CN106291652A - A kind of numeric class Gaussian particle filter recursive algorithm - Google Patents

Abstract

The invention discloses a kind of numeric class Gaussian particle filter algorithm.Including step: A, first CR nRC class Gaussian particle filter circuit is split as 1 rank CR circuit and n(general n=4) rank RC circuit connected in series.B, utilization Kirchhoff's current law (KCL) set up CR circuit and the current equations of RC circuit respectively.C, numerical differentiation is utilized to replace differentiating in step B current equations.D, set up the equation of input signal x [n] and output signal y [n], obtain the mathematics recurrence model of CR circuit and RC circuit.E, input signal is first passed through 1 rank CR circuit mathematics recurrence model process, again result is processed as input signal through RC circuit mathematics recurrence model, multistage RC circuit only needs upper level result as next stage input signal, finally gives class Gaussian pulse.Method proposes a kind of new numeric class Gaussian particle filter recursive algorithm, it is capable of core pulse signal class Gaussian particle filter, improves signal to noise ratio simultaneously.Algorithm calculating process is easy, it is simple to realize, it is adaptable to core pulse signal real-time class Gaussian particle filter.

Description

A kind of numeric class Gaussian particle filter recursive algorithm

Technical field

The present invention surveys based on radioactivity such as spentnuclear fuel measurement of concetration, the detection of food content of beary metal and environmental radiation evaluations Amount field, for core pulse number word processing method, it is proposed that a kind of new core pulse signal digital class Gaussian particle filter Recursive algorithm.

Background technology

Along with the development of electronic technology, traditional simulation nuclear spectrometer gradually develops to digitized direction, digital nuclear spectrometer There is higher stability, motility and adaptivity.In digital nuclear spectrometer system, radiation signal is through pre-amplification circuit Amplify and after front-end circuit filtering shaping, including pole-zero cancellation circuit, filter circuit and main amplifying circuit, quick by high-speed ADC Discretization；Data after discrete are sent directly into FPGA and carry out digit pulse shaping, overlapping pulses separation, amplitude discriminator, finally Form power spectrum transmission to show to host computer.

Pulse shaping algorithm is the key of digital nuclear spectrometer system, and its quality directly influences the accurate of measurement result Property.Gaussian particle filter is that core pulse signal is configured to Gaussian waveform or class Gaussian waveform, has good time response, frequently Rate response and higher signal to noise ratio, in Digital Nuclear Instrument System, detector output signal filtering is generally shaped by front-end circuit For Gaussian waveform or class Gaussian waveform.

Existing class Gaussian particle filter has analog circuit and two kinds of implementation methods of digital algorithm.Analog circuit implementation method Including Sallen-Key filter circuit (Li Dongcang, Yang Lei, the brave deng. in field core based on Sallen-Key wave filter pulse shaping Circuit studies [J]. nuclear electronics and Detection Techniques, 2008,28 (3): 536-566), CR-nRC wave-shaping circuit (Wang Jingjin, Fan Tian The people, Qian Yonggeng. nuclear electronics [M]. Beijing: Atomic Energy Press, 1983)；Digital algorithm includes Gauss based on wavelet analysis Pulse shaping (Chen Shiguo, Ji Shiyin, Liu Wansong. Gaussian pulse shaping of exponential decay signal [J] based on wavelet analysis. physics Journal, 2008,57 (5): 2882-2887) and class Gaussian particle filter based on z-transform analysis (M.Nakhostin.Recursive algorithm for real-time digital CR-(RC)ⁿ pulse shaping [J].IEEE TRANSACTIONS ONNUCLEAR SCIENCE,2011,58(5):2378-2381)。

Summary of the invention

It is an object of the invention to, based on CR-nRC class Gaussian particle filter analog circuit, utilize numerical differentiation method to build Vertical CR circuit and RC circuit mathematical model, propose a kind of new numeric class Gaussian particle filter recursive algorithm.

To achieve the above object of the invention, the technology used in the present invention method: CR-nRC wave-shaping circuit is split as CR electricity Road and RC circuit connected in series, utilize numerical differentiation method, sets up two kinds of circuit mathematical modeies, and recursive call realizes core pulse signal class Gaussian particle filter.

The principle of the present invention is: CR-nRC circuit is split as the CR circuit on 1 rank and the RC circuit connected in series on n rank；According to base That Hough current law, sets up CR circuit and RC circuital current equation respectively, and utilizes numerical differentiation to replace the differential in equation Computing, sets up CR circuit, RC circuit mathematical model；Class Gaussian particle filter passes through first to call CR circuit mathematics recurrence model, then Call RC mathematics recurrence model to realize.

Present invention have the advantage that the core pulse signal digital class Gaussian particle filter recursive algorithm computing of 1. propositions Journey is simple, easy to use, it is easy to hardware realizes；2. under the conditions of identical peak time, the trapezoidal one-tenth that the algorithm of proposition is more common Shape algorithm has more preferable filtering performance；3. it is capable of core pulse signal real-time digital class Gaussian particle filter.

Accompanying drawing explanation

Fig. 1 is CR-nRC circuit structure diagram.

Fig. 2 is CR circuit structure diagram

Fig. 3 is RC circuit structure diagram

Fig. 4 is different n value class Gaussian particle filter oscillograms.

Fig. 5 is identical peak time condition lower class Gaussian particle filter and trapezoidal shaping frequency response contrast effect figure.

Fig. 6 processes core pulse signal gained amplitude spectrogram respectively for using class Gaussian particle filter and trapezoidal shaping.

Specific implementation

A kind of numeric class Gaussian particle filter recursive algorithm:

Utilize CR-nRC class Gaussian particle filter analog circuit can realize core pulse signal class Gaussian particle filter, its circuit Structure is as shown in Figure 1.CR-nRC circuit is split as CR circuit and RC circuit, as shown in Figure 2,3.Build according to kirchhoff electric current The current equations of vertical CR circuit

$\frac{d(v_{\mathrm{in}}-v_{\mathrm{out}})}{\mathrm{dt}}\·C=\frac{v_{\mathrm{out}}}{R}$

Make x [n]=v_in, y [n]=v_out, x [n], y [n] represent the discrete series of input, output signal, n and n-1 respectively Between be spaced apart Δ t.Utilize numerical differentiation to replace differentiating in equation, can obtain

$x\left[n\right]-x[n-1]-\left(y\right[n]-y[n-1\left]\right)=\frac{\mathrm{\Δt}}{\mathrm{RC}}\·y\left[n\right]$

Make k_CR=Δ t/ (RC), arranges y [n] on the left of equation,

$y\left[n\right]=\frac{y[n-1]+x\left[n\right]-x[n-1]}{1+k_{\mathrm{CR}}}$

Above formula is CR circuit mathematics recurrence model, brings input signal x [n] into above formula, and recursive call can realize defeated Enter signal CR shaping to process.The current equations of RC circuit is

$\frac{v_{\mathrm{in}}-v_{\mathrm{out}}}{R}=\frac{{\mathrm{dv}}_{\mathrm{out}}}{\mathrm{dt}}\·C$

Replace differentiating in equation also with numerical differentiation, obtain RC circuit mathematics recurrence model

$y\left[n\right]=\frac{k\·y[n-1]+x\left[n\right]}{1+k_{\mathrm{RC}}}$

Wherein x [n], y [n] and the same meaning in C-R circuit, k_RC=RC/ Δ t.

Core pulse signal utilizes step signal to simulate, i.e. x [n]=1 (n > 0).Core pulse signal class Gaussian pulse to be realized Shaping and input signal is the most first brought into CR circuit mathematics recurrence model, the output obtained is re-used as RC circuit mathematics recurrence model Input, multistage RC circuits cascading mathematical model only need to be using the output of upper level model as the input of next stage model, Obtain class Gaussian pulse eventually.The class Gaussian particle filter result of different rank is as shown in Figure 4.Usually, arteries and veins is shaped as n=4 Punching is closer to Gaussian waveform.When Fig. 5 is n=4, class Gaussian particle filter and trapezoidal shaping process the core pulse letter of band noise respectively Number obtaining the frequency response of result, the shaped pulse that two kinds of methods obtain has identical peak time.As seen from the figure, class Gaussian particle filter algorithm relatively trapezoidal shaping has more preferable filtering performance.Fig. 6 for use class Gaussian particle filter with trapezoidal become Shape processes the core pulse signal gained amplitude spectrogram of 200,000 band noises respectively.Use class Gaussian particle filter gained amplitude spectrum Halfwidth is 3.5%, and the halfwidth using trapezoidal gained amplitude spectrum is 3.8%, illustrates to use class Gaussian particle filter to process core Pulse signal can obtain the amplitude spectrum of preferable energy resolution.

Claims (3)

1. a kind Gaussian particle filter recursive algorithm, it is characterised in that said method comprising the steps of:

A, it is primarily based on CR-nRC class Gaussian particle filter analog circuit, core pulse signal handling process is divided into 1 rank CR circuit With n rank (usually n=4) RC circuit connected in series.

B, utilization Kirchhoff's current law (KCL), set up CR circuit and the current equations of RC circuit respectively.

C, numerical differentiation method is utilized to replace differentiating in step B current equations.

D, set up input signal x [n] and output signal y [n] equation, obtain CR circuit mathematics recurrence model

$y\[n\]=\frac{y\[n-1\]+x\[n\]-x\[n-1\]}{1+k_{CR}}$

In like manner can get RC circuit mathematics recurrence model

$y\[n\]=\frac{k\·y\[n-1\]+x\[n\]}{1+k_{RC}}$

E, the CR circuit mathematics recurrence model that input signal first passes through 1 rank process, then using result as RC circuit mathematics The input signal of recurrence model.Multistage RC circuit only needs to export upper level result as next stage input signal, Input signal is configured to class Gaussian pulse at last.

2. according to the numeric class Gaussian particle filter algorithm described in claims 1, it is characterised in that utilize numerical differentiation method Setting up CR, RC circuit mathematical model, core pulse signal is configured to class Gaussian pulse by concatenated call.

3. according to the numeric class Gaussian particle filter algorithm described in claims 2, it is characterised in that resistance in CR, RC circuit Equal with the product of electric capacity, i.e. time constant 3. according to the numeric class Gaussian particle filter algorithm described in claims 2, and it is special Levying and be, resistance and the product of electric capacity in CR, RC circuit, i.e. time constant is equal.