RU2368002C2 - Device for separation of useful signal in case of single-sided law of adaptive noise component distribution - Google Patents

Abstract

FIELD: physics, computer engineering.

SUBSTANCE: this invention is related to the field of computer engineering and may be used in systems of signals control and processing. Device comprises units of storage, switchboards, unit for breakdown into intervals, approximation units, units of assessment storage, arithmetical summing device, unit of useful component assessment storage, subtraction units, unit for finding of minimum value, generator of random numbers, unit for elimination of connected values, ranging unit, register of random number selection storage, clock pulse generator.

EFFECT: compensation of systematic error in application of assessment multiplication method, which occurs in case additive noise component is available, having single-sided asymmetric distribution law.

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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 of 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 distributed according to a one-sided law with the mathematical expectation m ≠ 0 and variance σ ² .

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 у_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 the compensation of systematic error when using the method of multiplying estimates, which appears in the case of the presence of an additive noise component having a one-sided asymmetric distribution law. 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 method of smoothing is averaging over the implementation ensemble for _{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 is sufficient for ₁ , ₂ , ..., _{n for the} original process.

, и, определение длины m отрезка ряда у_k,

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

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 at _k ,

, and, the definition 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

, сдвиг «скользящего окна» на одно значение вправо (т.е. выбор вместо отрезка у_k+1, у_k+2, …, у_k+m-1 другого отрезка у_k, у_k+1, …, у_k+m-1), вычисление среднего арифметического выбранных значений реализации, и так до тех пор, пока не будет достигнут правый конец исходной дискретной реализации результатов измерений.at ₁ , at ₂ , ..., at _m , replacing the central of the values at ₁ , at ₂ , ..., at _{m with the} found average

, shift of the “sliding window” by one value to the right (i.e., instead of the segment _{k + 1} , _{k + 2} , ..., _{k + m-1,} another segment _k , _{k k + 1} , ..., _{k + m-1} ), 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.

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

The disadvantages of the known device is the following:

- 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);

- a large approximation error during signal processing in the case of the presence of an additive noise component having a one-sided asymmetric distribution law.

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 weights p _{k are} 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 for ₁ , ₂ , ..., _{n is} enough. 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 у₁, у₂, …, у_m медианой

, сдвиг «скользящего окна» на одно значение вправо (т.е. выбор вместо интервала у_k, у_k+1, …, у_k+m-1 реализации другого интервала у_k+1, у_k+2, …, у_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 method of median smoothing involves storing the initial discrete implementation of the measurement results for ₁ , y ₂ , ..., y _n , determining the length m of the interval interval of ₁ , y ₂ , ..., y _n (or the width of the "sliding window") for which the calculation will be performed medians, i.e. ranking the selected interval of the input implementation of the measurement results, determining the median

, replacing the central value of the interval at ₁ , at ₂ , ..., at _{m with the} median

, shift of the “sliding window” by one value to the right (i.e., instead of the interval at _k , at _{k + 1} , ..., at _{k + m-1, the} implementation of another interval at _{k + 1} , at _{k + 2} , ..., at _{k + m} ), the calculation of 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 is the following:

- 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 influence of median filtering on the signal and noise;

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

- a large approximation error during signal processing in the case of the presence of an additive noise component having a one-sided asymmetric distribution law.

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 p.]. 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 is sufficient for ₁ , ₂ , ..., _{n for the} original process.

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

replacing the initial values of the measurement results for ₁ , ₂ , ..., _{n for 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 = (for ₁ + for ₂ + for 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 is the following:

- 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 ;

- a large approximation error during signal processing in the case of the presence of an additive noise component having a one-sided asymmetric distribution law.

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 propagating estimates of its only initial implementation (ROSOTs) and a device for its implementation (patent No. 2207622, IPC 7 G06F 17/18).

The prototype device under consideration involves: 1) storing the input implementation for ₁ , ₂ , ..., _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 _i + ct _i ² using the least squares method; 5) repetition of 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 (ROCC) 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;

- a large approximation error during signal processing in the case of the presence of an additive noise component having a one-sided asymmetric distribution law.

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

- to use the method of propagating estimates, it is necessary to remember the entire implementation of the measurement results;

- the presence of a constant systematic error in the case of the presence of an additive noise component having a one-sided asymmetric distribution law.

The proposed device for extracting a useful signal with a one-sided distribution law of the additive noise component allows you to compensate for the systematic error that appears in the case of the presence of the additive noise component having a one-sided asymmetric distribution law. A simplified mathematical model of the measurement results is presented in accordance with expression (1). It is proposed to consider partitions of the original discrete sequence into intervals of random length. Partitions are formed by partitioning the interval (1, N) with random numbers α _{j, 1} , α _{j, 2} , ..., α _{j, m-1} into m intervals:

- текущее размножение, К - число размножений, m - количество интервалов.Δ is a random length of the interval,

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

The procedure for dividing a segment (1, N} into m intervals of random length is repeated K times in accordance with the ROCC method [Patent No. 2207622, IPC 7 G06F 17/18]. As a result, a matrix of values for dividing a segment (1, N) is obtained:

,

,

. Размножение оценок полезной составляющей осуществляется в соответствии со способом РАЗОЦ, результирующая оценка

,

, формируется как среднее арифметическое размноженных оценок

On each interval Δ _{j, k} from matrix (3), using the approximation of the values of the initial discrete implementation of the process under study by a quadratic least squares function, a set of estimates

,

,

. 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

между оценкой полезной составляющей

и входного сигнала у_i, т.е.

. Далее определяется минимальное значение разностного процесса, т.е. предполагается, что

аддитивного шума (фиг.1а), и осуществляется компенсация оценки полезного сигнала на эту величину, то есть из оценки входного сигнала вычитается минимальное значение разностного процесса

(фиг.1б).The difference process is determined.

between the evaluation of the useful component

and input signal at _i , i.e.

. Next, the minimum value of the difference process is determined, i.e. it is assumed that

additive noise (figa), and the evaluation of the useful signal is compensated by this value, that is, the minimum value of the difference process is subtracted from the input signal estimate

(figb).

A device for extracting a useful signal with a one-sided distribution law of the additive noise component (Fig. 2) contains an input implementation 1 storage unit, the input of which is the information input of the device, to the output of which the inputs of switches 2.K are connected, to the control inputs of which the output of the splitting unit is connected intervals 3, which contains a random number generator 12 distributed according to a uniform law, the output of which is connected to the input of the unit for eliminating related values 13, the output of which is connected to an ode to ranking block 14, the output of which is connected to the input of the register for storing random numbers 15, whose output is the information output of the interval block 3, to the outputs of switches 2.K the inputs of approximation blocks 3.K are connected, the outputs of which are connected to the inputs of the evaluation storage blocks 4.K, the outputs of which are connected to the inputs of the arithmetically summing device 5, the output of which is connected to the input of the storage unit for estimating the useful component 6, the output of which is connected to the first input of the subtraction unit 7, to the second input to the output of the input implementation storage unit 1 is connected, the output of the subtraction unit 7 is connected to the input of the storage unit 8, the output of which is connected to the input of the minimum value finding unit 9, the output of which is connected to the first input of the subtraction unit 10, the output of the evaluation storage unit is connected to its second input useful component 6, the output of the subtraction unit 10 is connected to the input of the storage unit 11, whose output is the information output of the device, the synchronization of the operation of the device is provided by the clock generator 16.

A device for extracting a useful signal with a one-sided distribution law of the additive noise component is implemented as follows. The initial discrete implementation arrives in each of the K channels, where it is divided into m intervals. The division is obtained by dividing the intervals of the original discrete implementation by random numbers of the uniform distribution law. On each of the m intervals for each partition, the values of the initial discrete implementation are approximated by a quadratic function using the least squares method. Thus, K estimates of the initial discrete implementation on each of m intervals for each partition are determined. The procedure for dividing the original discrete implementation into m intervals of random length is repeated K times in accordance with the method of Razots [Patent No. 2207622, IPC 7 G06F 17/18]. The resulting estimate of the useful component is determined as the arithmetic average of the volume of multiplied estimates at each time point. In order to compensate for the systematic error that appears in the case of the presence of an additive noise component having a one-sided asymmetric distribution law, a difference process is determined, obtained as the difference between the estimation of the useful component and the input implementation. In the resulting difference process, the minimum value is found, which is subtracted from the estimate of the useful component and the estimate of the useful signal is compensated by this value. The obtained values are output to the device.

A device for extracting a useful signal with a one-sided distribution law of the additive noise component works as follows. An input discrete implementation is recorded in the storage block of the input implementation 1. The interval partitioning unit 3 generates ranked sequences of random numbers distributed according to a uniform law with eliminated “bundles” that arrive sequentially at the control inputs of switches 2.K. At the intervals obtained in the approximation blocks 3. K, the initial discrete implementation is approximated by a quadratic function using the least squares method. The approximation results are recorded in the storage blocks of the 4.K. In each of the K channels, the values of the estimates from the outputs of the blocks 4.K go to the inputs of an arithmetically summing device 5, 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 obtained useful component estimate is input to the storage unit of the useful component estimate 6, from the output of which data is fed to the first input of the subtraction unit 7, which contains the difference between the values from the storage block of the input implementation 1 and the values from the storage unit of the estimate of the useful component 6 . The resulting difference process is recorded in the storage unit 8, the data from which is supplied to the unit for finding the minimum value 9, where the minimum value in the resulting difference process is determined, to which is fed to the first input of the subtraction unit 10, where it is subtracted from each value of the estimation of the useful component received at the second input of the unit of subtraction 10 from the storage unit of the estimate of the useful component 6, the obtained values are written to the storage unit 11, from the output of which they are output to the device. The synchronization of the device is provided by the clock generator 16.

EFFECT: compensation of systematic error when using the method of multiplying estimates, which appears in the case of the presence of an additive noise component having a one-sided asymmetric distribution law, in conditions of insufficient a priori information about the statistical characteristics of the additive noise component.

Claims (1)

A device for extracting a useful signal with a one-sided distribution law of an additive noise component, comprising an input implementation storage unit, the input of which is an information input of the device, K channels, each of which consists of a switch, an approximation unit, and an estimation storage unit, arithmetically summing the device, while the output the storage unit of the input implementation is connected to the first inputs of the switches, to the second inputs of which the output of the interval unit, which contains the generator random numbers distributed according to a uniform law, the output of which is connected to the input of the block of elimination of related values, the output of which is connected to the input of the ranking block, the output of which is connected to the input of the register for storing a sample of random numbers, whose output is the information output of the interval division block, to the outputs the switches are connected to the inputs of the approximation blocks, the outputs of which are connected to the inputs of the evaluation storage blocks, the outputs of which are connected to the inputs of an arithmetic summing device, the output of which connected to the input of the storage unit for estimating the useful component, characterized in that the output of the storage unit for estimating the useful component is connected to the first input of the first subtraction unit, the output of the storage unit of the input implementation is connected to the second input of the first subtraction unit, the input of the first block is connected to the output of the first subtraction unit storage, the output of which is connected to the input of the block finding the minimum value, the output of which is connected to the first input of the second subtraction block, to the second input of the second subtraction block the output of the storage unit for estimating the useful component is output, the output of the second subtraction unit is connected to the input of the second storage unit, the output of which is the information output of the device, the synchronization of the operation of the device is provided by the clock generator, the output of which is connected to all clock inputs of the device blocks.

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