CN106026919B - The punctual compensation method of crystal oscillator - Google Patents
The punctual compensation method of crystal oscillator Download PDFInfo
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03B—GENERATION OF OSCILLATIONS, DIRECTLY OR BY FREQUENCY-CHANGING, BY CIRCUITS EMPLOYING ACTIVE ELEMENTS WHICH OPERATE IN A NON-SWITCHING MANNER; GENERATION OF NOISE BY SUCH CIRCUITS
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Abstract
The present invention provides a kind of punctual compensation method of high-precision crystal oscillator, it include: to be handled by frequency of the FPGA analog input card to crystal oscillator, obtain the clock synchronization error between crystal oscillator and GPS second pulse, measure the operating temperature of crystal oscillator, construct temperature characteristics, obtain crystal oscillator temperature behavior model, Kalman filtering is carried out to the clock synchronization error information after temperature-compensating, the reference clock constructed, to obtain GPS error characteristic curve, after having separated temperature error and GPS error, it is kept time offset using least square model.The present invention is according to the error characteristics of GPS receiver, the phase random error characteristics of crystal oscillator, temperature frequency offset error characteristics and aging characteristics etc., the reconstruct of crystal oscillator temperature-frequency variation characteristic model is carried out to crystal oscillator time keeping error, and reference clock is constructed using the method for Kalman filtering, the characteristic that each error source is separated with this obtains high-precision punctual offset.
Description
Technical field
The present invention relates to relay protection of power system and synchronous sampling technique fields, in particular to based on real time temperature
Measurement updaue crystal oscillator temperature model parameters, the method that reference clock model is constructed with this and generates punctual offset.
Background technique
It is the second pulse signal locking local clock using GPS receiver output that crystal oscillator based on GPS, which tames technology, when
After GPS module losing lock or second pulse signal are lost, then the stability and preset compensation rate for relying primarily on crystal oscillator itself are come
Guarantee crystal oscillator in the accuracy in punctual stage.Therefore, when one timing of the stability of crystal oscillator itself, the compensation in stage of keeping time is calculated
The research of method is of great significance.
The punctual backoff algorithm of temperature compensating crystal oscillator is such as adopted primarily directed to the improvement of algorithm itself at present
With improving, kalman is filtered or sliding average scheduling algorithm is punctual to realize.Since kalman filtering knows error model for oneself
Prediction is more effective, and sliding average algorithm is mainly used in the error with normal distribution characteristic, and is wrapped in time keeping error
Containing all kinds of error characteristics, if being uniformly processed, it will cause as model inaccuracy and caused by prediction deviation.In addition also
Punctual offset is predicted in the way of fitting by historical data.Prediction need to be based on accurate model, special according to each error
Property superimposed clock synchronization error be analyzed and processed, will lead to the complexity that prediction algorithm is increased due to error characteristics aliasing
Degree, while reducing prediction accuracy.Therefore there is an urgent need to propose a kind of punctual method for separating each error characteristics.
Summary of the invention
Error unified Modeling is handled it is an object of the invention to the algorithm that solves to keep time at present and does not consider each error source
The problem of distribution character causes punctual precision to reduce.
In order to solve the above technical problems, the technical solution adopted in the present invention is as follows:
A kind of punctual compensation method of high-precision crystal oscillator, comprising the following steps:
It is handled by frequency of the FPGA analog input card to crystal oscillator, obtains crystal oscillator and GPS second pulse
Between clock synchronization error, using high-precision temperature transmitter measurement crystal oscillator operating temperature, construct temperature characteristics,
Crystal oscillator temperature behavior model is obtained, Kalman filtering is carried out to the clock synchronization error information after temperature-compensating, obtains structure
The reference clock made, so that GPS error characteristic curve is obtained, after having separated temperature error and GPS error, using minimum two
Multiplication predicts punctual offset.
In some embodiments, specific steps are as follows:
The first step counts oscillator itself clock, when obtaining opposite using the frequency of crystal oscillator as benchmark
Mark (program operation starts accumulative time value).Meanwhile judging whether the clock of GPS receiver is effective, if effectively further sentencing
Disconnected GPS second pulse whether misalignment, obtain the crystal oscillator clock synchronization error on the basis of GPS second pulse.
Second step obtains the initial temperature frequency characteristic of crystal oscillator.
Maximum value therein and minimum value removal (are avoided the Sudden Changing Rate of temperature sensor by the temperature data for choosing measurement
Measurement is affected greatly), residual value takes arithmetic average.It is also identical to the frequency processing mode of oscillator simultaneously, it will be maximum
Frequency removal corresponding with minimum temperature value, remaining frequency values take arithmetic average:
Wherein, NiFor i-th second crystal oscillator frequency count value, n was counts.By the sampled value of frequency and temperature
It substitutes into following equation and is solved:
In formula, Δ fiFor corresponding temperature TiWhen the frequency f that measuresiAnd f0Difference；ΔTiFor real time temperature TiWith T0Difference
Value；Δ E correction quantity of frequency.The a to cubic function is realized by pull-in frequency correction amount0、b0、c0Three temperature characteristics
Parameter is updated amendment, obtains the initial temperature frequency characteristic of crystal oscillator.
Third step obtains crystal oscillator temperature frequency characteristic curve.
After the high frequency random component in the composition error curve for filtering out GPS receiver and oscillator frequency deviation, adopt
It uses filtered data to take negative value as reference clock signal, again temperature collection and oscillator frequency, and then calculates new
Each subparameter of temperature frequency characteristic.Repeat the above steps, until temperature frequency characterisitic parameter updated value be less than setting range, then
Stop updating.Finally obtained temperature frequency characteristic curve.
4th step obtains reference clock using Kalman filtering.
The actually measured margin of error contains the randomized jitter of GPS and each error characteristics curve of crystal oscillator, table
It is up to formula
XGPS=ErrGPSIn+X (3) formula, XGPSIndicate total error curve；ErrGPSFor the randomized jitter of GPS receiver；X
For frequency shift (FS) caused by crystal oscillator initial temperature characteristic curve.
Using Kalman filtering algorithm to XGPSIt is pre-processed,.The core of Kalman filtering is made of 5 fundamental formulars,
It can be mainly divided into time update equation and measurement updaue equation.Wherein time update equation is responsible for calculating current shape forward in time
State variable and error covariance estimated value, to be that next time state constructs prior estimate, measurement updaue equation is by priori
Estimation and new measurand are combined to construct improved Posterior estimator.
Time update equation:
State renewal equation:
In formula,For k moment systematic perspective measured value,It is the k-1 moment to system
Control amount, A, B be system parameter, Pk -For error covariance, Q is the variance for observing random error；KkFor kalman gain, H
For measuring system parameter, ZkFor the measured value at k moment,For the predicted value at k moment.
The high fdrequency component that can be filtered out in GPS receiver randomized jitter is handled by Kalman filtering, so as to obtain
One accurate time reference.
5th step constructs GPS error characteristic curve.
The counting of two-way parallel frequencies is carried out to crystal oscillator counting module, wherein all the way using the frequency on the basis of GPS
Err1 is counted to get, frequency counting is carried out on the basis of the data that another way is passed through before using after Kalman filtering processing and obtains
Err2, expression formula are as follows:
Err1=S-XGPs=S-ErrGPs-X (6)
Err2S is the accurate reference clock that the 4th step constructs, Err in=S-X (7) formula1Have for GPS receiver
Time keeping error when effect, Err2After indicating that GPS loses, the time keeping error generated using S as reference clock, XGPSIt indicates
The composition error of GPS receiver and crystal oscillator, ErrGPSIndicate the error of GPS receiver.
Due to the form for using two-way parallel frequencies to count in Time keeping system, Err2It can directly obtain, Err1Through filtering
Involve to ask and obtain after difference.Therefore, by formula (6), the error E rr of formula (7) available GPSGPSAre as follows:
ErrGPS=Err2-Err1 (8)
6th step, on the basis of being reconstructed GPS error characteristic curve, according to formula
X=XGPS--ErrGPS (9)
The total error characteristics curve X of crystal oscillator is obtained, temperature sensor and the crystal oscillator temperature of building are utilized
Characteristic model compensates crystal oscillator temperature characterisitic, obtains the crystal oscillator error curve after temperature-compensating and is
Xtemp.After by temperature-compensating, which can be indicated are as follows: f '0=fB+f1(x0)+AT+f3
(t) in+δ (10) formula, Δ T is the error in view of temperature sensor；f1It (x) is the random phase offset of crystal oscillator；f3
It (x) is the aging deviation of crystal oscillator, δ is other systems error；f0' it is the crystal oscillator carried out after temperature-compensating
Output frequency.
To the f in formula (10)0' carry out least-squares prediction.The expression formula of least square method are as follows:
In formula, XpreIt is the punctual data using least-squares prediction.N is the data volume for carrying out least-squares algorithm use.Fitting
The variation of obtained line reflection crystal oscillator frequency, while also foundation is provided to generate offset.
It should be appreciated that as long as aforementioned concepts and all combinations additionally conceived described in greater detail below are at this
It can be viewed as a part of the subject matter of the disclosure in the case that the design of sample is not conflicting.In addition, required guarantor
All combinations of the theme of shield are considered as a part of the subject matter of the disclosure.
Can be more fully appreciated from the following description in conjunction with attached drawing present invention teach that the foregoing and other aspects, reality
Apply example and feature.The features and/or benefits of other additional aspects such as illustrative embodiments of the invention will be below
Description in it is obvious, or learnt in practice by the specific embodiment instructed according to the present invention.
Detailed description of the invention
Attached drawing is not intended to drawn to scale.In the accompanying drawings, identical or nearly identical group each of is shown in each figure
It can be indicated by the same numeral at part.For clarity, in each figure, not each component part is labeled.
Now, example will be passed through and the embodiments of various aspects of the invention is described in reference to the drawings, in which:
Fig. 1 is the flow chart of frequency division counter.
Fig. 2 is the schematic diagram of the crystal oscillator historical data based on GPS.
Fig. 3 is the schematic diagram of least square fitting result.
Fig. 4 is the schematic diagram of the punctual algorithm simulating curve of improvement based on error separate.
Fig. 5 is the schematic diagram of total simulation curve.
Fig. 6 is the punctual structure chart of crystal oscillator.
Specific embodiment
In order to better understand the technical content of the present invention, special to lift specific embodiment and institute's accompanying drawings is cooperated to be described as follows.
Various aspects with reference to the accompanying drawings to describe the present invention in the disclosure, shown in the drawings of the embodiment of many explanations.
It is not intended to cover all aspects of the invention for embodiment of the disclosure.It should be appreciated that a variety of designs and reality presented hereinbefore
Those of apply example, and describe in more detail below design and embodiment can in many ways in any one come it is real
It applies, this is because conception and embodiment disclosed in this invention are not limited to any embodiment.In addition, disclosed by the invention one
A little aspects can be used alone, or otherwise any appropriately combined use with disclosed by the invention.
According to an embodiment of the invention, proposing a kind of punctual method of high precision temperature compensation crystal oscillator.This method
It is special the error of GPS receiver, the phase random error of crystal oscillator, temperature frequency offset error and aging have been comprehensively considered
Property error fed back by error and update reference clock source using the historical data of clock synchronization error, obtain accurate crystal oscillator
Temperature behavior model further obtains crystal oscillator error characteristics on the basis of more newly-generated clock source, passes through minimum two
Multiplication predicts punctual offset.
In some specific embodiments, aforementioned side is explained in more detail below in conjunction with attached drawing 1- attached drawing 6 in we
The realization of method.
The first step counts oscillator itself clock, when obtaining opposite using the frequency of crystal oscillator as benchmark
Mark (program operation starts accumulative time value).Meanwhile judging whether the clock of GPS receiver is effective, if effectively further sentencing
Disconnected GPS second pulse whether misalignment, obtain the crystal oscillator clock synchronization error on the basis of GPS second pulse.Program flow diagram such as Fig. 1
It is shown.
Second step obtains the initial temperature frequency characteristic of crystal oscillator:
Use nominal frequency for the temperature compensating crystal oscillator of 25MHz, crystal is AT cut type, and temperature frequency offset is special
Property is cubic function:
In formula, f0For the frequency of reference temperature point, zero degree can be set or room temperature is reference temperature point；Δ f is practical
Deviation between temperature and reference temperature point；T is observed temperature；T0It is reference temperature；A0、B0、C0Respectively temperature characteristics
Primary, secondary, temperature coefficient three times.Therefore, the temperature characteristics that obtain AT cut type crystal oscillator need to only determine it
Three temperatures coefficient.GPS receiver standard deviation is 25ns.Historical data is that the crystal oscillator based on GPS receiver is defeated
Frequency deviation data out, the historical data in 24 hours (are sampled) for 1 second for interval as shown in Figure 2.
The temperature data for choosing measurement takes the data for continuously taking 5s, and maximum value therein and minimum value removal (are avoided
The Sudden Changing Rate of temperature sensor affects greatly measurement), residual value takes arithmetic average.Simultaneously to the frequency processing of oscillator
Mode is also identical, maximum frequency corresponding with minimum temperature value is removed, remaining frequency values takes arithmetic average:
Wherein, NiIt is counted for i-th second crystal oscillator frequency
Value, n is counts.The sampled value of frequency and temperature is substituted into following equation and is solved:
In formula, Δ fiFor corresponding temperature TiWhen the frequency f that measuresiAnd f0Difference；ΔTiFor real time temperature TiWith T0Difference
Value；Δ E correction quantity of frequency.The a to cubic function is realized by pull-in frequency correction amount0、b0、c0Three temperature characteristics
Parameter is updated amendment, obtains the initial temperature frequency characteristic of crystal oscillator.
Third step obtains crystal oscillator temperature frequency characteristic curve:
The high frequency filtered out in the composition error curve of GPS receiver and oscillator frequency deviation using Kalman filtering is random
Component takes negative value as reference clock signal using filtered data, and temperature collection and oscillator frequency, calculate new again
Temperature frequency characteristic each subparameter.Repeat the above steps, until temperature frequency characterisitic parameter updated value be less than setting range,
Then stop updating, finally obtains temperature frequency characteristic curve.In order to avoid obtaining ill-condition equation, temperature change is set at 0.1 degree
Data update is carried out when above again.
4th step obtains reference clock using Kalman filtering:
Actually measured error contains the randomized jitter of GPS and each error characteristics curve of crystal oscillator, expression
Formula are as follows:
XGPS=ErrGPSIn+X (4) formula, XGPSIndicate total error curve；ErrGPSFor the randomized jitter of GPS receiver；X
Frequency shift (FS) caused by initial temperature characteristic curve is used for crystal oscillator.
Using Kalman filtering algorithm to XGPSIt is pre-processed.The core of Kalman filtering is made of 5 fundamental formulars,
It can be mainly divided into time update equation and measurement updaue equation.Wherein time update equation is responsible for calculating current shape forward in time
State variable and error covariance estimated value, to be that next time state constructs prior estimate, measurement updaue equation is by priori
Estimation and new measurand are combined to construct improved Posterior estimator.
Time update equation:
State renewal equation:
In formula,For k moment systematic perspective measured value,It is the k-1 moment to the control amount of system, A, B are system parameter, Pk -For accidentally
Poor covariance, Q are the variance for observing random error；KkFor kalman gain, H is measuring system parameter, ZkFor the measurement at k moment
Value,For the predicted value at k moment.
The high fdrequency component filtered out in GPS receiver randomized jitter is handled by Kalman filtering, to obtain one more
Correct time benchmark.
5th step constructs GPS error characteristic curve:
The counting of two-way parallel frequencies is carried out to crystal oscillator counting module, wherein all the way using the frequency on the basis of GPS
Err1 is counted to get, frequency counting is carried out on the basis of the data that another way is passed through before using after Kalman filtering processing and obtains
Err2, expression formula are as follows:
Err1=S-XGPS=S-ErrGPS-X (7)
Err2S is the accurate reference clock that the 4th step constructs, Err in=S-X (8) formula1For GPS receiver
Time keeping error when effectively, Err2After indicating that GPS loses, the time keeping error generated using S as reference clock, XGPSTable
Show the composition error of GPS receiver and crystal oscillator, ErrGPSIndicate the error of GPS receiver.
Due to the form for using two-way parallel frequencies to count in Time keeping system, Err2It can directly obtain, Err1Through filtering
Involve to ask and obtain after difference.Therefore, by formula (7), the error E rr of formula (8) available GPSGPSAre as follows:
ErrGPS=Err2-Err1 (9)
6th step, on the basis of being reconstructed GPS error characteristic curve, according to formula
X=XGPS-ErrGPS (10)
The total error characteristics curve X of crystal oscillator is obtained, temperature sensor and the crystal oscillator temperature of building are utilized
Characteristic model compensates crystal oscillator temperature characterisitic.Obtaining the crystal oscillator error curve after temperature-compensating is
Xtemp.After by temperature-compensating, which can be indicated are as follows: f '0=fB+f1(x0)+ΔT+f3
(t) in+δ (11) formula, Δ T is the error in view of temperature sensor；f1It (x) is the random phase offset of crystal oscillator；f3
It (x) is the aging deviation of crystal oscillator, δ is other systems error；f0' it is the crystal oscillator carried out after temperature-compensating
Output frequency.
For straight line fitting y=a*x+b
According to straight line least square fitting formula:
B=E (y)-a*E (x)
So:
Here E (x) is to average.
According to above-mentioned formula, to the f in formula (11)0' carry out least-squares prediction.The expression formula of least square method are as follows:
X in formulaiFor tiMoment corresponding crystal oscillator error amount, XpreIt is the punctual data using least-squares prediction, N
For the data volume for carrying out least-squares algorithm use.Wherein
It is fitted the variation of obtained line reflection crystal oscillator frequency, while also providing foundation to generate offset.It is logical
Parameter of many experiments repeatedly in adjustment type is crossed, least square fitting is carried out to said frequencies characteristic curve by taking N=200 as an example,
As a result as shown in Figure 3.The punctual curve of punctual algorithm based on error separate is as shown in Figure 4.
The punctual algorithm of the improvement proposed by the present invention based on error separate is compared by emulating and is based only upon temperature-compensating
Algorithm and punctual algorithm based on prediction, it is as shown in Figure 5 to obtain 10 hours punctual curves.
By Fig. 5 curve (a) as it can be seen that due to traditional punctual compensation method do not account for the temperature characterisitic of crystal oscillator with
And the characteristic of GPS, 10 hours time keeping errors are 165 microseconds.In Fig. 5 curve (b) be based on temperature-compensating after crystal
Oscillator time keeping error curve, as seen from the figure, time keeping error is within 45 microseconds within 10 hours.This is because to crystal oscillator
It is modeled, it is contemplated that the influence of temperature, but due to the error of model itself, and the randomized jitter of GPS is had ignored,
Punctual precision still has room for improvement.Fig. 5 curve (c) uses punctual algorithm of the invention, it is seen that loses in reference signal GPS
After 10 hours, the downward trend of a shake is presented in time keeping error, and 10 hours time keeping errors of basic guarantee are within 2 microseconds.
Although oneself is disclosed above in the preferred embodiment the present invention, however, it is not to limit the invention.Skill belonging to the present invention
Has usually intellectual in art field, without departing from the spirit and scope of the present invention, when can be used for a variety of modifications and variations.Cause
This, the scope of protection of the present invention is defined by those of the claims.
Claims (4)
1. a kind of punctual compensation method of crystal oscillator, which comprises the following steps:
1) using the operating temperature of temperature transmitter measurement crystal oscillator, by FPGA analog input card to the frequency of crystal oscillator
Rate is handled to obtain clock synchronization error；
2) according to the operating temperature data of acquisition, the temperature characteristics of crystal oscillator is constructed, updates the temperature of crystal oscillator
Characteristic curve parameter is spent, crystal oscillator temperature behavior model is obtained and goes forward side by side trip temperature-frequency error compensation；
3) by the clock synchronization error information progress Kalman filtering after temperature-frequency error compensation, the reference clock constructed,
To obtain GPS error characteristic；
4) it after having separated temperature error and GPS error, is kept time offset using least square model；
In the step 2), processing carries out temperature-frequency error compensation in the following manner:
Initial temperature characterisitic parameter is first set, then it is modified to obtain temperature behavior model；Wherein choosing measurement
When data configuration temperature behavior model, if being removed maximum value therein and minimum value using the data continuously done, then will
Its residual value takes arithmetic average, while also identical to the frequency processing mode of crystal oscillator, will be maximum corresponding with minimum temperature value
Frequency removal, remaining frequency values is then taken into arithmetic average, specific processing is as follows:
Wherein, NiFor i-th second crystal oscillator frequency count value, n was counts；
The sampled value of frequency and temperature is substituted into following equation and is solved:
In formula, Δ fiFor corresponding temperature TiWhen the frequency f that measuresiAnd f0Difference；f0For benchmark frequency, Δ TiFor real time temperature Ti
With T0Difference；Δ E correction quantity of frequency, by introducing correction amount realization to a of cubic function0、b0、c0Three temperature characterisitics
The parameter of curve is updated amendment, realizes the amendment of temperature-frequency error compensation.
2. the punctual compensation method of crystal oscillator according to claim 1, which is characterized in that in the step 1),
The operating temperature of crystal oscillator is obtained by temperature sensor, and frequency dividing circuit is set in FPGA analog input card, obtains crystal
Clock synchronization error between the frequency and GPS second pulse of oscillator.
3. the punctual compensation method of crystal oscillator according to claim 1, which is characterized in that in the step 3),
Reference clock is obtained using Kalman filtering, specific as follows:
The data measured are the crystal oscillator frequency count value based on GPS clock, that is, the data measured are XGPS, wherein including
The randomized jitter of GPS and each error characteristics curve of crystal oscillator:
XGPS=ErrGPS+X (3)
In formula, XGPSIndicate total error curve namely the actually measured margin of error；ErrGPSFor the randomized jitter of GPS receiver；
X is frequency shift (FS) caused by crystal oscillator initial temperature characteristic curve；
Using Kalman filtering algorithm to XGPSIt being pre-processed, the core of Kalman filtering is made of 5 fundamental formulars, including
Time update equation and measurement updaue equation, wherein time update equation is responsible for calculating current state variable and error forward in time
Covariance estimated value, to be that next time state constructs prior estimate, measurement updaue equation is by prior estimate and new survey
Quantitative change amount is combined to construct improved Posterior estimator；
Time update equation:
State renewal equation:
In formula,For k moment systematic perspective measured value,It is the k-1 moment to the control amount of system, A, B are system parameter,For accidentally
Poor covariance, Q are the variance for observing random error；KkFor kalman gain, H is measuring system parameter, ZkFor the measurement at k moment
Value,For the predicted value at k moment；
Data after handling by Kalman filtering filter out the high fdrequency component in GPS receiver randomized jitter, so as to
To a correct time benchmark.
4. the punctual compensation method of crystal oscillator according to claim 3, it is characterised in that:
On the basis of being reconstructed GPS error characteristic curve, the total error characteristics curve X of crystal oscillator can be obtained:
X=XGPS-ErrGPS (6)
After obtaining the total error curve of crystal oscillator, the crystal oscillator temperature characterisitic based on temperature sensor and building
Model compensates crystal oscillator temperature characterisitic；
Obtaining the crystal oscillator error curve after temperature-compensating is Xtemp, after by temperature-compensating, the crystal oscillator
Error model can indicate are as follows:
f0'=fB+f1(x0)+ΔT+f3(t)+δ (7)
In formula, Δ T is the error in view of temperature sensor, takes the corresponding error of the resolution ratio of temperature transmitter herein；f1(x0)
For the random phase offset of crystal oscillator；f3It (t) is the aging deviation of crystal oscillator, δ is other systems error；f0' be into
The crystal oscillator output frequency gone after temperature-compensating；
Then, to the f in formula (7)0' carry out least-squares prediction, the expression formula of least square method are as follows:
In formula, xiFor tiMoment corresponding crystal oscillator error amount, XpreIt is the punctual data using least-squares prediction, N is
The data volume of least-squares algorithm use is carried out, wherein
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| CN101079687A (en) * | 2006-05-25 | 2007-11-28 | 上海欣泰通信技术有限公司 | A clock adjustment algorithm based on minimum two multiplexing model |
| CN103117742A (en) * | 2011-11-17 | 2013-05-22 | 沈阳工业大学 | Global position system (GPS)/compass dual-mode satellite clock crystal oscillator disciplined system |
| CN102629103A (en) * | 2012-03-30 | 2012-08-08 | 上海鸿晔电子科技有限公司 | Low-order adjusting method for network clock timekeeping module of satellite time service system |
| CN103427793A (en) * | 2013-07-29 | 2013-12-04 | 国电南瑞科技股份有限公司 | Time hacking and punctuality system and method based on temperature compensation |
| CN104570717A (en) * | 2013-10-25 | 2015-04-29 | 沈阳工业大学 | Time keeping system based on GPS /Beidou satellite and finite-state machine |
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