RU2616188C1 - Method of multistage filtration for auto support systems - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: signal coordinates of observation status is input to the multi-stage filter, which is a series of serially connected incremental dimension filters (n≥2) each of which forms the estimates used in the following as the measurement filter, according to the corresponding algorithm.

EFFECT: provision of support unstalled intense maneuvering targets with high precision estimation of derivatives of the third and fourth order with a small number of measuring instruments used.

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Description

The invention relates to electronic systems for tracking intensely maneuvering targets, in particular to tracking rangefinders and goniometers of airborne radars.

The expansion of the nomenclature of super-maneuverable (LSA) and hypersonic (GZLA) aircraft complicates the guidance process, which is manifested in a significant complication of the algorithms for trajectory control of interceptors [1, 2], associated with the need to take into account the high derivatives of the coordinates of the relative and absolute motion of the interceptor and goals [3]. In this regard, tracking systems of airborne radars must form estimates of the derived coordinates of the state of high (up to the fourth) orders.

It should be noted that in a number of radar systems, in particular, in goniometric systems, the estimation of high derivatives is difficult in view of the fact that only angles (side bearings) are directly measured [4]. Below we propose a multi-stage filtering method that allows one to estimate high derivatives of phase coordinates with high accuracy, even with a small number of directly observed coordinates.

Typically, to solve filtering problems, a Kalman filter is used, which generally allows for the system

in the presence of observations

to form optimal estimates by the criterion of the minimum of the total variance of error errors according to the rule [5]

- соответственно n-мерные векторы координат состояния оцениваемого процесса и их оценок; х_э - вектор экстраполяции оценок

, Ф - переходная матрица состояния системы; z(k) - m-мерный (m≤n) вектор измерений; Н - матрица формирования наблюдений, К_ф - матрица коэффициентов усиления невязки; D - ковариационная матрица ошибок фильтрации; D_и и D_x - соответственно ковариационные матрицы шумов измерений ξ_и (2) и возмущений ξ_х (1), k - номер шага, D_э - матрица ошибок экстраполяции.Here x (k) and

- respectively, n-dimensional vectors of the state coordinates of the process being evaluated and their estimates; x _e - vector extrapolation estimates

, Ф is the transition matrix of the state of the system; z (k) is the m-dimensional (m≤n) measurement vector; H is the matrix of the formation of observations, K _f is the matrix of the gain of the residual; D is the covariance matrix of filtering errors; D _and and D _x are the covariance matrices of measurement noise ξ _and (2) and perturbations ξ _x (1), k is the step number, D _e is the extrapolation error matrix, respectively.

From (3) it follows that in the Kalman filter the number of feedbacks formed in the residual (z (k) -H (k) x _e (k)) is determined by the number of meters used, which determines its disadvantage: a tendency to buckling (occurrence divergences) or deterioration in the accuracy of forming estimates of high derivatives of the process (1) - (7), when using a small number of meters.

This disadvantage can be compensated by applying several series-connected filters with increasing dimension.

The objective of the invention is to develop a method for forming estimates of the coordinates of the state, providing high accuracy in estimating high derivatives and filtering stability with a small number of measured coordinates.

The problem is achieved in that the signal of observation of the state coordinates is fed to the input of a multi-stage filter, which is a series of sequentially connected filters of increasing dimension (n≥2), each of which forms estimates used in the next filter as measurements, which determines the increase in their number feedbacks and, accordingly, increasing the stability and accuracy of the estimated derivatives.

The technical result that can be obtained from the use of the invention is to ensure the accuracy and stability of the formation of estimates of high derivatives with a small number of primary meters in promising tracking systems.

The principles of operation of the proposed method are illustrated by the example of a three-stage filter of the fourth order, provided that one meter is used. Its functional diagram is shown in figure 1, where:

и передающая их на вторую ступень в качестве измерений;F1 - the first stage of a multi-stage filter, forming estimates

and transmitting them to the second stage as dimensions;

и передающая их на вторую ступень в качестве измерений;F2 - the second stage of a multi-stage filter, forming estimates

and transmitting them to the second stage as dimensions;

и передающая их потребителю.F3 - the third stage of a multi-stage filter, forming estimates

and transmitting them to the consumer.

The effectiveness of the proposed multi-stage filtering method was tested on the example of forming estimates of the angle and its derivatives up to the fourth order in the presence of one meter (angle).

For comparison, a fourth-order classical Kalman filter was used as a prototype when using a single meter, obtained on the basis of (2) - (7).

In the application to the problem in question, a prototype model was used state

when using one meter

Where x ₁ , x ₂ , x ₃ , x ₄ are the coordinates of the state of the process being evaluated, ΔT is the time discrete.

Based on (8) and (9), according to algorithm (3) - (5), estimates are formed according to the rule

и х_э1, х_э2, х_э3, х_э4 - соответственно оценки координат состояния оцениваемого процесса х₁, х₂, х₃, х₄ и их экстраполяции; κ_ф1, κ_ф2, κ_ф3, κ_ф4 - компоненты матрицы усиления невязки К_ф, М - знак операции математического ожидания возможных значений координат состояния. Где вычисляются по правилу (6)-(7), при известной дисперсии DK ошибок измерений (9). Упрощенная структура такого фильтра, использованного в качестве прототипа, приведена на фигуре 2.Here

and x _e1 , x _e2 , x _e3 , x _e4 , respectively, estimates of the coordinates of the state of the evaluated process x ₁ , x ₂ , x ₃ , x ₄ and their extrapolation; κ _f1 , κ _f2 , κ _f3 , κ _f4 are the components of the residual gain matrix K _f , M is the sign of the mathematical expectation of possible values of the state coordinates. Where are calculated according to rule (6) - (7), with the known variance DK of measurement errors (9). The simplified structure of such a filter, used as a prototype, is shown in figure 2.

Analysis (10) - (12) shows that in this filter there is only one negative feedback, which will lead in some cases to a loss of stability and a decrease in the accuracy of forming estimates of the state coordinates.

It should be noted, however, that when accompanied by super-maneuverable (LSMS) and hypersonic (GZLA) flying targets moving along complex spatial trajectories even in the first filter, in which only the measured coordinate and its derivative are estimated (Figure 1), as a rule, a breakdown occurs accompaniment due to the discrepancy beyond the linear sections of direction-finding (discriminatory) characteristics (figure 3).

The most radical way to eliminate this drawback is to use an adaptive α, β filter as the first stage, the functioning algorithm of which is determined by the relations

- оценки координат х₁, х₂ на k-м шаге; х_э11(k) - экстраполяция координаты x₁₁(k); Δх(k) - невязка измерений; α(k), β(k) - коэффициенты усиления невязки, ΔT - дискрет времени; D₁ и D₂ - дисперсии ошибок фильтрации x₁₁(k) и х₁₂(k); Δх₀ - порог, определяющий начало адаптации х₁; Δx_max - максимальное значение ошибки сопровождения, определяемое шириной линейного участка дискриминационной характеристики.In (13):

- estimates of coordinates x ₁ , x ₂ at the kth step; x _e11 (k) - extrapolation of the coordinate x ₁₁ (k); Δх (k) is the residual of measurements; α (k), β (k) - residual gain, ΔT - time discrete; D ₁ and D ₂ - variance of filtering errors x ₁₁ (k) and x ₁₂ (k); Δx ₀ is the threshold that determines the beginning of adaptation x ₁ ; Δx _max - the maximum value of the tracking error, determined by the width of the linear section of the discriminatory characteristics.

, сформированные в первой ступени:As the second stage, it is proposed to use a fourth-order Kalman filter (2) - (5) using measurements

formed in the first step:

The functional diagram of the proposed two-stage filter, determined by relations (13) - (17), is shown in figure 4.

The analysis of the method (13) - (17) of the formation of estimates allows us to draw the following conclusions:

- the obtained law differs from the prototype (10) - (12) in that it performs multi-stage filtration when the adaptive α, β filter is used as the first stage, and the fourth-dimensional Kalman filter is used as the second stage, which improves the accuracy and stability of the formation estimates by increasing the number of feedbacks in the second stage;

- to use the algorithm does not require additional measurements compared to the prototype;

- the proposed algorithm for forming estimates does not impose fundamental restrictions on the possibility of its implementation.

The effectiveness of the proposed method of multi-stage filtration was checked according to the results of simulation modeling of the angular tracking system of an intensely maneuvering target moving according to the law

provided that a monopulse goniometer is used [4], with a linear portion of the direction-finding characteristic 2Δx _max = 0.2rad (figure 3), which forms a measurement

- его первая, вторая, третья и четвертая производные, ξ_и - шум измерений с известной дисперсией D_и.where ϕ _C - the current bearing of the target; but

- its first, second, third and fourth derivatives, ξ _and - measurement noise with a known dispersion D _and .

можно получить законы изменения ϕ_ц практически любой сложности.The advantage of model (18) is its adequacy to the real conditions of moving the target in a wide field of application conditions, since by manipulating

you can get the laws of change ϕ _C virtually any complexity.

As an indicator of the accuracy of the formation of estimates, the errors of estimating the bearing of the target, its first, second and third derivatives are used:

During the study, the following was modeled: monitored process (18), measurements (19), measurement noise, adaptive α, β - filter (13) with a second filter (14) - (17). For comparison, a single-stage Kalman filter (10) - (12) was simulated for the same conditions.

Figures 5 and 6 show the dependences of the relative errors of angle estimation obtained during modeling (Figure 5a), its first derivative (Figure 5b), the second derivative (Figure 6a), and the third derivative (Figure 6b) versus time, where different lines correspond to different lines filters: 1 - classic Kalman filter (10) - (12); 2 - adaptive α, β - filter (13); 3 - two-stage filter (13) - (17).

Since under the conditions used in the classical Kalman filter there is a breakdown of tracking (Δx> Δx _max , figure 5a), conditional transients that would occur if there were no breakdown are shown for it.

The simulation allows us to draw the following conclusions:

- a fourth-order Kalman filter, considered as a prototype, does not provide continuous tracking of intensely maneuvering targets, the law of which changes the spatial position of which contain high-order derivatives, and therefore cannot be used to evaluate them;

- the proposed method of multi-stage filtering allows for continuous tracking of intensely maneuvering targets with high-precision estimation of derivatives of the third and fourth order with a small number of meters used.

Literature

1. Merkulov V.I. The dynamism of aviation systems and on-board electronic systems. - M .: Radio engineering. - 2010, No. 1. - S. 88-96.

2. Ilchuk A.R., Merkulov V.I., Samarin O.A., Yurchik I.A. The effect of intensive maneuvering targets on the performance indicators of the primary signal processing system in airborne radars. Radio engineering. - 2003, No. 6.

3. Willow B.C., Merkulov V.I., Sokolov D.A. Maintenance of intensively maneuvering targets with an inertial goniometer in single-use systems. Information-measuring and control systems. - 2014, No. 3. - S. 13-18.

4. Merkulov V.I. [and etc]. Aircraft radio control systems. T.2. Electronic homing systems. / Ed. A.I. Kanaschenkova and V.I. Merkulova. - M .: Radio engineering, 2003 .-- 390 p.

5. Merkulov V.I., Drogalin V.V., Kanaschenkov A.I. and other Aviation systems of radio control. T. 1. The principles of building radio control systems. Fundamentals of synthesis and analysis. / Ed. A.I. Kanaschenkova and V.I. Merkulova. - M .: Radio engineering, 2003 .-- 390 p.

Claims (16)

A multi-stage filtering method for auto tracking systems that provides continuous tracking of intensively maneuvering targets with high-precision estimation of third and fourth order derivatives with a small number of meters used, which means that the signal for observing the state coordinates is fed to the input of a multi-stage filter, which is a series of series-connected filters of increasing dimension (n≥2), each of which forms the estimates used in the next filter as rhenium, according to the algorithm:

Here: x ₁ (k), x ₂ (k), x ₃ (k), x ₄ (k) are the coordinates of the state of the process being evaluated;

,

- estimates of coordinates x ₁ (k), x ₂ (k) at the kth step, formed in the first stage of the filter;

,

,

,

- estimates of coordinates x ₁ (k), x ₂ (k), x ₃ (k), x ₄ (k) at the kth step, formed in the second stage of the filter; x _e11 (k) - extrapolation of the coordinate x ₁₁ (k) in the first stage of the filter; x _e21 (k), x _e22 (k), x _e23 (k), x _e24 (k) - extrapolation of coordinates x ₁ (k), x ₂ (k), x ₃ (k), x ₄ (k) second stage of the filter; α (k), β (k) - residual gain in the first filter stage; D ₁ and D ₂ - variance of filtering errors x ₁₁ (k) and x ₁₂ (k); D ₁₁ , D ₂₁ , D _3l , D ₄₁ , D ₁₂ , D ₂₂ , D ₃₂ , D ₄₂ - variance of filtering errors x ₂₁ (k), x ₂₂ (k), x ₂₃ (k), x ₂₄ (k) ; Δx ₀ is the threshold that determines the beginning of adaptation x ₁ ; Δx _max - the maximum value of the tracking error, determined by the width of the linear section of the discriminatory characteristics; ΔT is the time discrete.

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