# Digital intelligent iterative filter

FIELD: computer engineering.

SUBSTANCE: invention relates to digital computer engineering and can be used in digital signal processing systems for optimum nonlinear filtering. The device contains six units for generating matrix functions, three correctors, three units for generating difference, three units for generating sum, three delay lines, unit for generating and outputting prior data, and two units for calculating regularisation parametre.

EFFECT: increased accuracy of evaluating information process parametres in measuring systems.

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The invention relates to digital computing and can be used in systems digital signal processing when 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 a heuristic 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 parameters of the information process.

Improving the accuracy characteristics of the filter parameters of random processes is relevant direction.

The claimed invention is directed to improving the accuracy of their estimates of the parameters of the information process in measuring systems, which is very important for radar nutrition the Institute goals. Digital intelligent iterative filter contains blocks: first, second, third blocks forming the difference; first, second, third correction blocks; block forming and outputting a priori data; first, second, third blocks forming amount; first, second, third, fourth, fifth and sixth blocks the formation of matrix functions; first, second and third delay lines; first and second blocks of the calculation of the regularization parameter, the first, second, third and fourth outputs of the block forming and outputting a priori data are connected respectively with the second, third, fourth and fifth information inputs first, second and third blocks of correction, 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 inputs of the first and second blocks 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 to the ninth informational input of the second error correction block, the output of the first processing unit Matri is Noah functions connected with information the input of the first 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 eighth informational input of the second error correction block, the first information output of which is connected to the first information input of the second processing unit sums the output of which is connected to the information input of the third block the formation of matrix functions and with the fourth information input of the second block of the calculation of the regularization parameter, the output of which is connected to the ninth informational input of the third error correction block, the output of the third processing unit matrix functions connected with 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 IP information input of the fourth processing unit matrix functions, the second information 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 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 informational input of the third error correction block, the first information 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 fifth processing unit amount, 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 input 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 with the first information in the Odom third error correction block.

One way to improve the accuracy of parameter estimation of dynamic systems is the use of methods of solving ill-posed problems based on the principles of regularization. The effectiveness of the regularization for the case of continuous systems proven and received its expression in the form of A. N. Tihonov's method [4] and its variants in the form of a method of iterative regularization [5]. Get the ltration equation using the method of iterative regularization for discrete systems [6, 9].

Let the dynamics of the estimated 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 system under investigation; η(k)=[η^{1}(k),η^{2}(k),...(η^{M}(k)]^{T}∈E^{M}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 matrix- has an inverse.

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

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

n(k)=[n^{l}(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(·)is a vector of Delta-function; H(x(k))=[H^{l}(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 minimum functionality that characterize the measurement error

In virtue of the continuity of the vector-function F(·) is the solution of the 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 [7]. Find the values of vector 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 the tee to the 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 conditionthere 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 the point η_{n}(k) has the form

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

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

The selection of the sequence of parameters α_{n}satisfying the condition

(9), will implement the digital filter processing of measuring information increased accuracy.

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 approximationwrite 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 panajim each of the equations for the adjoint vector Ψ_{i}the value α_{i}then equation (10)

take the following form

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 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). Producing the corresponding p is obrazovaniya taking into account the expression for

x_{n}(k+1) from (11) and using the decomposition in a Taylor series in a neighborhood of F(x_{n}(k),k), we obtain the following sequence DTCS

where the functions β and γ are introduced to reduce the entry.

We replace the condition at the end of 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

.

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

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

or, given (13), we obtain

where

According to (12) the expression for Δx_{n}and Δc have

To solve the differential equation (14) with respect to r(c,N), i.e. to find a General analytical solution is not possible, and usually turn to approximate methods. Suppose that r(c,N) is linear with

where- assessment of the state vector at time N, R_{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 neighborhoodand neglecting terms of order higher than the first, we can write equation (18) in the form

Equation (19) is executed when c→0, therefore, by equating the coefficients of the first and zero degree, obtain a differential equation forand R_{n}(N+1)

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, the estimates x_{i}are known functions of the parameter k. Thus, we have

Then equation (20) is converted as follows

where

Let us introduce notation

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 feedback factor in the equation to estimatewith estimatessignal vector function H and the matrices G, W. To include in the filter (24) in contrast to the filter [3], the regularization parameter is agreed in accordance with the principle of the residual errors of measurement, which allows to obtain a more accurate assessment procedure. 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: integrated within the project [0,t] is changed to [t-3s,t], where t represents 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 provides increased accuracy of the resulting estimates by a fraction of a percent when the increase in the number of necessary arithmetic operations several times.

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 algorithm estimates allow us to conclude about the possibility of its implementation in real-time based on the use of modern computer technology.

Studies have shown that the effectiveness of each re-processing with respect to the previous falls. Meanwhile, the amount of computation increases dramatically. Based on the analysis of numerical simulation results can recommend three iterative data processing.

The evaluation of the effectiveness of the designed filter is produced on the basis of numerical simulation of the problem of determining the unknown post is permanent 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 toare 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 10.8% compared with 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 characteristics, block sizing regular the organization, 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 includes a first block 1, the second block 7 and the third block 14 forming the difference between the first block 2, the second block 8 and the third correction unit 15, the first block 3, the second block 9, 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 and the first block 20, and the second unit 21 the 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 14 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 of matrices, block 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 functionsinformation 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 information output from the first block 14.3 forming compositions of the numerator of the regularization parameter is connected with the sixth and seventh informational inputs of the second unit 14.46 formation amount of the first information, the 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 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 calculations, the second details rmational 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 blocks 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 the input unit 14.15, the first information output of which is 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 calculations, the second information is th output of which is connected with the second information input of the third block 14.21 calculations and 14.23 forming compositions of the numerator of the regularization parameter, the second information input unit 14.22 calculations 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 wittingau 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 calculations, 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 calculations, 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 unit of calculation of the 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 informational inputs b is an eye 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 calculations connected with the second information output unit 13, and the first information input of the third 14.21, fifth 14.35, sixth 14.36 blocks calculations connected with the first information outputs, respectively, of the second 14.20, fourth 14.34 and fifth 14.35 blocks of prediction calculator, third information input units calculations connected with the fifth information output unit 13. The structure of the second unit of the calculation of the regularization parameter is similar.

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 and the second block 21 calculation of the regularization parameter, the output of which is connected to the ninth informational input of the third correction unit 15, 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, 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 information input WTO is on block 8 of correction, the second information output of the second correction unit 8 is connected with the eighth informational input of the third correction unit 15, the output of which is connected to the first information input of the third block 16 forming amount, the output of which is an output device 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 of the correction and the information input of the sixth block 19 forming the matrix functions, the second information, the output of which is connected with the sixth information input of the third block 15 correction; first output of the sixth block 19 forming the matrix functions connected with the second information input of 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 output of the first block of 20 calculation of the regularization parameter is connected with the ninth 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 with the fourth information input of the second block 21 calculation parameter reg the popularization and information input of the third block 10 forming the matrix functions, the output of which 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 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 the first block 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 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 and the information input of the first unit 2 correction; the 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 between the first information input of the second unit 7 forming the difference and the first information input of the third block 14 forming the difference, and the first information input of the first unit 20 calculation of the regularization parameter and the first information input of the second block 21 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 with the first information shall include the 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 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 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 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 output is om unit 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 14 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 the 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 unit 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 output the m 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), 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 the matrices W^{-1}, G, I, and 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 20, the calculation of the regularization parameter and the input unit 4 forming the matrix functions, on the other inputs of the block 20 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 functionsthe value with which the output of the 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^{-l}, 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 of; the output of block 20, starting from the third time, a value of 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, on the other inputs of the block 20 receives the values of α_{0}, G, W^{-1}, I; with one of the outputs of block 2 correction value 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 21 of the calculation of the regularization parameter and 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 isthat is summed with the value (27) in block 9, the output of which is formed isfrom the output of the block 11 is
to the input of the correction unit 8, the input unit 9 and to the input unit 12 forming the matrix functions, 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; with one of the outputs of block 8 of the correction value M_{1}(k+1/k) to the input of the correction unit 15, which is formed by the value of

which is fed to the input block 16 forming the sum;the output of block 16 is fed to the input unit 17 of the formation matrix functions, the output unit 17 isis fed to the input of the delay line 18, the output of which is formed iswhich is summed with the value (28) in block 16, the output of which is formed isfrom the output of block 18 isto the input of the correction unit 15, the input unit 16 and to the input of block 19 of the formation matrix functions, the output of which is formed issupplied to the input unit 15 and the input unit 14, the other input is vtorogo receives an input oscillation;
the discrepancy of measurementsfrom the output unit 14 is fed to the input unit 15, 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 residual measurement

and the values of W^{-1}α_{0}arrive at the inputs of the block 2.3 formation works, with which the value of 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 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_{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 follows (figure 4). The value of the matrix functionsto the input of the block 8.1 formation of partial derivatives with which the values offed to the input of the Loka transpose matrix functions 8.2,
with which the values ofand 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); 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_{1}(k+l), 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 similarly.

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 block 14 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 P value_{0}(k) from the output of the delay line 23, at the entrance of which is from the output of block 31 of formation works, is susegana output unit 2.3,
receives a 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+l/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_{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 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_{0}(k+1/k) from the output unit 26. The unit of calculation accuracy characteristics 8.5 second correction block works the same way. The output of block 8.5 formed a value of P_{1}(k+1).

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

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 value supplied by 14.8, 14.17, 14.30 delay line, the output of which is 2 the value of information process goes on to the input unit and 14.9 delay lines 14.18, 14.31; and similarly for and 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 31'll have to exit the x 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 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 do the values of G, W^{-1}, y, 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 G, W^{-1}, y, 14.23 block input 14.45 unit enters an expression analogous to (29), from the output of the block 14.21 comes forecast value for k-1 moment of time, in block 14.22 do the values of 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 with the responsibility
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 do the values of G, W^{-1}, y, 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 doblock 14.46 block 14.47 forming relationships is passed the value ofinput 14.47 unit 14.45 unit entersat the exit of block 14.47 forming relationships, we get the value of the regularization coefficient α_{n+1}. The second block 21 calculation of the regularization parameter works similarly.

The first shaping 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 transponer is of matrix functions,
where the input unit 14.3.5 formation works comeson the other inputs are values of G^{T},W^{-1}andc unit output 14.3.4, one input of which comes from the value 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 set of calculations 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 14.10.4supplied 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 is transferred to C is Uchenie

to another input of the block 10.2 enters the value of G_{n}(k)in the output 14.10.2 block whose output is the first output unit calculations are 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 unit calculations, the output of which have x_{ηn}(j). The remaining blocks of the calculations are similar.

Sources of information

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

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

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 intelligent 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.8-3.

7. Tikhonov A.N., Arsenin VIA Methods for solving ill-posed problems. - M.: Nauka, 1986. - 288 S.

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

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

Digital intelligent iterative filter, containing the 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, fourth, 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 and fifth information inputs of the first, second and third error correction block, the first the information output of the first error 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 the first processing unit matrix functions connected with the information input of the first delay line, the output of which is connected with the second information input of the first shaping unit amount with sevenths the information input of the first error correction block and the information input of the second shaping unit matrix functions, the second information 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 of the first shaping unit difference, the output of which is connected to the first information input of the first 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 first information output of which is connected to the first information input of the second processing unit amount, the output of which is connected to the information input of the third processing unit matrix functions, the output of the third processing unit matrix functions connected with 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 difference, the output of which is connected with the first information which was input of the second error correction block, the second information output of the second error correction block is connected with the eighth informational input of the third error correction block, the first information 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 input to the third error correction block, the first data output of the sixth block the formation of 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 block forming the difference between the first information input of the third block forming the difference of the input device, characterized in that it introduced the first and second blocks calculation parameter reg the polarization, the first informational inputs which are input devices, third, second and fifth informational inputs of the first and second blocks of the calculation of the regularization parameter are connected respectively to the first, second and fifth outputs of the block forming and outputting a priori data, the fourth information input of the first block of the calculation of the regularization parameter is connected to the output of the first processing unit amount, the fourth information input of the second block of the calculation of the regularization parameter is connected to the output of the second processing unit sums the outputs of the first and second blocks of the calculation of the regularization parameter is connected to the ninth meeting of the inputs respectively of the second and third error correction block.

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