CN104914428A - Speed measurement system based on ultrahigh frequency radio frequency identification label and measurement method - Google Patents

Abstract

The invention discloses a speed measurement system based on an ultrahigh frequency radio frequency identification label and a measurement method. The measurement system comprises a radio frequency identification label, a first antenna, a second antenna, a radio frequency identification reader and a data center. The first antenna and the second antenna are connected to the radio frequency identification reader respectively. The radio frequency identification reader receives signals emitted by the radio frequency identification label through the first antenna and the second antenna respectively and sends to the data center respectively. The method in the invention is based on an ultrahigh frequency RFID technology. A Lagrange interpolation method is used to expand a data source. Through a maximum value time difference method of Gaussian fitting between partitions and kalman filter combination and a correlation time difference method of a Phat processor and SCOT weighting, data read by a reader is processed so that accurate measurement of a walking speed is realized. By using the system and the method, an error can be effectively reduced and precision is increased, and a large calculated amount is not needed. The ultrahigh frequency RFID label possesses advantages that the size is small; a price is low; a reading distance is long and so on. The system and the method can be made into a sensor which can be worn on an elder so as to carry out accurate measurement of the walking speed.

Description

A kind of velocity measuring system based on super high frequency radio frequency identification label and measuring method

Technical field

The present invention relates to a kind of velocity measuring system based on super high frequency radio frequency identification label and measuring method, belong to RFID tag and read the technical field identified.

Background technology

Radio-frequency (RF) identification (Radio Frequency Identification, RFID) technology, it is a kind of contactless automatic identification technology, each RFID label tag has unique mark (ID) information, and RFID reader reads the id information of RFID label tag by the mode of radio frequency.This technology has the advantages such as recognition accuracy is high, antijamming capability strong, long service life, and the passive electronic label cost used is low, easy for installation, have also been obtained use widely in each field.

Interpolation, matching, filtering and cross-correlation are all conventional data processing methods.Interpolating function is the function of interpolation continuous data on the basis of discrete data, and make this continuous curve by all given discrete data point, it is the important method that discrete function approaches.Filtering is by the operation of specific band frequency filtering in signal, is the important measures suppressing and prevent to disturb.Matching is similar to, to data analysis important in inhibiting the one of raw data.Cross-correlation is used for the covariance of expression two between random vector X and Y in statistics; In signal transacting field, cross-correlation is used to a tolerance of similarity between expression two signals, usually by comparing the characteristic found in unknown signaling with known signal.

Senior health and fitness is a focus of contemporary scientific research, along with the quickening of aging population trend, health of older persons becomes more and more important, in recent years, researcher finds that the elderly's speed of travel and its health have close ties, therefore, will become more and more important to the accurate measurement of the elderly's speed of travel, but the correlative study of China in the measurement of human body walking speed is in space state substantially, also without any research to appearing a complete speed-measuring method.RFID in the past, in the application in the field of testing the speed, mostly is hot-short and tests the speed, and in the present invention, designed system and method aim at pedestrian and test the speed and provide.

Summary of the invention

Goal of the invention: the speed of travel measuring system and the method that the object of the present invention is to provide a kind of super high frequency radio frequency identification

Technical scheme: the speed of travel measuring system of super high frequency radio frequency identification of the present invention and method, radio-frequency identification reader is connected with RFID tag through radio frequency, radio-frequency identification reader is connected with data center through data line, radio-frequency identification reader is connected with microwave antenna, RFID tag is connected with reader by built-in transmitting antenna, specific measuring method is used to obtain data, Lagrange method of interpolation is used to carry out pre-service to raw data in speed calculation method successively, afterwards by the data that the relevant time difference method process interpolation of by stages Gauss curve fitting and the maximal value time difference method that Kalman filter combines and Phat processor and SCOT weighting obtains, thus obtain the speed of travel of pedestrian.

Described measuring method be carry electronic identification label pedestrian along the straight line moving parallel with two microwave antennas, under RFID device work, reader sends the radiofrequency signal of certain frequency by emitting antenna, electronic tag in emitting antenna perform region through activate after built-in information is sent, reader is to the information identification received, and send to data center's record, thus obtain a series of raw data.

Computational Method of Velocity Measurement:

1, Lagrange method of interpolation

The time interval of the signal intensity read due to RFID reader is inconstant, and signal intensity to be subject to the impact fluctuation of multiple factors such as indoor temperature, humidity, multipath effect very large, therefore need the data to reading to do pre-service.In order to avoid the loss of true value, adopt Lagrange method of interpolation to carry out interpolation to institute's read data, make generation time be spaced apart the sequence of Δ T.

If P, Q, H 3 are 3 points adjacent in the sequence of interpolation, its coordinate is respectively (x ₀, y ₀), (x ₁, y ₁), (x ₂, y ₂), suppose x ₀<x ₁<x ₂; A para-curve y=ax just can be determined by these 3 ²+ bx+c, three parameter a, b, c can be tried to achieve by Lagrange interpolation formula, and Lagrange interpolation formula is:

$y=\frac{(x-x_1)(x-x_2)}{(x_0-x_1)(x_0-x_2)}{y}_0+\frac{(x-x_0)(x-x_2)}{(x_1-x_0)(x_1-x_2)}{y}_1+\frac{(x-x_0)(x-x_1)}{(x_2-x_0)(x_2-x_1)}{y}_2$

After obtaining parameter, at interval [x ₀, x ₂] between, insert a sub-value every Δ T.After completing, reselect three adjacent points, constantly repeat above-mentioned way, make it to produce the sequence that the complete time interval is Δ T.

2, by stages Gauss curve fitting

The signal intensity P of certain position _rd () value can regard a probability problem as, P _rd () Distribution value is more intensive shows P _rd () value is truer.Now by stages Gauss curve fitting is adopted to the sequence that Lagrange interpolation produces, find out the P that probability is large _rd () value, rejects scattered misdata.Fitting function is:

$\left\{\begin{array}{c}{x}_c=\frac{\underset{i=1}{\overset{i=k}{\&Sigma;}}{P}_r{\left(d\right)}_i}{k}\\ \mathrm{\&omega;}=\sqrt{\frac{\underset{i=1}{\overset{i-k}{\&Sigma;}}{(P_r{\left(d\right)}_i-x_c)}^2}{k}}\\ Y={\mathrm{Ae}}^{-\frac{{(P_r{\left(d\right)}_i-x_c)}^2}{2{\mathrm{\&omega;}}^2}}\end{array}\right.$

Now the sequence that interpolation produces is divided into multiple interval, the P that each interval can produce under a certain distance d of approximate representation _rd () value, then by the P in this interval _rd () value substitutes into fitting function, retain 0.5<Y _ithe large probability data of <1.

3, Kalman filter

Because Gauss curve fitting method only eliminates scattered misdata, and some large probability noises can not eliminate its impact, now process by Kalman filter the data that Gauss curve fitting obtains, random disturbance eliminated by the measured value according to system, the true colors of playback system.According to the feature of the rfid system built, can process with without controlling discrete type Kalman filter, its algorithm describes by 5 equations.

The one-step prediction equation of state:

${\hat{x}}_{k/k-1}={\mathrm{\&Phi;}}_{k/k-1}*x_{k-1}$

The one-step prediction equation of square error:

${\hat{P}}_{k/k-1}={\mathrm{\&Phi;}}_{k/k-1}*P_{k-1}*{\mathrm{\&Phi;}}_{k/k-1}^T+{\mathrm{\&Phi;}}_{k-1}*Q_{k-1}*{\mathrm{\&Gamma;}}_{k-1}^T$

Filter gain equation (weight):

$H_k={\hat{P}}_{k/k-1}*C_k^T{\&lsqb;C_k*{\hat{P}}_{k/k-1}*C_k^T+R_k\&rsqb;}^{-1}$

Filtering estimate equation (optimal value in K moment):

$x_k={\hat{x}}_{k/k-1}+H_k\&lsqb;Z_k-C_k*{\hat{x}}_{k/k-1}\&rsqb;$

Square error upgrades matrix (the optimum square error in K moment):

$P_k=\&lsqb;I-H_k*C_k\&rsqb;*{\hat{P}}_{k/k-1}$

4, the broad sense cross-correlation of Phat processor and SCOT weighting

Broad sense cross-correlation be based on two signals between cross-power spectrum, and in frequency domain, give certain weighting, whitening processing can be carried out to signal and noise, strengthen the frequency content that in signal, signal to noise ratio (S/N ratio) is higher, thus the impact of restraint speckle, change (IDFT) to time domain by inverse discrete Fourier transform again, the broad sense cross correlation function obtaining two signals is:

$R_{12}^g\left(n\right)=IDFT\&lsqb;A\left(k\right)G_{12}\left(k\right)\&rsqb;$

Wherein, G ₁₂k () is the cross-spectral density between two signals, A (k) is broad sense cross-correlation weighting function.Choosing of weighting function determines according to different noises and reverberation situation, for native system, Phat processor and SCOT weighting proper.

Phat processor:

A(k)＝1/|G ₁₂(k)|

SCOT：

$A\left(k\right)=1/\sqrt{G_{11}\left(k\right)G_{22}\left(k\right)}$

The correlationship of two discrete signal frequency domain characteristics can describe with autopower spectral density and cross-spectral density, and autopower spectral density and autocorrelation function are a pair Fourier pairs, cross-spectral density and cross correlation function are also a pair Fourier pairs:

R ₁₂(n)＝IDFT[G ₁₂(k)]

According to the time domain circular convolution characteristic of discrete Fourier transformation, above formula can be changed into:

$R_{12}^g\left(n\right)=A\left(n\right)\&CircleTimes;R_{12}\left(n\right)=\underset{m=0}{\overset{N-1}{\&Sigma;}}A\left(m\right)R_{12p}(n-m)R_N\left(n\right)$

Wherein, A (n) obtains by A (k) discrete Fourier transformation (DFT); represent circular convolution operational symbol; R _12P(n-m) R _nn () represents circular shifting sequence; R _nn () is rectangle sequence.

In order to simplify the calculating of round convolution, can realize with matrix multiple, matrix representation is:

Y＝HX

Wherein:

$\mathrm{\&gamma;}=\left(\begin{array}{c}{R}_{12}^g\left(0\right)\\ R_{12}^g\left(1\right)\\ R_{12}^g\left(2\right)\\ \begin{array}{c}\&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\end{array}\\ R_{12}^g(N-1)\end{array}\right)$

$X=\left(\begin{array}{c}A\left(0\right)\\ A\left(1\right)\\ A\left(2\right)\\ \begin{array}{c}\&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\end{array}\\ A(N-1)\end{array}\right)$

The present invention proposes a kind of pedestrian's velocity-measuring system and method for super high frequency radio frequency identification, its beneficial effect not only effectively can reduce error in the process of testing the speed, and improves precision, and do not need large calculated amount.

Compared with prior art, its beneficial effect is in the present invention: 1, effectively can reduce error, improves precision, and does not need large calculated amount.

The measuring accuracy of 2, traditional speed-measuring method (as stopwatch tests the speed) is often not high, and the surveying instrument that precision is higher cannot large-scale popularization use because cost is higher, and these methods are all difficult to the daily speed of travel of Measurement accuracy the elderly.Ultra-high frequency RFID label has the advantages such as volume is little, price is low, reading distance, is suitable as sensor and is worn on the Measurement accuracy that the elderly carries out the speed of travel with it.

3, speed-measuring method precision comparison of the present invention is high, and whole system price is also more moderate, can be used for health care.

4, native system can test the speed to multiple people simultaneously, and RFID label tag preserves the data of subject person, by the different subject person of tag recognition.

Accompanying drawing explanation

Fig. 1 is velocity measuring system structured flowchart of the present invention;

Fig. 2 is velocity measuring system principle schematic of the present invention;

Fig. 3 is velocity measuring system of the present invention experiment schematic diagram;

Fig. 4 is embodiments of the invention 1 interpolation preprocessed data figure;

Fig. 5 is the Gauss curve fitting data plot of embodiments of the invention 1;

Fig. 6 is the Kalman filter process data plot of the embodiment of the present invention 1;

Fig. 7 is the relevant time difference method process data plot of the embodiment of the present invention 1.

Embodiment

Below technical solution of the present invention is described in detail, but protection scope of the present invention is not limited to described embodiment.

Embodiment 1:

As shown in Figure 1, native system is made up of RFID tag, radio-frequency identification reader (microwave antenna) and data center, identification information is preserved in RFID tag, radio-frequency identification reader is read the identification information of RFID tags by the method for radio-frequency (RF) identification and is sent to data center by data line, and data center shows and record data.

As shown in Figure 2, radio-frequency identification reader is connected with RFID tag through radio frequency, radio-frequency identification reader is connected with data center through data line, and radio-frequency identification reader is connected with microwave antenna, and RFID tag is connected with reader by built-in transmitting antenna.Pedestrian carries electronic tag and passes through from the straight line of two microwave antenna forward positions and two antenna parallel, reader sends the radiofrequency signal of certain frequency by emitting antenna, induction current is produced when electronic tag enters emitting antenna perform region, electronic tag obtains energy and is activated, and the information such as self coding is sent by the built-in transmitting antenna of card; System acceptance antenna receives the carrier signal of sending from electronic tag, is sent to reader through antenna adjustments device, and reader carries out demodulation code to the signal received and then delivers to backstage main system and carry out relevant treatment.The relation of signal propagation losses model reflected signal propagation path loss and propagation distance, the distance of electronic tag and antenna is nearer, loss in signal communication process is less, the signal intensity that reader receives is larger, and when the distance of electronic tag and antenna changes, will be there is corresponding change in the signal intensity that reader reads, distance is nearer, and the signal intensity read is larger.Distance D between antenna can set in advance, if measure two signal intensities maximum time mistiming Δ t, utilize formula the average velocity of this segment distance can be calculated.

1, system building

As shown in Figure 3, instrument used herein is purple battle-axe used in ancient China RFID, and by the Autopilot technology of SpeedwayRevolution, the operation of Automatic Optimal reader in applied environment, makes it measure and be in best performance state.Experimental apparatus is connected by figure, opening power, and set relevant parameter, the distance D adjusted between two antennas is 8m, allow the people that carry electronic tag along the straight line moving with two antenna parallel, reader record also preserves data, and the data read by maximum time difference method and relevant time difference method process reader, try to achieve the speed of travel of pedestrian.

2, Lagrange interpolation pre-service

As shown in Figure 4, herein by matlab programming realization Lagrange interpolation.As can be seen from the figure, raw data is some discrete points, and subregion is concentrated, and is not easy to process.When ensureing true value, by Lagrange interpolation expanding data source, make it the sequence that generation time is spaced apart 0.001s.

3, maximum time difference method

As shown in Figure 5, sequence interpolation produced the temporally interval division region such as interval 0.05s, then realize by stages matching by Gauss curve fitting function, fitting result utilizes Kalman filter to eliminate random disturbance.As we can see from the figure, curve changes not quite generally, but some small probability data and system random noise disallowable, make curve more level and smooth, the authenticity of data is higher.

As shown in Figure 6, to the P that Kalman filter process obtains _rd () value is averaged and just obtains under this interval and the corresponding time is P _rthe mean value of (d) corresponding time two antennas receive the time that the maximal value be worth is corresponding be respectively 3.123s and 9.862s.The speed of trying to achieve is:

$v=\frac{8}{9.862-3.123}=1.1871m\&CenterDot;s^{-1}$

4, relevant time difference method

As shown in Figure 7, utilize the sequence that Lagrange interpolation generation time interval delta T is 0.01s, carry out related operation by the sequence produced interpolation, adopt Phat processor and SCOT weighting.As seen from the figure, although Phat processor and SCOT curve are not very level and smooth, peak value clearly, is easily told, and more accurately can determine the time delay of two signals in actual measurement.Time delay number n after Phat processor and the process of SCOT weighting function is respectively 689 and 691, and corresponding mistiming Δ t is respectively 6.89s and 6.91s.The speed of trying to achieve is respectively:

$v=\frac{8}{6.89}1.1611m\&CenterDot;s^{-1}$

$v=\frac{8}{6.91}=1.1577m\&CenterDot;s^{-1}$

As mentioned above, although represented with reference to specific preferred embodiment and described the present invention, it shall not be construed as the restriction to the present invention self.Under the spirit and scope of the present invention prerequisite not departing from claims definition, various change can be made in the form and details to it.

Claims (7)

1. the velocity measuring system based on super high frequency radio frequency identification label, it is characterized in that, comprise RFID tag, first antenna, second antenna, radio-frequency identification reader and data center, wherein the first antenna and the second antenna are connected to radio-frequency identification reader respectively, described radio-frequency identification reader is also sent to described data center respectively by the first antenna and the second antenna signal that received RF identification label sends respectively, described data center calculates the speed of described RFID tag by maximum time difference method and relevant time difference method according to the signal received.

2. the measuring method of the velocity measuring system based on ultrahigh frequency RFID according to claim 1 is characterized in that, maximum time difference method comprises the following steps:

1) described data center reads the intensity data that the first antenna and the second antenna receive the signal that RFID tag sends;

2) by step 1) read the data that obtain with Δ T ₁the time interval carry out Lagrange's interpolation process and obtain the signal intensity sequence that the first antenna and the second antenna receive;

3) by step 2) the signal intensity sequence that obtains is according to time interval Δ T ₂equidistant zoning, then carries out by stages matching by Gauss curve fitting function, retains large probability data;

4) by step 3) fitting result eliminate random disturbance by Kalman filter;

5) by step 4) sequence results be averaged the average of trying to achieve signal intensity by the interval in step 3

6) according to two antennas the time t that maximal value is corresponding ₁and t ₂, calculate the speed of RFID tag wherein D is the distance between the first antenna and the second antenna.

3. the measuring method of the velocity measuring system based on ultrahigh frequency RFID according to claim 1 is characterized in that, relevant time difference method comprises the following steps:

1) described data center reads the intensity data that the first antenna and the second antenna receive the signal that RFID tag sends;

2) by step 1) read the data that obtain with Δ T ₃the time interval carry out Lagrange's interpolation process and obtain the signal intensity sequence that the first antenna and the second antenna receive;

3) by step 2) sequence results by the relevant time difference method process of Phat processor and SCOT weighting, the sequence number corresponding to peak value of trying to achieve relevant time difference method is M (i.e. the time delay number of two sequences);

4) speed of RFID tag is calculated wherein D is the distance between the first antenna and the second antenna.

4. it is characterized in that according to the measuring method of claim 2 and the velocity measuring system based on ultrahigh frequency RFID according to claim 3, described step 2): by step 1) read the data that obtain and carry out Lagrange's interpolation process with the time interval of Δ T and obtain the signal intensity sequence that the first antenna and the second antenna receive, be specially:

If P, Q, H 3 are 3 points adjacent in the sequence of interpolation, its coordinate is respectively (x ₀, y ₀), (x ₁, y ₁), (x ₂, y ₂), suppose x ₀<x ₁<x ₂; A para-curve y=ax just can be determined by these 3 ²+ bx+c, three parameter a, b, c can be tried to achieve by Lagrange interpolation formula, and Lagrange interpolation formula is:

$y=\frac{(x-x_1)(x-x_2)}{(x_0-x_1)(x_0-x_2)}{y}_0+\frac{(x-x_0)(x-x_2)}{(x_1-x_0)(x_1-x_2)}{y}_1+\frac{(x-x_0)(x-x_1)}{(x_2-x_0)(x_2-x_1)}{y}_2$

After obtaining parameter, at interval [x ₀, x ₂] between, insert a sub-value every Δ T; After completing, reselect three adjacent points, constantly repeat above-mentioned way, make it to produce the sequence that the complete time interval is Δ T.

5. the measuring method of the velocity measuring system based on ultrahigh frequency RFID according to claim 2 is characterized in that, described step 3): by step 2) the signal intensity sequence that obtains is according to time interval Δ T ₂equidistant zoning, zero padding during data deficiencies, then carry out by stages matching by Gauss curve fitting function, be specially:

$\left\{\begin{array}{c}{x}_c=\frac{\underset{i=1}{\overset{i=k}{\mathrm{\&Sigma;}}}{P}_r{\left(d\right)}_i}{k}\\ \mathrm{\&omega;}=\sqrt{\frac{\underset{i=1}{\overset{i=k}{\mathrm{\&Sigma;}}}{(P_2{\left(d\right)}_i-x_c)}^2}{k}}\\ Y_i={\mathrm{Ae}}^{-\frac{{(P_r{\left(d\right)}_i-x_c)}^2}{2{\mathrm{\&omega;}}^2}}\end{array}\right.$

Wherein x _crepresent the average of signal intensity; ω is the standard deviation of signal intensity in certain interval that RFID reader records; Y _irepresent probability; A is normalized parameter, determines by normalizing equation, and normalizing equation is:

$\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{Y}_i=1$

Now the sequence that interpolation produces is divided into multiple interval, the P that each interval can produce under a certain distance d of approximate representation _rd () value, then by the P in this interval _rd () value substitutes into fitting function, retain 0.5<Y _ithe large probability data of <1.

6. the measuring method of the velocity measuring system based on ultrahigh frequency RFID according to claim 2 is characterized in that, described step 4): by step 3) fitting result by Kalman filter eliminate random disturbance be specially:

The one-step prediction equation of state: (wherein Φ _k/k-1state variable drives matrix)

${\hat{x}}_{k/k-1}={\mathrm{\&Phi;}}_{k/k-1}*x_{k-1}$

The one-step prediction equation of square error: (wherein Q _k-1for the covariance of process noise; Г _k-1for noise drives matrix)

${\hat{P}}_{k/k-1}={\mathrm{\&Phi;}}_{k/k-1}*P_{k-1}*{\mathrm{\&Phi;}}_{k/k-1}^T+{\mathrm{\&Phi;}}_{k-1}*Q_{k-1}*{\mathrm{\&Gamma;}}_{k-1}^T$

Filter gain equation: (wherein R _kcovariance for measurement noises)

$H_k={\hat{P}}_{k/k-1}*C_k^T{[C_k*{\hat{P}}_{k/k-1}*C_k^T+R_k]}^{-1}$

Filtering estimate equation (wherein Z _kfor systematic observation variable):

$x_k={\hat{x}}_{k/k-1}+H_k[Z_k-C_k*{\hat{x}}_{k/k-1}]$

Square error upgrades matrix (wherein P _koptimum square error for the K moment):

$P_k=[I-H_k*C_k]*{\hat{P}}_{k/k-1}$

By above-mentioned equation, first the choosing of filtering initial value, often gets and P ₀=Cov [x ₀], then with the optimal estimation x in k-1 moment _k-1be as the criterion, the state variable in prediction k moment again this state is observed simultaneously, obtain observational variable Z _k, finally by observed quantity, premeasuring is revised, thus obtains the optimal State Estimation x in k moment _k.Kalman filtering is a kind of recursive algorithm, constantly repeats said process, just can determine not optimal estimation value in the same time.

7. the measuring method of the velocity measuring system based on ultrahigh frequency RFID according to claim 3 is characterized in that, described step 3): by step 2) sequence results by the relevant time difference method process of Phat processor and SCOT weighting, the sequence number corresponding to peak value of trying to achieve relevant time difference method is M, is specially:

Broad sense cross-correlation be based on two signals between cross-power spectrum, and in frequency domain, give certain weighting, whitening processing is carried out to signal and noise, strengthen the frequency content that in signal, signal to noise ratio (S/N ratio) is higher, thus the impact of restraint speckle, change (IDFT) to time domain by inverse discrete Fourier transform again, the broad sense cross correlation function obtaining two signals is:

$R_{12}^g\left(n\right)=\mathrm{IDFT}\left[A\left(k\right)G_{12}\left(k\right)\right]$

Wherein, G ₁₂k () is the cross-spectral density between two signals, A (k) is broad sense cross-correlation weighting function.Choosing of weighting function determines according to different noises and reverberation situation, for native system, Phat processor and SCOT weighting proper.

Phat processor:

A(k)＝1/|G ₁₂(k)|

SCOT：

$A\left(k\right)=1/\sqrt{G_{11}\left(k\right)G_{22}\left(k\right)}$

The correlationship of two discrete signal frequency domain characteristics can describe with autopower spectral density and cross-spectral density, and autopower spectral density and autocorrelation function are a pair Fourier pairs, cross-spectral density and cross correlation function are also a pair Fourier pairs:

R ₁₂(n)＝IDFT[G ₁₂(k)]

According to the time domain circular convolution characteristic of discrete Fourier transformation, above formula can be changed into:

$R_{12}^g\left(n\right)=A\left(n\right)\&CircleTimes;R_{12}\left(n\right)=\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}A\left(m\right)R_{12p}(n-m)R_N\left(n\right)$

Wherein, A (n) obtains by A (k) discrete Fourier transformation (DFT); represent circular convolution operational symbol; R _12P(n-m) R _nn () represents circular shifting sequence; R _nn () is rectangle sequence.

In order to simplify the calculating of round convolution, can realize with matrix multiple, matrix representation is:

Y＝HX

Wherein:

$Y=\left(\begin{array}{c}{R}_{12}^g\left(0\right)\\ R_{12}^g\left(1\right)\\ R_{12}^g\left(2\right)\\ .\\ .\\ .\\ R_{12}^g(N-1)\end{array}\right)$

$X=\left(\begin{array}{c}A\left(0\right)\\ A\left(1\right)\\ A\left(2\right)\\ .\\ .\\ .\\ A(N-1)\end{array}\right)$

Broad sense cross-correlation computation process is:

First, by two sequences y of interpolation generation ₁(n) and y ₂n (), makes two sequence lengths the same by zero padding, then utilizes basic computing cross-correlation, try to achieve R ₁₂(m), computing formula is:

$R_{12}\left(m\right)=\underset{n=0}{\overset{N}{\mathrm{\&Sigma;}}}{y}_1\left(n\right)y_2(n-m)$

Then, select Phat processor or SCOT weighting function A (k), obtain A (n) by Fourier inversion;

Finally, broad sense cross-correlation is tried to achieve by the rapid design method of above-mentioned round convolution according to maximal value determination time delay number M.