RU2713627C1 - Calculator of an extrapolated coordinate and its least-squares variation rate - Google Patents

Abstract

FIELD: radar ranging and radio navigation.SUBSTANCE: invention relates to the field of radar ranging, in particular, to tracking the target on the trajectory in the survey radar stations. To achieve technical result, probabilistic multipliers are introduced, in the role of which there are two-input conjunctors, shift registers, probabilistic subtractor and probabilistic adder.EFFECT: development of calculator of extrapolated coordinate and its rate of change by method of least squares for averaging obtained as a result of three successive, in equal time, measurements of radar coordinates.1 cl, 1 dwg

Description

The invention relates to the field of radar, in particular to the field of target tracking on the trajectory in the survey radar stations.

Known devices for a similar purpose, built on the basis of specialized arithmetic-logic devices, which consist of multipliers and adders [Satyga O.G. The fundamentals of building fire control systems for naval artillery systems and stabilization systems for naval weapons. Academy of Naval Forces named after P.S. Nakhimov. Sevastopol 2009. - S. 74-78]. Their main disadvantages are the relatively large hardware volume and low speed.

The problem to which the invention is directed is the development of a device for calculating a coordinate having a small hardware volume and the ability to process a signal in real time.

The solution to the technical problem is achieved by using the probabilistic form of data presentation, in connection with which the hardware implementation of the prototype under consideration changes.

The technical result provided by the given set of features is to reduce the hardware volume of the extrapolated coordinate calculator and the rate of its change using the least squares method while maintaining the accuracy characteristics and the possibility of processing the input signal in real time, achieved by replacing the amplifiers in the prototype with probabilistic multiplication units, and digital combination adder to a probabilistic adder and adding to the scheme a probabilistic subtractor and then nyh registers.

The invention is illustrated by the drawing of Fig., Which shows a functional diagram of a probabilistic calculator coordinates, where:

1.1, 1.2, 1.3 - registers for storing the values of the measured coordinates X ₁ , X ₂ and X ₃ ;

соответственно, где T - время поворота антенны РЛС;2.1, 2.2, 2.3, 2.4 - registers for storing values of correction factors

respectively, where T is the radar antenna turn time;

3.1, 3.2, 3.3 and 3.4 - two-input conjunctors that perform the function of arithmetic multipliers of probabilistically represented operands;

4 - probabilistic adder in the role of which may be a circuit [Pat. 171033 Russian Federation, IPC G06F 19/00 Parallel probabilistic adder / Moiseev D.V., Sapozhnikov N.E .; Applicant ChVVMU them. P.S. Nakhimov. - No. 2017100704; declared 01/10/2017; publ. 05/17/2017, bull. No. 14];

5 - probabilistic subtractor, in the role of which the circuit can act [Pat. 181260 Russian Federation, IPC G06F 7/70 (2006.01) G06F 17/18 (2006.01) Probabilistic subtractor / D.V. Moiseev, N.E. Shoemakers; applicant and patentee FGBVOU VO CHVVMU im. P.S. Nakhimov of the Ministry of Defense of the Russian Federation (RU). No. 2017139991, stated 11/16/2017; publ. 07/06/2018 Bull. No. 19].

The device is designed to calculate the extrapolated coordinate X _i and the rate of change in the i-th observation using the least squares method.

When solving the problem of determining the coordinate, it is necessary to know the coordinate estimate at the time of the last (n-th) measurement and the estimate extrapolated to one radar count period T. For n = 3, the coordinate estimate at the time of the last observation will be calculated by the formula:

по формулам:Using the least squares method (LSM) with the linear hypothesis of target movement, we define

according to the formulas:

Where:

Where:

Functions (3) and (5) are weighted functions of parameter estimation.

To obtain the coordinates extrapolated for one review period, it is necessary to substitute n into expression (1) instead of (n-1).

Then we get:

Where

X-coordinate extrapolation weight function.

Weighted functions (3), (5), and (7) when solving the problem of parameter estimation by the least-squares method are determined in advance and entered into registers specially designated for them.

For n = 3,

The calculator of the extrapolated coordinate and the rate of its change using the least squares method operates as follows - before starting work, the values of the correction coefficients and the values of the last three measured values are transmitted to the circuit inputs, after an equal period of time - T, corresponding to the antenna rotation time, presented in the form of probability maps.

In the simplest case of a probabilistic transformation, the value of the parameter of the converted quantity is either always positive or always negative, and the conversion process itself is performed in accordance with the rule

where x _i is the i-th parameter value of the converted signal X (t);

R (t _ij ) is the jth value of the parameter of the auxiliary random signal R (t), which varies in the interval of variation of X (t);

- число циклов преобразования сигнала X(t);

- the number of signal conversion cycles X (t);

- количество статистических испытаний каждого значения x_i внутри временного интервала Δt_i-t_i+1-t_i;

- the number of statistical tests of each value x _i inside the time interval Δt _i -t _{i + 1} -t _i ;

y _ij is the value of the probability mapping of the signal parameter x _i from the series Y _i (t) = {y _i1 ; y _i2 ; ... y _ij; ... y _iK }.

Probabilistic mapping has the properties of synchronism (clocking) and the independence of each member of the mapping from any other.

The first property is that the formation of the members of the probability mapping is performed through a constant time interval Δt _i = t _{i + 1} -t _i , determined by the frequency ƒ _j = 1 / Δt _j of rule (9).

The independence of each member of the probability map y _ij from any other follows from the fact that obtaining the probability map corresponds to the Bernoulli test scheme. For a random sequence obtained in accordance with this scheme, the autocorrelation function is a δ-function at τ = 0. To prove this, it should be shown that repeated tests in accordance with (9) are also independent. The values of the auxiliary random function R (t) are formed at discrete time instants. At any moment in time, a function can only be in one of its states r _ij with probability P _j (t). Obviously, for any t

and for given probabilities P _j (t), the distribution r _ij can be given by probability density:

Where

is the distribution of a fixed quantity r _ij determined by the Dirac function.

The use of these properties and the use of probabilistically represented discrete signals allows us to simplify the functional units for performing arithmetic and logical operations, in particular, addition, subtraction, multiplication, raising to the power, division, comparation, etc. and thereby dramatically reduce their hardware volume.

Taking into account the initial transformation rule, the probabilities of occurrence of “1” and “0” in the probability map are:

P (y _ij = 1) = P [R (t _ij ) 〈x _i ],

P (y _ij = 0) = 1-P [R (t _ij ) 〈x _i ].

The mathematical expectation of a probability mapping is determined through a series of distributions for a discrete random variable y _ij

Then

Thus, the probability of occurrence of “1” in the probability map is the mathematical expectation of the map and is numerically equal to the value of the integral distribution law of the auxiliary signal R (t) at the comparison level x _i .

Of particular interest is the case when the auxiliary random signal R (t) obeys the uniform distribution law in accordance with

For him, the last expression for MO is rewritten in the form:

M [Y _i (t)] = P (y _ij = 1) = x _i ,

those. we have the case of a linear probabilistic transformation.

Thus, the number of units in the probability mapping corresponds to the weight of the value converted to the probabilistic form, which in turn allows the operation of multiplying the probabilistically represented operand to the operand represented in binary positional codes. An example of a converter of information into probabilistic mappings is a circuit - Pat. 2660831 Russian Federation, IPC Н03М 7/00 (2006.01) Binary code converter - probabilistic mapping / D.V. Moiseev, N.E. Shoemakers; applicant and patentee FGBVOU VO CHVVMU im. P.S. Nakhimov of the Ministry of Defense of the Russian Federation (RU). No. 2017160609, claimed 01/10/2017; publ. 07/10/2018 Bull. Number 18.

The values from the inputs of the circuit are recorded in the shift registers, the measured coordinate values in the registers (1.1), (1.2) and (1.3), and the correction factors in the registers (2.1), (2.2), (2.3) and (2.4), respectively.

After recording the correction coefficients and the values of the measured coordinates presented in the form of probabilistic mappings in the corresponding shift registers, the calculator of the extrapolated coordinate and its rate of change using the least squares method starts: the values of the measured coordinates X _i and the corresponding correction coefficients M _i are input to the market conditions ( 3.1), (3.2) and (3.3), respectively.

To calculate the product of two quantities presented in the form of probabilistic reflections, one should use the relation:

whence it follows that in order to calculate the product of two probabilistically represented factors, one two-input conjunctor is needed.

The results of the product of X ₁ by M ₁ , X ₂ by M ₂ and X ₃ by M ₃ go to the parallel probabilistic adder circuit (4).

To find the sum of the probabilistically represented signals, we use the relation:

When performing the subtraction operation, we perform the same actions as for adding two terms, the second of which is taken with the opposite sign, we obtain an expression with a uniform distribution of auxiliary random signals:

Values from the registers (1.1) and (1.3) are fed to the inputs of the probabilistic subtractor (5), the output of which, together with the value of the correction coefficient from the output of the register (2.4), are fed to the conjunction 3.4.

The output of the adder (4) and the conjunctor (3.4) are the outputs of the entire circuit.

The technical and economic efficiency of the proposed probabilistic coordinate calculator consists in reducing its hardware volume while maintaining the accuracy characteristics and the possibility of processing the input signal in real time.

Claims (1)

The calculator of the extrapolated coordinate and the rate of change by the least squares method, characterized in that the circuit includes three sequential registers for storing the coordinate measurement results, four registers for storing the correction factors, four two-input conjunctors, one subtractor and one parallel adder for three inputs, at the beginning the operation of the circuit in the storage registers of the measurement results of the coordinates are loaded probabilistic display of the last three measured coordinates, in the storage registers mandrel coefficients are loaded probabilistic mappings of the corresponding correction coordinates for three coordinate measurements and one correction coefficient for measuring the rate of change of coordinates, after which the probabilistic mappings from the outputs of the corresponding registers of correction coefficients and registers of storage of the measurement results of the coordinates are paired in parallel to the inputs of two-input conjunctions that perform the function of multipliers devices, product of corresponding coordinates and corrections of the coefficients from the outputs of three conjunctors are fed in parallel to the inputs of the probabilistic adder, at the output of which the sum of the products of the measured coordinates and the corresponding correction coefficients is formed, in parallel with the values from the third and first registers for storing the measurement results, the coordinates are fed to the first and second inputs of the probabilistic subtracter, respectively, the difference from the output of which goes to the first input of the fourth conjunctor, to the second input of which a correction factor with h tvertogo register storing correction coefficients, the output of which forms the product of the difference of the first and third coordinates measuring the corresponding correction factor, and outputs a fourth adder conjunctor are the outputs of the whole circuit.

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