# Digital recursive filter

FIELD: computer science.

SUBSTANCE: device has sum forming blocks, matrix functions forming block, difference forming block, delay lines, apriori data output block.

EFFECT: higher precision.

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The invention relates to digital computing and can be used in systems of digital processing of radio signals for solving problems of optimal nonlinear filtering.

It is known device [1], the lack of which is the limited functionality due to the linear structure of the processed processes.

The closest to the technical nature of the claimed invention is the extended Kalman filter [2], containing the first unit forming the sum of the first and second blocks forming a matrix of functions, the first block forming the difference between the first delay line, the first correction block. The disadvantage of this device is the low accuracy of the generated estimates of the information process.

Improving the accuracy characteristics of the filtering of random processes is relevant direction.

The claimed invention is directed to improving the accuracy of their estimates of the information process in measuring systems, which is very important for radar target tracking, and contains blocks: first, second and third blocks forming the difference, the first, second and third correction blocks, the block forming and outputting a priori data, the first, second and third blocks forming the sum of the first, second, third, included four is th, the fifth and sixth blocks the formation of matrix functions, the first, second and third delay lines, the first, second, third and fourth outputs of the block forming and outputting a priori data are connected respectively with the second, third, fourth, fifth information inputs of the first, second and third error correction block, the first data output of the first correction block is connected with the first information input of the first shaping unit amount, the output of which is connected to the information input of the first shaping unit matrix functions, the output of which is connected to the information input of the first delay line, the output of which is connected with the second information input of the first processing unit amount with the seventh information input of the first error correction block and the information input of the second shaping unit matrix functions, the second information, the output of which is connected with the sixth information input of the first error correction block, the first data output of the second processing unit matrix functions connected with the second information input processing unit difference, the output of which is connected to the first information input of the first error correction block; a second information output of the first correction block is connected with the eighth informational input of the second error correction block, the output of which soy is inen with the first information input of the second processing unit amounts the output of which is connected to the information input of the third processing unit matrix functions, the output of which is connected to the information input of the second delay line, the output of which is connected with the second information input of the second processing unit amount, the seventh information input of the second error correction block and the information input of the fourth processing unit matrix functions, the second information, the output of which is connected with the sixth information input of the error correction block, the first data output of the fourth processing unit matrix functions connected with the second information input of the second processing unit difference, the output of which is connected to the first information input of the second error correction block; a second information output of the second error correction block is connected with the eighth information input to the third error correction block, the output of which is connected to the first information input of the third processing unit amount, the output of which is an output device connected to the information input of the fifth processing unit matrix functions, the output of which is connected to the information input of the third delay line, the output of which is connected with the second information input of the third unit forming the sum, the seventh information input to the third error correction block and with the information I the house of the sixth processing unit matrix functions, the second information output of which is connected with the sixth information input of the error correction block, the first data output of the sixth processing unit matrix functions connected with the second information input of the third processing unit difference, the output of which is connected to the first information input of the third error correction block; the first information input of the first block forming the difference between the first information input of the second shaping unit difference and the first information input of the third block forming the difference of the input device.

One way of improving the accuracy of the filter parameter estimation of dynamic systems, is the use of methods of solving ill-posed problems based on the principles of regularization. The effectiveness of regularization for continuous systems is proved for the case A. N. Tihonov's method [3] and its variants in the form of a method of iterative regularization [4]. We will show how to obtain the ltration equation using the method of iterative regularization for discrete systems [7].

Let the dynamics of the measured parameters is described by the system of difference equations in discrete-time

where x(k)=[x^{1}(k),x^{2}(k),... ,x^{M}(k)]^{T}∈^{}E^{M}the state vector of the investigated si theme;

η (k)=[η^{1}(k),η^{2}(k),... ,η^{M}(k)]^{T}∈^{}E^{M}the vector of unknown external influences;

F(x(k),k)=[F^{l}(x(k),k),F^{2}(x(k),k),... ,F^{M}(x(k),k)]^{T}∈^{}E^{M}- the transition function is continuous together with partial derivatives of the vector-function of its arguments.

G∈ E^{M}×^{}E^{M}matrix of the intensity of external influences;

k, N, M be positive integers. It is assumed that the matrixhas reverse.

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

where y(k)=[y^{1}(k),y^{2}(k),... ,y^{L}(k)]^{T}∈^{}E^{L}the vector of observations

n(k)=[n^{1}(k),n^{2}(k),... ,n^{L}(k)]^{T}∈^{}E^{L}the vector of discrete white Gaussian noise with known local characteristics

M[n(k)]=0,

M[n(k)n^{T}(l)]=Wδ (k-l),

W - covariance matrix of dimension L× L,

δ (· ) - vector Delta-function;

H(x(k))=[H^{1}(x(k)),H^{2}(x(k)),..., H^{L}(x(k))]^{T}∈^{}E^{L}signal vector function, continuous together with partial derivatives;

L, l be positive integers.

Pose the problem of synthesis of recurrent lter estimate x*(k), optimal in the sense of the minimum function is Nala, characterizing measurement error

In virtue of the continuity of the vector-function F(· ) the solution of equation (1) continuously depends on η (k), therefore the error function (3) for 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 equal to the task definition

Task(1), (2), (4) is an ill-posed inverse problem [5]. Find the values of vectors x^{*}(k), η^{*}(k)by solving the set of equations(1), (2), (4) in terms of the incorrectness of the original problem is quite difficult, therefore, widespread iterative gradient methods. However, the use of such methods may lead to divergent sequence of approximations. Therefore, the use of any iterative method for solving the problem(1), (2), (4) requires the definition of a regularizing family of operators, in which the regularization parameter is the number of the iteration.

In accordance with the General definition of regularizing family of operators Antigonos [5], we say that the iterative method

in which a numeric parameter α_{n}satisfies the conditions

generates a regularizing family of operators, in which the parameter is the number of the iteration, if for any initial approximation η_{0}and for any value of the error of the original data σ satisfying the condition of 0<|σ |<σ_{0}that σ_{0}=const, there is a number n(σ ) such that

that is, the obtained approximations converge to the exact solution in the norm spacewhen aiming error of the original data to zero.

For the implementation of the iterative method (5) is required to determine the gradient of the functional (3). According to [6] the expression to determine the gradient at the point η_{n}(k) has the form

gradJ[x_{n}(k),η_{n}(k)]=G^{T}ψ^{} _{n}(k)

where x_{n}(k) is the solution of (1) at η_{n}(k), and the vector ψ_{n}(k) is determined from conditions

Assuming zero approximation η_{0}(k)=0,will write the iterative sequence (5) in the expanded form for,

η_{0}(k)=0,

η_{1}(k)=η_{0}(k)-α_{0}G^{T}ψ^{} _{0}(k)=-α_{0}G^{T}ψ^{}Ȋ
_{0}(k),

η_{2}(k)=η_{1}(k)-α_{1}G^{T}ψ^{} _{1}(k)=-α_{0}G^{T}ψ^{} _{0}(k)-α_{1}G^{T}ψ^{} _{1}(k),

...

In consequence, taking into account (7) we have a sequence of discrete two-point boundary value problems (DTCS)

ψ_{i}(N)=0,x_{i}(0)=x^{*}(0),

,

Let us introduce the notationand multiply each of the equations for the adjoint vectors ψ_{i}the value of α_{i}then equation (8) take the following form

x_{n}(k+1)=F(x_{n}k),k)-GG^{T}λ^{} _{n},

λ_{n}(N)=0, x_{i}(0)=x^{*}(0),

To obtain the recurrent algorithm of estimation of the state vector, you must use the method of invariant embedding in discrete form. Note that the equation for the vector-functions λ DTCS (9) written in reverse time. This requires converting it to a form that shows the dependence of λ_{n}(k+1) from λ_{n}(k) and x_{n}(k). Producing the appropriate transformation is given expressions for x_{
n}(k+1) from (9) and using the decomposition in a Taylor series in a neighborhood of F(x_{n}(k),k), we obtain the following sequence DTCS:

x_{n}(k+1)=F(x_{n}(k),k)+GG^{T}λ^{} _{n}(k)=β [x_{n}(k),λ_{n}(k),k],

x_{i}(k+1/k)=F(x_{i}(k),k),

x_{i}(0)=x^{*}(0), λ_{n}(N)=0,

where options β and γ introduced to reduce the entry.

We replace the condition on the end λ_{n}(N)=0 a more General condition λ_{n}(N)=and let N and C - variables. Then the value of the vector x_{n}(N) is determined as a function of N and with

x_{n}(N)=r[c,N].

Change of size N by N+1 gives the increment Δ then

Let us write the expression for r(c+Δ c, N+1), using the apparatus finite difference

r (+Δ C,N+1)=r(c,N)+Δ r_{c}(C,N)+Δ r_{N}(C,N)+Δ^{2}r_{cN}(c,N),

or, given (11), we obtain

where

Δ r_{c}(c,N)=r(c+Δ c,N)-r(c,N),

Δ r_{N}(c,N)=r(c,N+1)-r(c,N),

Δ^{2}r_{cN}(c,N)=Δ r_{c}(c,N+1)-Δ r_{c}(c,N).

According to (10) the expression for Δ x_{n}and Δ have

To solve the differential equation (12) with respect to r(c,N}, i.e., to find a common analytical solved the e, fails, and generally turn to approximate methods. Suppose that r(c,N) is linear with

where- assessment of the state vector at time N, P_{n}(N) is some matrix with dimension M× M

Calculate the difference included in the expression (12)using the expression (14)

Substituting expressions(13), (14), (15) in (12), we obtain

Decomposing β and γ in a Taylor series in the neighborhoodand neglecting terms of order higher than the first, we can write equation (16) in the form

The relation (17) runs from→ 0, therefore, by equating the coefficients of the first and zero degree, obtain a differential equation forand P_{n}(N+1)

Write DTCS (10) for the case when k=N, taking into consideration that this is all DTCS for i=0,... ,n-1 are resolved and consequently the evaluation of x_{i}are known functions of the parameter k. Thus, we have

Then equation (18) is converted as follows:

p>where

Let us introduce notation

Then equation (20) we write in the form

Because of the difference in Perevoznaya matrices P_{n}andno, we record the sequence of equations for estimatingprocess (1), assuming that N is constantly changing and k=N,

The sequence of equations (22) is an iterative digital filter, which allows to process the digital processing of the measurement data for discrete dynamical systems. If we compare the equations with the equations of the discrete Kalman filter, it becomes clear that they are different from each other for the odd additional links assessment
with the previous set of estimatescarried with weighting factors determined by the sequence settings α_{i}and changing the overall feedback factor in the equation to estimate. Thus, the choice of the sequence settings α_{i}satisfying the conditions

allows you to implement the digital filter processing of the measurement data of high accuracy. It should be noted that the obtained result implies that the original system whose parameters are subject to estimation, nonlinear. The algorithm (22) gives the optimal nonlinear system parameter estimation in the sense of minimum of the functional characterizing the RMS error of the measuring channel. In contrast, the Kalman filter gives only a first approximation of the optimal estimate and thus is less accurate.

The evaluation of the effectiveness of the designed filter is produced on the basis of numerical simulation of the problem of determining the unknown constant parameter d discrete nonlinear system of the third order

x(k+1)=x(k)+τ · r(k)+τ · η^{1}(k),

d(k+1)=d(k)+τ · η
^{3}(k),

where the parameter τ sense of time interval which receives the measurement information in the form

The simulation was performed for the values of parameters α_{0}=1, α_{1}=0.333, α_{2}=0.1. Graphics estimates of the parameter d=0.25 for i=0,1,2 are given in figure 1 when the τ =0.3 when the total interval T=5. Visual analysis shows that the estimatesuperior accuracy assessment.

Thus, as follows from relations (22), the introduction of new structural elements and connections allows in combination with the overall characteristics to obtain the technical result consists in the reduction of the dispersion error is obtained at the output of the filter estimates of the input processes.

The claimed device can be applied in the information systems associated with the collection and processing of information, for example, in information systems radar and navigation systems.

The invention is illustrated figure 2-6, which shows the structural scheme of the iterative digital filter, the first, second and third blocks of correction unit of calculation accuracy characteristics.

Figure 2 presents a structural diagram of digital iterative filter. The device includes a first block 1, the second block 7 and the third block 14 forms the of the differences, the first block 2, the second block 8 and the third correction unit 15, the first block 3, the second block 9 and the third block 16 forming the sum of the first delay line 5, the second delay line 11 and the third delay line 18, the first block 4, the second block 6, the third block 10, fourth block 12, the fifth block 17 and the sixth block 19 of the formation matrix functions, block 13 forming and outputting a priori data.

3 shows the structural diagram of the first error correction block, which contains the block 2.1 formation of partial derivatives, unit 2.2 transpose matrix functions, block 2.3 formation works, unit 2.4 calculation accuracy characteristics, block 2.5 formation works.

4 shows the structural diagram of the second error correction block, which contains the block 8.1 formation of partial derivatives unit 8.2 transpose matrix functions, block 8.3 formation works, block 8.4 formation of the sum block 8.5 calculation accuracy characteristics, block 8.6 formation works.

Figure 5 presents the structural diagram of the third error correction block, which contains the block 15.1 formation of partial derivatives unit 15.2 transpose matrix functions, block 15.3 formation works, block 15.4 forming sums, unit 15.5 calculation accuracy characteristics, block 15.6 formation works.

Figure 6 presents the structural is a block circuit diagram of the calculation accuracy characteristics, included in the first, second and third blocks of corrections, which contains the block 20 forming the partial derivatives of matrix functions, block 21 transpose of matrices, block 22 forming compositions, line 23 of the delay unit 24 transpose of matrices, block 25 forming compositions, the block 26 forming the sum, unit 27 of the formation of partial derivatives of matrix functions, block 28 forming compositions, the block 29 forming the difference, the device 30 of conversion matrices, the block 31 of the formation of the work.

The first, second, third, fourth information output unit 13 forming and outputting a priori data (figure 2) are connected respectively with the second, third, fourth, fifth information inputs of the first block 2, the second unit 8 and the third correction unit 15, the second information output of the first correction unit 2 is connected with the eighth informational input of the second correction unit 8, the output of which is connected to the first information input of the second unit 9 forming amount, the output of which is connected to the information input of the third block 10 forming the matrix functions whose output is connected to the information input of the second delay line 11, the output of which is connected with the second information input of the second unit 9 forming the sum, with the seventh information input of the second correction unit 8 and the information is first input of the fourth block 12 forming the matrix functions, the second information output of which is connected with the sixth information input unit 8 correction; the first data output of the fourth block 12 forming the matrix functions connected with the second information input of the second unit 7 forming the difference, the output of which is connected to the first information input of the second correction unit 8; the first data output of the first correction unit 2 is connected with the first information input of the first unit 3 forming amount, the output of which is connected to the information input of the first block 4 forming the matrix functions whose output is connected to the information input of the first delay line 5, the output of which is connected with the second information input of the first unit 3 forming the sum with the seventh information input of the first correction unit 2 and the information input of the second block 6 forming the matrix functions, the second information, the output of which is connected with the sixth information input of the first unit 2 correction; first information output of the second block 6 forming the matrix functions connected with the second information input unit 1 forming the difference, the output of which is connected to the first information input of the first unit 2 correction; the second informational output of the second correction unit 8 is connected with the eighth informational input of the third BL is 15 ka correction, the output of which is connected to the first information input of the third block 16 forming amount, the output of which is the output of the device, and also connected to the information input of the fifth block 17 forming the matrix functions whose output is connected to the information input of the third delay line 18, the output of which is connected with the second information input of the third block 16 forming the sum, with the seventh information input of the third block 15 correction and data input of the sixth block 19 forming the matrix functions, the second information, the output of which is connected with the sixth information input unit 15 correction; first output of the sixth block 19 forming the matrix functions connected with the second information the entrance to the third block 14 forming the difference, the output of which is connected to the first information input of the third block 15 correction; the first information input of the first block 1 forming the difference between the first information input of the second unit 7 and the first information input of the third block 14 forming the difference of the input device.

The first and second information output unit 13 forming and outputting a priori data connected with the third and fourth information input unit 2.3 formation works (figure 3); the information output of the first unit 1 forms the of the differences connected with the first information input unit 2.3 formation works; the second information output of the second block 6 forming the matrix functions connected with the information input unit 2.1 the formation of the partial derivatives, the output of which is connected with the information input unit 2.2 transpose matrix functions, the output of which is connected with the second information input unit 2.3, the output of which is connected to the first information input unit 2.4 calculation accuracy characteristics, the output of which is connected to the first information input unit 2.5 the formation of works whose output is the output of the first correction unit 2; an information output of the delay line 5 (figure 2) is connected with the second information input unit 2.4 calculation accuracy characteristics; the third and fourth outputs of the block 13 forming and outputting a priori data connected with the third and fourth information input unit 2.4 calculation accuracy characteristics; an output unit 2.3 formation of works connected with the second information input unit 2.5 formation works and the second information input unit 8.4 formation amount (figure 4).

The information output of the second unit 7 forming the difference is connected with the first information input unit 8.3 formation works (figure 4). The first and second information output unit 13 forming the issuance of a priori data is connected to the second and Tr is Tim information input unit 8.3 formation works; the second information output of the fourth block 12 forming the matrix functions connected with the first information input unit 8.1 formation of partial derivatives, the output of which is connected with the information input unit 8.2 transpose matrix functions, the output of which is connected with the fourth information input unit 8.3, the output of which is connected to the first information input unit 8.4 formation amount of the second information input of which is connected to the information output unit 2.3 (3), the output unit 8.4 formation of the amounts connected with the first information output unit 8.5, with the second information input unit 15.4 formation amount (figure 5), and with the second information output unit 8.6 formation works; the third and fourth information output unit 13 forming the issuance of a priori data is connected to the second and third information input unit 8.5 calculation accuracy characteristics; information output of the delay line 11 is connected with the fourth information input unit 8.5 calculation accuracy characteristics, the output of which is connected to the first information input unit 8.6 formation works whose output is the output of the second correction unit 8 (figure 2).

The information output of the third block 14 forming the difference is connected with the first information input unit is 15.3 formation works (figure 5). The first and second information output unit 13 forming the issuance of a priori data is connected to the second and third information input unit 15.3 formation works; the second information output of the sixth block 19 forming the matrix functions connected with the first information input unit 15.1 formation of partial derivatives, the output of which is connected with the information input unit 15.2 transpose matrix functions, the output of which is connected with the fourth information input unit 15.3, the output of which is connected to the first information input unit 15.4 formation amount of the second information input of which is connected to the information output unit 8.4 (figure 4), the output of block 15.4 formation amounts connected with the first information the output unit 15.5, and with the second information output unit 15.6 formation works; the third and fourth information output unit 13 forming the issuance of a priori data is connected to the second and third information input unit 15.5 calculation accuracy characteristics; information output of the delay line 18 is connected with the fourth information input unit 15.5 calculation accuracy characteristics, the output of which is connected to the first information input unit 15.6 formation works whose output is the output of the second correction unit 15 (figure 2).

The output of block 2.3 formation works (figure 3) is connected with the information input unit 27 forming the partial derivatives of (6), the output of which is connected with the information input unit 28 forming compositions, the output of which is connected to the first information input unit 29 of the formation of the difference, the output of which is connected with the information input device 30 accesses matrices, the output of which is connected to the first information input unit 31 of the formation of works whose output is the output of 2.4 (figure 3) calculation accuracy characteristics; the fourth output unit 13 forming and outputting a priori data is connected with the second information input unit 29 of the formation of the difference; output unit 31 the formation of works connected with the information input line 23 of the delay, the output of which is connected with the third information input unit 22 forming compositions, the output of which is connected with the second information input unit 26 forming amount, the output of which is connected with the second information input units 28 and 31 forming compositions; the output of the first delay line 5 (figure 2) is connected with the information input unit 20 forming the partial derivatives, the output of which is connected with the information input unit 21 transpose matrices and the first information input unit 22 of creation the works the second information input connected to the output of block 21; the third information output unit 13 forming and outputting a priori data is connected with the information input unit 24 transpose matrices and the second information input unit 25 of the formation of the product, the first information input of which is connected to the information output unit 24; the output unit 25 is connected with the information input unit 26 forming amount.Blocks 8.5, 15.5 calculation accuracy characteristics (figure 4, 5) have the structure and relationships, similar to the 2.4 block.

The device works in the following way (figure 2). In the initial state in block 13 forming and outputting a priori data recorded values of the matrices W^{-1}, G, I, and values α_{1}that α_{2}that α_{3}. The value of the information process in the (k+1)-th timefrom the output unit 3 forming the sum is fed to the input of block 4 forming the matrix functions, the output of which isis fed to the input of the delay line 4, the output of which isis fed to the input unit 3 forming amount, the input correction unit 2 and the input unit 6 forming the matrix functionswhose value output unit 6 is fed to the input unit 2 and the input unit 1, the output to the which is formed is
residual measurement, which is fed to the input of the correction unit 2, the other input of which receives values α_{1}, G, W^{-1}, I; in block 2 is formed by the product of the matrix of gain and residual measurements, which is summarized in unit 3 with a value ofwith one of the outputs of block 2 correction value M_{1}(k+1/k) to the input of the correction unit 8, which is formed by the value of

which is fed to the input of block 9;the output unit 9 is fed to the input unit 10, the output of which isis fed to the input of the delay line 11, the output of which is formed isthat is summed with the value (25) in block 9, the output of which is formed is; output unit 11 isto the input of the correction unit 8, the input unit 9 and to the input unit 12, the output of which is formed issupplied to the input unit 8 and to the input unit 7 forming the difference, to the other input of which receives an input oscillation; the discrepancy of measurementsfrom the output unit 7 is fed to the input unit 8, the other input of which is the settlement of ouput value α
_{2}, G, W^{-1}, I; with one of the outputs of block 8 of the correction value M_{2}(k+1/k) to the input of the correction unit 15, which is formed by the value of

which is fed to the input of block 16;the output of block 16 is fed to the input unit 17, the output of which isis fed to the input of the delay line 18, the output of which is formed isthat is summed with the value of (26) in block 16, the output of which is formed is; from the output of block 18 isto the input of the correction unit 15, the input unit 16 and to the input unit 19, the output of which is formed iswhich is input to the block 15 and to the input unit 14 forming the difference, to the other input of which receives an input oscillation; the discrepancy of measurementsfrom the output unit 14 is fed to the input unit 17, the other input of which receives values α_{3}, G, W^{-1}, I.

The first correction unit 2 operates as follows (figure 3). The values of the matrix functionsgo to the input unit 2.1 the formation of the partial derivatives, with which the values ofthe village is ouput input block transpose matrix functions 2.2,
with which the values ofthe residual measurementand values α_{1}, W^{-1}arrive at the inputs of the block 2.3 formation works, with which the value of M_{1}(k+1/k) is fed to the input of block 2.4 calculation accuracy characteristics, to the other input of which receives the values G, I,and the output of which is formed a P value_{1}(k+1), which is fed to the input of block 2.5 formation works, the other input of which receives the value of M_{1}(k+1/k) from the output of the block 2.3. The output of the 2.5 block is the output of the correction unit 2.

The second correction unit 8 operates as follows (figure 4). The value of the matrix functionsto the input of the block 8.1 formation of partial derivatives with which the values ofgo on an input block transpose matrix functions 8.2, with which the values ofand the residual value measurementsthat α_{2}, W^{-1}fed to the input of block 8.3 formation works, the output of which isto the input of the block 8.4 summing up, the other input of which receives the value of M_{1}(k+1/k); value

output unit 8.4 fed to the input of block 8.5 calculation accuracy characteristics, to the other input of which receives the values of G, W^{-1},and the output is formed by the value of P_{2}(k+1), which is multiplied by (28) in block 8.6 formation works; output block 8.6 is the output of the correction unit 8. The third block 15 correction works in a similar way. The output of block 15 is formed a P value_{3}(k+1)M_{3}(k+1/k).

The first block 2.4 calculation of the accuracy characteristics of works in the following way (6). The value of the matrix functionsto the input of the block 20 forming the partial derivatives, the output of which isis fed to the input unit 21 of the transpose matrix functions and the input unit 22 forming compositions, the input of which also receives the value offrom the output of block 21 and a value of P_{1}(k) from the output of the delay line 23, at the entrance of which is from the output of block 31 of the formation of works, which is the output of unit 2.3, receives a value of P_{1}(k+1);from the output of the unit 22 is fed to the input of block 26 forming the sum, the other input of which receives the value of GG^{T}formed in the block 25 of the formation of a work, on which input goes mn the value of G and the value of G^{
T}formed in the block 24 of the transpose matrix, the input of which also receives the value of G; is the matrix functions M_{1}(k+1/k) is fed to the input of block 27 of the formation of partial derivatives, the output of which isto the input of the block 28, the other input of which receives a value of P_{1}(k+1/k)generated at the output of block 26;to the input of block 29 forming the difference, the other input of which receives the value of I; output unit 29 isis fed to the input device 30 accesses matrices, the output of which is connected to the input unit 31 of the formation of the work, the other input of which receives a value of P_{1}(k+1/k) from the output unit 26. The unit of calculation accuracy characteristics 8.5 second correction block and the block of calculation accuracy characteristics 15.5 third block correction function in the same way. The output of block 8.5 is formed a P value_{2}(k+1), and the output unit 15.5 - R_{3}(k+1).

Sources of information

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6. Vasiliev FP Methods for solving extremal problems. - M.: Nauka, 1981. p.106.

7. Kostoglotov A.A. Digital smart metering procedure // Measurement techniques, No. 7, 2002. p.16-21.

Digital recursive filter containing the first and second blocks forming a matrix of functions, the first correction block, the first block forming the difference between the first shaping unit amount of the first delay line and the output of the first processing unit amounts connected with the information input of the first shaping unit matrix functions, the output of which is connected to the information input of the first delay line, the output of which is connected with the second information input of the first shaping unit amounts and information input of the second processing unit matrix functions, the output of which is connected with the second information input of the first processing unit difference, the output of which is connected to the first information input of the first error correction block, the output of which is connected to the first information input of the first shaping unit amounts, characterized in that it introduced the second and third is Loki forming the difference, the second and third correction blocks, the block forming and outputting a priori data, the second and third blocks forming amount, third, fourth, fifth and sixth blocks the formation of matrix functions, second and third delay lines, the first, second, third and fourth outputs of the block forming and outputting a priori data are connected respectively with the second, third, fourth, fifth information inputs of the first, second and third error correction block, the second information output of the first correction block is connected with the eighth informational input of the second error correction block, the output of which is connected to the first information input of the second processing unit amount whose output is connected to the information input of the third processing unit matrix functions, the output of which is connected to the information input of the second delay line, the output of which is connected with the second information input of the second processing unit amount, the seventh information input of the second error correction block and the information input of the fourth processing unit matrix functions, the second information, the output of which is connected with the sixth information input of the second error correction block, the first data output of the fourth processing unit matrix functions connected with the second information input of the second processing unit RA is ing, the output of which is connected to the first information input of the second error correction block; a second information output of the second error correction block is connected with the eighth informational input of the third error correction block, the output of which is connected to the first information input of the third processing unit amount, the output of which is an output device connected to the information input of the fifth processing unit matrix functions, the output of which is connected to the information input of the third delay line, the output of which is connected with the second information input of the third unit forming the sum, the seventh information input of the third block of the correction and the information input of the sixth processing unit matrix functions, the second information, the output of which is connected with the sixth information the entrance to the third error correction block, the first data output of the sixth processing unit matrix functions connected with the second information input of the third processing unit difference, the output of which is connected to the first information input of the third error correction block; the output of the first delay line is connected with the seventh information input of the first error correction block, and the second information output of the second processing unit matrix functions connected with the sixth information input of the first error correction block; partyinvitations input of the first processing unit difference, the first information input of the second shaping unit difference and the first information input of the third block forming the difference of the input device.

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