# Digital intellectual recursive filter

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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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.

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

The closest to the technical nature of the claimed invention is a digital iterative filter [3], containing the first and second blocks forming the sum of the first, second, third and fourth blocks the formation of matrix functions, the first and second blocks forming the difference between the first and second delay lines, the first and second correction blocks, the block forming 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 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. Offers the proposed device contains a first the second blocks forming the difference, the first, second correction blocks, the block forming and outputting a priori data, the first and second blocks forming the sum of the first, second, third and fourth blocks the formation of matrix functions, first and second delay lines, the first block of the calculation of the regularization parameter, the first, second and third outputs of the block forming and outputting a priori data are connected respectively with the second, third, fourth information inputs of the first and second error correction block, and the fourth output unit for forming and issuing a priori data is connected with the fifth information input of the first error correction block, in addition, the first, second, fifth outputs of the block forming and outputting a priori data are connected respectively with the third, second and fifth information input unit of the calculation of the regularization parameter, 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 and fourth information input of the first block of the calculation of the regularization parameter, the output of which is connected with the fifth information input of the second error correction block, the output of the first processing unit matrix functions connected with information Photomerge delay line, the output of which is connected with the second information input of the first shaping unit amounts, 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 ninth 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, the output of which is an output device 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 information is hydrated 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.

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 [4], and its variants in the form of a method of iterative regularization [5]. We will show how to obtain the ltration equation using the method of iterative regularization for discrete systems [6].

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

wherethe state vector of the system under investigation;the vector of unknown external influences; a transition function- 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 feedback.

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

wherethe vector of observations

the vector of discrete white Gaussian noise with known local characteristics

**W**- covariance matrix of dimension L×L,**δ**(·) - vector Delta-function;

signal vector function, continuous together with partial derivatives; L, l be positive integers.

Pose the problem of synthesis of recurrent filter estimates**x***(k), optimal in the sense of minimum functionality that characterize the 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 task of determining estimates**x***(k), delivering a minimum of (3)is equal to the task definition

Task(1), (2), (4) is an ill-posed inverse problem [7].

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 the Finance 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 [7], we say that the iterative method

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

where Δ(**η**_{n}) - the discrepancy generates 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 initial data σ, satisfying the condition of 0<|σ| < σ_{0}, 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.

According to [8] the expression to determine the gradient at point**η**_{n}(k) has the form

where**x**_{n}(k) is the solution of (1) in**η**_{n}(k), and the vector**Ψ**_{n}(k) is determined from conditions

Knowing the expression for the gradient (7) the functional (3)can pen in order to write the expression (6) for the regularization parameter [9] in the following form α_{
0}=1,

The selection of the sequence of parameters α_{n}satisfying the condition (9), will implement the digital filter processing of the measurement data of high accuracy. Therefore, the question of the calculation of the regularization parameters is relevant.

For the implementation of the iterative method (5) is required to determine the gradient of the functional (3)defined by the expression (7). Assuming zero approximationwill write the iterative sequence (5) in the expanded form for,

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

,

Let us introduce the notationand multiply each of the equations for the adjoint vector Ψ_{i}the value α_{i}then equation (10) take the following form

,

To obtain algorithm recurren the aqueous 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 in DTCS (9) written in reverse time. This requires converting it to a form reflecting the dependence of λ_{n}(k+1) λ_{n}(k) and**x**_{n}(k). Making the proper conversions taking into account the expression for**x**_{n}(k+1) from (11) and using the decomposition in a Taylor series in the neighborhood of**F**(**x**_{n}(k),k), we obtain the following sequence DTCS:

where the function**β**and**γ**introduced to reduce the entry.

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

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

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

or, given (13), we obtain

where

According to (12) the expression for Δ**x**_{n}and Δ**with**have

To solve the differential equation (14) with respect to**r**(**c**,N), i.e. to find a common analytical R is the solution fails,
and usually turn to approximate methods. Suppose that**r**(**c**N) linear**with**

where**x***_{n}(N) is the estimation of the state vector at time N,**P**_{n}(N) is some matrix with dimension M×M

Calculate the difference included in the expression (14)using the expression (16)

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

Decomposing**β**and**γ**in a Taylor series in the vicinity (**x***_{n}(N),0,N) and neglecting terms of order higher than the first, we can write equation (18) in the form

Equation (19) is executed when**with**→0, therefore, by equating the coefficients of the first and zero degree**with**get a differential equation forand

Write DTCS (12) for the case when k=N, taking into consideration that this is all DTCS for i=0, ..., n-1 are resolved and, accordingly, evaluation of the**x**_{i}are known functions of the parameter k. Thus, we have

Then equation (20) is converted as follows

Then equation (22) 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, and taking into account the condition (7)is imposed on the regularization parameter, in the form

The sequence of equations (24) is a digital intellectual recursive filter, which allows to process the digital processing of the measurement data for discrete dynamical systems. If we compare the equations with the equations iterative digital filter [3], it becomes clear that they are different from each other due to the connection between the regularization parameter and the correction block, and additional links sequence parameters α_{i}changing the total coupling coefficient in equation for estimatingwith estimatesthe signal vector function**N**and matrices**G**,**W**. That is, in the filter (24) in contrast to the filter [3], the regularization parameter is coordinated by the discrepancy principle, which allows to obtain the optimal order and more accurate procedure. It should be noted that results is at implies,
that original system, the parameters of which are subject to evaluation, nonlinear. The algorithm (24) gives the optimal nonlinear system parameter estimation in the sense of minimum of the functional characterizing the RMS error of the measuring channel.

The calculation of the regularization parameter is organized as follows: the limits of integration are not [0, t]a [t-3s,t], where t denotes the current time, the s - step calculations; for discrete time you must take [N-1, N-4]. Studies have shown [6]that the use of data more than three steps back not increase the accuracy of the resulting estimates, and only increase the number of required arithmetic operations.

It should be noted that for the implementation of the 2nd iteration of the algorithm (24), you need to 1st iteration was implemented, for the implementation of the 3rd - 1st and 2nd. That is, the number of arithmetic operations required to compute the iterations of the algorithm will include the number of arithmetic operations of the previous iterations. Analysis of the computational cost required for the implementation of the developed estimation algorithm, allows to make a conclusion about the possibility of its implementation in real-time in the modern PEAK.

The evaluation of the effectiveness of the designed filter is produced on the basis of numerical modeling of the problem of determination of the nei is known constant parameter d discrete nonlinear system of the third order

,

,

where the parameter τ has the meaning of a time interval which receives the measurement information in the form

Graphics estimates of the parameter d=0.2 for i=0,l are given in figure 1 when τ=0.3 when the total interval T=5. It is evident that the assessment of intellectual recursive filter is superior in accuracy to the evaluation of iterative filter. Numerical simulation showed that the accuracy of determination of the parameter d using digital intellectual recursive filter is higher by 10.2% compared to the iterative digital filter.

Thus, as follows from relations (24), 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 2-8, which shows the structural scheme of intellectual recursive digital filter, the first and second correction blocks, block calculation accuracy features the istics of, block calculation of the regularization parameter, the first shaping unit works the numerator of the regularization parameter, unit calculations.

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

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 block circuit diagram of the calculation accuracy characteristics included in the first and second correction blocks, 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.

Figure 6 presents a structural block circuit diagram of the calculation of the regularization parameter, which contains the set of matrix functions 14.1, delay lines 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 forming compositions of the numerator of the regularization parameter, blocks 14.5, 14.14, 14.27, 14.44 transpose blocks 14.6, 14.15, 14.28, 14.45 formation works, blocks, 14.10, 14.20, 14.21, 14.34, 14.35, 14.36 calculations, blocks 14.46, 14.47 forming sums, unit 14.48 forming relationships.

Figure 7 presents a structural diagram of the first processing unit works the numerator of the regularization parameter included in the first block of the formation of the regularization parameter, which contains the block 14.3.1 the formation of matrix functions, block 14.3.2 partial derivatives of matrix functions, block 14.3.3 transpose matrix, b is OK 14.3.4, block 14.3.5 formation works, blocks 14.3.6 and 14.3.7 transpose matrices and block 14.3.8 formation works.

On Fig presents a structural diagram of the first block of calculation of the forecast, which is part of the shaping unit works the numerator of the regularization parameter, it includes blocks 14.10.1 and 14.10.5 formation works, blocks 14.10.2 and 14.10.6 forming sums, unit 14.10.3 the formation of the partial derivatives of matrix functions, block 14.10.4 the formation of matrix functions.

The information inputs of the delay lines 14.2, 14.7, 14.16, 14.29 (6) is connected with the information output unit 3 forming the sum (2), the first information input of the delay lines 14.4, 14.12, 14.24, 14.40, connected with the first information output unit 14.1 formation of matrix functionsan information input connected to the information output unit 3, the information output of the first delay line 14.2 is connected with the second information input of the first unit 14.3 forming compositions of the numerator of the regularization parameter, the first and the third information input is connected to the second and first information output unit 13 forming and outputting a priori data, respectively, and the fourth information input from the input device, the first data output of the first unit 14.3 forming pieces of the Oia, the numerator of the regularization parameter is connected with the sixth and seventh informational inputs of the second unit 14.46 forming amount, the first information output of which is connected to the first information input unit 14.48 forming relationship, the first output unit 14.48 forming relationships is the output of the unit 14; the first data output of the second delay line 14.4 connected to the first information input of the first block transpose 14.5 and the first information input of the first block 14.6 formation works, the first information output unit 14.5 connected with the second information input unit 14.6 formation works, the first information output of which is connected with the fourth information input of the first block 14.47 formation works, the first information output of which is connected with the second information input unit 14.48 forming relationships; a first data output of the third 14.7 a delay line connected to the first information input of the fourth 14.8 delay line, the first information output of which is connected with the second information input of the second block 14.9 forming compositions of the numerator of the regularization parameter and the second information input of the first block 14.10 calculation of the forecast, the second information, the output of which is connected with the second information input of the third block 14.11 forming compositions of the numerator of the regularization parameter, the third and fourth information input block is s 14.9, 14.11, connected with the first information output unit 13 and the input device, the first information output unit 14.9 connected with the third and fourth information input unit 14.46, the first information output unit 14.11 connected with the tenth information input unit 14.46; the first data output of the fifth 14.12 delay line connected to the first information input of the sixth 14.13 delay line, the first information output of which is connected to the first information input of the second block 14.14 transpose and the first information input of the second block 14.15 formation works, the first data output of the second 14.14 block transpose is connected with the second information input unit 14.15, first information which connected with the third information input unit 14.47 formation amount; the first information output of the seventh delay line 14.16 connected to the first information input of the eighth delay line 14.17, first information output of which is connected to the first information input of the ninth 14.18 delay line, the first information output of which is connected with the second information input of the fourth 14.19 block forming compositions of the numerator of the regularization parameter and the second unit 14.20 calculation of the forecast, the second information, the output of which is connected with the second information is nymi inputs of the third block 14.21 calculation of forecast and 14.23 forming compositions of the numerator of the regularization parameter, the second information input unit 14.22 calculate the forecast is connected with the second information output of the third block 14.21 computing, third and fourth information input blocks 14.19, 14.22 and 14.23 connected with the first information output unit 13 and the input device, respectively, the first information output unit 14.19 connected with the eleventh and twelfth informational inputs of the second unit 14.46 forming amount, the first information outputs blocks 14.23, 14.22 connected with the thirteenth and fourteenth informational inputs of the first block 14.46 respectively; the first information output of the tenth delay line 14.24 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 14.26 delay line, the first information output of which is connected with the first information input of the third block 14.27 transpose matrix functions and the first information input of the third block 14.28 formation works, the first data output of the third block 14.27 transpose is connected with the second information input of the third block 14.28 formation works, the first information output of which is connected to the first information input of the first block 14.47 formation amount; the first information you the od of the thirteenth delay line 14.29 connected to the first information input of the fourth 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 which in turn is connected to the first information input of the sixteenth delay line 14.32, the output of which is connected with the second information input of the seventh block 14.33 forming compositions of the numerator of the regularization parameter and the second information input of the fourth block 14.34 calculation of the forecast, the second information, the output of which is connected with the second information input of the ninth block 14.38 forming compositions of the numerator of the regularization parameter and the second information input of the fifth block 14.35 calculation of the forecast, the second information output of the latter is connected with the second information input of the tenth block 14.39 forming compositions of the numerator of the regularization parameter and with the second information input of the sixth computing unit forecast 14.36, the second information, the output of which is connected with the second information input of the eighth block 14.37 forming compositions of the numerator of the regularization parameter, the third and fourth information input blocks 14.33, 14.37, 14.38, 14.39 connected respectively with the first information output unit 13 and the input device, the first information output unit 14.33 connected to the eighth and ninth informatsionnymipotokami block 14.46 forming amount, the first information output unit 14.37 forming compositions of the numerator of the regularization parameter is connected with the fifth information input unit 14.46, the first information outputs blocks 14.38 and 14.39 forming compositions of the numerator of the regularization parameter is connected to the second and first information input unit 14.46 respectively; the first information output seventeenth delay line 14.40 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 which in turn is connected to the first information input of the twentieth delay line 14.43, the information output of which is connected with the first information input of the fourth block 14.44 transpose and fourth block 14.45 formation works, the first information output unit 14.44 connected with the second information input unit 14.45, first information output of which is connected with the second information input unit 14.47; the first information input of the second 14.9, fourth 14.19 and seventh 14.33 blocks forming compositions of the numerator of the regularization parameter is connected with the input device and the first information input of the third 14.11, fifth 14.22, sixth 14.23, eighth 14.37, deviator is 14.38 and tenth 14.39 blocks forming compositions of the numerator of the regularization parameter 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 blocks calculation of the forecast; the first information input of the first 14.10, second 14.20 and fourth 14.34 blocks calculate the forecast is connected to the second information output unit 13, and the first information input of the third 14.21, fifth 14.35, sixth 14.36 blocks calculate the forecast connected with the first information outputs, respectively, of the second 14.20, fourth 14.34 and fifth 14.35 blocks calculation of the forecast, the third information input blocks calculate the forecast is connected with the fifth information output unit 13.

First, second, and fifth information output unit 13 forming and outputting a priori data (figure 2) are connected respectively to the third, second and fifth information inputs of the first block 14 calculation of the regularization parameter, the output of which is connected with the fifth information input of the second correction unit 8, and the first, second, third, fourth information output unit 13 forming and outputting a priori data are connected respectively with the second, third, fourth, fifth information inputs of the first block 2 and the second, third, fourth information inputs of the second correction unit 8, the second information output of the first correction unit 2 is connected with the eighth information input of the second correction unit 8, the output of which is dine with the first information input of the second block 9 of the formation of the amounts the output which is the output of the device, and also 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 with the information input of the fourth block 12 forming the matrix functions, the second information, the 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 the 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 with the fourth information input of the first block 14 calculation of the regularization parameter and 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 block 2 corresponding the functions and information input of the second block 6 forming the matrix functions, the second information 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 correction unit 2; the first information input of the first block 1 forming the difference and the first information input of the second unit 7 forming the difference, and the first information input of the first block 14 calculation of the regularization parameter are input devices.

The first and fourth 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 block 1 forming the difference is connected with the first information input unit 2.3 formation works; the second informational 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 the different 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 second and third outputs of the unit 13 for forming and issuing 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 information output unit 13 forming the issuance of a priori data is connected with the third information input unit 8.3 formation works; output block 14.48 connected with the second 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 EN 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, 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 with 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 output of block 2.3 formation works (figure 3) is connected with the information input unit 27 of the formation of partial derivatives (figure 5), 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 vyhoda the block 2.4 (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; the output of block 31 of 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 the information input unit 22 forming compositions, 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.

Unit 8.5 calculation accuracy characteristics (figure 5) has a structure and communication, similar to the 2.4 block.

First adoptedand second information output unit 13 forming and outputting a priori data connected with the fourth information input unit 14.3.5 (7) and an information input unit 14.3.6 transpose matrix functions, the information output of which is connected with the third information input unit 14.3.5, the information output of which is connected with the information input unit 14.3.7 transpose matrix functions and the second information input unit 14.3.8 formation works, information output which is the output of the first shaping unit works the numerator of the regularization parameter, the information output unit 14.3.7 connected to the first information input unit 14.3.8; the first information input unit 14.3.5 connected with the information input unit 14.3.4, the second information input unit 14.3.5 connected with the information output unit 14.3.3 transpose of a matrix function, an information input connected to the information output unit 14.3.2 the formation of the partial derivatives of matrix functions, information the output of which in turn is connected with the information input processing unit matrix functions; structure of all blocks forming the product of the numerator of the regularization parameter are identical, they only differ in the relationships between information input blocks 14.3.1 (connected either with the information output of the corresponding delay line, or the first information output unit forecast and unit 14.3.6 (information input connected either with the second information o the house unit 13 forming and outputting a priori data, or the second information output unit calculations).

The first information input processing unit 14.10.1 works, which is the first information input of the first block of calculation of the forecast (Fig) is connected with the information output of the delay line, the second information input unit 14.10.1 connected with the fifth information output unit 13 forming and outputting a priori data, with the same information output connected to the first information input unit 14.10.2 formation amount and a second information output unit 14.10.5, third information input unit 14.10.1 connected with the information output unit 14.10.3 the formation of the partial derivatives of matrix functions, the second information input of which is connected with the fifth information input unit 13 forming and outputting a priori data, and the first information input from the information first access unit 14.10.4 the formation of matrix functions, the second information, the output of which is connected to the first information input unit 14.10.5 formation works and the second information input unit 14.10.6 formation the amount of information output unit 14.10.5 connected to the first information input unit 14.10.6; an information output unit 14.10.1 connected with the second information input unit 14.10.2, its informational output is the second information you the Odom block calculations and is connected with the third information input unit 14.3.6 the second shaping unit works the numerator of the regularization parameter (figure 2); the structure of the subsequent blocks calculations similar, differ only connections between the third information input unit 14.3.5 (it is connected either with the second information input unit forecast, or with the fifth information output unit 13 forming and outputting a priori data and the first information input unit 14.3.1 (it is connected or with the information output of the delay line, or the first information output of the previous block of the forecast).

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 matrices**W**^{-1},**G**,**I**and the values of α_{0}, Δt is the value of the sampling step. The value of the information process in the (k+1)-th timefrom the output unit 3 forming the sum is fed to the input unit 14 calculation of the regularization parameter and the input unit 4 forming the matrix functions, on the other inputs of the block 14 receives the values of**y**,**G**,**W**^{-1}with the output of block 4 forming the matrix functionsis fed to the input of the delay line 5, 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 functionsvalue is of which from the output unit 6 is fed to the input unit 2 and the input unit 1,
the output of block 1 is the value ofresidual measurement, which is fed to the input of the correction unit 2, the other input of which receives the values of α_{0},**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 ofthe output of block 14 from the third point in time is formed is α_{1}of the regularization parameter (until then have α_{1}=0.5), which is fed to the input of the second correction unit 8, to the other input unit 14 receives the values of**at**, Δt; with one of the outputs of block 2 correction value is**M**_{0}(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 of the formation of the sum;the output unit 9 is fed to the input unit 10 forming the matrix functions, from the output of block 10 isis fed to the input of the delay line 11, the output of which is formed iswhich is summed with the value (27) in block 9, the output of which is formed isfrom the output of the block 11 isto the input of the correction unit 8, on the stroke unit 9 and to the input unit 12 forming the matrix functions,
at the output of which is formed iswhich is supplied to the input unit 8 and the input unit 7, 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 receives the values of α_{1},**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 ofgo on an input block transpose matrix functions 2.2, the output of whichthe discrepancy of measurementsand**W**^{-1}α_{0}arrive at the inputs of the block 2.3 formation works, the output of which is**M**_{0}(k+1/k) is fed to the input of block 2.4 calculation accuracy characteristics, to the other input of which receives the values of**G**,**I**,and the output of which is formed by the value of**P**_{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**_{0}(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 about the time (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 ofas well as the residual value measurementsα_{1},**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**_{0}(k+1/k); the value ofoutput 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**_{1}(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 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 of the formation made the Denia
to the input of which also receives the value offrom the output of the block 21 and the value of**P**_{0}(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, comes the value of**P**_{0}(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 receives 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**_{0}(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 the value of**P**_{0}(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 the block 29 is

is 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 the value of**P**_{0}(k+1/k) from the output bloke.
The unit of calculation accuracy characteristics 8.5 second correction block works the same way. The output of block 8.5 formed**P**_{1}(k+1).

The unit of calculation of the regularization parameter works as follows. In the initial state to the input unit of the calculation of the regularization parameter goes- the value of the information process, where k is the current time, which, respectively, is transmitted to the delay line 14.2, 14.7, 14.16, 14.29 (6) and block the formation of matrix functionssince the output of which is

fed to the input of 14.4, 14.12, 14.24 and 14.40 delay lines; in the next iteration of the filter on the same blocks receives the current value assessment of the information process, from the outputs of the delay lines 14.2, 14.7, 14.16, 14.29 and 14.4, 14.12, 14.24, 14.40 on delay lines 14.8, 14.17, 14.30 and 14.13, 14.25, 14.41 act accordingly k-1 the value of evaluation and matrix functionsthese values are estimates and matrix functions are received at the inputs of blocks 14.3 forming compositions of the numerator of the coefficient regularization and blocks 14.5 transpose matrix functions, 14.6 formation works; next to the inputs of delay lines 14.2, 14.7, 14.16, 14.29 again enters the current value assessment of the information process, with these delay lines k-1 is estimated and fed to 14.8,
14.17, 14.30 delay line, the output of which k-2 is the assessment of the information process goes on to the input unit and 14.9 delay lines 14.18, 14.31; and similarly for 14.4, 14.12, 14.24, 14.40, and 14.13. 14.25, 14.41 delay lines, only for the matrix functions**N**to n+5 and subsequent iterations will have on the outputs of the delay lines 14.2, 14.8, 14.18, 14.32 values k-1, k-2, k-3, k-4 estimates of the information process, respectively, and outputs 14.4, 14.13, 14.26, 14.43 delay line values of the matrix functions for the same assessments. These values are estimates of the information process come into blocks 14.3, 14.9, 14.19, 14.33 forming compositions of the numerator of the coefficient regularization and 14.10, 14.20, 14.34 generation forecast; in blocks 14.3, 14.9, 14.19, 14.33 come from 13 block**G**,**W**^{-1}and**at**from input devices, the output of these blocks

for j=k, is fed to the input of block 14.46 formation amount; output 14.10 block on 14.11 block receives the value of the forecast for k-1 moment of time, in block 14.11 values arrive**G**,**W**^{-1},**at**with output 14.11 block input 14.46 unit enters an expression analogous to (29), 14.20 block 14.23 block and 14.21 block receives the value of the forecast for k-2 time, in block 14.23 transmitted values of**G**,**W**^{-1},**at**with 14.23 block to the input of 14.5 unit enters the expression,
similar to (29), from the output of the block 14.21 comes forecast value for k-1 moment of time, in block 14.22 values arrive**G**,**W**^{-1}, with output 14.22 block at 14.46 unit enters an expression analogous to (29), the inputs 14.34, 14.35, 14.36 blocks haveoutputs of these blocks have values for k-3, k-2, k-1 moment of time, which enter into blocks 14.38, 14.39, 14.37, respectively, in addition, the block 14.36 uses the results 14.35 block, and 14.35 block 14.36 block, and, finally, 14.34 block are transferred to the initial values at the inputs of blocks 14.37, 14.38. 14.39 values arrive**G**,**W**^{-1},**y**with output blocks 14.37, 14.38, 14.39 in block 14.46 do expressions analogous to (29); delay lines 14.4, 14.13, 14.26, 14.43 input blocks 14.5, 14.14, 14.27, 14.44 transpose matrix functions and 14.6, 14.15, 14.28, 14.45 formation of the work is transferredthen output blocks 14.6, 14.15, 14.28, 14.45 to the input unit 14.45 formation amounts do; block 14.46 block 14.47 forming relationships is passed the value ofinput 14.47 unit 14.45 unit entersthe output of block 14.47 forming relationships, we get the value of the regularization coefficient α_{n+1}.

P is the pout forming unit works the numerator of the regularization parameter 14.3 (7) works as follows.
To the input unit 14.3.1 formation matrix function receives the value of the information processoutput block input block 14.3.2 the formation of the partial derivatives of matrix functions and block 14.3.4, then from the output of the block 14.3.2 values are sent to the input unit 14.3.3 transpose matrix functions, where the input unit 14.3.5 formation works comeson the other inputs are values of**G**^{T},**W**^{-1}andfrom the output of the block 14.3.4, one input of which receives**at**the value of**G**^{T}to the input of the block 14.3.5 output unit 14.3.6 transpose matrix functions, on which input respectively from the output 13 of the block receives the value of**G**; output block 14.3.5 have the value ofwhich is supplied respectively to the input blocks 14.3.7 transpose matrix functions and 14.3.8 formation works, the output will have the value of

The first computing unit forecast is as follows. Input blocks 14.10.4 the formation of matrix functions and 14.10.3 the formation of partial derivatives receives the value of the information processfrom the output of the block 14.10.4
supplied to the other input of the block 14.10.3 and blocks 14.10.5 formation works, 14.10.6 formation amount output unit 14.10.3to the input of the block 14.10.1 formation works, the other input of which receives the values of**G**_{n}(k) and Δt, the output of this unit to the input unit 14.10.2 formation amount transferred is

to another input of the block 10.2 comes**G**_{n}(k)in the output 14.10.2 block whose output is the first output of the computing unit forecast, have forecast**G**_{n}(j), j=k+1; the second input of block 14.10.5 enters the value of Δt, the output of which issupplied to the second input unit 14.10.6 whose output is the second output of the computing unit of the forecast, the output of which have**x**_{ηn}(j). Other units of the calculation of the forecast operate in the same manner.

Sources of information

1. Ago, Washkansky. Applied questions of optimal linear filtering. - M.: Energoizdat, 1982, pp.96.

2. Aparina, Fluder. Digital processing of radar data. Support goals. - M.: Radio and communication, 1993, pp.118.

3. Patent No. 2209506. Russia. 2003. Digital iterative filter. // Kostoglotov A.A., Beans A.A., Kuznetsov A.A., Ceresin A.I., Black A.S.

4. Kostoglotov A.A. Synthesis of intellect the actual measurement procedures based on the principle of regularization A. N. Tihonov's. // Measurement techniques. No. 1, 2001, p.8-12.

5. Kostoglotov A.A. Method of successive approximations in theory of filtration. // Automatic control and computer engineering, No. 3, 2000, p.53-63.

6. Kostoglotov A.A., Kuznetsov A.A. Synthesis of intelligent measuring procedure based on the method of minimum error. // Measurement techniques, No. 7, 2005, p.8-13.

7. Tikhonov A. N., Arsenin C. J. Methods for solving ill-posed problems. - M.: Nauka, 1986.

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

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

Digital iterative filter, containing the first, second, third and fourth blocks the formation of matrix functions, the first and second correction blocks, the first and second blocks forming the difference between the first and second blocks forming the sum of the first and second delay lines, the block forming and outputting a priori data, 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 to the second info is to boost the input of the first shaping 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 unit forming the sum of the first, second, and third outputs of the block forming and outputting a priori data are connected respectively with the second, third, fourth information inputs of the first and second correction blocks, 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, the output of which is an output device connected to the information input of the third processing unit matrix functions, the output of which is connected with the information input 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, and the first information output connected to 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; the first Lin and delays 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, characterized in that it introduced the first block of the calculation of the regularization parameter, the data output of the first processing unit amounts connected with the fourth information input unit of the calculation of the regularization parameter, the first, second outputs of the block forming and outputting a priori data are connected respectively with the third and second information inputs of the first block of the calculation of the regularization parameter, and the fourth and fifth information output unit for forming and issuing a priori data are connected respectively with the fifth information inputs of the first error correction block and the first block of the calculation of the regularization parameter information the yield of the latter is connected with the fifth information input of the second 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 first block of the calculation of the regularization parameter are input devices.

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