RU2476904C1 - Method of tracking object and method of generating signal for controlling beam position of transceiver antenna of object tracking system - Google Patents

Abstract

FIELD: radio engineering, communication.SUBSTANCE: in the method of tracking an object, the novelty lies in that motion parameters of the object are estimated using a Kalman filter in initial conditions for estimates are set; the current signal-to-noise ratio in the signal received from the object is determined; a signal-to-noise ratio threshold value is set; the signal-to-noise ratio is used to determine the current root-mean-square error of the object coordinate measurement; said value is smoothed out and the obtained error value is used to determine Kalman filter gain constants; the current signal-to-noise ratio value is compared with the threshold and, if it less than the threshold, a feature indicating absence of a signal reflected from the signal is generated and further generation of extrapolated coordinates is carried out based on motion parameter estimates of the object which are stored at the beginning of generation of the feature indicating absence of a received signal, with subsequent correction of values thereof, taking into account reduction in information content of the stored parameters with progression of the current moment in time from the beginning of generation of the feature indicating absence of a signal; and when converting extrapolated coordinates of the object to coordinates for setting the antenna beam for emitting a probe signal, time lag of these coordinates relative the time when coordinates of the object are generated based on the signal received from the object is taken into account. In the method of generating a signal for controlling the beam position of a transceiver antenna of an object tracking system, the novelty lies in that the dynamic elements used to generate the control signal are a Kalman filter in which the model trajectory of the tracked object is given with an s-dimensional state vector of motion parameters, an positive feedback is realised based on the extrapolated coordinate of the object. In the positive feedback circuit, the extrapolated coordinate is delayed by a time equal to the time interval for extrapolating that coordinate.EFFECT: high accuracy of tracking and measuring coordinates of an object.9 cl, 2 dwg

Description

The group of inventions relates to location technology and is intended for use in systems of automatic tracking of objects.

A known method of tracking an object, including emitting a probe signal and receiving a signal reflected from the object, processing the received signal and generating, in each tracking plane, an object tracking error signal relative to the axis of the beam of the receiving and transmitting antenna device, generating, in accordance with the tracking signal error signal, a receiving position control signal - transmitting antenna device and continuous alignment of the axis of the beam of the antenna device with the line of sight of the object for the next radiation of the probe signal ([1], B.B. Vasin, OVVlasov and other Radar devices. M: Soviet radio, 1970, pp. 313-314, pp. 343-339).

This method of tracking an object has disadvantages determined by the low speed of viewing the space and low throughput, the lack of multifunctionality and significant weight and size characteristics associated with the presence of power drives in the tracking system that implements this method.

A known method of generating a signal for controlling the position of the beam of the receiving and transmitting antenna device of the object tracking system, including generating an error signal for tracking the object relative to the axis of the beam of the receiving and transmitting antenna device, generating, in accordance with the signal of the error of the tracking signal of the control signal of the rotation device of the receiving and transmitting antenna device, and subsequent correction of this control signal by means of integral regulation ([2], MV Maksimov, GI Gorgonov. Ra ioelektronnye homing - M .: Radio and Communications, 1982, str.226-228, str.235-237).

In this method, due to the integral regulation of the control signal (implemented by the inclusion of an appropriate number of integrators in the control system of the tracking system), the object tracking circuit as a dynamic system is given astatism properties that increase the accuracy of working out the input effect determined by the movement of the accompanied object. The order of astatism of the system is determined with respect to the derivatives of the input action, for example, with an object moving at the same speed, the steady-state tracking error will be zero in systems with second-order astatism ([3], Ed. By A. A. Krasovsky. Reference on the theory of automatic control . - M .: Nauka, 1987, pp. 107-113).

The known method has disadvantages, determined by the fact that the necessary order of astatism, providing the required dynamic accuracy, is limited by the possibilities of ensuring the stability of the tracking system, because already with the order of astatism above the first, the system becomes structurally unstable (due to the presence of integrators in the control channel), therefore, systems with first or second order astatism are practically realized. In addition, this method of generating a control signal with the astatism of the object tracking circuit is realized only when controlling the mechanical movement of the antenna device and its beam in space.

Closest to the proposed one is a method of tracking an object, including discrete radiation of a probing signal and receiving a signal reflected from the object, processing the received signal with simultaneous gating in range and generating, in each tracking plane, a signal for tracking an object with respect to the axis of the beam of the receiving and transmitting antenna device, taking into account the error signals of tracking the coordinates of the object in the coordinate system of the receiving and transmitting antenna device and converted e them into rectangular coordinates relative to the reference direction, estimating object motion parameters from them and generating extrapolated object coordinates, converting the extrapolated object coordinates to the coordinate system of the receiving and transmitting antenna device and electronically controlling the beam of the antenna device along them in the direction of the next radiation of the probe signal ([4 ], SZ Kuzmin, Fundamentals of Designing Systems for Digital Processing of Radar Information. - M.: Radio and Communications, 1986, pp. 212-217, pp. 160-164).

This method is based on the use of an antenna with non-mechanical movement in the space of its beam for tracking an object, the so-called phased antenna array (PAR) with electronic control of the beam position in the direction, which allows for multifunctionality and an increase in the tracking efficiency of the object.

In the known method for evaluating the parameters of the object’s movement (filtering its measured coordinates), the filter parameters are set in advance, at the design stage, based on the a priori accepted values of the coordinate measurement errors and the conditional probability of possible evolution in the movement of the accompanied object. In this case, specific current conditions of tracking are not taken into account: the position, type and parameters of the object’s movement at the moment of its tracking, as well as possible changes in the magnitude of the noise error of coordinate measurement during tracking. At a low level of the received reflected signal from the object (depending on the distance to the object, its reflecting properties, weather conditions, etc.), characterized by the signal-to-noise ratio, the process of forming the coordinates of the object may become unreliable or even interrupted. At the same time, the measured coordinates of the object and, accordingly, the coordinates of the AFR beam setup have large errors, and the moment of tying of the tracking trajectory and transitions from the state of coordinate estimation to the state of their extrapolation are accompanied by lengthy transient processes. Since in this case the tracking operations do not have a “memory” and do not take into account the decrease in the information content of retrospective coordinate measurements, when the signal is interrupted (with possible interference, fluctuations, and fading of the reflected signal, etc.), the accumulated information about the movement of the object is lost and the forecast accuracy from -for the "obsolescence" of the obtained coordinate estimates. Therefore, the subsequent installation of the beam in the direction of the object is carried out with an error, which leads to an increase in the tracking error or to the failure of the tracking of the object. Due to the limited computing resources of the tracking system, the moment of planning a new beam position for the emission of the probing signal has a time lag relative to the instant of formation of the object’s coordinates from the measured reflected signal, which, with a moving line of sight of the object or a moving headlamp carrier, also leads to an additional error of coordinate measurement. These circumstances determine the disadvantages of the known method of tracking an object.

Closest to the proposed one is a method of generating a control signal for the position of the object, including generating a control error, which is a differential signal between the signal of the driving signal and the signal of the output coordinate of the control object, generating, in accordance with this signal, an error in the signal for controlling the position of the object, organizing a positive feedback circuit, embracing dynamic links intended for the formation of a control signal, and the choice of the transfer function link in the chain of positive feedback in accordance with the transfer function of the dynamic links in the direct chain of the control signal formation ([5], Ya.Z. Tsypkin. Fundamentals of the theory of automatic systems. - M .: Nauka, 1977, pp. 76-77, pg. 123-128).

The known method of generating a control signal provides an increase in the astatism of the control loop of the object to the first order, i.e. such a system will have a zero steady-state error with a constant value of the driving action. However, the dynamic properties of a contour with first-order astatism do not provide the required accuracy characteristics of tracking moving objects, when the targeting effects on their tracking system change with certain speeds and accelerations, i.e. a system for tracking real objects to ensure the required accuracy should have an astatism order higher than the first. Thus, the known method provides low accuracy tracking of real moving objects.

A common drawback of these technical solutions is the low accuracy of tracking under conditions of uncertainty in the dynamics of the movement of the object and the changing energy of the signal reflected from the object, which leads to a decrease in the accuracy of measuring the coordinates of the object and a decrease in the potential area of the tracking system.

The objective of the proposed group of inventions is to increase the accuracy of tracking and measuring the coordinates of the object.

The problem is solved in that in the method of tracking the object, including discrete radiation of the probe signal and receiving the signal reflected from the object, processing the received signal with simultaneous gating in range and the formation in each tracking plane of the tracking signal of the tracking object relative to the axis of the beam of the receiving and transmitting antenna device, the formation, taking into account the error signals, of tracking the coordinates of the object in the coordinate system of the receiving and transmitting antenna device and conversion them into rectangular coordinates relative to the reference direction, estimating object motion parameters from them and generating extrapolated coordinates of the object, converting the extrapolated coordinates to the coordinate system of the receiving and transmitting antenna device and electronically controlling the beam of the antenna device in the direction of the next radiation of the probing signal, is new that the assessment of the parameters of the object’s movement and the generation of extrapolated coordinates of the object is carried out using a Kalman filter the model of the trajectory of the tracked object, set at the moment of tracking start the initial conditions for estimating the motion parameters of the object in the Kalman filter, determine the current signal-to-noise ratio in the received reflected signal from the object, set the threshold value of the signal-to-noise ratio, determine in accordance with the value of the signal ratio -noise the current value of the mean square error of measuring the coordinates of the object, conduct the current smoothing of the values of the mean square error of measuring the coordinates of the object kta, determine the Kalman filter gains taking into account the current smoothed value of the mean square error of measuring the coordinates of the object, compare the current value of the signal-to-noise ratio with a set threshold value of the signal-to-noise ratio and, if the current value of the signal-to-noise ratio is less than the threshold value, then a sign of absence the reflected signal received from the object and then, in the presence of this sign, the generation of extrapolated coordinates of the object is carried out according to estimates of the motion parameters of the object, memorized at the time of the start of formation of the sign of the absence of the received signal, followed by the current correction of their values, taking into account the decrease in the information content of the stored estimates of the motion parameters as the current moment moves away from the moment of the start of the formation of the sign of the absence of the received signal, and when the extrapolated coordinates of the object are converted to the coordinates for setting the beam of the receiving and transmitting antenna device for the emission of the probing signal take into account the time delay The building of the formation of extrapolated coordinates relative to the instant of formation of the object’s coordinates according to the received reflected signal from the object.

In the proposed method of tracking an object, initial conditions are set for estimating the parameters of the object’s movement by coordinates, equal to the values of the corresponding coordinates formed by the first measurement of the coordinates of the tracked object, and by the derivatives of the coordinates equal to the values of the corresponding derivatives of the coordinates of the tracked object, obtained from an external source or from a priori data of derivatives coordinates of the object.

In the proposed method of tracking an object, the current value of the mean square error of measuring the coordinates of the object σ _φ [n] is determined by the ratio

where Θ ₀ is the width of the beam pattern of the receiving and transmitting antenna device;

q ₀ [n] is the current signal-to-noise ratio of the received reflected signal from the object;

k _s - safety factor, taking into account the deviation of the value of the tracking error of the object from the error value determined by the potential accuracy of the tracking system;

n is the current number of the discrete time tracking step, n = 1, 2, 3, ....

In the proposed method of tracking an object, smoothing the current value of the mean square error of measuring the coordinates of the object is carried out by a discrete low-pass filter, determined by the ratio

with initial condition

also set each time at the time of renewal of the sign of the presence of the reflected signal received from the object after its absence,

- текущее значение сглаженной среднеквадратической ошибки измерения координат объекта - выходной сигнал;Where

- the current value of the smoothed mean square error of measuring the coordinates of the object is the output signal;

and _σ is the coefficient defining the passband of the filter;

σ _φ [n] is the current value of the standard error of the measurement of the coordinates of the object is the input signal;

k _c [n] - coefficient equal to

n is the current number of the discrete tracking step, n = 1, 2, 3, ....

In the proposed method of tracking an object in the Kalman filter, the model of the trajectory of the tracked object is set with a three-dimensional vector of the state of the motion parameters, determined by each rectangular coordinate by the relations

,

- текущие параметры траектории объекта, соответственно координата, скорость и ускорение, образующие трехмерный вектор состояния параметров движенияwhere x [n]

,

- current parameters of the trajectory of the object, respectively, coordinate, speed and acceleration, forming a three-dimensional vector of the state of motion parameters

;

;

T ₀ - time step for measuring the coordinates of the object;

n is the current number of the discrete step, n = 1, 2, 3, ....

In the proposed method of tracking an object, the generation of extrapolated coordinates of the object in the presence of a sign of the absence of a reflected signal received from the object is carried out in accordance with the ratios for each rectangular coordinate

,

- соответственно текущие экстраполированные координата, скорость и ускорение объекта;where x _e [n],

,

- respectively, the current extrapolated coordinate, speed and acceleration of the object;

,

,

- соответственно оценки координаты, скорости и ускорения объекта, запомненные на момент времени начала формирования признака отсутствия принимаемого от объекта отраженного сигнала;

,

,

- accordingly, estimates of the coordinate, speed and acceleration of the object, stored at the time point of the beginning of the formation of the sign of the absence of the reflected signal received from the object;

τ ₀ - time step of extrapolation of coordinates;

k _AND [n] is a weighting factor that takes into account the decrease in the information content of coordinate estimates as the current time moves away from the moment the formation of the sign of the absence of the received signal begins, k _И = 1 in the presence of the sign of the received signal and 0≤k _AND <1 in the absence of the sign of the received signal ;

n is the current number of the discrete time tracking step, n = 1, 2, 3, ...

In the proposed method of tracking an object, the time lag of forming the extrapolated coordinates of the object relative to the time of the formation of coordinates according to the received reflected signal from the object is taken into account by adjusting the angular extrapolated coordinates by the value Δφ, determined in each tracking plane by the ratio

- текущая угловая скорость перемещения оси приемно-передающего антенного устройства в соответствующей плоскости сопровождения;Where

- the current angular velocity of the axis of the receiving and transmitting antenna device in the corresponding tracking plane;

Δt is the time delay of the extrapolated coordinates of the object relative to the instant of formation of the coordinates of the object according to the received reflected signal from the object;

n is the current number of the discrete time tracking step, n = 1, 2, 3, ....

The problem is also solved by the fact that in the method of generating a signal for controlling the position of the beam of the receiving and transmitting antenna device of the object tracking system, including discrete generation of an object tracking error signal relative to the beam axis of the receiving and transmitting antenna device in each tracking plane, generating signal errors with this signal control of the position of the beam of the receiving and transmitting antenna device, organization of a positive feedback circuit spanning the The links designed for generating a control signal are new because the Kalman filter is used as dynamic links for generating a control signal by the position of the beam of the receiving and transmitting antenna device, in which the model of the trajectory of the tracked object is specified with the s-dimensional state vector of the motion parameters, and positive feedback is carried out according to the extrapolated coordinate of the tracking object from the output of the Kalman filter, and in the positive feedback circuit the delay of the extrapolated coordinate by a time equal to the time interval of extrapolation of this coordinate.

In the proposed method for generating a signal for controlling the position of the beam of the receiving and transmitting antenna device of the object tracking system in the Kalman filter, the model of the trajectory of the tracked object is set with a three-dimensional vector of the state of the motion parameters, determined by each tracking coordinate by the relations

,

- текущие параметры траектории объекта, соответственно координата, скорость и ускорение, образующие трехмерный вектор состояния параметров движенияwhere ϑ [n],

,

- current parameters of the trajectory of the object, respectively, coordinate, speed and acceleration, forming a three-dimensional vector of the state of motion parameters

;

;

T ₀ - time step for measuring the coordinates of the object;

n is the current number of the discrete step, n = 1, 2, 3, ....

The introduction of new operations and their relationships made it possible, in comparison with known methods, to increase the accuracy of tracking and measuring the coordinates of an object, the noise immunity of tracking, especially when tracking dynamic objects with intense noise, measuring their coordinates and a weak reflected signal, and also realizing high-order astatic properties tracking circuit when using a headlamp with electronic control of its beam.

A diagram explaining the proposed method for tracking an object is shown in FIG. 1, and a method for generating a beam position control signal (for one tracking plane) is shown in FIG. 2, which indicates:

12, 13, 15 - adders;

14 - block gain of the Kalman filter;

OOS - negative feedback;

PIC - positive feedback;

δε is the tracking error of the object relative to the axis of the beam of the receiving and transmitting antenna device;

- измеренная координата объекта сопровождения;

- the measured coordinate of the tracking object;

- вектор оценок параметров движения объекта;

- a vector of estimates of the parameters of the movement of the object;

Θ _e [n] - the vector extrapolated parameters of the object;

ϑ _Э [n] - extrapolated coordinate of the tracking object.

In Fig. 2, a double arrow denotes a vector connection, a single arrow denotes a scalar connection.

The way to maintain the facility is as follows. The beam of the receiving and transmitting antenna device of the tracking system at the current time t [n], where n is the measure number with a tempo T ₀ , is set in the direction of the angles ε _c [n] and β _c [n] of the expected position of the object for the next radiation of the probe signal , where ε _c [n], β _c [n] are the elevation angle and azimuth of the object in the coordinate system of the tracking antenna obtained from previous measurements and coordinate processing, and initially (at n = 1) from an external source of target designation (for example, object detector). The probe signal is emitted, the reflected signal from the object is received and processed, and the object tracking error signals δε [n] and δβ [n] are generated in the corresponding tracking planes relative to the beam axis of the receiving and transmitting antenna device (ie, the angular coordinates of the object relative to the beam axis antenna) with simultaneous gating along the range D [n] to the object. In the process of receiving the signal reflected from the object and measuring the coordinates δε [n] and δβ [n], the current signal-to-noise ratio q ₀ [n] in the received reflected signal is determined by a known method ([1], pp. 97-98). Preliminarily, before the start of tracking, a threshold value q _{0 is established} . The signal-to-noise ratio _pore below which the object coordinates formed by the received reflected signal are considered unreliable or absent altogether. Quantitatively, the threshold value of the signal-to-noise ratio q _{0 Pore is} set based on the admissible value of the probability of false alarm when a signal from an object is detected.

. Сглаживание среднеквадратической ошибки измерения координат проводят с учетом возможных прерываний измерений координат объекта, определяемых по критерию непревышения текущего значения сигнал-шум q₀[n] установленного порогового значения q_0Пор, посредством управления коэффициентом k_c[n] в соответствии с соотношением (4), а также переприсвоением начальных условий (3) на сглаживающем фильтре после восстановления процесса измерения координат.Then, in accordance with relation (1), based on the obtained signal-to-noise ratio q ₀ [n], the current value of the mean square error (RMS) of measuring the coordinates of the object σ _φ [n] is formed ([1], p. 314), where the safety factor k _h set from the range of values of k _s ≈ 1 ... 3, which is smoothed by a low-pass filter of the first order in accordance with relation (2) to the current value

. The root-mean-square error of the coordinate measurement is smoothed out taking into account possible interruptions in the measurements of the object’s coordinates, determined by the criterion of not exceeding the current signal-to-noise value q ₀ [n] of the established threshold value q _{0 Pore,} by controlling the coefficient k _c [n] in accordance with relation (4), as well as reassignment of initial conditions (3) on the smoothing filter after restoration of the coordinate measurement process.

The angular coordinates of the object ε _a [n], β _a [n] are generated in the coordinate system of the tracking antenna (for example, in a biconical coordinate system) as the sum of the measured corresponding error coordinates δε [n], δβ [n] and the coordinates of the beam position ε _c [n], β _c [n]

The angular coordinates ε _a [n], β _a [n], taking into account the measured distance D [n] to the object, are converted into rectangular coordinates x _a [n], y _a [n], z _a [n] in the antenna coordinate system ratio tracking

and further, taking into account the angular position ε _{0 of the} installation of the axis of the receiving and transmitting antenna device relative to the selected reference direction (for example, the base plane of the carrier of the antenna device) in the rectangular coordinates x [n], y [n], z [n] in the coordinate system of the system object tracking

,

,

и их первые

,

,

, вторые

,

,

и т.д. производные, получаемые по результатам обработки сформированных координат

,

,

объекта. Оценку текущих параметров движения объекта проводят посредством использования фильтра Калмана, определяемого известными соотношениями ([4], стр.163-164), который осуществляет оценку параметров движения посредством выполнения совместных и взаимосвязанных операций динамической фильтрации и экстраполяции координат, что обеспечивает оптимальную обработку результатов измерений. Структура фильтра Калмана содержит в качестве своей составной части математическую модель траектории объекта сопровождения (модель оцениваемого процесса), которая задается матрицей экстраполяции, определяющей размерность вектора состояния параметров движения объекта. Свойства фильтра Калмана определяются принятой моделью траектории движения и коэффициентами усиления (фильтрации), значения которых определяются принятыми ошибками измерения координат сопровождаемого объекта.Then carry out an assessment of the current parameters of the object’s movement, which means filtered rectangular coordinates of the object

,

,

and their first

,

,

second

,

,

etc. derivatives obtained by processing the generated coordinates

,

,

object. The current parameters of the object’s motion are estimated using the Kalman filter determined by the known relations ([4], pp. 163-164), which evaluates the motion parameters by performing joint and interconnected operations of dynamic filtering and extrapolating coordinates, which ensures optimal processing of measurement results. The Kalman filter structure contains as its component a mathematical model of the trajectory of the tracking object (model of the process being evaluated), which is defined by an extrapolation matrix that determines the dimension of the state vector of the object’s motion parameters. The properties of the Kalman filter are determined by the adopted model of the trajectory of motion and the amplification (filtering) coefficients, the values of which are determined by the accepted errors of measuring the coordinates of the tracked object.

When defining a model of the object’s trajectory with a three-dimensional state vector of motion parameters in the form (5) and, accordingly, with estimated parameters in the form of the coordinate, speed and acceleration of the object, the correlations for the Kalman filter, taking into account possible interruptions in the allocation of the object’s coordinates and decrease in the information content of the stored parameter estimates the movements on the interruption intervals (taken into account respectively by the controlled coefficients k _c [n] and k _AND [n]) have the form (written for one coordinate, for example, for the x coordinate)

- estimation equations

- extrapolation equations

,

,

- оценки координаты, скорости и ускорения объекта соответственно;Where

,

,

- estimates of the coordinate, speed and acceleration of the object, respectively;

,

- экстраполированные координата, скорость и ускорение объекта соответственно;x _e [n]

,

- extrapolated coordinate, speed and acceleration of the object, respectively;

k ₁ [n], k ₂ [n], k ₃ [n] - gain (filtering);

T ₀ - the period of sampling measurements and processing coordinates.

Gain factors k ₁ [n], k ₂ [n], k ₃ [n] are calculated in the current tracking time using the relations

where ψ _E11 [n], ψ _E12 [n], ψ _E13 [n] are the correlation coefficients of extrapolation errors, respectively, coordinates (index "1"), first (index "2") and second (index "3") derived coordinates, determined by known recurrence relations ([4], p. 163) for a given model of the trajectory of the tracking object in the form (5) taking into account the correlation coefficients of the estimation errors, respectively, of the coordinate of its first and second derivatives.

, связанной с измерениями принимаемого от объекта отраженного сигнала в реальном процессе сопровождения (по соотношению сигнал-шум), позволяет при оценке и экстраполяции координат учесть фактически сложившиеся точностные условия сопровождения объекта.The proposed definition of the coefficients k ₁ [n], k ₂ [n], k ₃ [n] Kalman filters, and, accordingly, the filtering and extrapolation parameters, taking into account the current value of the mean square error

associated with measurements of the reflected signal received from the object in the real tracking process (in terms of signal-to-noise ratio), when evaluating and extrapolating coordinates, it is possible to take into account the prevailing accuracy conditions for tracking the object.

,

,

, полученным по первому измерению координат сопровождаемого объекта, т.е. (записано для трехмерного вектора состояния параметров движения объекта, например, для координаты х)At the time of the start of escort, i.e. for n = 1, the initial conditions for the estimated motion parameters along the object’s coordinates are set in equations (12) of the Kalman filter equal to the values of the corresponding coordinates

,

,

obtained by the first measurement of the coordinates of the tracked object, i.e. (written for a three-dimensional state vector of the object motion parameters, for example, for the x coordinate)

and according to the speeds and accelerations of the object, equal to the values of the corresponding derived coordinates of the object obtained from an external source, or according to a priori data of the derived coordinates of the object, i.e.

,

,

,

,

- соответственно скорости и ускорения сопровождаемого объекта с внешнего источника или по априорным (ожидаемым) данным (например, равные нулевым значениям). Внешним источником данных по скоростям и ускорениям объекта может быть, например, система обнаружения объекта.Where

,

,

,

,

- respectively, the speed and acceleration of the tracked object from an external source or according to a priori (expected) data (for example, equal to zero values). An external source of data on the speeds and accelerations of an object can be, for example, an object detection system.

Next, the obtained extrapolated rectangular coordinates of the object x _E [n], for _E [n], z _E [n] are converted into angular coordinates ε _Ea , β _Ea in the coordinate system of the transmitter-receiver antenna, for example, according to the ratios

- экстраполированная дальность до объекта.Where

- extrapolated range to the object.

Then, angular corrections Δφ _ε [n], Δφ _β [n] are introduced into the generated extrapolated angular coordinates of the object ε _Ea [n], β _Ea [n] in the corresponding tracking planes, determined by a relation of the form (7), compensating for the delay Δt of the moment of formation of these extrapolated coordinates relative to the moment of formation of the tracking error signals δε [n], δβ [n] (coordinates) of the object

,

в плоскостях сопровождения для формирования поправок Δφ_ε[n], Δφ_β[n] могут измеряться датчиками угловой скорости, связанными с соответствующими осями антенного устройства, а запаздывание Δt определяется быстродействием конкретного устройства обработки и формирования координат.The current angular velocity of the transverse axes of the antenna device

,

in the tracking planes for the formation of corrections Δφ _ε [n], Δφ _β [n] can be measured by angular velocity sensors associated with the corresponding axes of the antenna device, and the delay Δt is determined by the speed of a particular processing device and the formation of coordinates.

According to the formed coordinates ε _c [n], β _c [n], the beam direction of the antenna device for emitting and receiving signals is electronically controlled at the next step of probing the object, for example, by converting them into phase shifts for phase shifters and the corresponding electronic movement of the beam in the direction of the object ([1], pp. 428-432).

,

,

, запомненными в момент начала формирования признака отсутствия принимаемого сигнала, с текущей коррекцией их значений на весовой коэффициент k_И[n], учитывающий снижение информативности запомненных координат по мере удаления текущего момента времени от момента начала формирования признака отсутствия принимаемого сигнала. Соотношения (6) получаются из соотношений фильтра Калмана (13) путем управления входящим в них коэффициентом k_c[n], формируемым в соответствии с соотношением (4).In the process of tracking, the current signal-to-noise ratio q ₀ [n] is compared with its set threshold value q _Por . If the current comparison value signal to noise ratio is less than a threshold, the formed sign of lack received from the object signal and further in the presence of this feature, generation of the extrapolated coordinate x _e [n], y _e [n], z _E [n] for the subsequent installation of the beam of the antenna device is carried out in accordance with relations (6) according to estimates of the parameters of the movement of the object

,

,

memorized at the time of the start of formation of the sign of the absence of the received signal, with the current correction of their values by the weight coefficient k _AND [n], taking into account the decrease in the information content of the stored coordinates as the current moment moves away from the moment of the start of the formation of the sign of the absence of the received signal. Relations (6) are obtained from the Kalman filter relations (13) by controlling the coefficient k _c [n] included in them, which is formed in accordance with relation (4).

Thus, when interrupting the process of measuring coordinates and then restoring it, when extrapolating the coordinates of the tracked object, the "aging" (decrease in information content) of the coordinates and their derivatives stored for forecasting is taken into account, which increases the accuracy of coordinate formation in the absence of measurements and, accordingly, increases the accuracy and reliability tracking facility.

The value of the weight coefficient k _AND [n] is determined by the adopted model of the movement of the object. Usually consider the maneuverability of an object in the form of a random process with a correlation function of the form ([6], V. A. Likharev. Digital methods and devices in radar. - M .: Soviet radio, 1973, p. 225)

- дисперсия ускорения объекта;Where

- dispersion of the acceleration of the object;

1 / α = T is the maneuver time constant.

In this regard, in practice, as a weight function of the acceleration estimate, as a rule, it is sufficient to use the exponential weighting function of the form

For an equal-discrete tracking time, the exponential function (21) at the current measurement step of coordinates can be approximated by a constant coefficient k _AND from the range of values 0≤k _AND ≤1.

The method of generating a signal for controlling the position of the beam of the receiving-transmitting antenna device of the object tracking system is as follows.

параметров движения (его s-составляющих компонентов

,

,

,

, …) и вектор Θ_Э[n] экстраполированных параметров движения (его s-составляющих компонентов ϑ_Э[n],

,

,

, …). Фильтр Калмана, как динамическая система, по доступным для наблюдения выходным координатам (по оценке координаты

и экстраполированной координате ϑ_Э[n] при разомкнутой его внутренней отрицательной обратной связи (разомкнута цепь ООС, фиг.2) представляет собой по отношению к входному воздействию (координате

) систему с астатизмом, порядок которого равен размерности s вектора состояния параметров движения Θ[n] в принятой модели траектории объекта. При этом фильтр Калмана как замкнутая система (замкнута цепь ООС, фиг.2) асимптотически устойчив и обладает свойством минимальности фазового запаздывания среди всех s-мерных фильтров с той же полосой пропускания. При организации положительной обратной связи по экстраполированной координате объекта ϑ_Э[n] с выхода фильтра Калмана по отношению к сигналу ошибки сопровождения объекта относительно оси луча ФАР δε[n] (цепь ПОС замкнута, фиг.2) динамическое звено, охватываемое этой связью, с учетом задержки экстраполированной координаты на время, равное интервалу времени экстраполяции этой координаты, по отношению к входному воздействию в виде ошибки сопровождения δε[n] представляет систему с астатизмом, порядок, которого равен размерности s вектора состояния параметров движения для принятой модели траектории. Таким образом, при сопровождении объекта ФАР реализуется астатическое регулирование порядка s сигнала управления положением ее луча без нарушения, в силу асимптотических свойств фильтра Калмана, условий устойчивости контура сопровождения объекта.For each object tracking plane, an error tracking signal is generated (δε [n], δβ [n]) relative to the axis of the beam of the receiving and transmitting antenna device with the PAR and then generating a control signal with this error using the Kalman filter, which is essentially structural The organization contains a model of the trajectory of the tracked object, defined in the general case by an s-dimensional state vector of motion parameters. At the output of such a filter, an estimate of the vector is obtained (for each coordinate)

motion parameters (its s-component components

,

,

,

, ...) and the vector Θ _Э [n] of extrapolated motion parameters (its s-component components ϑ _Э [n],

,

,

, ...). Kalman filter, as a dynamic system, by output coordinates available for observation (by coordinate estimation

and the extrapolated coordinate ϑ _Э [n] when its internal negative feedback is open (OOS circuit is open, figure 2) is in relation to the input action (coordinate

) a system with astatism whose order is equal to the dimension s of the state vector of motion parameters движения [n] in the adopted model of the object trajectory. In this case, the Kalman filter as a closed system (closed circuit of the OOS, figure 2) is asymptotically stable and has the property of minimizing phase delay among all s-dimensional filters with the same passband. When organizing positive feedback on the extrapolated coordinate of the object ϑ _Э [n] from the Kalman filter output with respect to the object tracking error signal relative to the beam axis δε [n] (the POS circuit is closed, Fig. 2), the dynamic link covered by this connection, with taking into account the delay of the extrapolated coordinate by a time equal to the time interval of extrapolating this coordinate with respect to the input action in the form of a tracking error δε [n] represents a system with astatism, the order of which is equal to the dimension s of the vector s ence of motion parameters for the model adopted path. Thus, when tracking a phased array object, astatic regulation of the order s of the signal to control the position of its beam is realized without breaking, due to the asymptotic properties of the Kalman filter and stability conditions for the object tracking loop.

и ускорения

, что соответствует физической картине сопровождения объекта, модель траектории движения объекта описывается соотношениями (8), а фильтр Калмана - соотношениями видаWhen defining a model of the trajectory of the tracked object with the state vector of motion parameters in the form of a three-dimensional vector with components of the coordinate ϑ [n], velocity

and acceleration

, which corresponds to the physical picture of the object tracking, the model of the object trajectory is described by relations (8), and the Kalman filter is described by relations of the form

In this case (for steady state), the discrete transfer function of the Kalman filter (based on the Z-transform) in the open state (open circuit of the OOS, figure 2) by the extrapolated coordinate has the form

those. contains in its circuit three series-connected digital integrators described by a transfer function of the form

and, therefore, is a system with third-order astatism.

The discrete transfer function of such a filter in the closed state has the form

In the presence of positive feedback on the extrapolated coordinate of the object ϑ _Э [n] with respect to the signal of the tracking error δε [n], covering the Kalman filter as a dynamic link and containing the delay element of the extrapolated coordinate for a time equal to the time interval of extrapolating the coordinate T ₀ , s the transfer function W _ass (z) = z ^-1 , the discrete transfer function of such a system has the form (i.e., coincides with the transfer function of the form (23)

and thus contains in its chain three series-connected digital integrators described by a transfer function of the form (24), and, therefore, is a system with third-order astatism. In this case, the input coordinate of the filter, i.e. The estimated coordinate of the object will be determined as

Thus, the proposed method in this case provides third-order astatic regulation in the control loop of the position of the PAR beam and, due to the fact that the orders of expressions in the numerator and denominator of the transfer function (25) differ by one (phase delay of not more than 90 °), the loop tracking facility will be stable. This ensures a zero value of the steady-state error of tracking the object during its movement with constant acceleration. Such a statement about stability is valid for any order of dimension s of the state vector of motion parameters and, accordingly, the order s of astatism of the tracking contour is realized, with the exception of the steady-state tracking error of the object with respect to the derivative of the s-th order of the coordinates of the object’s trajectory. Therefore, such a formation of a signal for controlling the position of the PAR beam improves the accuracy of object tracking and the accuracy of measuring its coordinates.

The proposed method of tracking an object and a method of generating a signal for controlling the position of the beam of a receiving and transmitting antenna device of an object tracking system are implemented by well-known standard elements of radar devices ([1], pp. 426-432) and a computer information processing and control system, construction principles, composition, structure and the functioning algorithm of which is given in [4], pp. 223-292.

Thus, the proposed technical solutions provide improved accuracy of tracking and measuring the coordinates of the object, which distinguishes them from known methods.

Information sources

1. VVVasin, OVVlasov and others. Radar devices. - M .: Soviet Radio, 1970.

2. M.V. Maksimov, G.I. Gorgonov. Radio-electronic homing systems - M .: Radio and communication, 1982.

3. Ed. A.A. Krasovsky. Handbook of the theory of automatic regulation. - M.: Science, 1987.

4.S.Z. Kuzmin. Fundamentals of designing systems for digital processing of radar information. - M.: Radio and Communications, 1986.

5. Ya. Z. Tsypkin. Fundamentals of the theory of automatic systems. - M .: Nauka, 1977.

6. V.A. Likharev. Digital methods and devices in radar. - M .: Soviet Radio, 1973.

Claims (9)

1. A method of tracking an object, including discrete radiation of a probing signal and receiving a signal reflected from the object, processing the received signal with simultaneous gating in range and generating an object tracking error signal in each tracking plane of the object relative to the beam axis of the receiving and transmitting antenna device, generating error signals taking into account tracking the coordinates of the object in the coordinate system of the receiving and transmitting antenna device and converting them into rectangular coordinates the reference direction, estimating the parameters of the object’s motion and generating extrapolated coordinates of the object, converting the extrapolated coordinates to the coordinate system of the receiving and transmitting antenna device and electronically controlling the beam of the antenna device in the direction of the next radiation of the probing signal, characterized in that it estimates the motion parameters of the object and the generation of extrapolated coordinates of the object is carried out using a Kalman filter containing a model of the trajectory of the object, set at the moment of tracking start the initial conditions for estimating the parameters of the object’s movement in the Kalman filter, determine the current signal-to-noise ratio in the received reflected signal from the object, set the threshold signal-to-noise ratio, determine the current signal-to-noise ratio in accordance with the signal-to-noise ratio the value of the standard error of the measurement of the coordinates of the object, conduct the current smoothing of the values of the standard error of the measurement of the coordinates of the object, determine the gains f Kalman filter, taking into account the current smoothed value of the mean square error of measuring the coordinates of the object, compare the current value of the signal-to-noise ratio with the set threshold value of the signal-to-noise ratio and, if the current value of the signal-to-noise ratio is less than the threshold value, then a sign of the absence of the reflected signal received from the object and further, in the presence of this feature, the generation of extrapolated coordinates of the object is carried out according to estimates of the parameters of the movement of the object, memorized at the time at the beginning of the formation of the sign of the absence of the received signal, with the subsequent current correction of their values, taking into account the decrease in the information content of the stored estimates of the motion parameters as the current moment moves away from the start of the formation of the sign of the absence of the received signal, and when the extrapolated coordinates of the object are converted into coordinates for setting the receiving beam the transmitting antenna device for the emission of the probe signal take into account the time delay of the extrapolar formation GOVERNMENTAL coordinate points in time relative to the formation of the object coordinates from the received reflected signal from the object. 2. The method according to claim 1, characterized in that the initial conditions for estimating the parameters of the object’s motion set along the coordinates equal to the values of the corresponding coordinates formed by the first measurement of the coordinates of the tracked object, and according to the derivatives of the coordinates equal to the values of the corresponding derivatives of the coordinates of the tracked object obtained from the external source or according to the a priori data of the derived coordinates of the object. 3. The method according to claim 1, characterized in that the current value of the mean square error of measuring the coordinates of the object σ _φ [n] is determined by the ratio

where Θ ₀ is the width of the beam pattern of the receiving and transmitting antenna device;
q ₀ [n] is the current signal-to-noise ratio of the received reflected signal from the object;
k _s - safety factor, taking into account the deviation of the value of the tracking error of the object from the error value determined by the potential accuracy of the tracking system;
n is the current number of the discrete time tracking step, n = 1, 2, 3, .... 4. The method according to claim 1, characterized in that the smoothing of the current value of the mean square error of measuring the coordinates of the object is carried out by a discrete low-pass filter, determined by the ratio

with initial condition

,
also set each time at the time of renewal of the sign of the presence of the reflected signal received from the object after its absence,
Where

- the current value of the smoothed mean square error of measuring the coordinates of the object is the output signal;
α _σ is the coefficient defining the passband of the filter;
σ _φ [n] is the current value of the standard error of the measurement of the coordinates of the object is the input signal;
k _c [n] - coefficient equal to

n is the current number of the discrete tracking step, n = 1, 2, 3, .... 5. The method according to claim 1, characterized in that in the Kalman filter, the model of the trajectory of the tracked object is set with a three-dimensional vector of the state of the motion parameters, determined by the relations

,

,
where x [n],

,

- current parameters of the trajectory of the object, respectively, coordinate, speed and acceleration, forming a three-dimensional vector of the state of motion parameters

T ₀ - time step for measuring the coordinates of the object;
n is the current number of the discrete step, n = 1, 2, 3, .... 6. The method according to claim 1, characterized in that the generation of extrapolated coordinates of the object in the presence of a sign of the absence of the reflected signal received from the object is carried out in accordance with the ratios for each rectangular coordinate

,

,
where x _e [n],

,

- respectively, the current extrapolated coordinate, speed and acceleration of the object;

,

,

- accordingly, estimates of the coordinate, speed and acceleration of the object, stored at the time point of the beginning of the formation of the sign of the absence of the reflected signal received from the object;
t ₀ - time step of extrapolation of coordinates;
k _AND [n] is a weighting factor that takes into account the decrease in the information content of coordinate estimates as the current time moves away from the moment the formation of the sign of the absence of the received signal begins, k _И = 1 in the presence of the sign of the received signal and 0≤k _AND <1 in the absence of the sign of the received signal ;
n is the current number of the discrete time tracking step, n = 1, 2, 3, .... 7. The method according to claim 1, characterized in that the time delay of the formation of the extrapolated coordinates of the object relative to the time of the formation of the coordinates according to the received reflected signal from the object is taken into account by adjusting the angular extrapolated coordinates by the value Δφ determined in each tracking plane by the ratio

,
Where

- the current angular velocity of the axis of the receiving and transmitting antenna device in the corresponding tracking plane;
Δt is the time delay of the extrapolated coordinates of the object relative to the instant of formation of the coordinates of the object according to the received reflected signal from the object;
n is the current number of the discrete time tracking step, n = 1, 2, 3, .... 8. A method of generating a signal for controlling the position of the beam of the receiving and transmitting antenna device of the object tracking system, including in each tracking plane discrete generating an error signal for tracking the object relative to the axis of the beam of the receiving and transmitting antenna device, generating, taking into account this signal, an error in the signal for controlling the position of the beam of the receiving and transmitting antenna antenna device, the organization of a positive feedback circuit spanning dynamic links designed to form control signal, characterized in that as dynamic links for generating a control signal by the position of the beam of the receiving and transmitting antenna device, a Kalman filter is used, in which the model of the trajectory of the tracked object is set with the s-dimensional vector of the state of the motion parameters, and the positive feedback is carried out by the extrapolated coordinate object tracking from the output of the Kalman filter, and in the positive feedback circuit delay the extrapolated coordinate by in emya equal time interval extrapolation of coordinates. 9. The method according to claim 8, characterized in that in the Kalman filter the model of the trajectory of the tracked object is set with a three-dimensional vector of the state of the motion parameters, determined by each tracking coordinate by the relations

,

,
Where

,

- current parameters of the trajectory of the object, respectively, coordinate, speed and acceleration, forming a three-dimensional vector of the state of motion parameters

T ₀ - time step for measuring the coordinates of the object;
n is the current number of the discrete step, n = 1, 2, 3, ....

Images