RU2452080C1 - Digital multi-iterative filter - Google Patents

Abstract

FIELD: information technology.

SUBSTANCE: filter comprises difference units, correction units, adder units, delay circuits, matrix function units, shaping and readout unit of apriori data, regularisation parameter unit.

EFFECT: accuracy of estimating information process parameters in measuring systems.

7 dwg

Description

The invention relates to digital computing and can be used in digital signal processing systems when solving problems of optimal non-linear filtering.

A device is known - an extended Kalman filter [1, 2], the disadvantage of which is the limited functionality due to the linear structure of the processes being processed and the device [3], as well as a heuristic setting of the regularization parameter.

Closest to the technical nature of the claimed invention is a digital intelligent iterative filter [3], containing the first, second, third difference generating units; first, second, third blocks of correction; a block for generating and issuing a priori data; first, second, third blocks of the formation of the amount; the first, second, third, fourth, fifth and sixth blocks of the formation of matrix functions; first, second and third delay lines; the first and second block of the calculation of the regularization parameter. However, this device in some practically important cases does not allow to obtain the required accuracy.

Improving the accuracy characteristics of filtering the parameters of random processes is an important area.

The claimed invention is aimed at improving accuracy in the formation of estimates of the parameters of the information process in measuring systems, which is very important for radar tracking of targets, containing blocks: the first, second, third, fourth blocks of the formation of the difference; first, second, third, fourth correction blocks; a block for generating and issuing a priori data; the first, second, third, fourth blocks of the formation of the amount; the first, second, third, fourth, fifth, sixth, seventh and eighth blocks of the formation of matrix functions; first, second, third and fourth delay lines; the first, second and third unit for calculating the regularization parameter, while the first, second, third and fourth outputs of the unit for generating and issuing a priori data are connected respectively to the second, third, fourth and fifth information inputs of the first, second, third and fourth correction units, in addition , the first, second, fifth outputs of the block for generating and issuing a priori data are connected respectively to the third, second, and fifth information inputs of the first, second, and third blocks for calculating the regularization parameter, the first information the output of the first correction block is connected to the first information input of the first sum forming block, the output of which is connected to the information input of the first matrix function forming block and the fourth information input of the first regularization parameter calculation block, the first information input of which is the device input; the output of the first regularization parameter calculation unit is connected to the ninth information input of the second correction unit, the output of the first matrix function formation unit is connected to the information input of the first delay line, the output of which is connected to the second information input of the first sum formation unit, with the seventh information input of the first correction unit and with information input of the second block of the matrix function formation, the second information output of which is connected to the sixth information input of the first block to rrektsii, first information output of the second forming unit matrix function is connected to a second data input of the difference forming unit, the output of which is connected to a first data input of the first correction block; the second information output of the first correction unit is connected to the eighth information input of the second correction unit, the first information output of which is connected to the first information input of the second summing unit, the output of which is connected to the information input of the third matrix function forming unit and with the fourth information input of the second regularization parameter calculation unit the output of which is connected to the ninth information input of the third correction unit, the output of the third block of matrix f The function is connected to the information input of the second delay line, the output of which is connected to the second information input of the second summing unit, the seventh information input of the second correction unit and the information input of the fourth matrix function forming unit, the second information output of which is connected to the sixth information input of the second correction unit, the first information output of the fourth matrix function generating unit is connected to the second information input of the second separation forming unit and whose output is connected to a first data input of the second correction unit; the second information output of the second correction unit is connected to the eighth information input of the third correction unit, the first information output of which is connected to the first information input of the third summing unit, the output of which is connected to the information input of the fifth matrix function forming unit, the output of which is connected to the information input of the third delay line the output of which is connected to the second information input of the third block of the formation of the sum, the seventh information input of the third block of cor and with the information input of the sixth matrix function generating unit, the second information output of which is connected to the sixth information input of the third correction unit, the first information output of the sixth matrix function forming unit is connected to the second information input of the third difference forming unit, the output of which is connected to the first information input of the third correction block; the second information output of the third correction unit is connected to the eighth information input of the fourth correction unit, the first information output of which is connected to the first information input of the fourth summing unit, the output of which is the output of the device and connected to the information input of the seventh matrix function forming unit, the output of which is connected to the information the input of the fourth delay line, the output of which is connected to the second information input of the fourth block of the formation of the sum, seventh the information input of the fourth correction unit and with the information input of the eighth matrix function forming unit, the second information output of which is connected to the sixth information input of the fourth correction unit, the first information output of the eighth matrix function forming unit is connected to the second information input of the fourth difference forming unit, the output of which is connected to the first information input of the fourth correction block.

One of the ways to increase the accuracy of estimating the parameters of dynamic systems is to use methods for solving ill-posed problems based on the principles of regularization. The effectiveness of the use of regularization for the case of continuous systems has been proved and has been expressed in the form of the method of A.N. Tikhonov [4] and its variants in the form of the method of iterative regularization [5]. We obtain filtering equations using the iterative regularization method for a discrete system [6–9].

Let the dynamics of the estimated parameters be described by a system of difference equations in discrete time

- вектор состояния исследуемой системы;

- вектор неизвестных внешних воздействий; переходная функция

- непрерывная вместе с частными производными вектор-функция своих аргументов; G∈E^M×E^M - матрица интенсивности внешних воздействий; k, N, М - натуральные числа. Предполагается, что матрица

имеет обратную матрицу.Where

- state vector of the studied system;

- vector of unknown external influences; transition function

- a continuous vector function of its arguments along with partial derivatives; G∈E ^M × E ^M - matrix of the intensity of external influences; k, N, M are natural numbers. It is assumed that the matrix

has an inverse matrix.

The observed signal obtained at the output of the measurement system model is described by a discrete equation

- вектор наблюдения,Where

- observation vector,

- вектор дискретного белого гауссовского шума с известными локальными характеристиками

is a vector of discrete white Gaussian noise with known local characteristics

- сигнальная вектор-функция, непрерывна вместе с частными производными; L, l - натуральные числа.W - covariance matrix of dimension L × L, δ (·) - vector delta - function;

- signal vector function, continuous with partial derivatives; L, l are natural numbers.

We pose the problem of synthesizing a recurrent filter for estimating x ^* (k), which is optimal in the sense of the minimum functional characterizing the measurement error

Due to the continuity of the vector - function F (), the solution of equation (1) continuously depends on η (k), therefore, the error functional (3) on each solution of system (1) continuously depends on η (k). Thus, the problem of determining the estimate x ^* (k), delivering a minimum of (3), is equivalent to the problem of determining

путем решения совокупности уравнений (1), (2), (4) в условиях некорректности исходной задачи достаточно сложно, в связи с этим широкое распространение получили итерационные градиентные методы. Однако использование таких методов может привести к расходящейся последовательности приближений. Поэтому применение любого итерационного метода для решения задачи (1), (2), (4) требует определения регуляризирующего семейства операторов, в котором параметром регуляризации является номер итерации.Problem (1), (2), (4) is an incorrectly posed inverse problem [7]. Find the values of the vectors x ^* (k), η ^* (k),

by solving the set of equations (1), (2), (4) under the conditions of the incorrectness of the original problem, it is quite difficult; in this regard, iterative gradient methods are widely used. However, the use of such methods can lead to a divergent sequence of approximations. Therefore, the application of any iterative method to solve problem (1), (2), (4) requires the determination of a regularizing family of operators in which the regularization parameter is the iteration number.

In accordance with the general definition of a regularizing family of operators according to A.N. Tikhonov [7], we say that the iterative method

in which the numerical parameter α _n satisfies the conditions:

where Δ (η _n ) is the residual, generates a regularizing family of operators in which the parameter is the iteration number if, for any initial approximation η ₀ and for any error value of the initial data σ, satisfying the condition 0 <| σ | <σ ₀ , σ ₀ = const, there exists a number n (σ) such that

при стремлении погрешности исходных данных к нулю.that is, the approximations obtained converge to the exact solution in the norm of space

when the error of the initial data tends to zero.

According to [8], the expression for determining the gradient at the point η _n (k) has the form

where x _n (k) is the solution to problem (1) for η _n (k), and the vector ψ _n (k) is determined from the conditions

Knowing the expression for the gradient (7) of functional (3), we can rewrite expression (6) for the regularization parameter [9] in the following form

The choice of a sequence of parameters α _n that satisfies condition (9) will make it possible to implement a filter for digital processing of measurement information of increased accuracy.

запишем итерационную последовательность (5) в развернутой форме для

To implement the iterative method (5), it is required to determine the gradient of functional (3) defined by expression (7). Taking for the zeroth approximation η ₀ (k) = 0,

we write the iterative sequence (5) in expanded form for

As a result, taking into account (7), we have a sequence of discrete two-point boundary value problems (DDTKZ) of the form

и помножим каждое из уравнений для сопряженных векторов ψ_i на величину α_i, тогда уравнения (10) принимают следующий видWe introduce the notation

and multiply each of the equations for the conjugate vectors ψ _i by the quantity α _i , then equations (10) take the following form

To obtain a recurrent estimation algorithm for the state vector, it is necessary to use the invariant immersion method in the discrete version. We note that the equation for the vector - functions λ in DDTKZ (9) is written in the inverse time. This requires its transformation to a form reflecting the dependence of λ _n (k + 1) on λ _n (k) and x _n (k). Performing the corresponding transformations taking into account the expression for x _n (k + 1) from (11) and using the Taylor series expansion in a neighborhood of F (x _n (k), k), we obtain the following DDTKZ sequence

where the functions β and γ are introduced to shorten the notation.

We replace the condition at the end of λ _n (N) = 0 with the more general condition λ _n (N) = c and let N and c be variables. Then the value of the vector x _n (N) is defined as a function of N and c

x _n (N) = r [s, N].

A change in the value of N Ha N + 1 gives an increment Δс, then

We write the expression for r (c + Δc, N + 1) using the apparatus of finite differences

r (s + Δc, N + 1) = r (c, N) + Δr _c (s, N) + Δr _N (s, N) + Δ ² r _cN (s, N),

or, given (13), we obtain

Where

According to (12), the expressions for Δx _n and Δс have the form

Allow difference equation (14) with respect to r (c, N), i.e. it is not possible to find a general analytical solution, and usually they turn to approximate methods. Suppose that r (c, N) is linear in c

- оценка вектора состояния в момент N, P_n(N) - некоторая матрица размерности М×М.Where

is an estimate of the state vector at the moment N, P _n (N) is some matrix of dimension M × M.

We calculate the differences in the expression (14) using the expression (16)

Substituting expressions (15), (16), (17) in (14), we obtain

и пренебрегая членами порядка выше первого, можно записать уравнение (18) в видеExpanding β and γ in a Taylor series in a neighborhood

and neglecting the terms of the order above the first one, we can write equation (18) in the form

и

Relation (19) is satisfied as c → 0; therefore, equating the coefficients for the first and zero powers of c, we obtain difference equations for

and

We write the DDTKZ (12) for the case when k = N while taking into account that all of the DDTKZ for i = 0, ..., n-1 are allowed and, accordingly, the estimates x _i are known functions of the parameter k. We have

нет, запишем последовательность уравнений для оценки

процесса (1), предполагая, что N постоянно изменяется и k=N, а также учитывая условие (7) налагаемое на параметр регуляризации, в видеSince the differences in the redesignation of the matrices P _n and

no, we write down the sequence of equations for estimating

process (1), assuming that N is constantly changing and k = N, and also taking into account condition (7) imposed on the regularization parameter, in the form

с оценками

сигнальной вектор-функцией Н и матрицами G, W. То есть в фильтре (24), в отличие от фильтра [3], параметр регуляризации согласован в соответствии с принципом невязки с ошибками измерений, что позволяет получить более точную процедуру оценивания. Алгоритм (24) дает оптимальную для нелинейной системы оценку параметров в смысле минимума функционала, характеризующего среднеквадратическую ошибку измерительного канала.The sequence of equations (24) is a digital intelligent multi-stage filter that allows the digital processing of measurement information for discrete dynamic systems. If we compare the obtained equations with the equations of the digital recursive filter [3], it becomes clear that they are different from each other due to the introduction of an additional iteration, as well as additional relationships of the sequence of parameters α _i , which change the overall feedback coefficient in the equation for estimating

with ratings

the signal vector function H and the matrices G, W. That is, in the filter (24), unlike the filter [3], the regularization parameter is matched in accordance with the principle of residuals with measurement errors, which allows a more accurate estimation procedure. Algorithm (24) gives an optimal estimate of the parameters for a nonlinear system in the sense of the minimum functional characterizing the mean square error of the measuring channel.

The calculation of the regularization parameter is organized as follows: the integration limits [0, t] are changed to [t-4s, t], where t is the current time, s is the calculation step; for discrete time it is necessary to take [N-1, N-5]. Studies have shown [6] that using the data more than four steps back provides an increase in the accuracy of the estimates obtained by fractions of a percent with an increase in the number of necessary arithmetic operations by several times. A method using more than four iterations will be called multi-iteration.

It should be noted that in order to implement the 2nd iteration of the developed algorithm (24), it is necessary that the 1st iteration be implemented, for the implementation of the 3rd - the 1st and 2nd, for the implementation of the 4th - 1st, 2 3rd and 3rd. That is, the number of arithmetic operations necessary to calculate the iteration of the algorithm will include the number of arithmetic operations of the previous iterations. Analysis of the computational costs required to implement the developed evaluation algorithm allows us to conclude that it can be implemented in real time based on the use of modern computer technology.

Studies have shown that the effectiveness of each reprocessing relative to the previous one decreases. Meanwhile, the volume of calculations is increasing dramatically. Based on the analysis of the results of numerical modeling, iterative data processing can be recommended four times.

The efficiency of the developed filter is estimated based on numerical simulation of the problem of determining the unknown constant parameter d of a third-order discrete nonlinear system

where parameter τ has the meaning of the time interval through which the measuring information arrives in the form

Thus, as follows from relations (24), the introduction of new structural elements and relationships allows, together with common features, to obtain a technical result consisting in reducing the variance of errors obtained at the output of the filter estimates of input processes.

The device relates to digital computing and can be used in digital processing systems of radio signals to solve problems of optimal non-linear filtering, as well as to detect target maneuvers, since this is very important both from a tactical and technical point of view. In technical terms, intensive target maneuvering can lead to a significant deterioration in the accuracy of stability of its auto tracking with tracking meters. In connection with the noted circumstances, it is advisable to include special devices (algorithms) for detecting, tracking, guiding, etc., and correcting (adapting) the parameters or structure of the filters in accordance with this situation in the composition of modern and promising converters.

The disadvantage of the selected prototype is the low accuracy of the formed estimates of the information process. By calculating the regularization parameter using the new formula in this paper, the accuracy of the estimates of the parameters of this device is increased.

The calculated weight coefficient of the regularization parameter has the form [10]:

Based on the prototype, the following is a description of the invention calculated by the formula (27).

The invention is illustrated in Figure 1-7, which shows the structural diagrams of a digital multi-iteration filter, first and second correction blocks, a block for calculating accuracy characteristics, a block for calculating the regularization parameter, a unit for generating the product of the numerator of the regularization parameter, and a prediction calculation block.

Figure 1 shows a block diagram of a digital multi-iteration filter. The device comprises a first block 1, a second block 7, a third block 14 and a fourth difference generating block 20; a first block 2, a second block 8, a third block 15, and a fourth correction block 21; the first block 3, the second block 9, the third block 16 and the fourth block 22 of the formation of the sum, the first delay line 5, the second delay line 11, the third delay line 18 and the fourth delay line 24; a first block 4, a second block 6, a third block 10, a fourth block 12, a fifth block 17, a sixth block 19, a seventh block 23, and an eighth block 25 for generating matrix functions, a block 13 for generating and outputting a priori data; the first block 26, the second block 27, and the third block 28 for calculating the regularization parameter.

Figure 2 shows the structural diagram of the first correction unit, which contains the partial derivative generation unit 2.1, the matrix function transposition unit 2.2, the product formation unit 2.3, the accuracy characteristics calculation unit 2.4, and the product formation unit 2.5.

Figure 3 shows the structural diagram of the second correction unit, which contains the partial derivative generation unit 8.1, the matrix function transposition unit 8.2, the product generation unit 8.3, the sum formation unit 8.4, the accuracy characteristics calculation unit 8.5, the product formation unit 8.6.

Figure 4 shows a structural diagram of a block for calculating accuracy characteristics included in the first, second, third and fourth blocks of correction, which contains a block 20 for forming partial derivatives of the matrix function, a block for transposing the matrices 21, a block for generating the product 22, a delay line 23, and a transposing block 24 matrices, a product generating unit 25, a sum generating unit 26, a partial function matrix generating unit 27, a product generating unit 28, a difference generating unit 29, an image processing device 30 eniya matrices forming unit 31 works.

Figure 5 shows the structural diagram of the block for calculating the regularization parameter, which contains the block for generating the matrix function 26.1, delay lines 26.2, 26.4, 26.8, 26.9, 26.13, 26.14, 26.18, 26.19, 26.20, 26.26, 26.27, 26.28, 26.32, 26.33, 26.34 , 26.35, 26.43, 26.44, 26.45, 26.46, blocks 26.3, 26.10, 26.12, 26.21, 26.24, 26.25, 26.36, 26.40, 26.41, 26.42 of the formation of the product of the numerator of the regularization parameter, transposition blocks 26.5, 26.15, 26.29, 26.29, 26.47, 26.6, 26.16, 26.30, 26.48 product generation, blocks 26.7, 26.17, 26.31, 26.49 difference formation, blocks 26.11, 26.22, 26.23, 26.37, 26.38, 26.39 forecast calculations, blocks 26.51, 26.50 formation of sums s, block 26.52 of forming the product of the denominator of the regularization parameter, block 26.53 of forming the relationship.

Figure 6 shows the structural diagram of the first block of forming the product of the numerator of the regularization parameter included in the first, second, and third blocks of forming the regularization parameter, which contains the matrix function generation block 26.3.1, the matrix function partial derivative block 26.3.2, the transposition block 26.3.3 matrices, difference block 26.3.4, block 26.3.5 for creating a product, blocks 26.3.6 and 26.3.7 for transposing matrices, and block 26.3.8 for creating a product.

Figure 7 shows the structural diagram of the first forecast calculation block, which is part of the unit for generating the product of the numerator of the regularization parameter, it includes blocks for generating the product 26.11.1 and 26.11.5, blocks for generating the sums 26.11.2 and 26.11.6, block 26.11.3 forming partial derivatives of a matrix function; block 26.11.4 forming a matrix function.

, информационный вход которого соединен с информационным выходом блока 3, информационный выход первой линии задержки 26.2 соединен со вторым информационным входом первого блока 26.3 формирования произведения числителя параметра регуляризации, первый и третий его информационные входы соединены со вторым и первым информационными выходами блока 13 формирования и выдачи априорных данных соответственно, а четвертый информационный вход - со входом устройства, первый информационный выход первого блока 26.3 формирования произведения числителя параметра регуляризации соединен с шестым и седьмым информационными входами второго блока 26.50 формирования суммы, первый информационный выход которого соединен с первым информационным входом блока 26.53 формирования отношения, первый выход блока 26.53 формирования отношения является выходом блока 26; первый информационный выход второй линии задержки 26.4 соединен с первым информационным входом первого блока транспонирования 26.5 и первым информационным входом первого блока 26.6 формирования произведения, первый информационный выход блока 26.5 соединен со вторым информационным входом блока 26.6 формирования произведения, первый информационный выход которого соединен со вторым информационным входом первого блока 26.7 формирования разности, первый информационный вход которого соединен с четвертым информационным входом блока 26.3, первый информационный выход блока 26.7 соединен с четвертым информационным входом первого блока 26.51 формирования суммы, первый информационный выход которого соединен с первым информационным входом блока 26.52 формирования произведения знаменателя параметра регуляризации, а второй вход блока 26.52 соединен с пятым выходом блока 13 формирования и выдачи априорных данных; первый информационный выход блока 26.52 формирования произведения знаменателя параметра регуляризации соединен со вторым входом блока 26.53 формирования отношения; первый информационный выход третей 26.8 линии задержки соединен с первым информационным входом четвертой 26.9 линии задержки, первый информационный выход которой соединен со вторым информационным входом второго блока 26.10 формирования произведения числителя параметра регуляризации и вторым информационным входом первого блока 26.11 вычисления прогноза, второй информационный выход которого соединен со вторым информационным входом третьего блока 26.12 формирования произведения числителя параметра регуляризации, третьи и четвертые информационные входы блоков 26.10, 26.12, соединены с первым информационным выходом блока 13 и входом устройства, первый информационный выход блока 26.10 соединен с четвертым и третьим информационными входами блока 26.50, первый информационный выход блока 26.12 соединен с десятым информационным входом блока 26.50 формирования суммы; первый информационный выход пятой 26.13 линии задержки соединен с первым информационным входом шестой 26.14 линии задержки, первый информационный выход которой соединен с первым информационным входом второго блока 26.15 транспонирования и первым информационным входом второго блока 26.16 формирования произведения, первый информационный выход второго 26.15 блока транспонирования соединен со вторым информационным входом блока 26.16, первый информационный выход которого соединен со вторым информационным входом второго блока формирования разности 26.17, первый информационный вход которого соединен с четвертым информационным входом блока 26.10 и первый информационный выход блока 26.17 соединен с третьим информационным входом блока 26.51 формирования суммы; первый информационный выход седьмой линии задержки 26.18 соединен с первым информационным входом восьмой линии задержки 26.19, первый информационный выход которой соединен с первым информационным входом девятой 26.20 линии задержки, первый информационный выход которой соединен со вторым информационным входом четвертого 26.21 блока формирования произведения числителя параметра регуляризации и второго блока 26.22 вычисления прогноза, первый информационный выход которого соединен с первыми информационными входами третьего блока 26.23 вычисления прогноза и 26.25 формирования произведения числителя параметра регуляризации, третьи и четвертые информационные входы блоков 26.21, 26.24 и 26.25 соединены с первым информационным выходом блока 13 и входом устройства, первый информационный выход блока 26.21 соединен с двенадцатым и одиннадцатыми информационными входами второго блока 26.50 формирования суммы, первые информационные выходы блоков 26.25, 26.24 соединены с тринадцатым и четырнадцатым информационными входами первого блока 26.50 соответственно; первый информационный выход десятой линии задержки 26.26 соединен с первым информационным входом одиннадцатой линии задержки 26.27, первый информационный выход которой соединен с первым информационным входом двенадцатой 26.28 линии задержки, первый информационный выход которой соединен с первыми информационным входом третьего блока 26.29 транспонирования матричной функции и первым информационным входом третьего блока 26.30 формирования произведения, первый информационный выход третьего блока 26.29 транспонирования соединен со вторым информационным входом третьего блока 26.30 формирования произведения, первый информационный выход которого соединен с первым информационным входом третьего блока формирования разности 26.31, первый информационный выход которого соединен с первым информационным входом блока 26.51 формирования суммы, и первый информационный вход третьего блока 26.31 соединен с четвертым информационным входом блока 26.21; первый информационный выход тринадцатой линии задержки 26.32 соединен с первым информационным входом четырнадцатой линии задержки 26.33, первый информационный выход которой соединен с первым информационным входом пятнадцатой 26.34 линии задержки, первый информационный выход которой в свою очередь соединен с первым информационным входом шестнадцатой линии задержки 26.35, выход которой соединен со вторым информационным входом седьмого блока 26.36 формирования произведения числителя параметра регуляризации и вторым информационным входом четвертого блока 26.37 вычисления прогноза, второй информационный выход которого соединен со вторым информационным входом девятого блока 26.41 формирования произведения числителя параметра регуляризации и вторым информационным входом пятого блока 26.38 вычисления прогноза, второй информационный выход последнего соединен со вторым информационным входом десятого блока 26.42 формирования произведения числителя параметра регуляризации и со вторым информационным входом шестого блока вычисления прогноза 26.39, второй информационный выход которого соединен со вторым информационным входом восьмого блока 26.40 формирования произведения числителя параметра регуляризации, третьи и четвертые информационные входы блоков 26.36, 26.40, 26.41, 26.42 соединены соответственно с первым информационным выходом блока 13 и входом устройства, первый информационный выход блока 26.36 соединен с девятым и восьмым информационными входами блока 26.50 формирования суммы, четвертый вход этого блока соединен с первым входом четвертого блока формирования разности 26.49; первый информационный выход блока 26.40 формирования произведения числителя параметра регуляризации соединен с пятым информационным входом блока 26.50, первые информационные выходы блоков 26.41 и 26.42 формирования произведения числителя параметра регуляризации соединены с первым и вторым информационными входами блока 26.50 соответственно; первый информационный выход семнадцатой линии задержки 26.43 соединен с первым информационным входом восемнадцатой линии задержки 26.44, первый информационный выход которой соединен с первым информационным входом девятнадцатой 26.45 линии задержки, первый информационный выход которой в свою очередь соединен с первым информационным входом двадцатой линии задержки 26.46, информационный выход которой соединен с первыми информационными входами четвертого блока 26.47 транспонирования и четвертого блока 26.48 формирования произведения, первый информационный выход блока 26.47 соединен со вторым информационным входом блока 26.48, первый информационный выход которого соединен со вторым информационным входом блока формирования разносности 26.49, который соединен со вторым информационным входом блока 26.51 формирования суммы; а также первый информационный вход блока 26.49 соединен с четвертым информационным входом блока 26.36; первые информационные входы второго 26.10, четвертого 26.21 и седьмого 26.36 блоков формирования произведения числителя параметра регуляризации соединены со вторым информационным выходом блока 13 формирования и выдачи априорных данных, а первые информационные входы третьего 26.12, пятого 26.24, шестого 26.25, восьмого 26.40, девятого 26.41 и десятого 26.42 блоков формирования произведения числителя параметра регуляризации соединены, соответственно, с первыми информационными выходами первого 26.21, третьего 26.23, второго 26.22, шестого 26.39, четвертого 26.37 и пятого 26.38 блоков вычисления прогноза; первые информационные входы первого 26.11, второго 26.22 и четвертого 26.37 блоков вычисления прогноза соединены со вторым информационным выходом блока 13, а первые информационные входы третьего 26.23, пятого 26.38, шестого 26.39 блоков вычисления прогноза соединены с первыми информационными выходами соответственно второго 26.22, четвертого 26.37 и пятого 26.38 блоков вычисления прогноза, третьи информационные входы блоков вычисления прогноза соединены с пятым информационным выходом блока 13. Структура и работа второго и третьего блока расчета параметра регуляризации аналогична.For the first block of the calculation of the regularization parameter (Figure 5), the information inputs of the delay lines 26.2, 26.8, 26.18, 26.32, are connected to the information output of the block 3 of the summing, (Figure 1) the first information inputs of the delay lines 26.4, 26.13, 26.26, 26.43 are connected to the first information output of the first block 26.1 formation of the matrix functions

the information input of which is connected to the information output of block 3, the information output of the first delay line 26.2 is connected to the second information input of the first regularization parameter numerator product block 26.3, its first and third information inputs are connected to the second and first information outputs of the a priori generation and output unit 13 data, respectively, and the fourth information input with the input of the device, the first information output of the first block 26.3 forming the product of the numerator of pairs the regularization meter is connected to the sixth and seventh information inputs of the second sum forming unit 26.50, the first information output of which is connected to the first information input of the ratio forming unit 26.53, the first output of the ratio forming unit 26.53 is the output of the block 26; the first information output of the second delay line 26.4 is connected to the first information input of the first transposition block 26.5 and the first information input of the first product formation block 26.6, the first information output of block 26.5 is connected to the second information input of the product formation block 26.6, the first information output of which is connected to the second information input the first block 26.7 forming the difference, the first information input of which is connected to the fourth information input of block 26.3, the first info mation output unit 26.7 is connected with the fourth informational input of the first block 26.51 formation amount, the first information output of which is connected to a first data input unit 26.52 denominator forming product of the regularization parameter and the second input unit is connected to 26.52 fifth output unit 13 for shaping and outputting a priori data; the first information output of the regularization parameter denominator product forming unit 26.52 is connected to the second input of the ratio forming unit 26.53; the first information output of the third delay line 26.8 is connected to the first information input of the fourth 26.9 delay line, the first information output of which is connected to the second information input of the second regularization parameter numerator product block 26.10 and the second information input of the first forecast calculation block 26.11, the second information output of which is connected to the second information input of the third block 26.12 forming the product of the numerator of the regularization parameter, the third and fourth information these inputs of blocks 26.10, 26.12 are connected to the first information output of block 13 and the input of the device, the first information output of block 26.10 is connected to the fourth and third information inputs of block 26.50, the first information output of block 26.12 is connected to the tenth information input of summing block 26.50; the first information output of the fifth delay line 26.13 is connected to the first information input of the sixth 26.14 delay line, the first information output of which is connected to the first information input of the second transposition block 26.15 and the first information input of the second transposition block 26.16, the first information output of the second transposition block 26.15 is connected to the second the information input of block 26.16, the first information output of which is connected to the second information input of the second difference generating unit 26 .17, the first information input of which is connected to the fourth information input of block 26.10 and the first information output of block 26.17 is connected to the third information input of summing block 26.51; the first information output of the seventh delay line 26.18 is connected to the first information input of the eighth delay line 26.19, the first information output of which is connected to the first information input of the ninth delay line 26.20, the first information output of which is connected to the second information input of the fourth regularization parameter numerator product block 26.21 and second block 26.22 calculation of the forecast, the first information output of which is connected to the first information inputs of the third block 26.23 calculation p hornoz and 26.25 forming the product of the numerator of the regularization parameter, the third and fourth information inputs of blocks 26.21, 26.24 and 26.25 are connected to the first information output of block 13 and the input of the device, the first information output of block 26.21 is connected to the twelfth and eleventh information inputs of the second sum forming block 26.50, the first information outputs of blocks 26.25, 26.24 are connected to the thirteenth and fourteenth information inputs of the first block 26.50, respectively; the first information output of the tenth delay line 26.26 is connected to the first information input of the eleventh delay line 26.27, the first information output of which is connected to the first information input of the twelfth 26.28 delay line, the first information output of which is connected to the first information input of the third matrix function transposition unit 26.29 and the first information input the third block 26.30 formation of the product, the first information output of the third block 26.29 transposition connected to the second information the input of the third block 26.30 of the formation of the product, the first information output of which is connected to the first information input of the third block of the difference 26.31, the first information output of which is connected to the first information input of the block 26.51 of the sum, and the first information input of the third block 26.31 is connected to the fourth information input of the block 26.21; the first information output of the thirteenth delay line 26.32 is connected to the first information input of the fourteenth delay line 26.33, the first information output of which is connected to the first information input of the fifteenth 26.34 delay line, the first information output of which is in turn connected to the first information input of the sixteenth delay line 26.35, the output of which connected to the second information input of the seventh block 26.36 forming the product of the numerator of the regularization parameter and the second information input of four of that forecast calculation unit 26.37, the second information output of which is connected to the second information input of the ninth regularization parameter numerator product generating unit 26.41 and the second information input of the forecast calculation unit 26.38, the second information output of the latter is connected to the second information input of the tenth regularization parameter numerator product formation block 26.42 and with the second information input of the sixth forecast calculation unit 26.39, the second information output of which is connected inen with the second information input of the eighth regularization parameter numerator product block 26.40, the third and fourth information inputs of blocks 26.36, 26.40, 26.41, 26.42 are connected respectively to the first information output of block 13 and the device input, the first information output of block 26.36 is connected to the ninth and eighth information the inputs of the sum forming block 26.50, the fourth input of this block is connected to the first input of the fourth difference forming block 26.49; the first information output of the regularization parameter numerator product generation unit 26.40 is connected to the fifth information input of the 26.50 block, the first information outputs of the regularization parameter numerator product generation blocks 26.41 and 26.42 are connected to the first and second information inputs of the 26.50 block, respectively; the first information output of the seventeenth delay line 26.43 is connected to the first information input of the eighteenth delay line 26.44, the first information output of which is connected to the first information input of the nineteenth 26.45 delay line, the first information output of which is in turn connected to the first information input of the twentieth delay line 26.46, information output which is connected to the first information inputs of the fourth transposition unit 26.47 and the fourth creation unit 26.48, the first inform the output of block 26.47 is connected to the second information input of block 26.48, the first information output of which is connected to the second information input of diversity block 26.49, which is connected to the second information input of summing block 26.51; and the first information input of block 26.49 is connected to the fourth information input of block 26.36; the first information inputs of the second 26.10, fourth 26.21 and seventh 26.36 of the generation unit numerator product of the regularization parameter are connected to the second information output of the a priori data generating and output unit 13, and the first information inputs of the third 26.12, fifth 26.24, sixth 26.25, eighth 26.40, ninth 26.41 and tenth 26.42 blocks of formation of the product of the numerator of the regularization parameter are connected, respectively, with the first information outputs of the first 26.21, third 26.23, second 26.22, sixth 26.39, fourth 26.37 and fifth 26. 38 forecast calculation blocks; the first information inputs of the first 26.11, second 26.22 and fourth 26.37 forecast calculation blocks are connected to the second information output of block 13, and the first information inputs of the third 26.23, fifth 26.38, sixth 26.39 forecast calculation blocks are connected to the first information outputs of the second 26.22, fourth 26.37 and fifth 26.38 forecast calculation blocks, the third information inputs of the forecast calculation blocks are connected to the fifth information output of the block 13. The structure and operation of the second and third blocks of the calculation of the reg parameter polarization is similar.

The first, second and fifth information outputs of the a priori data generation and generation block 13 (Figure 1) are connected respectively to the third, second and fifth information inputs of the first block 26, the second block 27 and the third regularization parameter calculation block 28, the output of which is connected to the ninth information input the fourth block 21 of the correction, and the first, second, third, fourth information outputs of the block 13 of the formation and issuance of a priori data are connected respectively to the second, third, fourth, fifth information inputs the first block 2, the second block 8, the third block 15 and the fourth correction block 21, the second information output of the first correction block 2 is connected to the eighth information input of the second correction block 8, the second information output of the second correction block 8 is connected to the eighth information input of the third correction block 15 , the second information output of the third correction unit 15 is connected to the eighth information input of the fourth correction unit 21, the output of which is connected to the first information input of the fourth block 22 of the formation su we, whose output is the output of the device, and is also connected to the information input of the seventh block 23 of the formation of the matrix function, the output of which is connected to the information input of the fourth delay line 24, the output of which is connected to the second information input of the fourth block 22 of the formation of the sum, with the seventh information input of the fourth block 21 correction and with the information input of the eighth block 25 of the formation of the matrix functions, the second information output of which is connected to the sixth information input of the fourth block 21 correction; the first information output of the eighth block 25 of the formation of the matrix functions is connected to the second information input of the fourth block 20 of the formation of the difference, the output of which is connected to the first information input of the fourth block 21 of the correction; the output of the first regularization parameter calculation unit 26 is connected to the ninth information input of the second correction unit 8, the output of which is connected to the first information input of the second summing unit 9, the output of which is connected to the fourth information input of the second regularization parameter calculation unit 27 and with the information input of the third block 10 forming a matrix function, the output of which is connected to the information input of the second delay line 11, the input of which is connected to the second information input of the second block 9 ph summing, with the seventh information input of the second correction unit 8 and with the information input of the fourth matrix function generating unit 12, the second information output of which is connected to the sixth information input of the correction unit 8; the first information output of the fourth block 12 of the formation of the matrix function is connected to the second information input of the second block 7 of the formation of the difference, the output of which is connected to the first information input of the second block 8 of the correction; the first information input of the first correction unit 2 is connected to the first information input of the first sum forming unit 3, the output of which is connected to the fourth information input of the first regularization parameter calculation unit 14 and to the information input of the first matrix function forming unit 4, the output of which is connected to the information input of the first line 5 delay, the output of which is connected to the second information input of the first block 3 of the formation of the sum, with the seventh information input of the first block 2 correction and information ion inlet of the second block 6 forming the matrix function, second information output connected with the sixth informational input of the first correction unit 2; the first information output of the second matrix function forming unit 6 is connected to the second information input of the difference forming unit 1, the output of which is connected to the first information input of the first correction unit 2; the first information input of the first difference forming unit 1, the first information input of the second difference forming unit 7, the first information input of the third difference forming unit 26 and the first information input of the fourth difference forming unit 20, as well as the first information input of the first regularization parameter calculation unit 26, the first information the input of the second regularization parameter calculation unit 27 and the first information input of the third regularization parameter calculation unit 28 are device inputs.

The first and fourth information outputs of the block 13 for generating and issuing a priori data are connected to the third and fourth information inputs of the block 2.3 for generating the work (Figure 2); the information output of the first difference generating unit 1 is connected to the first information input of the product generating unit 2.3; the second information output of the second matrix function generating unit 6 is connected to the information input of the partial derivative generating unit 2.1, the output of which is connected to the information input of the matrix function transposing unit 2.2, the output of which is connected to the second information input of block 2.3, the output of which is connected to the first information input of block 2.4 calculating accuracy characteristics, the output of which is connected to the first information input of the unit 2.5 of formation of the product, the output of which is the output of the first block 2 correction; the information output of the delay line 5 (Figure 1) is connected to the second information input of the block 2.4 for calculating the accuracy characteristics; the second and third outputs of block 13 for generating and issuing a priori data are connected to the third and fourth information inputs of block 2.4 for calculating accuracy characteristics; the output of the product formation unit 2.3 is connected to the second information input of the product formation unit 2.5 and the second information input of the sum formation unit 8.4 (Figure 3).

The information output of the second difference generating unit 7 is connected to the first information input of the product generating unit 8.3 (Figure 3). The first information output of the a priori data output generating unit 13 is connected to the third information input of the product generating unit 8.3; the output of block 26.53 is connected to the second information input of the block 8.3 forming the product; the second information output of the fourth matrix function generating unit 12 is connected to the first information input of the partial derivative generating unit 8.1, the output of which is connected to the information input of the matrix function transposition unit 8.2, the output of which is connected to the fourth information input of the 8.3 unit, the output of which is connected to the first information input of the block 8.4 the formation of the sum, the second information input of which is connected to the information output of block 2.3 (Figure 2), the output of block 8.4 of the formation of the sum is connected with the first information output of block 8.5, as well as with the second information output of block 8.6 of the formation of the work; the third and fourth information output of the a priori data output generating unit 13 is connected to the second and third information inputs of the accuracy characteristics calculating unit 8.5; the information output of the delay line 11 is connected to the fourth information input of the accuracy calculation unit 8.5, the output of which is connected to the first information input of the product formation unit 8.6, the output of which is the output of the second correction unit 8 (Figure 1).

The output of the product formation unit 2.3 (Figure 2) is connected to the information input of the partial derivative formation unit 27 (Figure 4), the output of which is connected to the information input of the product formation unit 28, the output of which is connected to the first information input of the difference formation unit 29, the output of which is connected to the information input of the matrix circulation device 30, the output of which is connected to the first information input of the product formation unit 31, the output of which is the output of the point calculation block 2.4 (Figure 2) ostnyh characteristics; the fourth output of the a priori data generating and generating unit 13 is connected to the second information input of the difference generating unit 29; the output of the product generating unit 31 is connected to the information input of the delay line 23, the output of which is connected to the third information input of the product forming unit 22, the output of which is connected to the second information input of the sum forming unit 26, the output of which is connected to the second information inputs of the product generating units 28 and 31 ; the output of the first delay line 5 (Figure 1) is connected to the information input of the partial derivative generation block 14, the output of which is connected to the information input of the matrix transpose block 21 and the first information input of the product formation block 22, the second information input of which is connected to the output of block 21; the third information output of the unit 13 for generating and issuing a priori data is connected to the information input of the matrix transpose unit 24 and the second information input of the product generating unit 25, the first information input of which is connected to the information output of the block 24; the output of block 25 is connected to the information input of the sum forming block 26.

Block 8.5 calculation of accuracy characteristics (Figure 3) has a structure and relationships similar to block 2.4.

The first and second information outputs of the a priori data generating and output unit 13 are connected to the fourth information input of the block 26.3.5 (Figure 6) and the information input of the matrix function transpose block 26.3.6, the information output of which is connected to the third information input of the 26.3.5 block, information the output of which is connected to the information input of the matrix function transposition block 26.3.7 and the second information input of the product formation block 26.3.8, the information output of which is the output of the first eye forming product of the numerator of the regularization parameter, the information output unit 26.3.7 connected to the first data input unit 26.3.8; the first information input of block 26.3.5 is connected to the information input of block 26.3.4, the second information input of block 26.3.5 is connected to the information output of matrix transposition block 26.3.3, the information input of which is connected to the information output of matrix derivative 26.3.2 functions, the information output of which, in turn, is connected to the information input of the block forming the matrix functions; the structure of all the blocks of formation of the product of the numerator of the regularization parameter is identical, they differ only by the connections between the information input of blocks 26.3.1 (connected either to the information output of the corresponding delay line or the first information output of the forecast calculation block) and block 26.3.6 (the information input of which is connected either with the second information output of block 13 for generating and issuing a priori data, or with the second information output of the forecast calculation block).

The first information input of the product formation unit 26.11.1, which is the first information input of the first forecast calculation unit (Figure 7), is connected to the information output of the delay line, the second information input of the block 26.11.1 is connected to the fifth information output of the unit 13 for generating and issuing a priori data , with the same information output is connected the first information input of the summing block 26.11.2 and the second information output of the block 26.11.5, the third information input of the block 26.11.1 is connected to the information output ohm of the block 26.11.3 forming partial derivatives of the matrix function, the second information input of which is connected to the fifth information input of the block 13 of forming and issuing a priori data, and the first information input is the information first output of the block of forming the matrix function 26.11.4, the second information output of which is connected with the first information input of the product formation block 26.11.5 and the second information input of the sum formation block 26.11.6, the information output of the block 26.11.5 is connected to the first information input Ohm block 26.11.6; the information output of block 26.11.1 is connected to the second information input of block 26.11.2, its information output is the second information output of the forecast calculation block and connected to the third information input of block 26.3.6 of the second regularization parameter numerator product formation block (Figure 6); the structure of the subsequent forecast calculation blocks is similar, they differ only in the connections between the third information input of block 26.3.5 (it is connected either with the second information input of the previous forecast block or with the fifth information output of block 13 for generating and issuing a priori data) and the first information input of block 26.3. 1 (it is connected either to the information output of the delay line, or the first information output of the previous forecast block).

с выхода блока 3 формирования суммы поступает на вход блока 26 вычисления параметра регуляризации и вход блока 4 формирования матричной функции, на остальные входы блока 26 поступают значения y, G, W^-1, с выхода блока 4 формирования матричной функции значение

поступает на вход линии задержки 5, с выхода которой значение

поступает на вход блока 3 формирования суммы, вход блока 2 коррекции и вход блока 6 формирования матричной функции

, значение которой с выхода блока 6 поступает на вход блока 2 и на вход блока 1, на выходе блока 1 формируется значение

невязки измерения, которое поступает на вход блока 2 коррекции, на остальные входы которого поступают значения α₀, G, W^-1, I; в блоке 2 формируется произведение матричного коэффициента усиления и невязки измерения, которое суммируется в блоке 3 со значением

; на выходе блока 26, начиная с четвертого момента времени, формируется значение α₁ параметра регуляризации (до этого имеем α₁=0.5), которое поступает на вход второго блока 8 коррекции, на остальные входы блока 26 поступают значения α₀, G, W^-1, I; с одного из выходов блока 2 коррекции значение M₀(k+1/k) поступает на вход блока 8 коррекции, в котором формируется значениеThe device operates as follows (Figure 1). In the initial state, in the block 13 for generating and outputting a priori data, the values of the matrices W ^-1 , G, I are recorded, as well as the values α ₀ , Δt are the values of the sampling step. The value of the evaluation of the information process at the (k + 1) th time

from the output of block 3 forming the sum goes to the input of block 26 calculating the regularization parameter and the input of block 4 forming the matrix function, the remaining inputs of block 26 receive the values y, G, W ^-1 , from the output of block 4 forming the matrix function

arrives at the input of the delay line 5, from the output of which the value

arrives at the input of the sum forming block 3, the input of the correction block 2 and the input of the matrix function forming block 6

, the value of which from the output of block 6 goes to the input of block 2 and to the input of block 1, at the output of block 1, a value is formed

the residuals of the measurement, which is fed to the input of the correction unit 2, to the remaining inputs of which the values α ₀ , G, W ^-1 , I are received; in block 2, the product of the matrix gain and the residual of the measurement is formed, which is summed in block 3 with the value

; at the output of block 26, starting from the fourth point in time, the value α _{1 of} the regularization parameter is formed (before that we have α ₁ = 0.5), which is fed to the input of the second correction block 8, the values of α ₀ , G, W ^are received at the other inputs of block 26 ¹ , I; from one of the outputs of the correction unit 2, the value of M ₀ (k + 1 / k) is fed to the input of the correction unit 8, in which the value is generated

на выходе блока 9 поступает на вход блока 27 вычисления параметра регуляризации и вход блока 10 формирования матричной функции, с выхода блока 10 значение

поступает на вход линии задержки 11, на выходе которой формируется значение

, которое суммируется со значением (27) в блоке 9, на выходе которого формируется значение

с выхода блока 11 значение

поступает на вход блока 8 коррекции, на вход блока 9 и на вход блока 12 формирования матричной функции, на выходе которого формируется значение

, которое подается на вход блока 8 и вход блока 7, на другой вход которого поступает входное колебание; невязка измерения

с выхода блока 7 поступает на вход блока 8, на остальные входы которого поступают значения α₁, G, W^-1, I; с одного из выходов блока 8 коррекции значение M₁(k+1/k) поступает на вход блока 15 коррекции, в котором формируется значениеwhich is input to the block 9 of the formation of the amount; value

at the output of block 9, it enters the input of block 27 for calculating the regularization parameter and the input of block 10 for generating the matrix function; from the output of block 10, the value

arrives at the input of the delay line 11, at the output of which a value is formed

, which is added to the value (27) in block 9, at the output of which a value is generated

output block 11 value

goes to the input of correction block 8, to the input of block 9 and to the input of block 12 of forming a matrix function, at the output of which a value is formed

which is fed to the input of block 8 and the input of block 7, to the other input of which an input oscillation is received; residual measurement

from the output of block 7 goes to the input of block 8, the remaining inputs of which receive the values α ₁ , G, W ^-1 , I; from one of the outputs of the correction unit 8, the value of M ₁ (k + 1 / k) is fed to the input of the correction unit 15, in which the value is generated

на выходе блока 16 поступает на вход блока 17 формирования матричной функции, с выхода блока 17 значение

) поступает на вход линии задержки 18, на выходе которой формируется значение

, которое суммируется со значением (28) в блоке 16, на выходе которого формируется значение

; с выхода блока 18 значение

поступает на вход блока 15 коррекции, на вход блока 16 и на вход блока 19 формирования матричной функции, на выходе которого формируется значение

, которое подается на вход блока 15 и вход блока 14, на другой вход которого поступает входное колебание; невязка измерения

с выхода блока 14 поступает на вход блока 15, на остальные входы которого поступают значения α₂, G, W^-1, I, с одного из выходов блока 15 коррекции значение M₂(k+1/k) поступает на вход блока 21 коррекции, в котором формируется значениеwhich is fed to the input of the block 16 forming the amount; value

at the output of block 16 enters the input of block 17 of the formation of the matrix function, from the output of block 17, the value

) enters the input of the delay line 18, at the output of which a value is formed

, which is added to the value (28) in block 16, at the output of which a value is generated

; block output 18 value

arrives at the input of block 15 of correction, at the input of block 16 and at the input of block 19 of the formation of the matrix function, at the output of which a value is generated

which is fed to the input of block 15 and the input of block 14, to the other input of which an input oscillation is received; residual measurement

from the output of block 14 goes to the input of block 15, to the other inputs of which the values α ₂ , G, W ^-1 , I are received, from one of the outputs of the correction block 15 the value M ₂ (k + 1 / k) goes to the input of the correction block 21 in which the value is formed

на выходе блока 22 поступает на вход блока 23 формирования матричной функции, с выхода блока 23 значение

поступает на вход линии задержки 24, на выходе которой формируется значение

, которое суммируется со значением (29) в блоке 22, на выходе которого формируется значение

; с выхода блока 24 значение

поступает на вход блока 21 коррекции, на вход блока 22 и на вход блока 25 формирования матричной функции, на выходе которого формируется значение

которое подается на вход блока 21 и вход блока 20, на другой вход которого поступает входное колебание; невязка измерения

с выхода блока 20 поступает на вход блока 21, на остальные входы которого поступают значения α₂, G, W^-1, I.which is input to the block 22 of the formation of the amount; value

at the output of block 22 goes to the input of block 23 of the formation of the matrix function, from the output of block 23, the value

arrives at the input of the delay line 24, at the output of which a value is formed

, which is added to the value (29) in block 22, at the output of which a value is generated

; block output 24 value

arrives at the input of the correction block 21, at the input of the block 22 and at the input of the block 25 of forming the matrix function, at the output of which a value is formed

which is fed to the input of block 21 and the input of block 20, to the other input of which an input oscillation is received; residual measurement

from the output of block 20 goes to the input of block 21, to the remaining inputs of which the values α ₂ , G, W ^-1 , I.

поступают на вход блока 2.1 формирования частных производных, с выхода которого значения

поступают на вход блока транспонирования матричной функции 2.2, с выхода которого значения

невязка измерения

и значения W^-1, α₀ поступают на входы блока 2.3 формирования произведения, с выхода которого значение M₀(k+1/k) поступает на вход блока 2.4 расчета точностных характеристик, на другие входы которого поступают значения G, I,

и на выходе которого формируется значение P₁(k+1), которое поступает на вход блока 2.5 формирования произведения, на другой вход которого поступает значение M₀(k+1/k) с выхода блока 2.3. Выход блока 2.5 является выходом блока 2 коррекции.The first block 2 correction works as follows (figure 2). Values of the matrix function

enter the input of block 2.1 of the formation of partial derivatives, from the output of which the values

arrive at the input of the transpose block of the matrix function 2.2, from the output of which the values

residual measurement

and the values W ^-1 , α ₀ are fed to the inputs of the block 2.3 of the formation of the product, from the output of which the value M ₀ (k + 1 / k) is fed to the input of the block 2.4 for calculating the accuracy characteristics, the other inputs of which receive the values G, I,

and at the output of which a value of P ₁ (k + 1) is generated, which is fed to the input of block 2.5 of the formation of the product, the other input of which receives the value M ₀ (k + 1 / k) from the output of block 2.3. The output of block 2.5 is the output of correction block 2.

поступает на вход блока 8.1 формирования частных производных, с выхода которого значения

поступают на вход блока транспонирования матричной функции 8.2, с выхода которого значения

, а также значение невязки измерения

, α₁, W^-1 поступают на вход блока 8.3 формирования произведения, с выхода которого значение

поступает на вход блока 8.4 суммирования, на другой вход которого поступает значение М₀(k+1/k); значениеThe second block 8 correction works as follows (figure 3). The value of the matrix function

enters the input of block 8.1 of the formation of partial derivatives, the output of which values

arrive at the input of the transpose block of the matrix function 8.2, from the output of which the values

, as well as the value of the measurement residual

, α ₁ , W ^-1 enter the input of block 8.3 of the formation of the product, the output of which value

arrives at the input of summation block 8.4, the other input of which receives the value M ₀ (k + 1 / k); value

, а на выходе формируется значение P₁(k+1), которое умножается на (28) в блоке 8.6 формирования произведения; выход блока 8.6 является выходом блока 8 коррекции.from the output of block 8.4, it enters the input of block 8.5 for calculating the accuracy characteristics, the other inputs of which receive the values G, W ^-1 ,

, and the output generates the value of P ₁ (k + 1), which is multiplied by (28) in block 8.6 of the formation of the product; the output of block 8.6 is the output of block 8 of correction.

поступает на вход блока 20 формирования частных производных, с выхода которого значение

поступает на вход блока 21 транспонирования матричной функции и на вход блока 22 формирования произведения, на вход которого также поступает значение

с выхода блока 21 и значение P₀(k) с выхода линии задержки 23, на вход которой с выхода блока 31 формирования произведения, являющегося выходом блока 2.4, поступает значение P₀(k+1); значение

с выхода блока 22 поступает на вход блока 26 формирования суммы, на другой вход которого поступает значение GG^T, сформированное в блоке 25 формирования произведения, на вход которого поступает значение G и значение G^T сформированное в блоке 24 транспонирования матриц, на вход которого также поступает значение G; значение матричной функции M₀(k+1/k) поступает на вход блока 27 формирования частных производных, с выхода которого значение

поступает на вход блока 28, на другой вход которого поступает значение P₀(k+1/k), сформированное на выходе блока 26; значение

поступает на вход блока 29 формирования разности, на другой вход которого поступает значение I; с выхода блока 29 значение

поступает на вход устройства 30 обращения матриц, выход которого соединен с входом блока 31 формирования произведения, на другой вход которого поступает значение Р₀(k+1/k) с выхода блока 26. Блок расчета точностных характеристик 8.5 второго блока коррекции работает аналогичным образом. На выходе блока 8.5 формируется значение P₁(k+1).The first block 2.4 calculation of the accuracy characteristics works as follows (Figure 4). The value of the matrix function

enters the input of the block 20 of the formation of partial derivatives, the output of which the value

arrives at the input of the transpose unit 21 of the matrix function and the input of the unit 22 of the formation of the product, the input of which also receives the value

from the output of block 21 and the value of P ₀ (k) from the output of the delay line 23, to the input of which from the output of block 31 of the formation of the work, which is the output of block 2.4, the value P ₀ (k + 1) is received; value

from the output of block 22, it passes to the input of the sum formation block 26, to the other input of which the GG ^T value generated in the product generation block 25 receives the G value and the G ^T value generated in the matrix transpose block 24, which also receives the input the value of G; the value of the matrix function M ₀ (k + 1 / k) is input to the block 27 of the formation of partial derivatives, from the output of which the value

enters the input of block 28, the other input of which receives the value P ₀ (k + 1 / k) formed at the output of block 26; value

arrives at the input of the difference forming unit 29, the other input of which receives the value I; block output 29 value

arrives at the input of the matrix reversal device 30, the output of which is connected to the input of the product forming unit 31, the other input of which receives the value P ₀ (k + 1 / k) from the output of block 26. The accuracy characteristics calculating unit 8.5 of the second correction block works in a similar way. At the output of block 8.5, the value P ₁ (k + 1) is generated.

- значение оценки информационного процесса, где k - текущий момент времени, которое, соответственно, передается на линии задержки 26.2, 26.8, 26.18, 26.32 (рисунок 5) и блок формирования матричной функции

, с выхода которого значение

поступает на вход 26.4, 26.13, 26.26 и 26.43 линий задержки; в следующей итерации фильтра на эти же блоки поступает текущее значение оценки информационного процесса, с выходов линий задержки 26.2, 26.8, 26.18, 26.32 и 26.4, 26.13, 26.26, 26.43 на линии задержки 26.9, 26.19, 26.33 и 26.14, 26.27, 26.44 поступают соответственно k-1 значение оценки и матричной функции

, эти же значения оценок и матричной функции поступают на входы блоков 26.3 формирования произведения числителя коэффициента регуляризации и блоков 26.5 транспонирования матричной функции, 26.6 формирования произведения; далее на входы линий задержки 26.2, 26.8, 26.18, 26.32 опять поступает текущее значение оценки информационного процесса, с этих линий задержки k-1 значение оценки поступает на 26.9, 26.19, 26.33 линий задержки, с выхода которых k-2 значение оценки информационного процесса поступает дальше на вход блока 26.10 и линий задержки 26.20, 26.34; аналогично и для и 26.4, 26.13, 26.26, 26.43, а также 26.14, 26.27, 26.44 линий задержки, только для матричной функции Н; в результате на n+5 и последующих итерациях будем иметь на выходах линий задержки 26.2, 26.9, 26.20, 26.35 значения k-1, k-2, k-3, k-4 оценок информационного процесса, соответственно, и на выходах 26.4, 26.14, 26.28, 26.46 линий задержки значения матричной функции для тех же оценок. Эти значения оценок информационного процесса поступают на блоки 26.3, 26.10, 26.21, 26.36 формирования произведения числителя коэффициента регуляризации и 26.11, 26.22, 26.37 формирования прогноза; в блоки 26.3, 26.10, 26.21, 26.36 поступают из 13 блока G, W^-1 и у со входа устройства, с выхода этих блоков значенияThe unit for calculating the regularization parameter works as follows. In the initial state, the input of the calculation unit of the regularization parameter receives

- the value of the evaluation of the information process, where k is the current point in time, which, respectively, is transmitted to the delay line 26.2, 26.8, 26.18, 26.32 (Figure 5) and the matrix function generating unit

whose output value

arrives at the input 26.4, 26.13, 26.26 and 26.43 delay lines; in the next iteration of the filter, the current value of the information process assessment is received for these blocks, from the outputs of the delay lines 26.2, 26.8, 26.18, 26.32 and 26.4, 26.13, 26.26, 26.43 and the delay lines 26.9, 26.19, 26.33 and 26.14, 26.27, 26.44, respectively k-1 value of the estimate and matrix function

, the same values of the estimates and the matrix function arrive at the inputs of the blocks 26.3 of the formation of the product of the numerator of the regularization coefficient and the blocks 26.5 of transposition of the matrix function, 26.6 of the formation of the product; further, the inputs of the delay lines 26.2, 26.8, 26.18, 26.32 again receive the current value of the evaluation of the information process, from these delay lines k-1 the evaluation value is sent to 26.9, 26.19, 26.33 delay lines, from the output of which the k-2 value of the evaluation of the information process further to the input of block 26.10 and delay lines 26.20, 26.34; similarly for and 26.4, 26.13, 26.26, 26.43, as well as 26.14, 26.27, 26.44 delay lines, only for the matrix function H; as a result, at n + 5 and subsequent iterations, we will have at the outputs of the delay lines 26.2, 26.9, 26.20, 26.35 the values of k-1, k-2, k-3, k-4 estimates of the information process, respectively, and at the outputs 26.4, 26.14 , 26.28, 26.46 delay lines of the value of the matrix function for the same estimates. These values of the estimates of the information process go to blocks 26.3, 26.10, 26.21, 26.36 of the formation of the product of the numerator of the regularization coefficient and 26.11, 26.22, 26.37 of the formation of the forecast; in blocks 26.3, 26.10, 26.21, 26.36 come from block 13 G, W ^-1 and at the input of the device, from the output of these blocks values

для j=k, поступают на вход блока 26.50 формирования суммы; с выхода 26.11 блока на 26.12 блок поступает значение прогноза для k -1 момента времени, в блок 26.12 поступают значения G, W^-1, y, с выхода 26.12 блока на вход 26.50 блока поступает выражение, аналогичное (29), с 26.22 блока в 26.25 блок и 26.23 блок поступает значение прогноза для k-2 момента времени, в блок 26.25 передаются значения G, W^-1, у, с 26.25 блока на вход 26.50 блока поступает выражение, аналогичное (29), с выхода блока 26.23 поступает значение прогноза для k-1 момента времени, в блок 26.24 поступают значения G, W^-1, y, с выхода 26.24 блока на 26.50 блок поступает выражение, аналогичное (29), на входах 26.37, 26.38, 26.39 блоков имеем

с выходов этих блоков имеем значения для k-3, k-2, k-1 момента времени, которые поступают на блоки 26.41, 26.42, 26.40, соответственно, кроме того, блок 26.39 использует результаты работы 26.38 блока, а 26.38 блок 26.37 блока и, наконец, в 26.37 блок передаются начальные значения, на входы блоков 26.40,26.41, 26.42 поступают значения G, W^-1, y, с выхода блоков 26.40, 26.41, 26.42 в блок 26.50 поступают выражения, аналогичные (29); с линий задержки 26.4, 26.14, 14.28, 26.46 на вход блоков 26.5, 26.15, 26.29, 26.47 транспонирования матричной функции и 26.6, 26.16, 26.30, 26.48 формирования произведения передается

, после чего с выхода блоков 26.6, 26.16, 26.30, 26.48 на вход блоков формирования разности 26.7, 26.17, 26.31, 26.49 поступает выражение

на выходе которых формируется невязка измерений

поступающая на 26.51 блок формирования сумм; с блока 26.50 в блок 26.53 формирования отношения передается значение

, на первый вход 26.52 формирования произведения знаменателя параметра регуляризации с блока 26.51 поступает выражениеfor

for j = k, they enter the input of block 26.50 of the formation of the sum; from the block output 26.11 to the 26.12 block, the forecast value for k -1 time instant arrives, the values G, W ^-1 , y are sent to the block 26.12, the expression similar to (29) is received from the block output 26.12 to the block 26.50, from block 26.22 to 26.25 block and 26.23 block the forecast value for the k-2 moment of time arrives, values G, W ^-1 , y are transferred to block 26.25, from 26.25 of the block an expression similar to (29) is received at the block 26.50 input, the forecast value comes from the output of block 26.23 for k-1 moment of time, values G, W ^-1 , y are received in block 26.24, from the output of block 26.24 at 26.50 the block receives an expression similar to (2 9), at the inputs 26.37, 26.38, 26.39 blocks we have

from the outputs of these blocks, we have values for the k-3, k-2, k-1 points in time that arrive at blocks 26.41, 26.42, 26.40, respectively, in addition, block 26.39 uses the results of operation 26.38 of the block, and 26.38 uses block 26.37 of the block and finally, at 26.37 the block initial values are transmitted, the inputs of blocks 26.40,26.41, 26.42 receive the values G, W ^-1 , y, from the output of blocks 26.40, 26.41, 26.42, expressions similar to (29) are sent to block 26.50; from the delay lines 26.4, 26.14, 14.28, 26.46 to the input of the blocks 26.5, 26.15, 26.29, 26.47 of the transposition of the matrix function and 26.6, 26.16, 26.30, 26.48 of the formation of the product is transmitted

then after the output of blocks 26.6, 26.16, 26.30, 26.48 to the input of the blocks of the formation of the difference 26.7, 26.17, 26.31, 26.49 the expression

at the output of which a discrepancy of measurements is formed

arriving at 26.51 summing unit; from block 26.50 to block 26.53 formation of the relationship is transmitted value

, the first input 26.52 of the formation of the product of the denominator of the regularization parameter from block 26.51 receives the expression

and the second input of block 26.52 receives the value Δt from the fifth information output of block 13 for generating and issuing a priori data (Figure 1); at the output of block 26.52, we obtain the expression

From the first output of block 26.52 of the formation of the product of the denominator of the regularization parameter, the expression

At the output of block 26.53, forming the ratio, we obtain the value of the regularization coefficient α _{n + 1} .

, с выхода блока 26.3.1 на вход блоков 26.3.2 формирования частных производных матричной функции и блока 26.3.4 поступает значение

, далее с выхода блока 26.3.2 значения поступают на вход блока 26.3.3 транспонирования матричной функции, откуда на вход блока 26.3.5 формирования произведения поступает

на другие входы поступают значения G^T, W^-1 и значение

с выхода блока 26.3.4, на один из входов которого поступает у, значение G^T поступает на вход блока 26.3.5 с выхода блока 26.3.6 транспонирования матричной функции, на вход которого соответственно с выхода 13 блока поступает значение G; с выхода блока 26.3.5 имеем значение

которое поступает соответственно на вход блоков 26.3.7 транспонирования матричной функции и 26.3.8 формирования произведения, в результате на выходе устройства будем иметь значенияThe first block of formation of the product of the numerator of the regularization parameter 26.3 (Figure 6) works as follows. At the input of the block 26.3.1 formation of the matrix function receives the value of the evaluation of the information process

, from the output of block 26.3.1 to the input of blocks 26.3.2 of the formation of partial derivatives of the matrix function and block 26.3.4, the value

, then, from the output of block 26.3.2, the values go to the input of the transposition matrix block 26.3.3 of the matrix function, whence the input of the block 26.3.5 of the formation of the product

the other inputs receive the values of G ^T , W ^-1 and the value

from the output of block 26.3.4, at one of the inputs of which y arrives, the value of G ^T goes to the input of block 26.3.5 from the output of block transposition 26.3.6 of the matrix function, the input of which, respectively, from the output 13 of the block receives the value G; from the output of block 26.3.5 we have the value

which is supplied respectively to the input of the matrix function transposition blocks 26.3.7 and the product formation 26.3.8, as a result, we will have the values at the output of the device

, с выхода блока 26.11.4 значение

поступает на другой вход блока 26.11.3 и блоков 26.11.5 формирования произведения, 26.11.6 формирования суммы, с выхода блока 26.11.3 значение

поступает на вход блока 26.11.1 формирования произведения, на другие входы которого поступают значения G_n(k) и Δt, с выхода этого блока на вход блока 26.11.2 формирования суммы передается значение

на другой вход блока 26.11.2 поступает значение G_n(k), в результате на выходе 26.11.2 блока, выход которого является первым выходом блока вычисления прогноза, имеем прогноз G_n(j),j=k+1; на второй вход блока 26.11.5 поступает значение Δt, с выхода которого значение

поступает на второй вход блока 26.11.6, выход которого является вторым выходом блока вычисления прогноза, с выхода которого имеем х_ηn(j). Остальные блоки вычисления прогноза работают аналогично.The first forecast calculation unit works as follows. At the input of blocks 26.11.4 of the formation of the matrix function and 26.11.3 of the formation of partial derivatives, the value of the evaluation of the information process

, from the block output 26.11.4 value

arrives at another input of block 26.11.3 and blocks 26.11.5 of the formation of the product, 26.11.6 of the formation of the sum, from the output of block 26.11.3 the value

arrives at the input of the product formation block 26.11.1, the other inputs of which receive the values of G _n (k) and Δt, from the output of this block, the value is transmitted to the input of the sum formation block 26.11.2

to another input of the block 26.11.2 the value G _n (k) is received, as a result, on the output 26.11.2 of the block, the output of which is the first output of the forecast calculation block, we have the forecast G _n (j), j = k + 1; the second input of block 26.11.5 receives the value Δt, from the output of which the value

arrives at the second input of block 26.11.6, the output of which is the second output of the forecast calculation block, from the output of which we have x _ηn (j). The remaining forecast calculation blocks work similarly.

Information sources

1. A.A. Vengerov, V.A. Shcharensky. Applied questions of optimal linear filtration. - M .: Energoizdat, 1982. - 96 p.

2. A. Farina, F. Studer. Digital processing of radar information. Tracking goals. - M .: Radio and communications, 1993. - 118 p.

3. Patent No. 2362255. Russia. 2009. Digital Intelligent Recursive Filter. // Kostoglotov A.A., Kuznetsov A.A., Ponomarev A.S., Lazarenko S.V.

4. Kostoglotov A.A. The synthesis of intelligent measuring procedures based on the principle of regularization A.N. Tikhonov // Measuring equipment, No. 1, 2001. S.8-12.

5. Kostoglotov A.A. The method of successive approximations in the theory of filtration // Automation and Computer Engineering, No. 3, 2000. P.53-63.

6. Kostoglotov A.A., Kuznetsov A.A. Synthesis of an intelligent measuring procedure based on the method of minimal errors // Measuring technique, No. 7, 2005. P.8-13.

7. Tikhonov A.N., Arsenin V.Ya. Methods for solving incorrect tasks. - M .: Nauka, 1986 .-- 288 p.

8. Vasiliev F.P. Methods for solving extreme problems. - M .: Nauka, 1981. - 106 p.

9. Kostoglotov A.A. Digital intelligent measuring procedure // Measuring technique, No. 7, 2002. S.16-21.

10. Detistov V.A., Taran V.N. Synthesis of optimal control by the gradient method based on the predictive model // A and T. - 1990. - No. 10. - S. 46-56.

Claims (1)

The digital intelligent multistage filter contains the blocks: the first, second, third, fourth blocks of the formation of the difference; first, second, third, fourth correction blocks; a block for generating and issuing a priori data; the first, second, third, fourth blocks of the formation of the amount; the first, second, third, fourth, fifth, sixth, seventh and eighth blocks of the formation of matrix functions; first, second, third and fourth delay lines; the first, second and third unit for calculating the regularization parameter, while the first, second, third and fourth outputs of the unit for generating and issuing a priori data are connected respectively to the second, third, fourth and fifth information inputs of the first, second, third and fourth correction units, in addition , the first, second, fifth outputs of the block for generating and issuing a priori data are connected respectively to the third, second, and fifth information inputs of the first, second, and third blocks for calculating the regularization parameter, the first information the output of the first correction unit is connected to the first information input of the first sum forming unit, the output of which is connected to the information input of the first matrix function generating unit and the fourth information input of the first regularization parameter calculation unit, the first information input of which is the device input, the output of the first regularization parameter calculation unit connected to the ninth information input of the second correction unit, the output of the first matrix function forming unit is connected to and the formation input of the first delay line, the output of which is connected to the second information input of the first summing block, with the seventh information input of the first correction block and with the information input of the second matrix function forming block, the second information output of which is connected to the sixth information input of the first correction block, the first information the output of the second matrix function forming unit is connected to the second information input of the difference forming unit, the output of which is connected to your information input of the first correction block; the second information output of the first correction unit is connected to the eighth information input of the second correction unit, the first information output of which is connected to the first information input of the second summing unit, the output of which is connected to the information input of the third matrix function forming unit and with the fourth information input of the second regularization parameter calculation unit the output of which is connected to the ninth information input of the third correction unit, the output of the third block of matrix f The function is connected to the information input of the second delay line, the output of which is connected to the second information input of the second summing unit, the seventh information input of the second correction unit and the information input of the fourth matrix function forming unit, the second information output of which is connected to the sixth information input of the second correction unit, the first information output of the fourth matrix function generating unit is connected to the second information input of the second separation forming unit and whose output is connected to a first data input of the second correction unit; the second information output of the second correction unit is connected to the eighth information input of the third correction unit, the first information output of which is connected to the first information input of the third summing unit, the output of which is connected to the information input of the fifth matrix function forming unit, the output of which is connected to the information input of the third delay line the output of which is connected to the second information input of the third block of the formation of the sum, the seventh information input of the third block of cor and with the information input of the sixth matrix function generating unit, the second information output of which is connected to the sixth information input of the third correction unit, the first information output of the sixth matrix function forming unit is connected to the second information input of the third difference forming unit, the output of which is connected to the first information input of the third correction block; the second information output of the third correction unit is connected to the eighth information input of the fourth correction unit, the first information output of which is connected to the first information input of the fourth summing unit, the output of which is the output of the device and connected to the information input of the seventh matrix function forming unit, the output of which is connected to the information the input of the fourth delay line, the output of which is connected to the second information input of the fourth block of the formation of the sum, seventh the information input of the fourth correction unit and with the information input of the eighth matrix function forming unit, the second information output of which is connected to the sixth information input of the fourth correction unit, the first information output of the eighth matrix function forming unit is connected to the second information input of the fourth difference forming unit, the output of which is connected to the first information input of the fourth correction block, into the device, into the structure of the block for calculating the regularization parameter The first, second, third, and fourth difference generating blocks and the regularization parameter denominator product generating unit that define new connections, the first information input of the first difference forming unit is connected to the fourth information input of the first regularization parameter numerator product generating unit, and the second information input of the first a difference generating unit is connected to a first information output of a first product generating unit; the first information output of the first difference generating unit is connected to the fourth information input of the first sum forming unit; the first information input of the second difference forming unit is connected to the fourth information input of the first regularization parameter numerator product generating unit, and the second information input of the second difference forming unit is connected to the first information output of the second product forming unit; the first information output of the second difference forming unit is connected to the third information input of the first sum forming unit; the first information input of the third difference generating unit is connected to the fourth information input of the fourth regularization parameter numerator product generating unit, and the second information input of the third difference forming unit is connected to the first information output of the third product generating unit; the first information output of the third difference forming unit is connected to the first information input of the first sum forming unit; the first information input of the fourth difference forming unit is connected to the fourth information input of the seventh regularization parameter numerator product generating unit, and the second information input of the fourth difference forming unit is connected to the first information output of the fourth product forming unit; the first information output of the fourth difference generating unit is connected to the second information input of the first sum forming unit; the first information input of the product formation unit of the regularization parameter denominator product is connected to the first information output of the first sum formation unit, and the second information input is connected to the fifth information output of the unit for generating and issuing a priori data; the first information output of the formation unit of the product of the denominator of the regularization parameter is connected to the second information input of the relationship formation unit.

Images