RU2313826C1 - Device for extracting useful signal with liquidation of tear points with usage of estimate multiplication method - Google Patents

Abstract

FIELD: computer engineering, possible use in systems for controlling and processing signals.

SUBSTANCE: device contains block for storing measurement results, control block, clock impulse generator, arithmetic adding device, block for storing estimate of useful component, k channels, each one of which consists of two commutators, two approximation blocks, two blocks for storing estimate, additional division block, block for removing tear points and block for storing estimate of useful component, block for division onto intervals, consisting of random numbers generator, block for removing connected values, ranking block and register for storing a selection of random numbers.

EFFECT: reduced error of estimation of useful signal function with usage of estimate multiplication method.

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Description

The present invention relates to the field of computer technology and can be used in control systems and signal processing.

.The input implementation of the measurement results is the only discrete sequence y ₁ , y ₂ , ..., y _n , where y _k = y (t _k ),

.

The mathematical model of the measurement results can be represented as:

where S _k is a useful component; u _k is the additive noise component.

With respect to the random noise component, it is assumed that Mu _k = 0, Du _k = σ ² , and its values at different instants of time are uncorrelated (i.e., cov (u _k , u _s ) = 0, k ≠ s).

принадлежит известному классу функций и определяется конечным числом параметров, используются параметрические методы оценивания (сюда входят методы регрессионного анализа, основу которых составляет классическая теория наименьших квадратов). В случаях, когда отсутствует априорная информация о функции полезной составляющей, для ее оценивания используются непараметрические методы, такие как сглаживание. Известно, что наилучший способ сглаживания - усреднение по ансамблю реализации y_i,k,

исходного процесса. Однако, на практике, как правило, предполагается наличие единственной реализации измеряемого процесса. В этом случае целесообразно пользоваться способами сглаживания.The main problem to be solved is smoothing the initial measurement results and isolating the useful component with the elimination of the break points of the estimates when using the method of multiplying estimates under conditions of insufficient a priori information about the statistical characteristics of additive noise and the function of the useful component in the presence of a single discrete implementation of the measured process. It is a priori assumed that the initial useful component is Anderson-smooth, i.e. at some intervals, it can be fairly accurately approximated by a polynomial not higher than the second degree. A similar problem may arise: 1) in the operation of transceiver devices for long-distance or space communications; 2) in radio engineering when evaluating the noise immunity of signal processing circuits (algorithms); 3) in meteorology when changing various characteristics of the state of the atmosphere, etc. In cases where the useful component S _k ,

belongs to a well-known class of functions and is determined by a finite number of parameters, parametric estimation methods are used (this includes methods of regression analysis, which are based on the classical theory of least squares). In cases where there is no a priori information about the function of the useful component, non-parametric methods such as smoothing are used to evaluate it. It is known that the best smoothing method is averaging over the ensemble of the implementation of y _{i, k} ,

source process. However, in practice, as a rule, it is assumed that there is a single implementation of the measured process. In this case, it is advisable to use smoothing methods.

The known method of the moving average [Anderson T. Statistical analysis of time series. - M .: Mir, 1976. - 765 p.]. This is one of the easiest methods to smooth out measurement results. To use it, one implementation y ₁ , y ₂ , ..., y _{n of the} original process is enough.

, определение длины m отрезка ряда y_k,

(или ширины "скользящего окна"), для которого производится вычисление среднего арифметического,

значений y₁, y₂,..., y_m, замену центрального из значений y₁, y₂,..., y_m найденным средним

, сдвиг "скользящего окна" на одно значение вправо (т.е. выбор вместо отрезка y_k, y_k+1,..., y_k+m-1 другого отрезка y_k+1, y_k+2,...,y_k+m), вычисление среднего арифметического выбранных значений реализации, и так до тех пор, пока не будет достигнут правый конец исходной дискретной реализации результатов измерений.For the initial discrete implementation of the measurement results, the smoothing interval m is determined, i.e. natural number m <n. The moving average method involves storing the initial discrete implementation of the measurement results y _k ,

, determination of the length m of a segment of the series y _k ,

(or the width of the "sliding window") for which the arithmetic mean is calculated,

values of y ₁ , y ₂ , ..., y _m , replacing the central of the values of y ₁ , y ₂ , ..., y _{m by the} found average

, shift of the "sliding window" by one value to the right (i.e., choosing instead of the segment y _k , y _{k + 1} , ..., y _{k + m-1} another segment y _{k + 1} , y _{k + 2} , .. ., y _{k + m} ), calculating the arithmetic mean of the selected implementation values, and so on, until the right end of the original discrete implementation of the measurement results is reached.

The width of the "window" is chosen odd, because The theoretical value is calculated for the central value. The expression for calculating the smoothed values of the initial discrete implementation of the measurement results is written in the form:

where p = (m-1) / 2 (m is an odd number).

Often, smoothing based on a moving average transforms the implementation of the measurement results, so that small but important parts for the analysis of the useful component (waves, bends, etc.) are not highlighted.

Signs of an analog device that coincide with the features of the claimed technical solution are as follows: discretization of a signal by time, storing a digital signal, allocation of time intervals, finding the arithmetic mean of the signal falling into the selected time intervals, replacing the original discrete implementation of the measurement results with smoothed values.

The disadvantages of the known device are:

- The first p and last p values of the measurement results are not smoothed; this drawback is especially noticeable in the case when the volume of implementation of the measurement results is small, or if it is necessary to extrapolate beyond the considered time interval;

- the moving average method causes autocorrelation of residues, even if it was absent in the original useful component, i.e. in the evaluation of the useful component, a correlation of neighboring values of the measurement results occurs (Slutsky-Yul effect).

The reasons that impede the achievement of the required technical result are as follows:

- if the width of the “window” of smoothing is 2p + 1, then the first p and last p values of the initial implementation of the measurement results are not processed;

- since the central value of the “window” of smoothing is calculated as the arithmetic average of the neighboring ones, the values of the estimation of the useful component become dependent.

The structural diagram of a device that implements the considered method contains a pulse generator, a switch, a control unit, first and second registers, an adder whose output is connected to the information input of the first register, the output of which is connected to the first information input of the switch, the second input of which is the input of the device.

используется выражение:There is a method of weighted moving average [Economic and mathematical methods and applied models: Textbook for universities. / Ed. V.V. Fedosova. - M .: UNITI, 1999. - 399 pp.], Which differs from the simple sliding smoothing method in that the values of the initial discrete implementation of the measurement results included in the smoothing interval are summed with different weights. To calculate the score

expression is used:

where the weight p _k is determined using the least squares method.

For a weighted moving average, the disadvantage is the inability to smooth the values of the initial discrete implementation of the measurement results at the ends of the implementation. In addition, the use of this method without negative weights causes autocorrelation of residues, i.e. the Slutsky-Yule effect takes place.

In the moving average method, both the arithmetic average (simple and with weights) and the median can be used. This method of smoothing is called median smoothing [Kolemaev V.A., Kalinina V.N. Theory of Probability and Mathematical Statistics. - M .: INFRA-M, 1997. - 302]. To apply this method, one discrete implementation of the measurement results y ₁ , y ₂ , ..., y _{n is} sufficient. The main advantage of median smoothing is emission resistance. The basis of the method is the calculation of the moving median.

, замена центрального значения интервала y₁, y₂,...,y_n медианой

, сдвиг "скользящего окна" на одно значение вправо (т.е. выбор вместо интервала y_k, y_k+1,...,y_k+m-1 реализации другого интервала y_k+1, y_k+2,...,y_k+m), вычисление медианы на новом интервале входной реализации результатов измерения, и так до тех пор, пока не будет достигнуто правого конца исходной реализации результатов измерений.The median smoothing method involves storing the initial discrete implementation of the measurement results y ₁ , y ₂ , ..., y _n , determining the length m of the interval interval of the series y ₁ , y ₂ , ..., y _n (or the width of the "sliding window"), for which will calculate the median, that is, ranking the selected interval of the input implementation of the measurement results, determine the median

, replacing the central value of the interval y ₁ , y ₂ , ..., y _{n by the} median

, shift of the "sliding window" by one value to the right (i.e., choosing instead of the interval y _k , y _{k + 1} , ..., y _{k + m-1 to} implement another interval y _{k + 1} , y _{k + 2,.} .., y _{k + m} ), calculating the median on the new interval of the input implementation of the measurement results, and so on, until the right end of the original implementation of the measurement results is reached.

The features of the analog device, which coincide with the features of the claimed technical solution, are as follows: discretization of the signal by time, storing the input implementation of the measurement results, allocation of time intervals, replacing the input implementation of the measurement results with smoothed values.

The disadvantages of the known device are:

- The first p and last p values of the measurement results are not smoothed.

- Due to the nonlinearity of the processing method, it is impossible to strictly distinguish between the effects of median filtering on signal and noise.

- Median smoothing can only be considered as an effective method of pre-processing the input implementation of the measurement results in the case of impulse noise.

The reasons that impede the achievement of the required technical result are as follows:

- If the width of the smoothing window is 2p + 1, then the first p and last p values of the initial implementation of the measurement results are not processed.

- Median filtering is a non-linear processing method.

- The dependence of the smoothing efficiency of the measurement results on the shape of the useful and noise component.

The block diagram of a device that implements the considered method contains a pulse generator, a switch, a control unit, a storage register, a ranking unit, an average value selection unit, an output register, where an estimate of the initial discrete implementation of the measurement results is stored.

A known method of exponential smoothing [Bendat J., Piersol A. Applied analysis of random data. - M .: Mir, 1989. - 540 s]. Its peculiarity lies in the fact that in the procedure for finding the estimate of the useful component, only the previous values of the input implementation of the measurement results taken with a certain "weight" are used, and the value of the "weights" decreases to the beginning of the implementation. To apply this method, one implementation y ₁ , y ₂ , ..., y _{n of the} original process is sufficient.

The method of exponential smoothing involves storing the initial discrete implementation of the measurement results y ₁ , y ₂ , ..., y _{n of a} random process, choosing the smoothing parameter α (0 <α <1), the value of Q ₀ , calculating the estimate of the useful component using the recurrence formula:

replacing the initial values of the measurement results y ₁ , y ₂ , ..., y _{n with the} smoothed values of Q ₁ , Q ₂ , ..., Q _n .

To use exponential smoothing of the measurement results, the initial value Q _{0 of the} estimate of the useful component and the smoothing parameter α are determined. Wrong choice of initial conditions can have a significant impact on the result of processing the initial discrete implementation of the measurement results. In practical recommendations on the use of exponential smoothing [Bendat J., Pirsol A. Applied analysis of random data. - M .: Mir, 1989. - 540 p.] It is proposed to choose as the initial value Q ₀ either the first value of the measurement results or the arithmetic average of several first members of the measurement results, for example, Q ₀ = (y ₁ + y ₂ + y ₃ ) / 3. On the other hand, the influence of the initial conditions decreases with an increase in the number of measurement results and becomes insignificant with a large number of measurements.

The characteristics of the analog device, which coincide with the features of the claimed technical solution, are as follows: time signal discretization, digital signal storing, presentation of useful component evaluation values in the form of a polynomial from the values of the initial discrete implementation of the measurement results, replacement of the values of the initial implementation of the measurement results with smoothed values.

The disadvantages of the known device are:

- the uncertainty of the choice of the smoothing parameter α, in some cases it is proposed (unreasonably) to determine the value of α based on the volume of the smoothed implementation: α = 2 / (n + 1);

- the uncertainty of the choice of the parameter Q ₀ , which leads to the groundlessness of repeated re-application of the method of exponential smoothing for other values of α and Q ₀ .

The reasons that impede the achievement of the required technical result are as follows: the method of exponential smoothing is not a "self-adjusting" method, since the choice of parameters α and Q _{0 is} carried out subjectively and depends on the experience and practical skills of the researcher, the values of α and Q ₀ are functions of the waveform, noise, sample size.

The structural diagram of a device that implements the considered method comprises a pulse generator, a switch, a control unit, a storage register, an adder, a multiplication unit, an output register for storing the useful component estimate.

Closest to the invention is a method for highlighting a trend by multiplying estimates of its only initial implementation (ROSOTs) and a device for its implementation (patent No. 2207622, IPC 7 G06F 17/18).

The device under consideration - the prototype assumes: 1) remembering the input implementation y ₁ , y ₂ , ..., y _n ; 2) dividing the input implementation into sub-intervals by random numbers having a uniform distribution law; 3) checking the condition that the sub-intervals include at least L values of the original implementation, if the condition is not met, then random partition numbers are regenerated; 4) finding at each sub-interval of the input implementation the estimates of the coefficients of the approximating polynomial a + bt + ct ² using the least squares method; 5) repeating the procedures described in paragraphs 2-4 K times; 6) finding the smoothing function as the arithmetic mean of “piecewise quadratic” approximating functions at each moment in time.

A device for highlighting a trend by the method of multiplying estimates of its only initial implementation (Razots) contains a block for storing measurement results, switches, a random number generator, a block for eliminating related values, a ranking block, a register for storing random numbers, approximation blocks, register for storing estimates, an arithmetic summing device , storage unit estimates useful component, a clock generator.

The disadvantages of the known prototype device are:

- the impossibility of implementing the known method Razots in real time;

- the presence of break points in the estimation of the useful component as a result of the approximation at the boundaries of the intervals of the partition.

The reasons that impede the achievement of the required technical result are as follows:

- as a result of the approximation at each interval of the partition, the maximum error in the estimation of the useful component of the measurement results falls on their boundaries, where there are gaps in the estimation of the useful component;

- increasing the error of smoothing the measurement results due to an unlimited increase in the number of reproductions, which increases the likelihood of coincidence of the boundaries of the partition intervals and the accumulation of approximation errors.

, на m интервалов:The proposed device for extracting a useful signal with the elimination of break points when using the method of multiplying estimates allows you to reduce the error of estimation of the useful component S _k and eliminate the break points when using the method of multiplying estimates. It is proposed to consider simultaneously two options for dividing the initial discrete implementation of the measurement results into intervals of random length. According to the results of the main partition of the initial discrete implementation of the measurement results, an additional partition is formed. The main partition is formed by partitioning the interval (1, n) with random numbers

, at m intervals:

- текущее размножение, K - число размножений, m - количество интервалов.where the superscript 1 denotes the main partition, Δ is the random length of the interval,

is the current breeding, K is the number of breeding, m is the number of intervals.

на m интервалов:An additional partition is formed by partitioning the interval (1, n) by numbers

on m intervals:

вычисляются с помощью выражения:where superscript 2 denotes an additional partition, numbers

are calculated using the expression:

Additional tiling intervals are obtained so that their boundaries fall in the middle of the tiling intervals. Moreover, the right boundary of the first interval of the additional partition and the left boundary of the last interval are in the middle of the first interval and the penultimate interval, respectively, of the main partition. The procedure for dividing the segment (1, n) into m intervals of random length into the main and additional partitions is repeated K times in accordance with the Razots method [Patent No. 2207622, IPC 7 G06F 17/18.]. As a result, we obtain two sets of partitions of the segment (1, n):

и

из ряда (5) и (6) с помощью аппроксимации значений исходной дискретной реализации исследуемого процесса квадратичной функцией методом наименьших квадратов получается набор оценок

и

,

(фиг.1а и б). Для основного и дополнительного разбиения погрешность оценки полезной составляющей минимальна в середине интервалов и максимальна на их границах. При этом, минимальная погрешность оценки в середине интервалов дополнительного разбиения приходится на границы интервалов основного разбиения. Для уменьшения погрешности оценки полезной составляющей, значения оценок, относящихся к границам основного интервала, заменяются значениями оценок, приходящихся на середины интервалов дополнительного разбиения. Производится замена значений оценок, полученных на интервалах

, соответствующими значениями оценок, полученными на интервалах

, q - число заменяемых отсчетов и формируется оценка

(фиг.1в). Размножение оценок полезной составляющей осуществляется в соответствии со способом РАЗОЦ, результирующая оценка

, формируется как среднее арифметическое размноженных оценок

.At each interval

and

from series (5) and (6) by approximating the values of the initial discrete implementation of the process under study by a quadratic function by the least squares method, a set of estimates is obtained

and

,

(figa and b). For the main and additional partitions, the error in estimating the useful component is minimal in the middle of the intervals and maximal at their boundaries. Moreover, the minimum estimation error in the middle of the intervals of the additional partition falls on the boundaries of the intervals of the main partition. To reduce the estimation error of the useful component, the values of the estimates related to the boundaries of the main interval are replaced by the values of the estimates falling in the middle of the intervals of the additional partition. The values of estimates obtained at intervals are replaced.

corresponding values of estimates obtained at intervals

, q is the number of replaced samples and an estimate is formed

(figv). The reproduction of the estimates of the useful component is carried out in accordance with the Razots method, the resulting estimate

is formed as the arithmetic mean of the multiplied estimates

.

As a result of the studies, it was found that the number of replaced samples q should not exceed one, two values symmetrically with respect to the boundaries of the intervals of the main partition. Otherwise, the effectiveness of the proposed method of reducing the error of estimation of the useful component is reduced.

A device for extracting a useful signal with the elimination of break points when using the method of multiplying estimates (figure 2) contains a storage unit for measurement results 1, the input of which is the information input of the device, the output of which is connected to the inputs of the switches 2.K and the inputs of the switches 8.K, to the control inputs of the switches 2.K connected to the output of the interval unit 3, which contains a random number generator 14, distributed according to a uniform law, the output of which is connected to the input of the block eliminating related values 15, the output of which is connected to the input of the ranking block 16, the output of which is connected to the input of the register of storing random numbers 17, whose output is the information output of the block for dividing into intervals 3, the inputs of the approximation blocks 3.K are connected to the outputs of the switches 2.K, the outputs which are connected to the inputs of the storage units of the 4.K grade, the outputs of which are connected to the first inputs of the blocks to eliminate the break points 5.K, to the second inputs of which the output of the block to the intervals 3 is connected, to the control inputs of the blocks to eliminate the break points and 5.K the output of the control unit 11 is connected, the output of the interval partitioning unit 3 is connected to the inputs of the additional splitting units 7.K, the outputs of which are connected to the control inputs of the 8.K switches, the outputs of which are connected to the inputs of the 9.K approximation units, the outputs of which connected to the inputs of the storage units of the assessment 10.K, the outputs of which are connected to the inputs of the blocks to eliminate the break points 5.K, the outputs of which are connected to the inputs of the storage units of the assessment of the useful component 6.K, the outputs of which are connected to the inputs of the arithmetic summing device -keeping 12 whose output is connected to the input of the evaluation unit storing a useful component 13 whose output is the data output device. The synchronization of the device is provided by the clock generator 18.

A device for extracting a useful signal with the elimination of break points when using the method of multiplying estimates is implemented as follows. The initial discrete implementation of the results of measurements of a physical quantity arrives in each of the K channels, where it is twice divided into m intervals. The main partition is obtained by dividing the intervals of the original discrete implementation by random numbers of the uniform distribution law. Based on the results of the main partition of the initial discrete implementation of the measurement results, an additional partition is formed. The boundaries of the intervals of the additional partition are defined as the middle of the intervals of the main partition, with the right border of the first interval and the left border of the last interval of the additional partition fall in the middle of the first and penultimate interval, respectively, of the main partition. On each of the m intervals for the main and additional partitions, the values of the initial discrete implementation of the process under study are approximated by a quadratic least squares function. Thus, K estimates of the initial discrete implementation of the measurement results on each of m intervals are determined for the main and additional partitions. Further, the values of estimates related to the boundaries of the main interval are replaced by the values of estimates falling in the middle of the intervals of the additional partition. The resulting estimate of the useful component is defined as the arithmetic average of the volume of multiplied estimates at each time point and the resulting estimate of the useful component is output to the device.

A device for extracting a useful signal with the elimination of break points when using the method of multiplying estimates works as follows. In the storage unit of the measurement results 1 is recorded the initial discrete implementation of the measurement results of a physical quantity. The interval partitioning unit 3 generates ranked sequences of random numbers distributed according to a uniform law with eliminated “connectives”, which are fed sequentially to the control inputs of the switches 2.K, to the inputs of the blocks of the additional partitioning 7.K, and to the inputs of the blocks for eliminating the break points 5.K . On the obtained intervals in the approximation blocks 3.K, the initial discrete implementation of the measurement results is approximated by a quadratic function using the least squares method. The approximation results are written to the storage units of the 4.K. In blocks of the additional partition 7.K, the boundaries of the intervals of the additional partition are defined as the midpoints of the intervals of the main partition, with the right boundary of the first interval and the left boundary of the last interval of the additional partition fall in the middle of the first and penultimate interval, respectively, of the main partition. The partition numbers after the additional partition block 7.K are supplied sequentially to the control inputs of the switches 8.K. On the obtained intervals in the approximation blocks 9.K, the initial discrete implementation is approximated by a quadratic function using the least squares method. The approximation results are written to the storage units of the 10.K estimate. Values of the estimates of the useful component from the outputs of the storage blocks are estimated at 4.K and 10.K and are input to the blocks for eliminating the break points 5.K, where the values of the estimates related to the boundaries of the main interval are replaced by the values of the estimates that are in the middle of the intervals of the additional partition. The values of the boundaries of the intervals of the main partition come from the output of the partition block into intervals of 3, and the values of the length of the interval for replacing estimates of the useful component come from the output of the control unit 11. The values of the estimates of the useful component after eliminating the break points are recorded in the storage blocks of the estimate of the useful component 6.K. In each of the K channels, the values of the estimates from the outputs of the 6.K blocks are input to the arithmetic summing device 12, where the resulting estimate of the useful component is determined as the arithmetic average of the estimates obtained in each of the K channels of the device at fixed times. Thus, the resulting evaluation of the useful component is fed to the input of the storage unit for estimating the useful component 13, from the output of which the data are output to the device. The synchronization of the device is provided by the clock generator 18.

EFFECT: reduced error of estimation of useful signal function when using the method of multiplying estimates, which is achieved by eliminating the break points of the estimation of the useful component.

Claims (1)

A device for extracting a useful signal with the elimination of break points when using the method of multiplying estimates, containing a storage unit for the measurement results, the input of which is the information input of the device, k channels, each of which consists of a switch, an approximation unit, an approximation estimation storage unit, to the output of the storage unit the measurement results are connected to the inputs of the switches, the control inputs of which are connected to the output of the interval unit, which contains a random number generator, the distribution according to a uniform law, the output of which is connected to the input of the unit for eliminating related values, the output of which is connected to the input of the ranking unit, the output of which is connected to the input of the register for storing random numbers, the output of which is the information output of the unit for dividing into intervals, the inputs of the blocks are connected to the outputs of the switches approximations, the outputs of which are connected to the inputs of the approximation estimation storage blocks, an arithmetic summing device, the output of which is connected to the input of the estimation estimation storage block useful component, the output of which is the information output of the device, characterized in that an additional splitting unit, an additional switch, an additional approximation unit, an additional approximation estimation storage unit, a break point elimination unit, a useful component evaluation storage unit, are added to the output of the storage unit the results of measurements are connected to the inputs of additional switches, the outputs of additional evaluation storage units are connected to the first inputs of point elimination units breaks, to the second inputs of which the output of the interval unit is connected, to the control inputs of the blocks to eliminate the break points, the output of the control unit is connected, from which the values of the length of the interval for replacing estimates of the useful component are received, the output of the interval unit is connected to the inputs of the units of additional partition, the outputs of which connected to the control inputs of additional switches, the outputs of which are connected to the inputs of additional approximation blocks, the outputs of which are connected to the inputs of additional Storage evaluation approximation block outputs the storage estimate the approximation of blocks connected to inputs of eliminating the discontinuity points blocks whose outputs are connected to inputs of the storage units useful evaluation component whose outputs are connected to inputs of an arithmetic adder, synchronism of operation of all elements of the device provided by clock generator.

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