RU2357357C2 - Digital intellectual recursive filter - Google Patents

Abstract

FIELD: information technology.

SUBSTANCE: present invention relates to digital computer technology and can be used in systems for digital processing radio signals for optimum non-linear filtration. The device has blocks for generating matrix functions (4, 6, 10, 12), corrector units (2, 8), differential generating units (1, 7), summing units (3, 9), delay line (5, 11), unit for generating and output of priori data (13). The device also has a unit for calculating regularisation parametre (14), which is linked to the rest of the units.

EFFECT: more accurate evaluation of the information process in measuring systems.

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Description

The invention relates to digital computing and can be used in digital processing systems of radio signals to solve problems of optimal non-linear filtering.

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

The closest in technical essence to the claimed invention is a digital iterative filter [3], containing the first and second blocks of the formation of the sum, the first, second, third and fourth blocks of the formation of matrix functions, the first and second blocks of the formation of the difference, the first and second delay lines, the first and the second correction blocks, a block for generating and outputting a priori data. The disadvantage of this device is the low accuracy of the generated estimates of the information process.

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

The claimed invention is aimed at improving accuracy in the formation of an assessment of the information process in measuring systems, which is very important for radar tracking of targets. The proposed device contains the first, second blocks of the formation of the difference, the first, second blocks of correction, the block of formation and output of a priori data, the first and second blocks of the formation of the sum, the first, second, third and fourth blocks of the formation of matrix functions, the first and second delay lines, the first block calculation of the regularization parameter, while the first, second and third outputs of the block for generating and issuing a priori data are connected respectively to the second, third, fourth information inputs of the first and second correction blocks and, and the fourth output of the a priori data generating and issuing unit is connected to the fifth information input of the first correction unit, in addition, the first, second, fifth outputs of the a priori data generating and issuing unit are connected to the third, second, and fifth information inputs of the regularization parameter calculation unit, the first information 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 forming unit function and the fourth information input of the first regularization parameter calculation unit, the output of which is connected to the fifth information input of the second correction unit, the output of the first matrix function generation 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 summing unit, with the seventh information input of the first correction unit and with the information input of the second block of the matrix function formation, the second information output of which of the connections with the sixth informational input of the first correction unit, the first information output of the second forming unit matrix function is connected to a second data input of the difference forming unit whose output 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 ninth information input of the second correction unit, the output of which is connected to the first information input of the second summing unit, the output of which is the output of the device and connected to the information input of the third matrix function forming unit, the output of which is connected to the information input of the second a 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 unit correction and with 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 forming unit is connected to the second information input of the second difference forming unit, the output of which is connected to the first information input of the second block correction.

One of the ways to improve the accuracy of filters for estimating the parameters of dynamic systems is to use methods for solving incorrect problems based on the principles of regularization. The effectiveness of the use of regularization for continuous systems has been proved for the case of A. N. Tikhonov’s method [4], and its variations in the form of an iterative regularization method [5]. We show how to obtain filtration equations using the iterative regularization method for a discrete system [6].

Let the dynamics of the measured 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;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;

имеет обратную связь. G ∈Е ^М × Е ^М - matrix of intensity of external influences; k, N, M are natural numbers. It is assumed that the matrix

has feedback.

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

W is the covariance matrix of dimension L × L, δ (·) is the vector delta function;

- сигнальная вектор-функция, непрерывна вместе с частными производными; L, l - натуральные числа.

- 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

Since the vector function F (·) is continuous, 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

Problem (1), (2), (4) is an incorrectly posed inverse problem [7].

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.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 α ₀ = 1,

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. Therefore, the issue of calculating the regularization parameters is topical.

, 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). Taken as a zero approximation

, 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 домножим 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 value 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. 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 that reflects 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 the 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

Changing the value of N by N + 1 gives an increment of Δ s , then

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

or, given (13), we obtain

Where

According to (12), the expressions for Δ x _n and Δ s 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

where x * _n (N) is the 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

Expanding β and γ in a Taylor series in a neighborhood ( x * _n (N), 0, N) and neglecting terms of order higher than the first, 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 DDTKZ (12) for the case when k = N, while taking into account that all DDTKZ for i = 0, ..., n-1 are allowed and, accordingly, the estimates x _i are known functions of the parameter k. Thus, we have

Then equation (20) is transformed as follows

Then we write equation (22) in the form

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 отличии от фильтра [3] параметр регуляризации согласован по принципу невязки, что позволяет получить оптимальную по порядку и более точную процедуру. Следует отметить, что полученный результат предполагает, что исходная система, параметры которой подлежат оценке, нелинейна. 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 recursive filter, which allows the digital processing of measurement information for discrete dynamic systems. If we compare the obtained equations with the equations of the digital iterative filter [3], it becomes clear that they are different from each other due to the relationship between the regularization parameter and the correction unit, as well as additional relationships of the sequence of parameters α _i that change the overall coupling coefficient in the equation for assessments

with ratings

signal vector function H and matrices G , W. That is, in the filter (24), unlike the filter [3], the regularization parameter is matched according to the principle of residual, which allows one to obtain an optimal order and more accurate procedure. It should be noted that the result assumes that the original system, the parameters of which are to be evaluated, is non-linear. 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 are taken not [0, t], but [t-3s, t], where t is the current time, s is the calculation step; for discrete time it is necessary to take [N-1, N-4]. Studies have shown [6] that using the data more than three steps back does not provide an increase in the accuracy of the estimates obtained, but only increase the number of necessary arithmetic operations.

It should be noted that for the implementation of 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. 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. An analysis of the computational costs required to implement the developed evaluation algorithm allows us to conclude that it can be implemented in real time in modern PICs.

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

The graphs of the estimates of the parameter d = 0.2 for i = 0, l are shown in Fig. 1 at τ = 0.3 for the total interval T = 5. It can be seen that the estimate of an intelligent recursive filter exceeds the estimate of an iterative filter in accuracy. Numerical modeling showed that the accuracy of determining the parameter d using a digital intelligent recursive filter is 10.2% higher compared to a digital iterative filter.

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 claimed device can be used in information systems related to the collection and processing of information, for example, in information systems of radar and radio navigation systems.

The essence of the invention is illustrated in Fig.2-8, which shows the structural diagrams of an intelligent recursive digital filter, the first and second correction blocks, the block for calculating the accuracy characteristics, the block for calculating the regularization parameter, the first block for generating the product of the numerator of the regularization parameter, and the forecast calculation block.

Figure 2 presents the structural diagram of a digital intelligent recursive filter. The device comprises a first block 1 and a second difference forming block 7, a first block 2 and a second correction block 8, a first block 3, a second sum forming block 9, a first delay line 5 and a second delay line 11, a first block 4, a second block 6, and a third block 10 and the fourth block 12 of the formation of matrix functions, block 13 of the formation and issuance of a priori data and block 14 of the calculation of the regularization parameter.

Figure 3 presents the structural diagram of the first block of correction, which contains block 2.1 of the formation of partial derivatives, block 2.2 of transposing the matrix functions, block 2.3 of the formation of the product, block 2.4 of calculating the accuracy characteristics, block 2.5 of the formation of the product.

Figure 4 presents a structural diagram of a second correction unit, which contains a private derivative generating unit 8.1, a matrix function transposing unit 8.2, a product generating unit 8.3, a sum generating unit 8.4, a precision characteristics calculating unit 8.5, a product generating unit 8.6.

Figure 5 presents a structural diagram of a block for calculating accuracy characteristics included in the first and second blocks of correction, which contains a block 20 for generating partial derivatives of the matrix function, a block 21 for transposing matrices, a block 22 for generating a product, a delay line 23, a block 24 for transposing the matrices, a block 25 product generation, summing unit 26, matrix partial function derivation unit 27, product generating unit 28, difference generating unit 29, matrix inversion device 30, form unit 31 mira of the work.

Figure 6 presents a structural diagram of a block for calculating a regularization parameter, which contains a block for generating a matrix function 14.1, a delay line 14.2. 14.4, 14.7, 14.8, 14.12, 14.13, 14.16, 14.17, 14.18, 14.24, 14.25, 14.26, 14.29, 14.30, 14.31, 14.32, 14.40, 14.41, 14.42, 14.43, blocks 14.3, 14.9, 14.11, 14.19, 14.22, 14.23 , 14.33, 14.37. 14.38, 14.39 formation of the product of the numerator of the regularization parameter, transposition blocks 14.5, 14.14, 14.27, 14.44, production formation blocks 14.6, 14.15, 14.28, 14.45, forecast calculation blocks 14.10, 14.20, 14.21, 14.34, 14.35, 14.36, generation blocks 14.46, 14.47 amount, block 14.48 formation of the relationship.

Fig. 7 is a structural diagram of a first regularization parameter numerator product forming unit product block included in a first regularization parameter generating unit, which comprises a matrix function generating unit 14.3.1, a matrix function partial derivative block 14.3.2, matrix transposition unit 14.3.3, a block 14.3.4, block 14.3.5 formation of the product, blocks 14.3.6 and 14.3.7 transposition of matrices and block 14.3.8 formation of the product.

On Fig presents a structural diagram of the first forecast calculation unit, which is part of the unit of formation of the product of the numerator of the regularization parameter, it includes blocks 14.10.1 and 14.10.5 formation of the product, blocks 14.10.2 and 14.10.6 formation of the sum, block 14.10. 3 formation of partial derivatives of the matrix function, block 14.10.4 formation of the matrix function.

информационный вход которого соединен с информационным выходом блока 3, информационный выход первой линии задержки 14.2 соединен со вторым информационным входом первого блока 14.3 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 14.3 формирования произведения числителя параметра регуляризации соединен с шестым и седьмым информационными входами второго блока 14.46 формирования суммы, первый информационный выход которого соединен с первым информационным входом блока 14.48 формирования отношения, первый выход блока 14.48 формирования отношения является выходом блока 14; первый информационный выход второй линии задержки 14.4 соединен с первым информационным входом первого блока транспонирования 14.5 и первым информационным входом первого блока 14.6 формирования произведения, первый информационный выход блока 14.5 соединен со вторым информационным входом блока 14.6 формирования произведения, первый информационный выход которого соединен с четвертым информационным входом первого блока 14.47 формирования произведения, первый информационный выход которого соединен со вторым информационным входом блока 14.48 формирования отношения; первый информационный выход третьей 14.7 линии задержки соединен с первым информационным входом четвертой 14.8 линии задержки, первый информационный выход которой соединен со вторым информационным входом второго блока 14.9 формирования произведения числителя параметра регуляризации и вторым информационным входом первого блока 14.10 вычисления прогноза, второй информационный выход которого соединен со вторым информационным входом третьего блока 14.11 формирования произведения числителя параметра регуляризации, третьи и четвертые информационные входы блоков 14.9, 14.11, соединены с первым информационным выходом блока 13 и входом устройства, первый информационный выход блока 14.9 соединен с третьим и четвертым информационными входами блока 14.46, первый информационный выход блока 14.11 соединен с десятым информационным входом блока 14.46; первый информационный выход пятой 14.12 линии задержки соединен с первым информационным входом шестой 14.13 линии задержки, первый информационный выход которой соединен с первым информационным входом второго блока 14.14 транспонирования и первым информационным входом второго блока 14.15 формирования произведения, первый информационный выход второго 14.14 блока транспонирования соединен со вторым информационным входом блока 14.15, первый информационный выход которого соединен с третьим информационным входом блока 14.47 формирования суммы; первый информационный выход седьмой линии задержки 14.16 соединен с первым информационным входом восьмой линии задержки 14.17, первый информационный выход которой соединен с первым информационным входом девятой 14.18 линии задержки, первый информационный выход которой соединен со вторыми информационными входами четвертого 14.19 блока формирования произведения числителя параметра регуляризации и второго блока 14.20 вычисления прогноза, второй информационный выход которого соединен со вторыми информационными входами третьего блока 14.21 вычисления прогноза и 14.23 формирования произведения числителя параметра регуляризации, второй информационный вход блока 14.22 вычисления прогноза соединен со вторым информационным выходом третьего блока 14.21 вычисления, третьи и четвертые информационные входы блоков 14.19, 14.22 и 14.23 соединены с первым информационным выходом блока 13 и входом устройства соответственно, первый информационный выход блока 14.19 соединен с одиннадцатым и двенадцатым информационными входами второго блока 14.46 формирования суммы, первые информационные выходы блоков 14.23, 14.22 соединены с тринадцатым и четырнадцатым информационными входами первого блока 14.46 соответственно; первый информационный выход десятой линии задержки 14.24 соединен с первым информационным входом одиннадцатой линии задержки 14.25, первый информационный выход которой соединен с первым информационным входом двенадцатой 14.26 линии задержки, первый информационный выход которой соединен с первыми информационным входом третьего блока 14.27 транспонирования матричной функции и первым информационным входом третьего блока 14.28 формирования произведения, первый информационный выход третьего блока 14.27 транспонирования соединен со вторым информационным входом третьего блока 14.28 формирования произведения, первый информационный выход которого соединен с первым информационным входом первого блока 14.47 формирования суммы; первый информационный выход тринадцатой линии задержки 14.29 соединен с первым информационным входом четырнадцатой линии задержки 14.30, первый информационный выход которой соединен с первым информационным входом пятнадцатой 14.31 линии задержки, первый информационный выход которой в свою очередь соединен с первым информационным входом шестнадцатой линии задержки 14.32, выход которой соединен со вторым информационным входом седьмого блока 14.33 формирования произведения числителя параметра регуляризации и вторым информационным входом четвертого блока 14.34 вычисления прогноза, второй информационный выход которого соединен со вторым информационным входом девятого блока 14.38 формирования произведения числителя параметра регуляризации и вторым информационным входом пятого блока 14.35 вычисления прогноза, второй информационный выход последнего соединен со вторым информационным входом десятого блока 14.39 формирования произведения числителя параметра регуляризации и со вторым информационным входом шестого блока вычисления прогноза 14.36, второй информационный выход которого соединен со вторым информационным входом восьмого блока 14.37 формирования произведения числителя параметра регуляризации, третьи и четвертые информационные входы блоков 14.33, 14.37, 14.38, 14.39 соединены соответственно с первым информационным выходом блока 13 и входом устройства, первый информационный выход блока 14.33 соединен с восьмым и девятым информационными входами блока 14.46 формирования суммы, первый информационный выход блока 14.37 формирования произведения числителя параметра регуляризации соединен с пятым информационным входом блока 14.46, первые информационные выходы блоков 14.38 и 14.39 формирования произведения числителя параметра регуляризации соединены со вторым и первым информационными входами блока 14.46 соответственно; первый информационный выход семнадцатой линии задержки 14.40 соединен с первым информационным входом восемнадцатой линии задержки 14.41, первый информационный выход которой соединен с первым информационным входом девятнадцатой 14.42 линии задержки, первый информационный выход которой в свою очередь соединен с первым информационным входом двадцатой линии задержки 14.43, информационный выход которой соединен с первыми информационными входами четвертого блока 14.44 транспонирования и четвертого блока 14.45 формирования произведения, первый информационный выход блока 14.44 соединен со вторым информационным входом блока 14.45, первый информационный выход которого соединен со вторым информационным входом блока 14.47; первые информационные входы второго 14.9, четвертого 14.19 и седьмого 14.33 блоков формирования произведения числителя параметра регуляризации соединены со входом устройства, а первые информационные входы третьего 14.11, пятого 14.22, шестого 14.23, восьмого 14.37, девятого 14.38 и десятого 14.39 блоков формирования произведения числителя параметра регуляризации соединены соответственно с первыми информационными выходами первого 14.10, третьего 14.21, второго 14.20, шестого 14.36. четвертого 14.34 и пятого 14.35 блоков вычисления прогноза; первые информационные входы первого 14.10, второго 14.20 и четвертого 14.34 блоков вычисления прогноза соединены со вторым информационным выходом блока 13, а первые информационные входы третьего 14.21, пятого 14.35, шестого 14.36 блоков вычисления прогноза соединены с первыми информационными выходами соответственно второго 14.20, четвертого 14.34 и пятого 14.35 блоков вычисления прогноза, третьи информационные входы блоков вычисления прогноза соединены с пятым информационным выходом блока 13.The information inputs of the delay lines 14.2, 14.7, 14.16, 14.29 (FIG. 6) are connected to the information output of the sum forming unit 3 (FIG. 2), the first information inputs of the delay lines 14.4, 14.12, 14.24, 14.40 are connected to the first information output of the block 14.1 matrix function formation

the information input of which is connected to the information output of block 3, the information output of the first delay line 14.2 is connected to the second information input of the first regularization parameter numerator product block 14.3, its first and third information inputs are connected to the second and first information outputs of the a priori data generation and generation block 13 respectively, and the fourth information input is with the input of the device, the first information output of the first block 14.3 forming the product of the numerator of steam Etra regularization is connected to the sixth and seventh data inputs of the second block 14.46 formation amount, the first information output of which is connected to a first data input unit forming relations 14.48, 14.48 forming a first output unit is an output ratio unit 14; the first information output of the second delay line 14.4 is connected to the first information input of the first transposition block 14.5 and the first information input of the first product formation block 14.6, the first information output of block 14.5 is connected to the second information input of the product formation block 14.6, the first information output of which is connected to the fourth information input the first block 14.47 forming the product, the first information output of which is connected to the second information input of the block 14.48 forming IAOD relations; the first information output of the third delay line 14.7 is connected to the first information input of the fourth delay line 14.8, the first information output of which is connected to the second information input of the second regularization parameter numerator product block 14.9 and the second information input of the first forecast calculation block 14.10, the second information output of which is connected to the second information input of the third block 14.11 forming the product of the numerator of the regularization parameter, the third and fourth information nnye inputs 14.9 units, 14.11, connected to the first data output unit 13 and the input device, the first information output unit 14.9 is connected with the third and fourth data inputs of block 14.46, the first information output unit is connected to 14.11 tenth data input unit 14.46; the first information output of the fifth delay line 14.12 is connected to the first information input of the sixth delay line 14.13, the first information output of which is connected to the first information input of the second transposition block 14.14 and the first information input of the second product formation block 14.15, the first information output of the second transposition block 14.14 is connected to the second the information input of block 14.15, the first information output of which is connected to the third information input of the summing block 14.47; the first information output of the seventh delay line 14.16 is connected to the first information input of the eighth delay line 14.17, the first information output of which is connected to the first information input of the ninth delay line 14.18, the first information output of which is connected to the second information inputs of the fourth regularization parameter numerator product block 14.19 and second block 14.20 calculation of the forecast, the second information output of which is connected to the second information inputs of the third block 14.21 calculation forecast and 14.23 the formation of the product of the numerator of the regularization parameter, the second information input of the prediction calculation block 14.22 is connected to the second information output of the third calculation block 14.21, the third and fourth information inputs of the blocks 14.19, 14.22 and 14.23 are connected to the first information output of the block 13 and the device input, respectively the first information output of block 14.19 is connected to the eleventh and twelfth information inputs of the second summing block 14.46, the first information outputs of blocks 14.23, 14.22 with united with the thirteenth and fourteenth information inputs of the first block 14.46, respectively; the first information output of the tenth delay line 14.24 is connected to the first information input of the eleventh delay line 14.25, the first information output of which is connected to the first information input of the twelfth delay line 14.26, the first information output of which is connected to the first information input of the third matrix function transposition block 14.27 and the first information input the third block 14.28 forming the product, the first information output of the third transposition block 14.27 is connected to the second information the input of the third block 14.28 of the formation of the work, the first information output of which is connected to the first information input of the first block 14.47 of the formation of the sum; the first information output of the thirteenth delay line 14.29 is connected to the first information input of the fourteenth delay line 14.30, the first information output of which is connected to the first information input of the fifteenth 14.31 delay line, the first information output of which is in turn connected to the first information input of the sixteenth delay line 14.32, the output of which connected to the second information input of the seventh block 14.33 forming the product of the numerator of the regularization parameter and the second information input of the four of that forecast calculation block 14.34, the second information output of which is connected to the second information input of the ninth regularization parameter numerator block 14.38 and the second information input of the forecast calculation block 14.35, the second information output of the latter is connected to the second information input of the tenth regularization parameter numerator block 14.39 and with the second information input of the sixth forecast calculation block 14.36, the second information output of which is connected inen with the second information input of the eighth regularization parameter numerator product block 14.37, the third and fourth information inputs of blocks 14.33, 14.37, 14.38, 14.39 are connected respectively to the first information output of block 13 and the device input, the first information output of block 14.33 is connected to the eighth and ninth information the inputs of block 14.46 forming the sum, the first information output of block 14.37 forming the product of the numerator of the regularization parameter is connected to the fifth information input of block 14.46, per s information outputs blocks 14.38 and 14.39 numerator forming product of the regularization parameter connected with the first and second data inputs respectively block 14.46; the first information output of the seventeenth delay line 14.40 is connected to the first information input of the eighteenth delay line 14.41, the first information output of which is connected to the first information input of the nineteenth 14.42 delay line, the first information output of which is in turn connected to the first information input of the twentieth delay line 14.43, information output which is connected to the first information inputs of the fourth transposition unit 14.44 and the fourth creation unit 14.45, the first inform the output of block 14.44 is connected to the second information input of block 14.45, the first information output of which is connected to the second information input of block 14.47; the first information inputs of the second 14.9, the fourth 14.19 and the seventh 14.33 of the regularization parameter numerator product generation blocks are connected to the device input, and the first information inputs of the third 11.11, fifth 14.22, sixth 14.23, eighth 14.37, ninth 14.38 and tenth 14.39 regularization parameter numerator product blocks are connected respectively, with the first information outputs of the first 14.10, third 14.21, second 14.20, sixth 14.36. fourth 14.34 and fifth 14.35 forecast calculation blocks; the first information inputs of the first 14.10, second 14.20 and fourth 14.34 forecast calculation blocks are connected to the second information output of block 13, and the first information inputs of the third 14.21, fifth 14.35, sixth 14.36 forecast calculation blocks are connected to the first information outputs of the second 14.20, fourth 14.34 and fifth 14.35 forecast calculation blocks, the third information inputs of the forecast calculation blocks are connected to the fifth information output of the block 13.

The first, second and fifth information outputs of the a priori data generation and generation unit 13 (FIG. 2) are connected respectively to the third, second and fifth information inputs of the first regularization parameter calculation unit 14, the output of which is connected to the fifth information input of the second correction unit 8, and the first the second, third, fourth information outputs of the block 13 for generating and issuing a priori data are connected respectively to the second, third, fourth, fifth information inputs of the first block 2 and the second, third, fourth inf by the education inputs of the second correction unit 8, the second information output of the first correction unit 2 is connected to the eighth 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 the output of the device, and also connected to 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 output 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 output 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 of the correction and inform input of the second insulating 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 generating unit 1 and the first information input of the second difference forming unit 7, as well as the first information input of the first regularization parameter calculation unit 14 are the 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 (Fig. 3); 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 about block 2 correction; the information output of the delay line 5 (FIG. 2) is connected to the second information input of the accuracy characteristics calculation unit 2.4; 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 generation 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 (FIG. 4).

The information output of the second difference forming unit 7 is connected to the first information input of the product forming unit 8.3 (Fig. 4). 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 14.48 is connected to the second information input of the block 8.3 forming the product; the second information output of the fourth matrix function generation block 12 is connected to the first information input of the partial derivative generation block 8.1, the output of which is connected to the information input of the matrix function transposition block 8.2, the output of which is connected to the fourth information input of the block 8.3, the output of which is connected to the first information input of the block 8.4 of the formation of the sum, the second information input of which is connected to the information output of the block 2.3 (Fig.3), the output of the block 8.4 of the formation of the sum is connected to vym data output unit 8.5 and the second data output unit 8.6 the formation of a 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 (Fig. 2).

The output of the product formation unit 2.3 (FIG. 3) is connected to the information input of the partial derivative formation unit 27 (FIG. 5), 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 connected to the information input of the matrix reversal device 30, the output of which is connected to the first information input of the product forming unit 31, the output of which is the output of the precision characterization block 2.4 (Fig. 3) teristic; the fourth output of the block 13 forming and issuing a priori data is connected to the second information input of the block 29 forming the difference; 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 (FIG. 2) is connected to the information input of the partial derivative generation unit 20, the output of which is connected to the information input of the matrix transpose unit 21 and the first information input of the product formation unit 22, the second information input of which is connected to the output of the 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 5) has a structure and relationships similar to block 2.4.

The first and second information outputs of the block 13 for generating and issuing a priori data are connected to the fourth information input of the block 14.3.5 (Fig. 7) and the information input of the transpose block 14.3.6 of the matrix function, the information output of which is connected to the third information input of the block 14.3.5, the information output of which is connected to the information input of the matrix function transposition block 14.3.7 and the second information input of the product formation block 14.3.8, the information output of which is the output of the first block forming the product of the numerator of the regularization parameter, the information output of block 14.3.7 is connected to the first information input of block 14.3.8; the first information input of block 14.3.5 is connected to the information input of block 14.3.4, the second information input of block 14.3.5 is connected to the information output of matrix transposition block 14.3.3, the information input of which is connected to the information output of matrix derivative block 14.3.2 functions, the information output of which is in turn connected to the information input of the matrix function forming unit; the structure of all 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 14.3.1 (connected either to the information output of the corresponding delay line or the first information output of the forecast calculation block) and block 14.3.6 (the information input of which is connected either with the second information output of the block 13 for generating and issuing a priori data, or the second information output of the forecast calculation block).

The first information input of the product generation unit 14.10.1, which is the first information input of the first forecast calculation unit, (Fig. 8) is connected to the information output of the delay line, the second information input of the unit 14.10.1 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 block 14.10.2 forming the sum and the second information output of the block 14.10.5, the third information input of the block 14.10.1 is connected to the information output b lock 14.10.3 forming partial derivatives of the matrix function, the second information input of which is connected to the fifth information input of the block 13 for generating and issuing a priori data, and the first information input with the information first output of the block for generating the matrix function 14.10.4, the second information output of which is connected to the first the information input of the block 14.10.5 forming the product and the second information input of the block 14.10.6 forming the sum, the information output of the block 14.10.5 is connected to the first information input bl ka 14.10.6; the information output of block 14.10.1 is connected to the second information input of block 14.10.2, its information output is the second information output of the forecast calculation block and connected to the third information input of block 14.3.6 of the second regularization parameter numerator product formation block (Fig. 2); the structure of the subsequent forecast calculation blocks is similar, they differ only in the connections between the third information input of block 14.3.5 (it is connected either to the second information input of the previous forecast block or to the fifth information output of the block 13 for generating and issuing a priori data) and the first information input of block 14.3. 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 14 вычисления параметра регуляризации и вход блока 4 формирования матричной функции, на остальные входы блока 14 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 14 начиная с третьего 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 14 поступают значения у, Δt; с одного из выходов блока 2 коррекции значение М ₀(k+1/k) поступает на вход блока 8 коррекции, в котором формируется значениеThe device operates as follows (figure 2). In the initial state, in the block 13 for generating and issuing a priori data, the values of the matrices W ^-1 , G , I and 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 14 for calculating the regularization parameter and the input of block 4 for forming the matrix function, the remaining inputs of block 14 receive the values y , G , W ^-1 , from the output of block 4 for 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, the value is formed at the output of block 1

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 14, starting from the third moment of 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 remaining inputs of block 14 receive the values of y , Δt; 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 formed

на выходе блока 9 поступает на 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.which is input to the block 9 of the formation of the amount; value

at the output of block 9 goes to the input of block 10 of the formation of 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 summed with 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.

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 М ₀(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 P ₁(k+1), которое поступает на вход блока 2.5 формирования произведения, на другой вход которого поступает значение M ₀(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 3). 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 of W ^-1 , α ₀ are fed to the inputs of the block 2.3 forming 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 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 М ₀(k+1/k); значение

с выхода блока 8.4 поступает на вход блока 8.5 расчета точностных характеристик, на другие входы которого поступают значения G, W ^-1,

а на выходе формируется значение P ₁(k+1), которое умножается на (28) в блоке 8.6 формирования произведения; выход блока 8.6 является выходом блока 8 коррекции.The second block 8 correction works as follows (figure 4). 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 go to 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

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 a 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 P ₀(k) с выхода линии задержки 23, на вход которой с выхода блока 31 формирования произведения, являющегося выходом блока 2.3, поступает значение P ₀(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 М ₀(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 P ₀(k+1/k), сформированное на выходе блока 26; значение

The first block 2.4 calculation of the accuracy characteristics works as follows (Fig.6). 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 2.3, 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, the input of which also G value arrives; 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 14.2, 14.7, 14.16, 14.29 (фиг.6) и блок формирования матричной функции

с выхода которого значение

The 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 time, which, respectively, is transmitted on the delay line 14.2, 14.7, 14.16, 14.29 (Fig.6) and the block forming the matrix functions

whose output value

эти же значения оценок и матричной функции поступают на входы блоков 14.3 формирования произведения числителя коэффициента регуляризации и блоков 14.5 транспонирования матричной функции, 14.6 формирования произведения; далее на входы линий задержки 14.2, 14.7, 14.16, 14.29 опять поступает текущее значение оценки информационного процесса, с этих линий задержки k-1 значение оценки поступает на 14.8, 14.17, 14.30 линий задержки, с выхода которых k-2 значение оценки информационного процесса поступает дальше на вход блока 14.9 и линий задержки 14.18, 14.31; аналогично и для 14.4, 14.12, 14.24, 14.40, а также 14.13. 14.25, 14.41 линий задержки, только для матричной функции Н; в результате на n+5 и последующих итерациях будем иметь на выходах линий задержки 14.2, 14.8, 14.18, 14.32 значения k-1, k-2, k-3, k-4 оценок информационного процесса соответственно и на выходах 14.4, 14.13, 14.26, 14.43 линий задержки значения матричной функции для тех же оценок. Эти значения оценок информационного процесса поступают на блоки 14.3, 14.9, 14.19, 14.33 формирования произведения числителя коэффициента регуляризации и 14.10, 14.20, 14.34 формирования прогноза; в блоки 14.3, 14.9, 14.19, 14.33 поступают из 13 блока G, W ^-1 и у со входа устройства, с выхода этих блоков значения

arrives at the input of 14.4, 14.12, 14.24 and 14.40 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 14.2, 14.7, 14.16, 14.29 and 14.4, 14.12, 14.24, 14.40 to the delay lines 14.8, 14.17, 14.30 and 14.13, 14.25, 14.41, 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 14.3 of the product of the numerator of the regularization coefficient and the transposition blocks 14.5 of the matrix function, 14.6 of the product; Further, the inputs of the delay lines 14.2, 14.7, 14.16, 14.29 again receive the current value of the evaluation of the information process, from these delay lines k-1 the evaluation value is supplied to 14.8, 14.17, 14.30 delay lines, from the output of which the k-2 value of the evaluation of the information process further to the input of block 14.9 and delay lines 14.18, 14.31; similarly for 14.4, 14.12, 14.24, 14.40, and also 14.13. 14.25, 14.41 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 14.2, 14.8, 14.18, 14.32 the values of k-1, k-2, k-3, k-4 estimates of the information process, respectively, and at the outputs 14.4, 14.13, 14.26 , 14.43 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 14.3, 14.9, 14.19, 14.33 of the formation of the product of the numerator of the regularization coefficient and 14.10, 14.20, 14.34 of the formation of the forecast; in blocks 14.3, 14.9, 14.19, 14.33 come from 13 blocks G , W ^-1 and at the input of the device, from the output of these blocks values

для j=k, поступают на вход блока 14.46 формирования суммы; с выхода 14.10 блока на 14.11 блок поступает значение прогноза для k-1 момента времени, в блок 14.11 поступают значения G, W ^-1, у, с выхода 14.11 блока на вход 14.46 блока поступает выражение, аналогичное (29), с 14.20 блока в 14.23 блок и 14.21 блок поступает значение прогноза для k-2 момента времени, в блок 14.23 передаются значения G, W ^-1, у, с 14.23 блока на вход 14.45 блока поступает выражение, аналогичное (29), с выхода блока 14.21 поступает значение прогноза для k-1 момента времени, в блок 14.22 поступают значения G,W ^-1, у, с выхода 14.22 блока на 14.46 блок поступает выражение, аналогичное (29), на входах 14.34, 14.35, 14.36 блоков имеем

с выходов этих блоков имеем значения для k-3, k-2, k-1 момента времени, которые поступают на блоки 14.38, 14.39, 14.37 соответственно, кроме того, блок 14.36 использует результаты работы 14.35 блока, а 14.35 блок - 14.36 блока, и, наконец, в 14.34 блок передаются начальные значения, на входы блоков 14.37, 14.38. 14.39 поступают значения G, W ^-1, y, с выхода блоков 14.37, 14.38, 14.39 в блок 14.46 поступают выражения, аналогичные (29); с линий задержки 14.4, 14.13, 14.26, 14.43 на вход блоков 14.5, 14.14, 14.27, 14.44 транспонирования матричной функции и 14.6, 14.15, 14.28, 14.45 формирования произведения передается

после чего с выхода блоков 14.6, 14.15, 14.28, 14.45 на вход блока 14.45 формирования сумм поступают значения

; с блока 14.46 в блок 14.47 формирования отношения передается значение

на вход 14.47 блока с 14.45 блока поступает

на выходе блока 14.47 формирования отношения получаем значение коэффициента регуляризации α_n+1.for

for j = k, they enter the input of the summing block 14.46; from the block output 14.10 to the 14.11 block, the forecast value for the k-1 moment of time arrives, the values G , W ^-1 , y arrive at the block 14.11, the expression similar to (29) comes from the block output 14.11 to the block input 14.46, from block 14.20 to 14.23 block and 14.21 block, the forecast value for the k-2 moment of time is received, values G , W ^-1 , y are transmitted to block 14.23; from 14.23 of the block, an expression similar to (29) is received at the block input 14.45, the forecast value is received from the output of block 14.21 k-1 for a time at block received values 14.22 G, W ^-1, y, output from block 14.22 to 14.46 board receives expression similar e (29), at the inputs 14.34, 14.35, 14.36 blocks 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 14.38, 14.39, 14.37, respectively, in addition, block 14.36 uses the results of 14.35 blocks, and 14.35 block - 14.36 blocks, and finally, at 14.34 the block initial values are transmitted to the inputs of the blocks 14.37, 14.38. 14.39, the values G , W ^-1 , y are received; from the output of blocks 14.37, 14.38, 14.39, expressions similar to (29) are received in block 14.46; from the delay lines 14.4, 14.13, 14.26, 14.43 to the input of the transposition of the matrix function blocks 14.5, 14.14, 14.27, 14.44 and the product formation transmissions 14.6, 14.15, 14.28, 14.45 transmitted

after which, from the output of blocks 14.6, 14.15, 14.28, 14.45, the values

; from block 14.46 to block 14.47 of the formation of the relationship is transmitted value

at the entrance of the block 14.47 from 14.45 block

at the output of the relationship formation block 14.47, we obtain the value of the regularization coefficient α _{n + 1} .

с выхода блока на вход блоков 14.3.2 формирования частных производных матричной функции и блока 14.3.4, далее с выхода блока 14.3.2 значения поступают на вход блока 14.3.3 транспонирования матричной функции, откуда на вход блока 14.3.5 формирования произведения поступает

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

с выхода блока 14.3.4, на один из входов которого поступает у, значение G ^T поступает на вход блока 14.3.5 с выхода блока 14.3.6 транспонирования матричной функции, на вход которого соответственно с выхода 13 блока поступает значение G; с выхода блока 14.3.5 имеем значение

которое поступает соответственно на вход блоков 14.3.7 транспонирования матричной функции и 14.3.8 формирования произведения, в результате на выходе устройства будем иметь значения

The first block forming the product of the numerator of the regularization parameter 14.3 (Fig. 7) works as follows. At the input of block 14.3.1 of the formation of the matrix function, the value of the evaluation of the information process

from the output of the block to the input of blocks 14.3.2 of the formation of the partial derivatives of the matrix function and block 14.3.4, then from the output of the block 14.3.2, the values are sent to the input of the block 14.3.3 of transposition of the matrix function, from where the input of the block of the formation of the product 14.3.5 receives

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

from the output of block 14.3.4, at one of the inputs of which y arrives, the value of G ^T goes to the input of block 14.3.5 from the output of transposition block 14.3.6 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 14.3.5 we have the value

which is supplied respectively to the input of the matrix function transposition blocks 14.3.7 and 14.3.8 of the product formation, as a result, we will have the values at the output of the device

с выхода блока 14.10.4 значение

поступает на другой вход блока 14.10.3 и блоков 14.10.5 формирования произведения, 14.10.6 формирования суммы, с выхода блока 14.10.3 значение

поступает на вход блока 14.10.1 формирования произведения, на другие входы которого поступают значения G _n(k) и Δt, с выхода этого блока на вход блока 14.10.2 формирования суммы передается значение

The first forecast calculation unit works as follows. At the input of blocks 14.10.4 of the formation of the matrix function and 14.10.3 of the formation of partial derivatives, the value of the evaluation of the information process

from the output of the block 14.10.4 value

arrives at another input of block 14.10.3 and blocks 14.10.5 of product formation, 14.10.6 of forming the sum, from the output of block 14.10.3 the value

arrives at the input of the product formation block 14.10.1, 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 14.10.2

поступает на второй вход блока 14.10.6, выход которого является вторым выходом блока вычисления прогноза, с выхода которого имеем x _ηn(j). Остальные блоки вычисления прогноза работают аналогично.to another input of block 10.2, the value G _n (k) is received, as a result, on the output of 10/14/2 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 14.10.5 receives the value Δt, from the output of which the value

arrives at the second input of block 14.10.6, 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, p. 96.

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

3. Patent No. 2209506. Russia. 2003. Digital Iterative Filter. // Kostoglotov A.A., Fasol A.A., Kuznetsov A.A., Cheremsin A.I., Chernykh A.S.

4. Kostoglotov A.A. Synthesis of intelligent measurement procedures based on the principle of regularization A.N. Tikhonov. // Measuring technique. No. 1, 2001, pp. 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 measurement procedure based on the method of minimal errors. // Measuring equipment, No. 7, 2005, pp. 8-13.

7. Tikhonov A. N., Arsenin V. Ya. Methods for solving ill-posed problems. - M.: Science, 1986.

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

9. Kostoglotov A.A. Digital intelligent measurement procedure. // Measuring equipment, No. 7, 2002. p.16-21.

Claims (1)

A digital iterative filter containing the first, second, third and fourth blocks of the formation of matrix functions, the first and second blocks of correction, the first and second blocks of the formation of the difference, the first and second blocks of the formation of the sum, the first and second delay lines, the block of generation and output of a priori data, wherein the output of the first sum forming unit is connected to the information input of the first matrix function forming unit, the output of which is connected to the information input of the first delay line, the output of which is connected to the second and the formation input of the first sum forming unit and the information input of the second matrix function forming unit, the output of which is connected to the second information input of the first difference forming unit, the output of which is connected to the first information input of the first correction unit, the output of which is connected to the first information input of the first sum forming unit, the first, second, third outputs of the a priori data generation and output unit are connected respectively to the second, third, fourth information input the first and second correction units, the second information output of the first correction unit is connected to the eighth information input of the second correction unit, the output of which is connected to the first information input of the second summing unit, the output of which is the output of the device and connected to the information input of the third matrix function forming unit, the output of which 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, seventh the information input of the second correction unit and with the information input of the fourth matrix function generating unit, the second information output of which is connected to the sixth information input of the second correction unit, and the first information output is connected to the second information input of the second difference forming unit, the output of which is connected to the first information input the second block of correction; the output of the first delay line is also connected to the seventh information input of the first correction unit, and the second information output of the second matrix function generating unit is connected to the sixth information input of the first correction unit, characterized in that the first regularization parameter calculation unit is introduced into it, while the information output of the first the summing unit is connected to the fourth information input of the regularization parameter calculation unit, the first, second outputs of the unit for generating and issuing a priori data inens respectively with the third and second information inputs of the first regularization parameter calculation unit, and the fourth and fifth information outputs of the a priori data generation and output unit are connected respectively to the fifth information inputs of the first correction unit and the first regularization parameter calculation unit, the information output of the latter is connected to the fifth information input the second block of correction; the first information input of the first difference forming unit, the first information input of the second difference forming unit and the first information input of the first regularization parameter calculation unit are device inputs.

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