Fig.6

Fig.7

2. For want of choice of errors MIS it is important to adhere to a system approach. In this plan the elements MIS can be distributed on three groups in the correspondence with the following transformations:
             - analog transformations;
             - digital conversions;
  &           - digitization.

In a Fig. 7 the dependence of the integrated costs on an equipment - G is shown depending on requests to an exactitude of this equipment. Integrated costs are understood as all kinds of the required costs on an equipment, namely: weights, dimensions, power consumption, cost price etc. the Curve -a- corresponds to digital conversions. Really, the exactitude of digital conversions depends on word length of numbers. it is connected to an exactitude by a parity: 

N=log₂(80/2D_п),                    (4.1)

Where D_п the indicated error of a measurement.

Really: N = log2m, where m number of levels of a partition of a range of a measurement in a geometric measure. But within the limits of one level the parameter before quantization is determined on uniform to the law (by virtue of it of indeterminacy) with expectation in the middle of level. With allowance for Р = 0,95 and s  = 1,65 corresponds 0,8. Thus D_п corresponds to magnitude of a level of quantization 2D_п/0,8. Taking into account, that the indicated error is expressed in percentage, the effective range is equal 100 %, that allows to receive the formula (4.1).Obviously, that for want of growth of an exactitude of a measurement G will grow under the logarithmic law.
                As to an error of digitization, it is connected to frequency of inquiry by the formula: f_д  = К Ö( 1/ Dд), where K - constant of proportionality. For want of use of the first derivative: f_д=К(1/D_д). Generally, it is possible to consider, that dependence f_д(D_д )  there will pass between linear dependence and dependence to the proportional radical square - curve -b- in a Fig. 7. 
              The maintenance of a necessary exactitude by analog means requires the greatest costs. It is well-known, that the magnification of these costs with growth of a required exactitude is close to degree dependence - curve -c-. It is meant an error of analog transformations both methodical, and tool errors of gauges.

                     3. For want of choice of parities of errors of transformations it is necessary to use a principle of an insignificant error. The essence it consists in the following. It is known, that the addition of errors is made under the formula: 

This dependence is shown in a Fig. 8. Obviously, that taking into account the recommendations [9], it is possible to suppose, that the deviation of a specific error from nominal up to 0,1 its magnitudes practically does not change a degree of confidence to an information. Usually and the determination of norms of an error has rather approximate,  qualitative character.

Fig.8

Proceeding from this, it is possible to suppose, that for want of D₂ is less than or equal 0,5, the influence it can be neglected. Usually accept for a criterion of an insignificant smallness 0,3.

                4. Proceeding from above-stated, it is possible to accept such methodology: errors of quantization for want of of sufficient word length of analog-to-digitial converter, computing devices and accumulators of an information it is possible to neglect. Really, already for want of eight categories the error of quantization makes less than 0,1 %. Usually word length of quantization is much more. The error of digitization because of of criterion of an insignificant smallness can be accepted three times less than cumulative methodical and tool error. In this case it is possible to suppose, that the process of digitization of errors does not introduce to process of a measurement at all.

THE CHAPTER 5. THE INFLUENCE of PARASITES TO DIGITIZATION
             
                The Important stochastic property of digitization is influence to it of parasites. Parasites usually imply anomalous measurements and noise. 
                 1. The noise have frequencies were outside of frequency band of measurements, in this connection effect of a noise on adjacent readout noncorrelated. In a Fig. 9 the influence of a noise to digitization is shown provided that the sample t1 is subjected to effect of a noise parasite.

For want of to magnitude of a noise parasite D1 the point of a maximum error of digitization will proceed from a point and, exactly b. For want of D2 - exactly c. The dependence of a total error on a noise parasite is shown in a Fig. 10. Obviously, that on a criterion of an insignificant error, already for want of D_ш < 0,5 it can be not taken into account, and for want of D_ш > 2,2, it the influence becomes defining. The noise, generally speaking, acts on both adjacent samples.  

In a Fig. 11 is shown, that in this case, supposing, that the noise is distributed close to the normal law (though it not that and important), the influence of a noise to an error decreases.

Really, for want of to magnitude D_ш <D_д  the Influence it is exhibited in the field of a point (t2 - t1) /2, as from sample t1, and t2. Obviously for want of it an error

Thus, the digitization with a piecewise linear interpolation has property of kill, reducing influence of a noise in 0,7 times. For want of it the noise in 0,7 times is less than the error of digitization can not be taken into account generally, as the influence it is insignificant. For want of amplitude of a noise has more 0,7, the magnification of frequency of inquiry is necessary with the purpose of further fulfilment of operations on kill.
                2. The theory of kill is the important part of an information theory. From the point of view of communication this problem is considered for a long time, including for want of of discrete communication. Concerning problems of kill in appendix to the informational - measuring system of clearness is not present till now. The kill is that other, as a comparison of a population of measurements with t _i   on  t _{i + n}  and their averaging. Therefore all filters, in a general view, are recursive. The difference them consists in an amount direct and feedback. The general scheme of such filter is shown in a Fig. 12 [11] . Choice of factors a₀  - a_n and b₀  - b_m determine transfer function of a filter and it the order.

The transfer function is described by functions of a various kind, that allows them to classify of a different kind by titles. For example: a Batteruorts filter, sine Batteruorts filter , tangens filters, filter of the Chebyshev etc. If in a filter b_i= 0, such filter name as a nonrecursive filter have various varieties. The number of poles or zero of a filter determines it the order, that is reflected in a title, for example: a filter Баттеруорта of the second order. The realization of this or that filter is made automatically on the COMPUTER under the appropriate programs.

As a whole problem of kill is pleased combined. But it is necessary to notice, that the complexity of such filters then is exhibited, when for kill the large number of readout is used. However, for want of determination of frequencies of inquiries on a method of cosine approximation, as shown earlier, the interval between readout is selected such, that the readout outside of this interval stochastically are not connected to this interval. Therefore their use for kill has no the basis. You see the kill is use of a population of readout stochastically interconnected among themselves. Therefore for kill it is necessary to increase frequency of inquiry. The analysis of materials of actual measurements shows, that the performances of parasites are those, as will be shown further, that the redundancy of frequency of readout is necessary small (in two - three times). Therefore problem of kill limits by the elementary cases. Thus, the in-depth study circumscribed in [12] of filters, within the framework of the given work, is not necessary. 

As to kill on Kalman-Biusy algorithms [13], this kill is developed for multiparameter systems and reflects reflects a structure of these systems. In the elementary production of a problem, when there is one measured parameter and the mathematical model of object is unknown, the kill on Kalman is reduced to a method of a minimum of average guadrates (method of the Gauss), which in turn for want of number of samplings equal to two is reduced to determination their arithmetic mean. 

Variants of recursive filters are the filters based on splain-functions. The algorithm of the given filter is created on application of linear transformation on basis of a mobile interval, that is the filtered significances are calculated for an average point of an interval. This method also means, that all readout is informational are connected, but, as was shown, the readout outside of an interval between readout determined on a method of cosine approximation with this interval are not connected. Therefore for kill it is necessary to increase number of readout. Therefore, the method because of of splain-functions is transformed simply to averaging. 

3. The analysis of materials of actual measurements shows, that the noise parasites are reduced to two kinds, a gaussian  noise and sinusoidal oscillations with imposed  by a gaussian noise more often. The source of a noise of the first kind as a rule are the thermal noise in analog circuits of primary converters. By  second source - vibration of design elements of object. As was shown above, the casual sample of a sinusoid gives arccosinusoidal distribution.  The superposition of a gaussian noise on it smoothes  side ejections and distribution of probability comes nearer to uniform. As was shown above, the boundary frequency of a spectrum of a measured parameter is a priori is determined as an approximating cosinusoid. For want of magnification of sampling rate, concerning the given cosinusoid, the error in it  measurement will decrease under the law circumscribed in APPENDIX 2.

As the process of digitization, together with an interpolation was shown earlier,, reduces parasites approximately in 0,7 times. Let's assume, that the parasite as sinusoidal oscillation adjoins to boundary frequency of a parameter. The maximum error for want of digitizations and further interpolation   for various N =T/DT looks like shown on a Fig. 13, where T period of a sinusoid, and  DT period of digitization.

The restoring   of function     depends on a phase of readout in relation to samples. If the maxima of sinusoidal function is  on middle of an interval between readout, an error greatest (а), if on readout, least. In the latter case (Fig. 14) the error Dx on an edge of a range is equal sinx - 2x/p. Let's define it maximum magnitude:D'x=(cosx-2/p)dx;    D'x=0  if cosx=2/p; from here: x=arccos(2/p).
    

Therefore: Dx_max = [(sinarccos(2/p))-(2/p)arccos(2/p)] =

On the average, taking into account a rectangular distribution of readout and arccosinusoidal distribution of the readouts on a sinusoid, the error will be approximately twice less than 100 % of an error (в). That is the sinusoid on an edge of a range will be distorted on the average twice. Therefore AFC in a zone of a passband will have on the average kind   (Fig. 15). This Figure means amplitude appropriate to a range     of an error of digitization.   Frequencies lower have large amplitude. But, anyway, error of digitization does not exceed a specific error.

4. If the level of parasites is more allowable, it is possible to take measures on their kill. But for this purpose, as is shown it was above necessary to have redundant readout, that is the frequency of inquiries needs to be increased. As the process of kill uniform of discrete readout is reduced to their averaging, the number them should be increased to multiply initial sampling rate.
                Is valid, as the Kalman filter for want of these conditions is reduced to a method of the Gauss, and the recursive methods are reduced to summation of two significances with factor equal - 1/2 and with determination of a middle of an interval. Therefore, not rejecting all variety of methods of kill, it is possible to make one conclusion, that for want of availability of two readout a method of kill one, this averaging.

Let's assume, that for maintenance of kill we have increased sampling rate twice. For want of it, we shall increase frequency of a parasite from w_в (Fig. 15). For the beginning let's assume, that it is a little bit more than frequency w_в. Besides taking into account, that the sinusoidal parasites together with   a gaussian noise have close to uniform distribution of probability and can be replaced by a model have the same distribution that further as a model the oscillation as triangular is accepted. 

Fig.16

Graphically fulfilment of operation of averaging expreses in junction of adjacent points of reference direct and definition of significance in a middle of this direct (Fig. 16). Further we average obtained points (а) and we shall receive a point (б). Thus, we make two stages of averaging, in which outcome all information in an interval  t_i-t_i+1.   This operation Is algebraic looks like: [(а₁+а₂)/2+(а₂+а₃)/2]/2[, that is equal:  а₁/4+а₂/2+а₃/4 , that corresponds to a recursive filter with factors 1/4 and 1/2. 

Let's construct AFC of such filter having limited by frequency 4w. On frequency w_в the parasite is suppressed twice (Fig. 17а). On frequency 2w_в the parasite is suppressed completely (Fig. 17б). On frequency 3wв again twice, and on frequency 4w_в is not suppressed at all. Thus, AFC will look like (Fig. 18).

If the large degree of kill is necessary  , it is necessary still to increase frequency of readout twice. In this case AFC will look like (Fig. 19)

Fig.17

Fig.18

Fig.19

Fig.20

Fig.21

Fig.22

Fig.23

Fig.24

Fig.25

Thus, such filter not only suppresses parasites, but also has a large band of this suppression. For want of it it is necessary to mean the following. Here we consider a maximum deviation of a noise signal on amplitude, but this deviation changes periodically, at the expense of stroboscopic effect, from zero up to maximum magnitude.  Besides the point position of a parasite is not known, therefore we can mean average value in the given frequency band. Therefore, approaching stochastically to a potency of a noise it is possible to accept, that AFC look like (Fig. 20 and 21). That is the first filter suppresses a parasite approximately on 20dB, and second on 25dB. Taking into account also that the interpolation suppresses a parasite still twice, the suppression of noise in the first case will be approximately on 25dB, and in second on 30dB, that in practice of measurements is quite enough.

As to higher frequencies of noise, for want of their kills can be accepted them with the normal law of distribution, as a  gaussian  noise.

                                         ____
            For want of it s_ф = Ös_ш²/N  where  N  number of readout used for kill. For want of s_ф/s_ш = 1/ÖN ., if to accept s_ш = 1 ,  s_ф = 1/ÖN . That is, for want of N=2 , s_ф=0,7, and for want of N=4 , s_ф=0,25. Taking into account filtering properties of an interpolation: for want of N=2, s_ф=0,35 ; for want of  N=4  s_ф=0,25.  With allowance for it AFC of filters will look like (Fig. 22 and 23).

It is necessary to mean the following. At first, the models, considered by us, are artificial a little. Therefore at low-frequency sinusoidal - similar noise there are also high-frequency parasites. Secondly, the efficiency of kill of a sinusoid for want of magnification of number readouts grows all more slowly (see. The fig. 24) also is subject to dependence of a Fig. 25. Therefore increase of frequencies of inquiries for kill N > 4 is not meaningful.

Thus, the process of kill requires magnification of frequencies of inquiries, but algorithms of calculations simple and effective enough.

2. Now consider problems connected to anomalous measurements. The anomalous measurements can have the various physical reasons. The defects of a fillet of magnetic accumulators, failures in digital transmission lines, throws of a feed of gauges, jinglingof contacts etc. can concern to a him.  However in the information plan all of them are identical. When we look at an anomalous measurement, we can tell one -  it can not be, because can be never  . The problem arises then, when the problems is put how to define, can it be whether or not. Obviously, what to answer this problem it is possible only then, when is a priori dynamics of registered process is known. For example, if we see, that there is recording height of a flight vehicle equal 5000м and suddenly. Through 0,1с. the mark 200м has appeared, hardly who or will doubt, that available typical anomalous measurement. But when the mark 5020м has appeared, it is already difficult to refer it to an anomalous measurement. The criterion reliable enough and idle time in realization as computing algorithm for definition of an anomalous measurement is necessary.

There are various algorithms of liquidation of anomalous measurements. Here we shall consider one from possible methods, which can be useful when for want of dynamics of process because of with which is known to preparation MIS, and also for want of of specific exactitude of measurements, sampling rate  of a measured parameter is determined.

In the event that the frequency of inquiry of a parameter is determined because of theories  of a approximated cosinusoid, it is possible to assert, that for want of next sampling the parameter can not deviate from previous more than on 3D. Really, in this case speech goes about an extrapolation, as the next sampling is not known to us. We can only assume it significance. Therefore, using the formula for case of an extrapolation and taking into account, that the recording is made for case of an interpolation, we consider, that the parameter can be changed to magnitude no more 3D. In case sampling rate generally was determined on case extrapolation, as a criterion it is necessary to take magnitude D.

What to do with an anomalous measurement? It is natural, if anomalous, it and at all measurement. It is possible to consider, that it and at all was not. If it is necessary for restoring, it is necessary to take the next readout and by an interpolation to define passed. Naturally, we want it whether or not, but the information for us is lost, therefore error on an interval of a passed anomalous measurement will be more specific. But the probability it small and with it is possible to be reconciled.  Further, in spite of the fact that we define frequency of inquiries, it is exact is not maintained for a variety of reasons a system character, for example, at the expense of a multiplicity of frequencies of inquiries on different parameters. Therefore frequently actual frequency of inquiries exceeds settlement. Besides precisely to know dynamics measured of parameters hardly it is possible, therefore even the most competent expert will overestimate significances of performances dynamics measured of parameters. And, at last, taking into account, that the parameter seldom leaves on a limit of dynamics it is possible as a criterion to take not 3D, and 2D. In this case error of determination of an anomalous measurement and error of its restoring will be agreed almost completely. 

The anomalous measurements concern to that case, when the operations, which are necessary for undertaking, have the logic basis and special researches with application of a diverse and complicated mathematical means simply it is not required. In this problem two methodical approaches are possible. First corresponds to that case, when the information arrives to us in accordance with it of origin. We receive the next significance measured of a parameter, and that will be farther, we do not know. The second case - when all information or even part it the ambassador of the last anomalous measurement is known to us. Because of of these approaches can be developed and various algorithms. 

The anomalous measurements can follow as single measurements (Fig. 26а), packs or packages (б), or as ruptures in a measurement of a parameter (в). First can be connected, for example, to failures in a digital equipment, second about violation of contacts in potenciametrical gauges or miss of power supply voltage, third, for example, with a glueing together of various sites of a magnetic fillet of the registrars.

Let's consider this problem from the point of view of the first methodical approach. Is a priori we have a criterion of detection 3D. Therefore, to detect an anomalous measurement, we make with each obtained measurement operation of a comparison (Fig. 27):

If |a_i – a_i+1 | there is more 3D, it corresponds 1, if |a_i – a_i+1 | is less than or equal 3D, it corresponds   0.

The number of points for want of restoring in case (в), Fig. 26, will be equal Da/3Dд. For example, if the rupture Dа is equal 50 % of a range and Dд = 1 %, N = 50/3 or 15 points are approximately equal. The character of restoring on a circumscribed method will look like (Fig. 28). Obviously, that this method, being rather simple, has that defect, that the information is lost in case of ruptures of function. Let's try to remove this defect.

To restore function after it of the consequent analysis the reminder it of the previous significances is necessary. Let's assume, that we have such memory. Here there can be two cases. At first, anomalous measurement represented by a number readouts, which number, nevertheless, less than the dynamic characteristics of object allow. That is ambassador of the last anomalous readout there is a true readout, which in relation to anomalous looks as an anomalous measurement. In this case each next measurement is checked up on a criterion anomalousity. When will jump, all previous anomalous measurements are throwed and are substituted by a linear interpolation.

If through specific number of measurements new the horse racing does not occur, it is considered, that it is a rupture of function and all previous anomalous measurements are considered valid and are transmitted on processing. The restored function for want of it will look like (Fig. 29).

However, as it was marked, the large main memory is in this case necessary, and also the delay on processing is necessary which can be invalid in case the information processing owes is made in real time.

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