneuvering target in the movement process. Firstly, clutter suppression is carried out on echo data, then Keystone correction distance walking is carried out, Wigner-Hough transformation is carried out after airspace beam forming to estimate acceleration and compensate, and finally space-time two-dimensional beam forming is carried out to complete accumulation. The method can overcome distance walking and Doppler walking, and improve the accumulated signal-to-noise ratio, but when the target speed is high, the algorithm needs to perform traversal search on Doppler ambiguity, the calculated amount is high, and real-time processing is not facilitated.

A fast long-time accumulation algorithm based on frequency domain correction is provided for the problems of distance walking and Doppler walking by a fast long-time accumulation algorithm disclosed by Wangzhe in journal of aviation weapons in 2 nd 2016. The method can effectively realize envelope compensation and Doppler compensation, but the method needs to perform one-dimensional search in the acceleration dimension, and when the range of the prior acceleration is large, the search time is long, so that the real-time performance of the algorithm is influenced.

The methods can not realize weak, high-speed and high-mobility multi-target detection under long-time irradiation, and improve the expected effect of detection performance.

Disclosure of Invention

The invention relates to the field of pulse Doppler radars, and provides a multi-target particle swarm long-time accumulation detection method based on a CLEAN algorithm.

In order to achieve the purpose, the invention adopts the following technical scheme:

the multi-target particle swarm long-time accumulation detection method based on the CLEAN algorithm comprises the following steps of:

s1, after the target radar echo is obtained, segmenting the target echo to ensure that the movement of the target does not exceed a range Doppler unit in each segmentation time;

s2, performing coherent accumulation on each section of echo data by utilizing segmented Fourier transform to obtain multi-section echo coherent accumulation data;

s3, performing target detection by using a particle swarm algorithm to obtain single-target information;

s4, eliminating the response of the target in each section of echo coherent accumulation data by utilizing a CLEAN algorithm;

the above steps S3-S4 are repeated until all targets have been successfully detected.

The method comprises the following steps:

(1) the radar transmits N pulse pulses in sequence with carrier frequency f₀The transmitted pulse signal is expressed as A.exp (j2 pi f)₀t) over a distance R₀At a relative velocity v₀After the target is reflected, the received target echo is A.exp { j2 pi f₀[t-2(R₀-v₀t)/c]}。

(2) The echo signal and the local oscillator signal exp (j2 pi f)₀t) mixing, and obtaining a mixed signal A' exp { j [2 ] after down-conversionπf₀(-2R₀/c+2v₀t/c)]}。

(3) Using prior knowledge to accumulate the whole coherent integration time t_totalThe echoes in each segment are divided into M segments, each segment has L pulses, and the distance deviation of the target in each segment is ensured to be less than one range-Doppler unit.

(4) And performing FFT on each section of target echo according to a range gate to obtain time-frequency coherent accumulation data of the target in the section.

(5) Initializing N particles of the particle swarm optimization algorithm, and randomly distributing the initial values of the particles in the prior range [ R ] of the target_min～R_max,v_min～v_max,a_min～a_max]In this case, the number of particle group iterations k is 1.

(6) And calculating the distance walking and the speed walking of the particle i among the M sections of coherent accumulation data at the k iteration, and assuming the initial distance, the speed and the acceleration of the particle to be R_i,k,v_i,k,a_i,k]The distance and velocity of the particle in the m-th segment are R_i,k-v_i,kt_m-1/2a_i,kt_m ²、v_i,k-a_i,kt_mWherein t is_m＝m(t_totaland/M) represents the interval time between the mth section data and the first section data. And obtaining a range Doppler unit and a frequency unit in the m-th time-frequency coherent accumulation data by using the distance and the speed of the particles, and performing phase compensation.

(7) Adding FFT module values of corresponding distance Doppler units in M-section time-frequency coherent accumulation data to serve as fitness A of kth iteration of particle i_i,k. Taking the particle with the highest fitness of the particle i in the previous k iterations as the individual optimal value [ RPbest ] of the particle i_i,vPbest_i,aPbest_i]Taking the particle with highest fitness in the N individual particle optima as the particle swarm optimization [ RGbest_k,vGbest_k,aGbest_k]。

(8) Judging the possible situations:

the first condition is as follows: if the current iteration number k is more than or equal to k_minAnd the k-th iteration to the k-k_minPopulation optimum between sub-iterationsIf the difference is smaller than the threshold value, turning to the step (10);

case two: if the current iteration number k is more than or equal to k_minAnd the k-th iteration to the k-k_minIf the group optimal value variance between the secondary iterations is larger than the threshold value, turning to the step (9);

case three: if k is<k_minTurning to the step (9);

case four: if k is not less than k_maxGo to step (10).

k_minDenotes the minimum number of iterations, k_maxThe maximum number of iterations is indicated.

(9) Updating the particles, and the distance updating increment of the particle i is delta R_i,k+1＝ωΔR_i,k+C₁·rand·(RPbest_i-R_i,k)+C₂·rand·(RGbest_k-R_i,k) The distance is updated to R_i,k+1＝R_i,k+ΔR_i,k+1(ii) a Speed update increment of Δ v_i,k+1＝ωΔv_i,k+C₁·rand·(vPbest_i-v_i,k)+C₂·rand·(vGbest_k-v_i,k) Velocity is updated to v_i,k+1＝v_i,k+Δv_i,k+1(ii) a Acceleration update increment is Δ a_i,k+1＝ωΔa_i,k+C₁·rand·(aPbest_i-a_i,k)+C₂·rand·(aGbest_k-a_i,k) Acceleration is updated to a_i,k+1＝a_i,k+Δa_i,k+1。C₁And C₂Represents the update coefficient, and rand represents a random quantity between 0 and 1. And (6) turning to the step.

(10) And taking the optimal value of the particle swarm as a target value, and adding 1 to the number of detected targets.

The first condition is as follows: if the number of the detected targets meets the requirement, the detection is finished;

case two: and (5) if the number of the detected targets is less than the requirement, turning to the step (11).

(11) Assume target distance, velocity and acceleration as [ R ]_T,v_T,a_T]Then the distance R of the target in the mth phase-coherent data segment_T,m＝R_T-v_Tt_m-1/2a_Tt_m ²Velocity v_T,m＝v_T-a_Tt_mDoppler f_d＝2v_T,mLambda, distance unit G_R＝mod(R_T,m/dR), dR represents the range resolution. In the distance unit G_RThe reconstructed target signal is α. sin [ pi (l-f)_d/df)]/[π(l-f_d/df)]And L is 0,1,2, …, L-1, α represents an amplitude correction factor, df represents frequency resolution, the reconstructed signal is removed from the coherent accumulated data, and the step (5) is returned.

For high maneuvering targets, it is difficult to achieve long-term accumulation by means of parameter compensation and coherent accumulation. Compared with the prior art, the invention has the following beneficial effects:

the invention is applied to the field of pulse Doppler radars, and can provide a method for long-time accumulation detection, which utilizes segmented Fourier transform to improve the signal-to-noise ratio, utilizes particle swarm optimization to heuristically detect targets, utilizes CLEAN algorithm to solve the problem that the particle swarm optimization can only detect a single target, can overcome the phenomenon that the detection accumulation performance is reduced due to the fact that the targets span a distance unit and span a Doppler unit during long-time accumulation, improves the detection performance, and obtains the information of a plurality of detection targets.

Drawings

FIG. 1: a flow chart of a multi-target particle swarm long-time accumulation detection method based on a CLEAN algorithm;

FIG. 2: coherent accumulation of the cross-range gate phenomenon;

FIG. 3: segmented coherent accumulation data;

FIG. 4: target 1, 1 st iteration particle distribution map;

FIG. 5: the 21 st iteration particle distribution map of target 1;

FIG. 6: the 201 st iteration particle distribution map of the target 1;

FIG. 7: reconstructing an image of the object 1;

fig. 8a, 8 b: removing front and back coherent accumulated data from the target 1;

FIG. 9: object 2 iterates the particle distribution map 201 th time.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings and examples.

As shown in FIG. 1, the invention provides a multi-target particle swarm long-time accumulation detection method based on a CLEAN algorithm, which comprises the following steps:

(1) The detection scene is set as a double-target scene, and the distance, the speed and the acceleration of two targets are set as 550m,1245m/s and 100m/s²]、[700m,1220m/s,100m/s²]. The radar emitting a pulse signal with a pulse repetition period T_r5.5 mus, pulse width τ 0.5 mus, accumulation time t_totalThe whole echo is shown in fig. 2 at 0.1s, and the two targets cross the gate during the whole coherent accumulation time. Direct accumulation can result in an accumulated signal-to-noise ratio that is too low to detect.

(2) The entire echo data is divided into M-10 segments with L-1818 pulses per segment. The prior range of the distance of the target is 375 m-750 m, the prior range of the speed is 1200 m/s-1260 m/s, and the prior range of the acceleration is-10 m/s²～10m/s²The segmentation time is 1818 × T_rThe maximum displacement in the segment is 1260m/s × 0.01.01 s 12.6m which is less than the width 75m of the range gate, and the cross-range gate phenomenon of the target can not occur in 0.01s according to the prior knowledge.

(3) Coherent accumulation is performed for each segment 1818 pulses according to the distance gate, and the obtained segmented FFT result is shown in fig. 3. Theoretically, two targets should be located at the 8 th range gate and the 10 th range gate respectively, and the FFT result of the 8 th range gate of the 10-segment pulse is shown in the figure, and the echo pulse completes coherent accumulation under the condition of not crossing the range gates.

(4) The initial range of the distance of the particles is set to 375 m-750 m, the initial range of the speed is set to 1200 m/s-1260 m/s, and the initial range of the acceleration is set to-10 m/s²～10m/s²In this range, the number of initialized particles is set to 300. Assume that the initial value of the ith particle is [ R ]_i,0,v_i,0,a_i,0]。

(5) Assuming that it is the kth iteration that is present, the range-doppler index of particle i in the 10-segment coherent accumulation data is calculated. The distance walk of the particle i in the mth segment can be expressed as

In the formula: t is t_mRepresents the interval time between the m-th pulse and the 1 st pulse, where t_m＝LT_r0.1 s. The speed walking can be expressed as

v_route,m＝v_i,k+a_i,kt_m

By means of R_route,mAnd v_route,mCalculating the distance index G of the particle i in the mth section of coherent accumulation data_RmAnd Doppler index G_fmThe expression is as follows

G_Rm＝mod(R_route,m/dR)

G_fm＝mod(2v_route,m/λ/df)

In the formula: dR denotes the distance resolution, here dR ═ c τ/2 ═ 75 m; df denotes the frequency resolution, where df is 1/(LT)_r) 100 Hz; λ represents a wavelength.

(6) Performing phase compensation on M sections of coherent accumulation data of the particles i, and performing phase compensation factor H on the mth section of coherent accumulation data_i,mCan be expressed as

In the formula:f₀representing the carrier frequency. After compensation, the FFT module values of corresponding distance Doppler indexes in the M sections of coherent accumulation data are added to obtain the fitness A of the particle i_i,k。

(7) When multiple iterations are carried out, the particle value corresponding to the maximum fitness in the multiple iterations is taken as the individual optimal value [ RPbest ] of the particle i_i,vPbest_i,aPbest_i]. Taking the particle value with highest fitness in the individual optima as the particle swarm optima [ RGbest_k,vGbest_k,aGbest_k]。

(8) Assuming a minimum number of iterations k _min200, maximum number of iterations k_max3000, the iteration end threshold k_Threshold＝10^-5。

The first condition is as follows: if the current iteration number k is more than or equal to k_minAnd the k-th iteration to the k-k_minTurning to the step (10) if the group optimal value variance between the secondary iterations is smaller than a threshold value;

case three: if k is<k_minTurning to the step (9);

case four: if k is not less than k_maxGo to step (10).

(9) Updating the particle, the distance updating increment Delta R of the particle i_i,k+1Speed update delta Δ v_i,k+1Acceleration update increment is Δ a_i,k+1Can be expressed as

ΔR_i,k+1＝ωΔR_i,k+C₁·rand·(RPBest_i-R_i,k)+C₂·rand·(RGBest-R_i,k)

Δv_i,k+1＝ωΔv_i,k+C₁·rand·(vPBest_i-v_i,k)+C₂·rand·(vGBest-v_i,k)

Δa_i,k+1＝ωΔR_i,k+C₁·rand·(aPBest_i-a_i,k)+C₂·rand·(aGBest-a_i,k)

In the formula: c₁Representing individual optimal value influence factors, and taking 1.8; c₂Representing the influence factor of the optimal value of the population, and taking 1.8; rand represents a random quantity between 0 and 1, w represents an update coefficient, and can be expressed as

In the formula: omega_minRepresenting the minimum update coefficient, and taking the minimum update coefficient as 0.1; omega_maxRepresenting the maximum update coefficient, is taken to be 0.8. And (5) returning to the step (5) after the updating is finished.

(10) Optimizing the particle swarm [ RGbest_k,vGbest_k,aGbest_k]The target value is the optimal value of the population of particles, and 1 is added to the number of detected targets.

(11) Distance R of target in mth section of coherent data_T,m＝RGbest_k-vGbest_kt_m-1/2aGbest_kt_m ²Velocity v_T,m＝vGbest_k-aGbest_kt_mDoppler f_d＝2v_T,mLambda, distance unit G_R＝mod(R_T,m/dR). In the distance unit G_RThe reconstructed target signal is α. sin [ pi (l-f)_d/df)]/[π(l-f_d/df)]And L is 0,1,2, …, L-1, α represents an amplitude correction factor, and df represents frequency resolution.

(12) The particle swarm distribution diagrams of the 1 st iteration and the 21 st iteration of the particle swarm in the first particle swarm detection algorithm are respectively shown in FIG. 4 and FIG. 5, the whole particle swarm changes towards the optimal value, the particle swarm judges the termination condition before the 201 st iteration, and the variance of the 1 st iteration to the 200 th iteration is-1.4681 × 10^-6Is less than the iteration end threshold k_Threshold＝10^-5The final iteration result of the first target detection is shown in FIG. 6The distance, speed and acceleration of the target are 585m, 1245m/s and 100m/s respectively²。

(13) The number of detection targets is 1, which is less than the required number 2, and therefore, the second detection is required. The reconstruction of the target image using the CLEAN algorithm is shown in fig. 7. Images before and after the first-stage coherent accumulated data is removed are shown in fig. 8a and 8b, and the response of the first target in the coherent accumulated data is removed.

(14) In the second detection, the particle swarm judges the termination condition before the 201 st iteration, and the variance from the 1 st iteration to the 200 th iteration is-5.2381 × 10^-6Is less than the iteration end threshold k_Threshold＝10^-5The final iteration result of the second target detection is shown in FIG. 9, where the distance, velocity and acceleration of the target are 730m, 1219m/s and 100m/s, respectively²。

(15) The number of the detection targets is 1, the required number is 2, and the detection is finished.

In conclusion, the invention uses segmented FFT to realize long-time accumulation, and solves the phenomena of target span units and frequency span units; the particle swarm algorithm is used for realizing the detection of the target, so that meaningless search paths are reduced, the detection performance is improved, and the detection time is shortened; and eliminating the response of the detected target in the coherent accumulation data by utilizing a CLEAN algorithm to realize multi-target detection.

While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims

1. A multi-target particle swarm long-time accumulation detection method based on a CLEAN algorithm is characterized by comprising the following steps:

2. The multi-target particle swarm long-time accumulation detection method based on the CLEAN algorithm as claimed in claim 1, comprising the following steps:

(1) the radar transmits N pulses in sequence with a carrier frequency of f₀The transmitted pulse signal is expressed as A.exp (j2 pi f)₀t) over a distance R₀At a relative velocity v₀After the target is reflected, the received target echo is A.exp { j2 pi f₀[t-2(R₀-v₀t)/c]}；

(2) The echo signal and the local oscillator signal exp (j2 pi f)₀t) mixing, and obtaining a mixed signal A' exp { j [2 pi f ] after down-conversion₀(-2R₀/c+2v₀t/c)]}；

(3) Using prior knowledge to accumulate the whole coherent integration time t_totalThe echo in each section is divided into M sections, each section has L pulses, and the offset of a target in each section is ensured to be smaller than a range Doppler unit; the priori knowledge comprises a distance priori range, a speed priori range and an acceleration priori range of the target;

(4) performing FFT on each section of target echo according to a range gate to obtain time-frequency coherent accumulation data of the target in the section;

(5) initializing N particles of the particle swarm optimization algorithm, and randomly distributing the initial values of the particles in the prior range [ R ] of the target_min～R_max,v_min～v_max,a_min～a_max]In the method, the particle swarm iteration number k is 1;

(6) in the k iteration, calculating the coherent accumulation data of the particle i in the M sectionsAssuming the initial distance, velocity and acceleration of the particle are [ R ]_i,k,v_i,k,a_i,k]The distance and velocity of the particle in the m-th segment are R_i,k-v_i,kt_m-1/2a_i,kt_m ²、v_i,k-a_i,kt_mWherein t is_m＝m(t_total/M) represents the interval time between the mth section of data and the first section of data; obtaining a distance Doppler unit and a frequency unit in the m-th time-frequency coherent accumulation data by using the distance and the speed of the particles, and performing phase compensation;

(7) adding FFT module values of corresponding distance Doppler units in M-section time-frequency coherent accumulation data to serve as fitness A of kth iteration of particle i_i,k(ii) a Taking the particle with the highest fitness of the particle i in the previous k iterations as the individual optimal value [ RPbest ] of the particle i_i,vPbest_i,aPbest_i]Taking the particle with highest fitness in the N individual particle optima as the particle swarm optimization [ RGbest_k,vGbest_k,aGbest_k]；

(8) Judging the possible situations:

case three: if k is<k_minTurning to the step (9);

case four: if k is not less than k_maxTurning to the step (10);

k_mindenotes the minimum number of iterations, k_maxRepresenting the maximum number of iterations;

(9) updating the particle, the distance of the particle i is updated by increment

ΔR_i,k+1＝ωΔR_i,k+C₁·rand·(RPbest_i-R_i,k)+C₂·rand·(RGbest_k-R_i,k)，

Distance is updated to R_i,k+1＝R_i,k+ΔR_i,k+1；

Speed update increment of

Δv_i,k+1＝ωΔv_i,k+C₁·rand·(vPbest_i-v_i,k)+C₂·rand·(vGbest_k-v_i,k)，

Velocity is updated to v_i,k+1＝v_i,k+Δv_i,k+1；

Acceleration update increment of

Δa_i,k+1＝ωΔa_i,k+C₁·rand·(aPbest_i-a_i,k)+C₂·rand·(aGbest_k-a_i,k)，

Acceleration is updated to a_i,k+1＝a_i,k+Δa_i,k+1；

C₁And C₂Representing an updating coefficient, and rand representing a random quantity between 0 and 1; turning to step (6);

(10) taking the optimal value of the particle swarm as a target value, and adding 1 to the number of detected targets;

case two: if the number of the detected targets is less than the requirement, turning to the step (11);

(11) assume target distance, velocity and acceleration as [ R ]_T,v_T,a_T]Then the distance R of the target in the mth phase-coherent data segment_T,m＝R_T-v_Tt_m-1/2a_Tt_m ²Velocity v_T,m＝v_T-a_Tt_m，

Doppler f_d＝2v_T,mLambda, distance unit G_R＝mod(R_T,mdR), dR represents the distance resolution;

in the distance unit G_RThe reconstructed target signal is α. sin [ pi (l-f)_d/df)]/[π(l-f_d/df)]，

L-0, 1,2, …, L-1, α denotes the amplitude correction factor, df denotes the frequency resolution;

removing the reconstructed signal from the coherent accumulation data; and (5) returning.