CN105608317A - Linear system based digital filtering apparatus and method - Google Patents

Abstract

The invention relates to a linear system based digital filtering apparatus and method. The method comprises the following steps: firstly, analyzing a system type and judging and determining whether a noise type of a linear system belongs to white noise following Gaussian distribution and having uniform power spectrum density distribution or not; secondly, judging the change trend of data and estimating the size of next data according to the change trend of the data; thirdly, judging the reliability degrees of a measured value and an estimated value; and finally, according to the reliability degrees of the measured value and the estimated value, dynamically distributing the weights of the two values in an optimal value, and according to the weights of the two values, calculating the optimal value. The method provided by the invention is small in calculation amount, good in filtering effect and especially suitable for the situation of poor capability of a processor in the system.

Description

A kind of digital filter apparatus and method based on linear system

Technical field

The present invention relates to data filtering technical field, more particularly, relate to one based on measured value and estimateThe linear system data filtering device and method that evaluation optimal value is calculated.

Background technology

Along with the develop rapidly of computer technology, sensor technology and information technology, data acquisition and processingSystem has also extensively obtained application. This system can be monitored the information of production scene exactly, and then improvesProduct quality, reduces production costs.

Data acquisition is more timely with processing, and operating efficiency and the ratio of performance to price are just higher, the economy effect obtainingBenefit is just better. But, because actual working site environment is generally more severe, exist variousNoise and Interference. In order to carry out Measurement accuracy and control, must eliminate these in measured signal unfavorable because ofElement, this just requires, in the time of system, fully take into account the source of various interference, seeks from design angleAsk, take some Compensation measures, to improve data acquisition quality, and then the reliability that improves system is with steadyQualitative. The general policy of general design is: filtering, shielding, ground connection, isolation and absorption, and filtering techniqueRequisite a kind of means of removing interference in data collecting system.

It will be apparent to those skilled in the art that hardware filtering device just improves arranging of real-time system data acquisition qualityOne of execute, but be difficult to thoroughly suppress various interference, so digital filtering arises at the historic moment. Digital filtering refers toWork out corresponding program to reach the object of signal filtering, because being uses program according to predetermined filtering methodRealize filtering, therefore its stability is high, and filtering parameter amendment is convenient.

At present, classical digital filtering method is more; For example, more simple method has arithmetic mean of instantaneous valueMethod, the filter method that overflows, comparison pass-fail, slip arithmetic mean method and single order low pass filtering method etc.; RatioMore complicated have Kalman filtering and a complementary filter etc. The simple general filter effect of filtering method alsoBe not fine, after filtering still there is a large amount of noises in system, more senior filtering method complexityLarger, it is many that processor moves the time of cost. If wanting to do some filtering on single-chip microcomputer calculatesMethod processing, the system delay that senior filtering algorithm brings is very serious.

Therefore, how to calculate by some simple digital filtering methods, reach the height that complexity is largerThe degree of accuracy of the filtering method of level.

Summary of the invention

The object of the present invention is to provide a kind of data filtering device and method based on linear system, it is adoptedWith some simply calculate, can calculate more accurately filtering output optimal value.

For achieving the above object, technical scheme of the present invention is as follows:

Based on a digital filter apparatus for linear system, described device comprises the linear systematic survey value of detectionSensor and data filtering module; It is characterized in that, described data filtering module comprise memory cell,Processing unit, parameter initialization unit and output unit; The parameter that described memory cell is stored comprises phaseAdjacent two optimal value variable P0 and P1, two optimal value variable P0 and 2 formations of P1 of obtaining for twiceSlope K, estimated value P_E, measured value P_N, estimated value P_E and the measured value P_N's of straight line is poorThe acquisition time interval T of value △ P and sensor; Described processing unit is for analytical system type and noiseType, sends measured value P_N and obtains estimated value P_E by slope K in each interval T according to sensor,The difference △ P of estimated value P_E and measured value P_N, what obtain estimated value P_E and measured value P_N canLetter degree, and according to degree of reliability dynamic assignment estimated value P_E, measured value P_N in optimal valueWeight, and go out this optimal value variable P_R according to the weight calculation of two numerical value, and by described outputEach optimal value is exported in unit.

Preferably, described data filtering module is micro-control unit.

For achieving the above object, the present invention also provides a kind of technical scheme as follows:

A digital filtering method that adopts said apparatus, comprises the steps:

Step S1: described processing unit analysis and judge whether system type is linear system; If so,Execution step S2, if not, execution step S7;

Step S2: described parameter initialization unit initializes measured linear system correlated variables and calculatingData variation rate, and the parameter after initializing is stored into described memory cell; Wherein, described twoThe initial value of figure of merit variable P0 and P1 is the straight of 0, two optimal value variable P0 and 2 formations of P1The slope K of line is 0;

Step S3: go to estimate next sensor measurement data estimation value by the rate of change K of step S2The size of P_E, and described sensor obtains gathering measured value P_N according to acquisition time interval T;

Step S4: according to the difference △ P of estimated value P_E and measured value P_N obtain estimated value P_E andThe credibility of measured value P_N;

Step S5: the credibility of analyzing by step S4 divides to estimated value P_E and measured value P_NJoin weight, and go out this optimal value variable P_R according to weight calculation;

Step S6: assignment again, recursive operation; The optimal value P_R assignment first this computing being obtainedGive P0, then by P0 assignment to P1; Continue execution step S3, until data processing is complete;

Step S7: finish.

Preferably, in described step S3, if two variable P_E and P_N are set, P_E is used for protectingDeposit the estimated value obtaining, the current data value that P_N representative sensor records,

The big or small calculating formula that obtains estimated value is:

$\frac{(P0-P1)}{t}=\frac{(P\_E-P0)}{t}$

Calculate estimated value:

P_E＝2*P0-P1

And the current data value that described sensor measurement obtains is saved in P_N.

Preferably, the step S4 of institute specifically comprises: the difference that estimated value P_E and measured value P_N are set is△ P sets a reduced value R simultaneously;

When the difference △ of estimated value and measured value P is than R hour, estimated value P_E and measured value P_N comparisonApproach, measured value is more approaching with the situation of expection, occurs that the possibility ratio of noise does not have noisy possibilityProperty is little, and measured value P_N is more reliable than estimated value P_E, and estimated value P_E and measured value P_NDifference △ P less, the reliability of measured value P_N is higher, and the degree of reliability is linear with difference △ PChange;

In the time that the difference △ of estimated value and measured value P is zero, estimated value P_E and measured value P_N equally canLean on, the degree of reliability is identical;

In the time that the difference △ of estimated value and measured value P is larger than R, estimated value P_E and measured value P_N gapLarger, there is larger sudden change in measured value, and a lot of noises that adulterated in data now, are estimatedBe worth more reliably, and the degree of reliability is linear change with difference △ P.

Preferably, in the step S5 of institute, by two numerical value of Reliability Distribution, the weight in optimal value is specifically wrappedDraw together:

The weight of measured value P_N is A, and the weight of estimated value P_E is 1-A, R be one self-definedNumerical value; :

△P＝|P_E-P_N|

Analyzed by step S4, the weight A that can obtain measured value P_N is:

$A=\frac{\left|P\_E-P\_N\right|}{R+\left|P\_E-P\_N\right|}$

Optimal value is P_R, and optimal value is that estimated value and measured value form according to certain weight, finalObtain optimal value:

P_R＝(1-A)*P_N+A*P_E

Preferably, the acquisition time interval T of described sensor is that 1ms is to a value between 10ms.

Preferably, described step S1 also comprises: judge whether intrasystem noise type is to obey GaussDistribute and the equally distributed white noise of power spectral density, if so, execution step S2, if not, holdRow step S7.

Can find out from technique scheme, the present invention is based on the data filtering device and method of linear system,Solve the deficiency of current techniques, realized that filter effect is obvious and computational complexity is little, due to eachThere is the autoregression rolling average system (AutoregressiveIntegratedMoving of external variableAverage, is called for short ARIMA) or the system that represents of available Rational Transfer can convert the state of using toThe system of space representation, thus can calculate with this linear system filtering method. In addition, the present invention is non-Often be suitable for the more weak microprogram control unit (MicroprogrammedControl of disposal abilityUnit, is called for short MCU) do the system of digital filtering processing. Its beneficial effect is summarized as follows:

(1) this method for designing good reliability, efficiency is high, has alleviated greatly workload, is conducive to filterThe optimization of ripple device design.

(2) the present invention estimates the data that obtain and the data that measure according to dynamic straight line variation tendencyAssign weight, make the result reliability that finally obtains higher.

Brief description of the drawings

Fig. 1 is the block diagram that the present invention is based on linear system data filtering device

Fig. 2 is the process blocks schematic diagram that the present invention is based on linear system data filtering method

Fig. 3 is the principle schematic that the present invention is based on linear system data filtering method

Figure 4 shows that and use filtering method of the present invention to carry out filtered waveform and use Kalman filteringCarry out filtered comparison of wave shape figure

Detailed description of the invention

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in further detail.

It should be noted that, the present invention adopt digital filtering method taking based on differential thought as theoretical foundation. In mathematics, differential is the linear description of the one of the localized variation to function, and differential also can be similar toGround is described when the variable quantity value of function argument and is done enough hour, and how the value of function changes. RootAccording to the character of differential, when a variable quantity that can carry out its independent variable of function of differential is obtained enough littleTime, in the scope of this section of variation, can think that dependent variable is linear change.

It will be apparent to those skilled in the art that independent variable is exactly processor when sensor is carried out to filteringTo the time in sampling interval of sensing data, dependent variable is exactly the output data of sensor. Conventionally sensorBe used for measure environment variables, due to environmental variance change slow, namely its change curveSmoother, so its variation function forming certainly can be micro-, i.e. the comparison of curvilinear motionSmoothly; Therefore, on this curve, get one section of very little constant interval, so just can be similar to and think thisSection curve is straight line, that is to say that this section of curve is linear change.

Refer to Fig. 1, Fig. 1 is the block diagram that the present invention is based on linear system data filtering device.As shown in the figure, this linear system data filtering device is that the optimal value based on measured value and estimated value is calculated,It comprises the sensor and the data filtering module that detect linear systematic survey value; This data filtering module comprisesMemory cell, processing unit, parameter initialization unit and output unit. The parameter that memory cell is storedComprise adjacent two optimal value variable P0 and P1, two optimal value variable P0 and the P1 two of obtaining for twiceSlope K, estimated value P_E, measured value P_N, estimated value P_E and the measured value of the straight line that point formsThe parameters such as difference △ P, the reduced value R of P_N and the acquisition time interval T of sensor.

Refer to Fig. 2, Fig. 2 is the linearity system that the present invention is based on the optimal value calculating of measured value and estimated valueThe process blocks schematic diagram of system data filtering method. As shown in the figure, of the present invention based on measured value and estimationThe linear system digital filtering method that the optimal value of value is calculated, comprises following step:

Step S1: analyze and judge whether system type is linear system and intrasystem noise type

More than narration shows, this filtering method is applicable to linear system, therefore, first will determine and filterThe attribute of the system of ripple, only has linear system just can use the method. The characteristic of linear system is fairly simple,Linear system need meet linear characteristic.

That is to say, state variable and output variable are for all possible input variable and original state allThe system that meets principle of stacking, principle of stacking refers to:

If system is during corresponding to any two kinds of inputs and original state (u1 (t), x01) and (u2 (t), x02)State and output are respectively (x1 (t), y1 (t)) and (x2 (t), y2 (t));

When input and original state be:

(C1u1(t)+C2u2(t),C1x01+C2x02)

The state of system and output must be:

(C1x1(t)+C2x2(t),C1y1(t)+C2y2(t))

Wherein: x represents state, y represents output, and u represents input, and C1 and C2 are any real number.

It will be apparent to those skilled in the art that a system being made up of linear element parts must be linear system.But contrary proposition may be false in some cases. State variable (or the input of linear systemVariable) and output variable between causality can describe with one group of linear differential equation or difference equation,This equation is called the Mathematical Modeling of system. As the direct result of sumproperties, of linear systemCritical nature is that the response of system can be decomposed into two parts: zero input response and zero state response. BeforePerson refers to by the caused response of non-zero initial conditions; Latter refers to the response being caused by input. Both can divideJi Suan not. It is linear system that this character can be used for judging whether. If system meets linear systemFeature, can be judged as linear system, can carry out filtering with filtering method of the present invention.

Then, also need further to judge the noise type in this linear system, the method be applicable to filtering orReduce the white noise in linear system, this white noise is wanted Gaussian distributed simultaneously, its power spectral densityEqually distributed. The method is applicable to filtering or reduces the white noise in linear system.

Step S2: initialization survey system correlated variables and calculated data rate of change

In embodiments of the present invention, linear system is carried out before digital filtering, need first to two optimal valuesThe rate of change K of the straight line of variable P0 and P1, two optimal value variable P0 and 2 formations of P1, estimateDifference △ P, the reduced value R of evaluation P_E, measured value P_N, estimated value P_E and measured value P_NInitialize with parameters such as the acquisition time interval T of sensor.

Two optimal value variable P0 and P1 initialize:

While measurement for the first time, P0, P1 are set to 0, at this time turn on sensor is carried out the collection of data,The time interval T of collection is set to 1ms between 10ms, by front two groups of data that collect successivelyDeposit optimal value variable P0 and P1 in, had these two groups of data just can calculate the variation of these two groups of dataRate K, taking the time as X-axis, sensor output data is the coordinate system (as shown in Figure 3) that Y-axis formsIn, the slope of the straight line of optimal value variable P0 and 2 formations of P1 is the rate of change K of two groups of data.

Suppose, the sampling interval is t, and the slope of the straight line that two optimal value variable P0 and P1 form is k,The slope of this straight line is:

$k=\frac{(P0-P1)}{t}---\left(1\right)$

Because the sampling interval is very little, also can find out the variation tendency of data from the rate of change of these data.When system is not in the starting stage time, what preserved optimal value variable P0 and P1 the inside is meter aboveThe optimal value drawing, rate of change computational methods are identical with above step.

Step S3: the size of going to estimate next sensor measurement data by the rate of change K of step S2And gather current sensor data.

Obtain a data k by step S2, it has represented the variation tendency of front twice optimal value. According to micro-The character of integration, when the variable quantity of function argument takes fully enough little time, in the scope of this section of variationCan think that dependent variable is linear change, so, can roughly think what the sensor next one collectedThe slope of the variation of front two secondary data of Data Comparison is the same, that is to say that this estimated value is in the first twoOn the extended line of straight line that data form, but this estimated value is not 100% reliable.

As shown in Figure 3, two variable P_E and P_N are set; Wherein, P_E is used for preserving and obtainsEstimated value, the current data value that P_N representative sensor records.

According to analysis above, the big or small calculating formula that can obtain estimated value is:

$\frac{(P0-P1)}{t}=\frac{(P\_E-P0)}{t}---\left(2\right)$

Calculate estimated value:

P_E＝2*P0-P1(3)

Meanwhile, current data value sensor measurement being obtained is saved in the P_N of memory cell.

Step S4: the credibility that relatively obtains estimated value P_E and measured value P_N.

By above step, obtain an estimated value P_E and a measured value P_N, lastExcellent calculated value obtains by these two data.

Which is more reliable on earth will to analyze now two data, although the data of estimation are according to beforeThe Changing Pattern of data calculates, but accuracy exists certain problem, cannot accurately embody oneIndividual small changing value, the difference that estimated value P_E and measured value P_N are set is △ P,, sets meanwhileA reduced value R.

When the difference △ of estimated value and measured value P is than R hour, estimated value P_E and measured value P_N ratioMore approaching, measured value is more approaching with the situation of expection, the possibility ratio that occurs noise do not have noisy canEnergy property is little, at this time thinks that measured value P_N is more reliable than estimated value P_E, and estimated value P_ELess with the difference △ P of measured value P_N, think that the reliability of measured value P_N is higher, and reliable journeyDegree is linear change with difference △ P.

In the time that the difference △ of estimated value and measured value P is zero, estimated value P_E and measured value P_N are sameReliably, the degree of reliability is identical.

In the time that the difference △ of estimated value and measured value P is larger than R, estimated value P_E and measured value P_N are poorApart from larger, at this time can think that larger sudden change has occurred measured value, such situation substantially canTo think a lot of noises that adulterated in data, at this time can determine and more should go to believe estimated value. AndThe difference △ P of estimated value P_E and measured value P_N is larger, thinks that estimated value is more reliable, and reliableDegree is linear change with difference △ P.

Step S5: the analysis by step S4 assigns weight to estimated value and measured value, and according to weightCalculate optimal value variable P1.

By analyzing above, can obtain the reliability situation of estimated value P_E and two values of measured value P_N,Can go to distribute estimated value P_E and two numerical value of measured value P_N in optimal value variable by reliabilityWeight. The weight that measured value P_N is set is A. :

△P＝|P_E-P_N|(4)

Analyzed by step S4, the weight A that can obtain measured value P_N is:

$A=\frac{\left|P\_E-P\_N\right|}{R+\left|P\_E-P\_N\right|}---\left(5\right)$

The weight of measured value P_N is A, and the weight of estimated value P_E is 1-A, and R is one and makes by oneselfJustice numerical value, removes to represent weight A by the form of formula (5), in the time that difference is R, can think estimated value withThe weight of measured value is the same.

Obtained weight, remaining calculating optimal value variable is just fairly simple. That is to say, in the present inventionEmbodiment in, optimal value variable is that estimated value and measured value form by certain weight.

The in the situation that of mass data, the optimal value variable calculating is with respect to estimated value P_E and measurementValue P_N has higher reliability, and the data wide fluctuations causing for noise has good inhibitionEffect. Owing to having added the estimated value of data variation trend inside optimal value, very effectively filter outNot according to the data of trend variation or saltus step.

Step S6: assignment again, recursive operation

The filtering method of this invention is a kind of recursive operation method, under the result data that this computing obtains isParameter in inferior calculating process:

The optimal value assignment that this computing is obtained is given the variable arranging in our calculating process, first willP_R assignment is to P0, then by P0 assignment to P1, formula is expressed as follows:

P0＝P_R(7)

P1＝P0(8)

The optimal value assignment that this computing is obtained participates in next round fortune to the variable arranging in calculating processCalculate, be about to again P0 and P1 that assignment obtains, recurrence is gone down always, and data also continue to keep upgrading.Next round computing repeating step S1 is to step S6.

In sum, filtering method of the present invention is applicable to same system type with Kalman filtering, butHave a lot of advantages with respect to the latter, first, operand of the present invention is little, only has several steps fairly simpleAddition subtraction multiplication and division computing, and the algorithm complex of Kalman filtering is large comparatively speaking a lot. Meanwhile, filterRipple effect is also very good.

Refer to Fig. 4, Figure 4 shows that and use filtering method of the present invention carry out filtered waveform and makeCarry out filtered comparison of wave shape figure by Kalman filtering. Wherein, curve 1 waveform is that use is of the present inventionFiltering method carries out filtered waveform, and curve 2 is to use Kalman filtering to carry out filtered waveform.Can be found out by comparison of wave shape figure, the effect of this filtering method and Kalman filtering is more approaching, for oneA little wave energies are made rapidly response, and, more responsive than Kalman filtering, also can for little fluctuationEmbody more accurately, as shown in waveform in figure, before the shake of one section of system, filtering side of the present inventionMethod has been made response in time, and Kalman filtering has filtered out when noise signal, and trembling greatly afterwardsMoving, the effect of filtering method and Kalman filtering is almost consistent; Final stage is that sensor is actionlessTime waveform, the filter effect of two methods is also more approaching.

Therefore, filtering method of the present invention has less operand with respect to Kalman filtering, and sensitiveDu Genggao, hysteresis quality is also more weak, the crucial filter effect larger Kalman filtering of operand that matches in excellence or beauty completely.

Above-described is only the preferred embodiments of the present invention, and described embodiment is not in order to limit the present inventionScope of patent protection, the equivalent structure that therefore every utilization description of the present invention and accompanying drawing content are doneChange, in like manner all should be included in protection scope of the present invention.

Claims (8)

1. the digital filter apparatus based on linear system, described device comprises the sensor and the data filtering module that detect linear systematic survey value; It is characterized in that, described data filtering module comprises memory cell, processing unit, parameter initialization unit and output unit; The parameter that described memory cell is stored comprises adjacent two optimal value variable P0 and P1, two optimal value variable P0 and the difference △ P of the P1 straight slope K of structure, estimated value P_E, measured value P_N, estimated value P_E and measured value P_N and the acquisition time interval T of sensor of obtaining for twice at 2; Described processing unit is for analytical system type and noise type, send measured value P_N and obtain estimated value P_E by slope K in each interval T according to sensor, the difference △ P of estimated value P_E and measured value P_N, obtain the credibility of estimated value P_E and measured value P_N, and according to degree of reliability dynamic assignment estimated value P_E, the weight of measured value P_N in optimal value, and go out this optimal value variable P_R according to the weight calculation of two numerical value, and export each optimal value by described output unit.

2. digital filter apparatus according to claim 1, is characterized in that, described data filtering module is micro-control unit.

3. a digital filtering method that adopts device described in claim 1, is characterized in that, described method comprises the steps:

Step S1: described processing unit analysis and judge whether system type is linear system; If so, execution step S2; If not, execution step S7;

Step S2: described parameter initialization unit initializes measured linear system correlated variables and calculated data rate of change, and the parameter after initializing is stored into described memory cell; Wherein, the initial value of described two optimal value variable P0 and P1 is that the slope K of the straight line of 0, two optimal value variable P0 and 2 formations of P1 is 0;

Step S3: go to estimate the size of next sensor measurement data estimation value P_E by the rate of change K of step S2, and described sensor obtains gathering measured value P_N according to acquisition time interval T;

Step S4: the credibility that obtains estimated value P_E and measured value P_N according to the difference △ P of estimated value P_E and measured value P_N;

Step S5: the credibility of analyzing by step S4 assigns weight to estimated value P_E and measured value P_N, and go out this optimal value variable P_R according to weight calculation;

Step S6: assignment again, recursive operation; The optimal value P_R assignment first this computing being obtained is to P0, then by P0 assignment to P1; Continue execution step S3, until data processing is complete;

Step S7: finish.

4. digital filtering method according to claim 3, is characterized in that, in described step S3, the big or small calculating formula that obtains estimated value is:

Calculate estimated value:

P_E＝2*P0-P1

And the current data value that described sensor measurement obtains is saved in P_N.

5. digital filtering method according to claim 3, is characterized in that, the step S4 of institute specifically comprises: the difference that estimated value P_E and measured value P_N are set is △ P, sets a reduced value R simultaneously;

When the difference △ of estimated value and measured value P is than R hour, measured value P_N is more reliable than estimated value P_E, and the degree of reliability is linear change with difference △ P;

In the time that the difference △ of estimated value and measured value P is zero, estimated value P_E and measured value P_N are reliable equally, and the degree of reliability is identical;

In the time that the difference △ of estimated value and measured value P is larger than R, estimated value P_E is more reliable than measured value P_N, and the degree of reliability is linear change with difference △ P.

6. digital filtering method according to claim 5, is characterized in that, the step S5 of institute specifically comprises:

If the weight of measured value P_N is A, the weight of estimated value P_E is 1-A, and R is a self-defined numerical value; :

△P＝|P_E-P_N|

Analyzed by step S4, the weight A that can obtain measured value P_N is:

Optimal value is P_R, and optimal value is that estimated value and measured value form according to certain weight, finally obtains optimal value:

P_R＝(1-A)*P_N+A*P_E。

7. digital filtering method according to claim 3, is characterized in that, the acquisition time interval T of described sensor is that 1ms is to a value between 10ms.

8. digital filtering method according to claim 3, is characterized in that, described step S1 also comprises: judge whether intrasystem noise type is the equally distributed white noise of Gaussian distributed and power spectral density, if, execution step S2, if not, execution step S7.