CN105044702A - Fitting method for pulse waveforms - Google Patents

Abstract

The invention provides a fitting method for pulse waveforms. The fitting method for the pulse waveforms comprises the following steps that firstly, the pulse waveform PObs and the template waveform PModel are obtained respectively, wherein the ratio of the sampling rate SDaq of the template waveform and the sampling rate SModel of the pulse waveform is larger than 10; secondly, the implicit function that y equals to f(x) is used for expressing the template waveform PModel, the target function y=A*f[B(x-C)] is obtained through translation and zooming operation of the function, and A, B and C are undermined factors; thirdly, the numerical value of a sampling point of the pulse waveform PObs is substituted into the target function, and the undermined factors A, B and C are obtained through the nonlinear least square method. By means of the method, a new method is provided on the aspect of pulse laser ranging and pulse laser three-dimensional measuring, and the fitting method is suitable for full-waveform laser radar systems in any waveform shape and suitable for other electronic systems needing waveform fitting.

Description

The approximating method of pulse waveform

Technical field

The present invention relates to waveform fitting, particularly the approximating method of pulse waveform.

Background technology

Transponder pulse signal and echo pulse signal all carry out sampling and record with very little sampling interval by Full wave shape laser radar (Waveform-DigitizingLiDAR), user is according to practical application request, the Wave data of record is processed and analyzed, compare conventional laser radar, abundanter return laser beam number of times and target signature information can be obtained.

The key content of wave data processing and analysis is that the waveform how carrying out accurate stable decomposes.Model fitting method is the most frequently used waveform decomposition method, and the pulse waveform of its hypothesis laser radar meets certain mathematical model, then uses nonlinear least square method to calculate the design parameter of mathematical model.Wherein, the most frequently used mathematical model is Gaussian function or Generalized Gauss function, but affects by pulsed laser and photodetector output characteristics, and laser pulse signal meets class Gaussian function, therefore use Gaussian function or Generalized Gauss function as mathematical model, be inaccurate.

Summary of the invention

For solving the deficiency in above-mentioned prior art, the invention provides that a kind of precision is high, structure is simple, the pick-up unit of weak absorbing gas in the complex environment of low cost.

The object of the invention is to be achieved through the following technical solutions:

The approximating method of pulse waveform, the approximating method of described pulse waveform comprises the following steps:

(A1) pulse waveform P is obtained respectively _obsand template waveforms P _model, wherein, the sampling rate S of template waveforms _daqwith the sampling rate S of pulse waveform _modelratio be greater than 10;

(A2) described template waveforms P is represented with implicit function y=f (x) _model, by translation and the zoom operations of function, obtain objective function:

Y=Af [B (x-C)], A, B and C are undetermined multipliers;

(A3) by described pulse waveform P _obsthe numerical value of sampled point substitute into described objective function, and utilize nonlinear least square method to obtain described undetermined multipliers A, B and C.

According to the approximating method of above-mentioned pulse waveform, preferably, in step (A1), described pulse waveform P _obsacquisition pattern be:

It is S that electric pulse simulating signal sends into sampling rate _daqdata collector be converted to digital signal P _daq=(p _daq(1, v ₁) ..., p _daq(i, v _i) ..., p _daq(m, v _m)), wherein m represents sampling number, v _irepresent the magnitude of voltage of i-th sampled point;

P _daq(i, v _i) be digital signal P _daqpeak point, get this peak point and front m thereof ₁individual and rear m ₂individual m altogether ₁+ 1+m ₂individual composition pulse waveform $P_{Obs}=\left(p_{Daq}\right(i-m_1,v_{i-m_1}),...,p_{Daq}(i,v_i),...,p_{Daq}(i+m_2,v_{i+m_2}\left)\right);$ M ₁and m ₂selection rule be:

$\left\{\begin{array}{c}{m}_1=floor\left(t_{rise}{S}_{Daq}\right)\\ m_2=floor\left(t_{fall}{S}_{Daq}\right)\end{array}\right.,m_1+m_2<m,$ Floor () represents to zero direction bracket function, t _riseand t _fallrepresent electric impulse signal rising edge and negative edge duration respectively;

Get peak point p _daq(i, v _i) front l ₁individual and rear l ₂sampling time summation between individual point is the halfwidth τ of pulse waveform _{hw_Daq}:

${\mathrm{\&tau;}}_{Hw\_Daq}=\frac{l_2-l_1}{S_{Daq}},$ L ₁and l ₂selection rule be: $\left\{\begin{array}{c}{v}_{i-l_1}\&le;0.5v_i\\ v_{i-l_1+1}>0.5v_i\end{array}\right.,\left\{\begin{array}{c}{v}_{i+l_2}\&GreaterEqual;0.5v_i\\ v_{i+l_2+1}<0.5v_i\end{array}\right..$

According to the approximating method of above-mentioned pulse waveform, preferably, in step (A1), described template waveforms P _modelacquisition pattern be:

It is S that electric impulse signal sends into sampling rate _modeldata collector be converted to digital signal P _raw=(p _raw(1, u ₁) ..., p _raw(j, u _j) ..., p _raw(n, u _n)), n is sampling number, and interpolation multiple is n _inter, u _jrepresent the magnitude of voltage of a jth sampled point;

P _raw(j, u _j) be the peak point of waveform, get this peak point and front n thereof ₁individual point and rear n ₂individual point is (n altogether ₁+ 1+n ₂) individual composition template waveforms, n ₁and n ₂selection rule be:

$\left\{\begin{array}{c}{n}_1=floor\left(\frac{m_1{S}_{Model}{n}_{Inter}}{S_{Daq}}\right)\\ n_2=floor\left(\frac{m_2{S}_{Model}{n}_{Inter}}{S_{Daq}}\right)\end{array}\right.,n_1+n_2<n;$

Get peak point p _raw(j, u _j) front k ₁individual and rear k ₂sampling time summation between individual is the halfwidth τ of template waveforms _{hw_Model}:

${\mathrm{\&tau;}}_{Hw\_\_Model}=\frac{k_2-k_1}{S_{Model}{N}_{Inter}};$ K ₁and k ₂selection rule be: $\left\{\begin{array}{c}{u}_{j-k_1}\&le;0.5u_j\\ u_{j-k_1+1}>0.5u_j\end{array}\right.,\left\{\begin{array}{c}{u}_{j+k_2}\&GreaterEqual;0.5u_j\\ u_{j+k_2+1}<0.5u_j\end{array}\right.;$

Template signal is moved integrally j sampling interval along time shaft to initial point direction, obtains template waveforms $P_{Model}=\left(p_{Model}\right(-n_1,u_{j-n_1}),...,p_{Model}(0,u_j),...,p_{Model}(n_2,u_{j+n_2}\left)\right).$

According to the approximating method of above-mentioned pulse waveform, preferably, in step (A3), the acquisition pattern of described undetermined multipliers A, B and C is:

The initial value of setting undetermined multipliers A, B and C is respectively:

$A_0=\frac{v_i}{u_j},B_0=\frac{{\mathrm{\&tau;}}_{Hw\_Daq}}{{\mathrm{\&tau;}}_{Hw\_Model}};C_0=\frac{i}{S_{Daq}};$

According to the numerical evaluation implicit function derivative f ' of the sampled point of described pulse waveform _estwith target function value y _est; A _est, B _estand C _estrepresent the intermediate iteration value of undetermined multipliers A, B and C respectively; Undetermined multipliers partial derivative with account form be:

$\left\{\begin{array}{c}\frac{\&part;f}{\&part;A}=\frac{y_{est}}{A_{est}}\\ \frac{\&part;f}{\&part;B}=A_{est}{f}_{est}^{\&prime;}\\ \frac{\&part;f}{\&part;C}==-A_{est}{f}_{est}^{\&prime;}{B}_{est}\end{array}\right.;$

The optimum undetermined multipliers that matching obtains is A _lm, B _lmand C _lm, then the pulse waveform crest voltage v that obtains of matching _pk, pulsewidth τ _hwwith peak value moment t _pkbe respectively:

$\left\{\begin{array}{c}{v}_{pk}=A_{lm}{u}_j\\ {\mathrm{\&tau;}}_{hw}=B_{lm}{\mathrm{\&tau;}}_{Hw\_Model}\\ t_{pk}=C_{lm}\end{array}\right..$

Compared with prior art, the beneficial effect that the present invention has is:

The present invention creatively uses implicit function model representation template waveforms, completely eliminates the deficient accurate shortcoming of explicit function (as Gaussian function or Generalized Gauss function) model, by implicit function translation and zoom operations, achieves the matching of pulse waveform.

Due to the waveform that template waveforms can have any shape, therefore the method provides new method in waveform fitting, is applicable to the electronic system of random waveform form fit.

Accompanying drawing explanation

With reference to accompanying drawing, disclosure of the present invention will be easier to understand.Those skilled in the art it is easily understood that: these accompanying drawings only for illustrating technical scheme of the present invention, and and are not intended to be construed as limiting protection scope of the present invention.In figure:

Fig. 1 is pulse waveform of the present invention and template waveforms matching schematic diagram;

Fig. 2 is implicit function derivative and the target function value calculation flow chart of nonlinear least square method of the present invention.

Embodiment

Fig. 1 ~ 2 and following description describe Alternate embodiments of the present invention and how to implement to instruct those skilled in the art and to reproduce the present invention.In order to instruct technical solution of the present invention, simplifying or having eliminated some conventional aspects.Those skilled in the art should understand that the modification that is derived from these embodiments or replace will within the scope of the invention.Those skilled in the art should understand that following characteristics can combine to form multiple modification of the present invention in every way.Thus, the present invention is not limited to following Alternate embodiments, and only by claim and their equivalents.

Embodiment:

The approximating method of the pulse waveform of the embodiment of the present invention, the approximating method of described pulse waveform comprises the following steps:

(A1) obtain pulse waveform, be specially with under type:

A () electric pulse simulating signal sends into sampling rate is S _daqdata collector be converted to digital signal P _daq=(p _daq(1, v ₁) ..., p _daq(i, v _i) ..., p _daq(m, v _m)), wherein m represents sampling number, v _irepresent the magnitude of voltage of i-th sampled point; The sampling rate of data collector need meet Sampling Theorem;

B () establishes p _daq(i, v _i) be digital signal P _daqpeak point, get this peak point and front m thereof ₁individual and rear m ₂individual m altogether ₁+ 1+m ₂individual composition pulse waveform $P_{Obs}=\left(p_{Daq}\right(i-m_1,v_{i-m_1}),...,p_{Daq}(i,v_i),...,p_{Daq}(i+m_2,v_{i+m_2}\left)\right);$ M ₁and m ₂selection rule be:

$\left\{\begin{array}{c}{m}_1=floor\left(t_{rise}{S}_{Daq}\right)\\ m_2=floor\left(t_{fall}{S}_{Daq}\right)\end{array}\right.,m_1+m_2<m---\left(1\right)$

Wherein, floor () represents to zero direction bracket function, t _riseand t _fallrepresent electric impulse signal rising edge and negative edge duration respectively;

C () gets peak point p _daq(i, v _i) front l ₁individual and rear l ₂sampling time summation between individual point is the halfwidth τ of pulse waveform _{hw_Daq}:

${\mathrm{\&tau;}}_{Hw\_Daq}=\frac{l_2-l_1}{S_{Daq}}---\left(2\right)$

Wherein l ₁and l ₂selection rule be:

$\left\{\begin{array}{c}{v}_{i-l_1}\&le;0.5v_i\\ v_{i-l_1+1}>0.5v_i\end{array}\right.,\left\{\begin{array}{c}{v}_{i+l_2}\&GreaterEqual;0.5v_i\\ v_{i+l_2+1}<0.5v_i\end{array}\right.---\left(3\right)$

Obtain template waveforms, be specially with under type:

A () uses sampling rate to be S _modeldata collector gather electric impulse signal, possess and use interpolation function, interpolation multiple is n _inter; For elimination pulse energy instability and detector electric noise are on the impact of electric impulse signal, data collector possesses and uses average function; For collecting more accurate template waveforms, sampling rate S _modelat least than sampling rate S _daqhigh 10 times;

B () electric impulse signal collects digital signal P through data collector _raw=(p _raw(1, u ₁) ..., p _raw(j, u _j) ..., p _raw(n, u _n)), wherein n is sampling number, u _jrepresent the magnitude of voltage of a jth sampled point.If p _raw(j, u _j) be the peak point of waveform, get this peak point and front n thereof ₁individual point and rear n ₂individual point is (n altogether ₁+ 1+n ₂) individual composition template waveforms, n ₁and n ₂selection rule be:

$\left\{\begin{array}{c}{n}_1=floor\left(\frac{m_1{S}_{Model}{n}_{Inter}}{S_{Daq}}\right)\\ n_2=floor\left(\frac{m_2{S}_{Model}{n}_{Inter}}{S_{Daq}}\right)\end{array}\right.,n_1+n_2<n---\left(4\right)$

C () gets peak point p _raw(j, u _j) front k ₁individual and rear k ₂sampling time summation between individual is the halfwidth τ of template waveforms _{hw_Model}:

${\mathrm{\&tau;}}_{Hw\_\_Model}=\frac{k_2-k_1}{S_{Model}{N}_{Inter}}---\left(5\right)$

Wherein k ₁and k ₂selection rule be:

$\left\{\begin{array}{c}{u}_{j-k_1}\&le;0.5u_j\\ u_{j-k_1+1}>0.5u_j\end{array}\right.,\left\{\begin{array}{c}{u}_{j+k_2}\&GreaterEqual;0.5u_j\\ u_{j+k_2+1}<0.5u_j\end{array}\right.---\left(6\right)$

D template signal is moved integrally j sampling interval along time shaft to initial point direction by (), obtain template waveforms $P_{Model}=\left(p_{Model}\right(-n_1,u_{j-n_1}),...,p_{Model}(0,u_j),...,p_{Model}(n_2,u_{j+n_2}\left)\right);$

According to translation of functions and convergent-divergent principle, waveform fitting specific implementation process is as follows:

(A2) implicit function y=f (x) is used to represent template waveforms P _model, by translation of functions and zoom operations, obtain objective function:

y＝Af[B(x-C)](7)

Wherein, A represents the zoom factor along y-axis, and B represents the zoom factor along x-axis, and C represents the shift factor along x-axis, as shown in Figure 1;

(A3) nonlinear least square method determination undetermined multipliers A, B and C is used.

The concrete principle of nonlinear least square method and algorithm are not described in detail, here with pulse waveform P _obsmiddle sampled point p _daq(i, v _i) be example, describe content related to the present invention in detail:

Calculate undetermined multipliers initial value A ₀, B ₀and C ₀:

Computing method are such as formula shown in (8):

$A_0=\frac{v_i}{u_j},B_0=\frac{{\mathrm{\&tau;}}_{Hw\_Daq}}{{\mathrm{\&tau;}}_{Hw\_Model}};C_0=\frac{i}{S_{Daq}}---\left(8\right)$

Calculate implicit function derivative f ' _estwith target function value y _est;

Fig. 2 shows implicit function derivative f ' _estwith target function value y _estcalculation flow chart, wherein A _est, B _estand C _estrepresent the intermediate iteration value of undetermined multipliers respectively;

Undetermined multipliers partial derivative with computing method such as formula shown in (9):

$\left\{\begin{array}{c}\frac{\&part;f}{\&part;A}=\frac{y_{est}}{A_{est}}\\ \frac{\&part;f}{\&part;B}=A_{est}{f}_{est}^{\&prime;}\\ \frac{\&part;f}{\&part;C}==-A_{est}{f}_{est}^{\&prime;}{B}_{est}\end{array}\right.---\left(9\right)$

If the optimum undetermined multipliers that matching obtains is A _lm, B _lmand C _lm, then the pulse waveform crest voltage v that obtains of matching _pk, pulsewidth τ _hwwith peak value moment t _pk, can calculate by through type (10):

$\left\{\begin{array}{c}{v}_{pk}=A_{lm}{u}_j\\ {\mathrm{\&tau;}}_{hw}=B_{lm}{\mathrm{\&tau;}}_{Hw\_Model}\\ t_{pk}=C_{lm}\end{array}\right.---\left(10\right)$ 。

Claims (4)

1. the approximating method of pulse waveform, the approximating method of described pulse waveform comprises the following steps:

(A1) pulse waveform P is obtained respectively _obsand template waveforms P _model, wherein, the sampling rate S of template waveforms _daqwith the sampling rate S of pulse waveform _modelratio be greater than 10;

(A2) described template waveforms P is represented with implicit function y=f (x) _model, by translation and the zoom operations of function, obtain objective function:

Y=Af [B (x-C)], A, B and C are undetermined multipliers;

(A3) by described pulse waveform P _obsthe numerical value of sampled point substitute into described objective function, and utilize nonlinear least square method to obtain described undetermined multipliers A, B and C.

2. the approximating method of pulse waveform according to claim 1, is characterized in that: in step (A1), described pulse waveform P _obsacquisition pattern be:

It is S that electric pulse simulating signal sends into sampling rate _daqdata collector be converted to digital signal P _daq=(p _daq(1, v ₁) ..., p _daq(i, v _i) ..., p _daq(m, v _m)), wherein m represents sampling number, v _irepresent the magnitude of voltage of i-th sampled point;

P _daq(i, v _i) be digital signal P _daqpeak point, get this peak point and front m thereof ₁individual and rear m ₂individual m altogether ₁+ 1+m ₂individual composition pulse waveform $P_{Obs}=\left(p_{Daq}\right(i-m_1,v_{i-m_1}),...,p_{Daq}(i,v_i),...,p_{Daq}\left(i+m_2,v_{i+m_2}\right));$ M ₁and m ₂selection rule be:

$\left\{\begin{array}{c}{m}_1=floor\left(t_{rise}{S}_{Daq}\right)\\ m_2=floor\left(t_{fall}{S}_{Daq}\right)\end{array}\right.,m_1+m_2<m,$ Floor () represents to zero direction bracket function, t _riseand t _fallrepresent electric impulse signal rising edge and negative edge duration respectively;

Get peak point p _daq(i, v _i) front l ₁individual and rear l ₂sampling time summation between individual point is the halfwidth τ of pulse waveform _{hw_Daq}:

${\mathrm{\&tau;}}_{Hw\_Daq}=\frac{l_2-l_1}{S_{Daq}},$ L ₁and l ₂selection rule be: $\left\{\begin{array}{c}{v}_{i-l_1}\&le;0.5v_i\\ v_{i-l_1+1}>0.5v_i\end{array}\right.,\left\{\begin{array}{c}{v}_{i+l_2}\&GreaterEqual;0.5v_i\\ v_{i+l_2+1}<0.5v_i\end{array}\right..$

3. the approximating method of pulse waveform according to claim 1, is characterized in that: in step (A1), described template waveforms P _modelacquisition pattern be:

It is S that electric impulse signal sends into sampling rate _modeldata collector be converted to digital signal P _raw=(p _raw(1, u ₁) ..., p _raw(j, u _j) ..., p _raw(n, u _n)), n is sampling number, and interpolation multiple is n _inter, u _jrepresent the magnitude of voltage of a jth sampled point;

P _raw(j, u _j) be the peak point of waveform, get this peak point and front n thereof ₁individual point and rear n ₂individual point is (n altogether ₁+ 1+n ₂) individual composition template waveforms, n ₁and n ₂selection rule be:

$\left\{\begin{array}{c}{n}_1=floor\left(\frac{m_1{S}_{Model}{n}_{Inter}}{S_{Daq}}\right)\\ n_2=floor\left(\frac{m_2{S}_{Model}{n}_{Inter}}{S_{Daq}}\right)\end{array}\right.,n_1+n_2<n;$

Get peak point p _raw(j, u _j) front k ₁individual and rear k ₂sampling time summation between individual is the halfwidth τ of template waveforms _{hw_Model}:

${\mathrm{\&tau;}}_{Hw\_Model}=\frac{k_2-k_1}{S_{Model}{N}_{Inter}};$ K ₁and k ₂selection rule be: $\left\{\begin{array}{c}{u}_{j-k_1}\&le;0.5u_j\\ u_{j-k_1+1}>0.5u_j\end{array}\right.,\left\{\begin{array}{c}{u}_{j+k_2}\&GreaterEqual;0.5u_j\\ u_{j+k_2+1}<0.5u_j\end{array}\right.;$

Template signal is moved integrally j sampling interval along time shaft to initial point direction, obtains template waveforms $P_{Model}=\left(p_{Model}\right(-n_1,u_{j-n_1}),...,p_{Model}(0,u_j),...,p_{Model}\left(n_2,u_{j+n_2}\right)).$

4. the approximating method of pulse waveform according to claim 1, is characterized in that: in step (A3), and the acquisition pattern of described undetermined multipliers A, B and C is:

The initial value of setting undetermined multipliers A, B and C is respectively:

$A_0=\frac{v_i}{u_j};B_0=\frac{{\mathrm{\&tau;}}_{Hw\_Daq}}{{\mathrm{\&tau;}}_{Hw\_Model}};C_0=\frac{i}{S_{Daq}};$

According to the numerical evaluation implicit function derivative f ' of the sampled point of described pulse waveform _estwith target function value y _est; A _est, B _estand C _estrepresent the intermediate iteration value of undetermined multipliers A, B and C respectively; Undetermined multipliers partial derivative with account form be:

$\left\{\begin{array}{c}\frac{\&part;f}{\&part;A}=\frac{y_{est}}{A_{est}}\\ \frac{\&part;f}{\&part;B}=A_{est}{f}_{est}^{\&prime;}\\ \frac{\&part;f}{\&part;C}==-A_{est}{f}_{est}^{\&prime;}{B}_{est}\end{array}\right.;$

The optimum undetermined multipliers that matching obtains is A _lm, B _lmand C _lm, then the pulse waveform crest voltage v that obtains of matching _pk, pulsewidth τ _hwwith peak value moment t _pkbe respectively:

$\left\{\begin{array}{c}{v}_{pk}=A_{lm}{u}_j\\ {\mathrm{\&tau;}}_{hw}=B_{lm}{\mathrm{\&tau;}}_{Hw\_Model}\\ {\mathrm{\&tau;}}_{pk}=C_{lm}\end{array}\right..$