EP0607070A1 - Device for stabilisation of the beam direction of an electronic scanning antenna rigidly fixed on a vehicle - Google Patents

Abstract

This device decouples the aiming of the beam of an electronic scanning antenna from the movements of its platform which is assumed to be mobile. It includes two independent tracking suites. The latter determine the directional cosines of the beam along the pitch and yaw axes of a three-reference system which is related to the platform, and the roll axis of which is collinear with the direction of orientation of the antenna. They are each decoupled from the movements of the platform by introduction of a variable deduced by a stabilisation circuit (6), from the gyrometric measurements of an inertial unit (2) linked to the platform. This device makes it possible to make the beam of the antenna easily carry out a surveillance or target-tracking scanning which is independent of the movements of the platform. In the case in which the electronic scanning antenna forms part of a homing head of the missile, it can easily be incorporated into a device for guidance by proportional navigation. <IMAGE>

Description

The present invention relates to the decoupling of the beam pointing of an antenna with electronic scanning with respect to the movements of the mobile which supports it, whether the beam pointing is done by scanning during a standby or by tracking of deviation signals in target tracking mode. It also relates to the guidance of a mobile equipped with a radar with electronic scanning antenna for the pursuit of a target followed by means of deviation signals delivered by the electronic scanning antenna.

It is known to decouple, in relation to the movement of its support platform, the pointing of an antenna which can be mechanically orientable in elevation and in azimuth. A conventional way of doing this consists in equipping the antenna with gyroscopic mechanisms which, through a servo, prevent it from following the rotational movements of its support. However, such mechanisms are bulky and bulky so that an attempt has been made to eliminate them.

Another method for decoupling the pointing of a mechanically steerable antenna from the movements of its support consists in using the indications given by an inertial unit linked to the support to eliminate the effects of the movement of the support on the pointing of the antenna by means of two servos controlling the pointing angles in elevation and in azimuth of the antenna. It is then necessary to translate, using trigonometric relations, the components of the natural speed of rotation of the support given by the inertial unit with respect to a reference frame linked to the support, in variations in elevation angle and azimuth.

It has been proposed, in particular by American patent US-A-5,052,637 to apply this latter method of decoupling to electronically scanned antennas although they are rigidly fixed to their support and the elevation and azimuth angles are not not the quantities which are natural to electronic pointing. This results in complications in the calculations which can lead to harmful couplings.

The object of the present invention is to decouple the pointing of the beam of an antenna with electronic scanning of the movements of its platform which is simple to implement and reliable.

• un circuit de recouvrement qui détermine le cosinus directeur u, selon l'axe de roulis du référentiel lié au mobile, de la direction du faisceau à partir des deux autres cosinus directeurs v et w, selon les axes de tangage et de lacet du référentiel lié au mobile; de la direction du faisceau appliqués au pointeur, par mise en oeuvre de la relation : $$\mathit{\text{u}}\text{=}\sqrt{\text{1-}\mathit{\text{v}}\text{²-}\mathit{\text{<figure-callout id="2" label="w" filenames="imgf0001.png,imgf0002.png" state="{{state}}">w</figure-callout>}}\text{²}}$$
  
• un circuit de stabilisation recevant les composantes p, q, r de la vitesse propre de rotation du mobile délivrées par la centrale à inertie, les cosinus directeurs v et w appliqués au pointeur et le cosinus directeur u engendré par le circuit de recouvrement, et délivrant une première composante de stabilisation pw-ru selon l'axe de tangage du référentiel lié au mobile et une deuxième composante de stabilisation qu-pv selon l'axe de lacet du référentiel lié au mobile
• un premier circuit intégrateur sommateur additionnant et intégrant par rapport au temps la composante, selon l'axe de tangage du référentiel lié au mobile, de la consigne de modification de déflexion délivrée par le circuit de commande de déflexion, et la première composante de stabilisation, selon l'axe de tangage du référentiel lié au mobile, délivrée par le circuit de stabilisation pour obtenir le cosinus directeur v, selon l'axe de tangage du référentiel lié au mobile, de la direction du faisceau, et
• un deuxième circuit intégrateur sommateur additionnant et intégrant par rapport au temps la composante, selon l'axe de lacet du référentiel lié au mobile, de la consigne de modification de déflexion délivrée par le circuit de commande de déflexion, et la deuxième composante de stabilisation, selon l'axe de lacet du référentiel lié au mobile, délivrée par le circuit de stabilisation pour obtenir le cosinus directeur w, selon l'axe de lacet du référentiel lié au mobile de la direction du faisceau.

It relates to a device for stabilizing the pointing of the beam of an electronic scanning antenna rigidly fixed on a mobile, equipped with a pointer operating from an orientation control consisting of the direction cosines v and w of the direction. of the beam along axes of pitch and yaw of a direct orthogonal frame of reference linked to the mobile whose roll axis is collinear with the direction of orientation of the antenna and controlled by a deflection control circuit of the beam delivering components, according to the axes of pitch and yaw of the frame of reference linked to the mobile, of a set point for modifying deflection of the beam independent of the speed of rotation of the mobile, said mobile being equipped with an inertial unit giving the components p, q and r of its own speed of rotation, along the roll, pitch and yaw axes of the frame of reference linked to the mobile. This stabilization device is remarkable in that it comprises:

• an overlap circuit which determines the director cosine u, along the roll axis of the frame of reference linked to the mobile, of the direction of the beam from the other two director cosines v and w, along the pitch and yaw axes of the linked frame of reference mobile; of the direction of the beam applied to the pointer, by implementing the relation: $$\mathit{\text{u}}\text{=}\sqrt{\text{1-}\mathit{\text{v}}\text{²-}\mathit{\text{<figure-callout id="2" label="w" filenames="imgf0001.png,imgf0002.png" state="{{state}}">w</figure-callout>}}\text{²}}$$
  
• a stabilization circuit receiving the components p, q, r of the natural speed of rotation of the mobile delivered by the inertial unit, the director cosines v and w applied to the pointer and the director cosine u generated by the recovery circuit, and delivering a first stabilization component pw-ru along the pitch axis of the frame of reference linked to the mobile and a second stabilization component qu-pv along the yaw axis of the frame of reference linked to the mobile
• a first summing integrator circuit adding and integrating with respect to time the component, along the pitch axis of the reference frame linked to the mobile, of the deflection modification setpoint delivered by the deflection control circuit, and the first stabilization component, along the pitch axis of the frame of reference linked to the mobile, delivered by the circuit stabilization to obtain the director cosine v, along the pitch axis of the frame of reference linked to the mobile, of the beam direction, and
• a second summing integrator circuit adding and integrating with respect to time the component, along the yaw axis of the reference frame linked to the mobile, of the deflection modification setpoint delivered by the deflection control circuit, and the second stabilization component, along the yaw axis of the referential linked to the mobile, delivered by the stabilization circuit to obtain the director cosine w, along the yaw axis of the referential linked to the mobile of the direction of the beam.

The beam deflection control circuit can be a scanning control circuit supplying the components, along the pitch and yaw axes of the frame of reference linked to the mobile, of a scanning setpoint speed independent of the rotation speed of the mobile. . It can also be a deviation circuit associated with the electronic scanning antenna and delivering errors on the direction cosines v, w of the direction of the beam relative to those of the direction of a target being tracked.

The invention also relates to a proportional navigation guidance device using the above-mentioned beam stabilization device.

• une figure 1 représente le schéma d'un dispositif de stabilisation du pointage du faisceau d'une antenne à balayage électronique par rapport aux mouvements du support de l'antenne permettant d'assurer un balayage du faisceau découplé des mouvements du support d'antenne ;
• une figure 2 représente le schéma d'une variante du dispositif de stabilisation de la figure 1 ;
• une figure 3 représente le schéma d'un dispositif de guidage de mobile par navigation proportionnelle incorporant un dispositif de stabilisation du pointage du faisceau d'une antenne à balayage électronique fixée au mobile et utilisée pour une poursuite de cible ; et
• une figure 4 représente un diagramme vectoriel illustrant le principe de la navigation proportionnelle.

Other characteristics and advantages of the invention will emerge from the description below of several embodiments given by way of example. This description will be made with reference to the drawing in which:

• FIG. 1 represents the diagram of a device for stabilizing the pointing of the beam of an electronic scanning antenna with respect to the movements of the antenna support making it possible to scan the beam decoupled from the movements of the antenna support;
• 2 shows the diagram of a variant of the stabilization device of Figure 1;
• FIG. 3 represents the diagram of a mobile guidance device by proportional navigation incorporating a beam pointing stabilization device of an electronic scanning antenna fixed to the mobile and used for target tracking; and
• FIG. 4 represents a vector diagram illustrating the principle of proportional navigation.

To decouple the orientation control of the beam of an antenna from the movements of rotation of the mobile on which it is fixed, it is necessary to be able to give to the beam of the antenna rotation orders according to a reference trihedron orthogonal inertial in translation linked to the mobile translate them in order of rotation according to an orthogonal reference trihedron linked to the mobile to have them executed by the antenna pointing circuit.

qui exprime que la vitesse absolue de l'extrémité du vecteur unitaire U dans le référentiel inertiel suivant le mobile en translation est égale à la vitesse relative de l'extrémité de ce vecteur unitaire U dans le référentiel lié au mobile et à l'antenne augmentée de la vitesse d'entraînement en rotation du mobile.To do this, we use the classical vector relationship between the derivative dU / dt with respect to time in the inertial frame of reference of the unit vector U of the pointing direction of the antenna beam, the derivative δU / δt with respect to time in the referential linked to the mobile and the antenna of this same unit vector U and the vector product of the instantaneous rotation vector ω of the mobile and of the antenna with respect to the inertial referential by the unit vector U: $$\frac{\mathit{\text{of}}}{\mathit{\text{dt}}}\text{=}\frac{\text{δ}\mathit{\text{U}}}{\text{δ}\mathit{\text{t}}}\text{+ ω∧}\mathit{\text{U}}$$

which expresses that the absolute speed of the end of the unit vector U in the inertial frame of reference according to the mobile in translation is equal to the relative speed of the end of this unit vector U in the frame of reference linked to the mobile and to the augmented antenna of the rotational driving speed of the mobile.

We then express this vector relation in the frame of reference linked to the mobile, which we assume, according to the conventions usually adopted, that it is direct and that it has an axis Ox _a corresponding to the main axis of pointing of the antenna with respect to to which the roll movements take place, an axis Oy _a in the plane of the antenna with respect to which the pitching movements take place and an axis Oz _a in the plane of the antenna with respect to which the movements take place lace.

le vecteur de rotation instantanée ω, les composantes p de roulis, q de tangage et r de lacet du mobile délivrées par une centrale à inertie solidaire de ce dernier : $$\text{[ω]=[}\mathit{\text{p}}\text{,}\mathit{\text{q}}\text{,}\mathit{\text{r}}{\text{]}}^{\mathit{\text{T}}}$$

le vecteur dérivée dU/dt par rapport au temps dans le référentiel inertiel, les composantes x', y', z' définissant la vitesse de rotation dans le référentiel inertiel imposée au faisceau d'antenne par une commande d'orientation découplée des mouvements de rotation du mobile

et le vecteur dérivée δU/δt par rapport au temps dans le référentiel lié, les composantes u', v', w' définissant la vitesse de rotation dans le référentiel lié, imposée au faisceau d'antenne par la commande d'orientation

In this frame of reference linked to the mobile, the unit vector U has for components the directing cosines u, v, w which are used by the antenna pointer to orient its beam: $$\text{[}\mathit{\text{U}}\text{] = [}\mathit{\text{u}}\text{,}\mathit{\text{v}}\text{,}\mathit{\text{w}}{\text{]}}^{\mathit{\text{T}}}$$

the instantaneous rotation vector ω, the components p of roll, q of pitch and r of yaw of the mobile delivered by an inertial unit integral with the latter: $$\text{[ω] = [}\mathit{\text{p}}\text{,}\mathit{\text{q}}\text{,}\mathit{\text{r}}{\text{]}}^{\mathit{\text{T}}}$$

the derivative vector dU / dt with respect to time in the inertial frame of reference, the components x ', y', z 'defining the speed of rotation in the frame of reference inertial imposed on the antenna beam by an orientation control decoupled from the rotational movements of the mobile

and the derived vector δU / δt with respect to time in the linked reference frame, the components u ', v', w 'defining the speed of rotation in the linked reference frame, imposed on the antenna beam by the orientation command

puisque u, v, w sont les cosinus directeurs définissant dans le référentiel lié le vecteur unitaire U de la direction d'orientation du faisceau de l'antenne.We note that : $$\mathit{\text{<figure-callout id="2" label="u" filenames="imgf0001.png,imgf0002.png" state="{{state}}">u</figure-callout>}}\text{² +}\mathit{\text{<figure-callout id="2" label="v" filenames="imgf0001.png,imgf0002.png" state="{{state}}">v</figure-callout>}}\text{² +}\mathit{\text{<figure-callout id="2" label="w" filenames="imgf0001.png,imgf0002.png" state="{{state}}">w</figure-callout>}}\text{² = 1}$$

since u, v, w are the guiding cosines defining in the linked reference frame the unit vector U of the direction of orientation of the antenna beam.

We also have due to the definition of the derived vector δU / δt $$\mathit{\text{u}}\text{'=}\frac{\mathit{\text{of}}}{\mathit{\text{dt}}}\text{,}\mathit{\text{v}}\text{'=}\frac{\mathit{\text{dv}}}{\mathit{\text{dt}}}\text{and}\mathit{\text{w}}\text{'=}\frac{\mathit{\text{dw}}}{\mathit{\text{dt}}}$$

$$\mathit{\text{ux}}\text{'+}\mathit{\text{vy}}\text{'+}\mathit{\text{wz}}\text{'=0}$$

There are also two other relationships that will be useful later: $$\mathit{\text{uu}}\text{'+}\mathit{\text{vv}}\text{'+}\mathit{\text{ww}}\text{'= 0}$$

$$\mathit{\text{ux}}\text{'+}\mathit{\text{vy}}\text{'+}\mathit{\text{wz}}\text{'= 0}$$

The first (4) results from a derivation with respect to the time of relation (2) and can also be written: $$\mathit{\text{U}}\frac{\text{δ}\mathit{\text{U}}}{\text{δ}\mathit{\text{t}}}\text{= 0}$$

dans laquelle on tient compte du fait que le terme UδU/δt est nul en raison de la relation (6) de même que le produit mixte U.(ω∧U) qui comporte deux fois le même vecteur.The second (5) follows from the expression of the dot product UdU / dt using the relation (1): $$\mathit{\text{U}}\text{.}\frac{\mathit{\text{of}}}{\mathit{\text{dt}}}\text{=}\mathit{\text{U}}\text{.}\frac{\text{δ}\mathit{\text{U}}}{\text{δ}\mathit{\text{t}}}\text{+}\mathit{\text{U}}\text{. (ω∧}\mathit{\text{U}}\text{)}$$

in which one takes account of the fact that the term UδU / δt is zero due to the relation (6) as well as the mixed product U. (ω∧U) which contains twice the same vector.

qui donne un système de trois équations permettant d'exprimer les cosinus directeurs u, v, w, dans le référentiel lié au mobile, de la direction de pointage du faisceau et leurs dérivées dans le temps u', v', w', en fonction d'une vitesse de rotation par rapport au référentiel inertiel de composantes x', y', z' dans le référentiel lié au mobile, imposée par une commande d'orientation découplée des mouvements de rotation du mobile et de l'antenne.We then obtain, by expressing the vectors of relation (1) from their components in the frame of reference linked to the mobile, the matrix relation:

which gives a system of three equations making it possible to express the guiding cosines u, v, w, in the frame of reference linked to the mobile, of the pointing direction of the beam and their derivatives in time u ', v', w ', in function of a speed of rotation relative to the inertial frame of reference of components x ', y', z 'in the frame of reference linked to the mobile, imposed by an orientation control decoupled from the rotational movements of the mobile and the antenna.

Aussi, pour assurer le découplage de la direction d'orientation du faisceau de l'antenne on ne met en oeuvre que les deux dernières équations associées à la relation : $$\mathit{\text{u}}\text{=}\sqrt{\text{1-}\mathit{\text{v}}\text{²-}\mathit{\text{w}}\text{²}}$$

The first equation of this system is superfluous since we suppose that the antenna beam always points towards the front of the mobile, that is to say that the director cosine u is always positive, and that we have the relation between guiding cosines: $$\mathit{\text{<figure-callout id="2" label="u" filenames="imgf0001.png,imgf0002.png" state="{{state}}">u</figure-callout>}}\text{² +}\mathit{\text{<figure-callout id="2" label="v" filenames="imgf0001.png,imgf0002.png" state="{{state}}">v</figure-callout>}}\text{² +}\mathit{\text{<figure-callout id="2" label="w" filenames="imgf0001.png,imgf0002.png" state="{{state}}">w</figure-callout>}}\text{² = 1}$$

Also, to ensure the decoupling of the direction of orientation of the antenna beam, only the last two equations associated with the relationship are implemented: $$\mathit{\text{u}}\text{=}\sqrt{\text{1-}\mathit{\text{v}}\text{²-}\mathit{\text{<figure-callout id="2" label="w" filenames="imgf0001.png,imgf0002.png" state="{{state}}">w</figure-callout>}}\text{²}}$$

Figure 1 gives an example of such an implementation for scanning the beam of an electronic scanning antenna decoupled from the rotational movements of the mobile which supports it.

We distinguish in this figure 1 an electronic scanning antenna 1 fixed on a mobile equipped with an inertial unit 2 which delivers three components in roll p, in pitch q and in yaw r of the rotational movement of the mobile relative to a frame of reference inertial the following in translation in a linked frame of reference having a roll axis Ox _a corresponding to the orientation axis of the antenna and of the pitch axes Oy _a and of yaw Oz _a in the plane of the antenna.

The antenna 1 is provided with a pointing computer 3 operating from the guiding cosines v and w along the axes of pitch and yaw of the linked frame of reference while a device 4 for controlling the deflection of the antenna beam delivers the components y 'and z', according to the axes of pitch and yaw of the linked frame of reference, of an instruction for modifying the deflection of the antenna beam relative to the inertial frame of reference.

The cosine directors v and w applied to the pointing calculator 3 are also applied to an overlap circuit 5 which determines the third cosine director u of the direction of the beam of the antenna with respect to the referential linked by implementation of the relation: $$\mathit{\text{u}}\text{=}\sqrt{\text{1-}\mathit{\text{v}}\text{²-}\mathit{\text{<figure-callout id="2" label="w" filenames="imgf0001.png,imgf0002.png" state="{{state}}">w</figure-callout>}}\text{²}}$$

The components p, q, r in the linked frame of reference of the speed of rotation of the mobile with respect to the inertial frame of reference delivered by the inertial unit 2 are applied, as well as the guiding cosines v, w arriving at the pointing computer 3 and the cosine director u generated by the covering circuit 5, to a stabilization circuit 6 which calculates the components pw-ru and qu-pv.

qui est intégrée par un intégrateur 8 pour obtenir le cosinus directeur v selon l'axe de tangage, de la direction du faisceau destiné au calculateur de pointage 3, au circuit de recouvrement 5 et au circuit de stabilisation 6.The pw-ru component delivered by the stabilization circuit 6 is added by a summing circuit 7 to the pitch component y ′ of the deflection modification instruction of the antenna beam relative to the inertial reference frame delivered by the control device 4 of deflection. This summation makes it possible to obtain the derivative v ′ of the director cosine v along the pitch axis: $$\mathit{\text{v}}\text{'=}\mathit{\text{y}}\text{'+}\mathit{\text{pw}}\text{-}\mathit{\text{ru}}$$

which is integrated by an integrator 8 to obtain the director cosine v along the pitch axis, of the direction of the beam intended for the pointing computer 3, the covering circuit 5 and the stabilization circuit 6.

qui est intégrée par un intégrateur 10 pour obtenir le cosinus directeur w selon l'axe de lacet, de la direction du faisceau destiné au calculateur de pointage 3, au circuit de recouvrement 5 et au circuit de stabilisation 6.The component qu-pv delivered by the stabilization circuit 6 is added by a summing circuit 9 to the yaw component z 'of the modification instruction of deflection of the antenna beam relative to the inertial reference frame delivered by the control device 4 of deflection. This summation makes it possible to obtain the derivative w 'of the director cosine w along the yaw axis: $$\mathit{\text{w}}\text{'=}\mathit{\text{z}}\text{'+}\mathit{\text{that}}\text{-}\mathit{\text{pv}}$$

which is integrated by an integrator 10 to obtain the director cosine w along the yaw axis, of the direction of the beam intended for the pointing computer 3, the covering circuit 5 and the stabilization circuit 6.

Alternatively, instead of placing the integrators 8, 10 downstream of the summing circuits 7, 9, they can be split into 8a, 8b and 10a, 10b and placed, as shown in FIG. 2, upstream of the reindexed summing circuits 7 'and 9'.

The deflection control circuit 4 can be a sweep control circuit delivering as components y ′, z ′ along the pitch and yaw axes of the deflection modification instruction, the components along the pitch and yaw axes d '' a desired speed of rotation of the antenna beam independent of the movement of the mobile. We then obtain a scanning of the horizon by the antenna beam decoupled from the movements of the mobile which can be useful during a standby period.

Instead of searching for the scanning beam for the antenna beam, one may want to track the target by deviation. It then suffices to use as a deflection control circuit 4 a deviation circuit. It is shown in fact that a deviation circuit associated with an electronic scanning antenna directly delivers the errors Δv and Δw existing along the axes of pitch and yaw, between the cosines directing the direction of the beam and those of the target being tracked .

λ étant la longueur d'onde émise ou reçue. Le champ reçu d'une direction de vecteur unitaire U' : $$\text{[}\mathit{\text{U}}\text{']=[}\mathit{\text{u}}\text{+Δ}\mathit{\text{u}}\text{,}\mathit{\text{v}}\text{+Δ}\mathit{\text{v}}\text{,}\mathit{\text{w}}\text{+Δ}\mathit{\text{w}}{\text{]}}^{\mathit{\text{T}}}$$

est alors pour une cellule rayonnante C_i et après déphasage par celle-ci :

a_i étant un coefficient de pondération avec lequel le signal de la cellule rayonnante C_i est ajouté aux signaux des autres cellules rayonnantes pour engendrer le signal global de l'antenne.To be convinced of this, we consider the constitution of an electronic scanning antenna. This is formed by a number of radiating cells C _i distributed in a plane identified by the axes of pitch Oy _a and of yaw Oz _a of the referential linked according to coordinates (Y _i , Z _i ) so that said axes of pitch Oy _a and of yaw Oz _a are axes of symmetry. The radiation of the antenna in the direction of the unit vector U of director cosines u, v, w with respect to the linked frame of reference is obtained by assigning to each radiating cell C _i a phase: $${\text{ψ}}_{\mathit{\text{i}}}\text{= -2π (}{\mathit{\text{vy}}}_{\mathit{\text{i}}}\text{+}{\mathit{\text{wz}}}_{\mathit{\text{i}}}\text{) / λ}$$

λ being the wavelength transmitted or received. The field received from a unit vector direction U ': $$\text{[}\mathit{\text{U}}\text{'] = [}\mathit{\text{u}}\text{+ Δ}\mathit{\text{u}}\text{,}\mathit{\text{v}}\text{+ Δ}\mathit{\text{v}}\text{,}\mathit{\text{w}}\text{+ Δ}\mathit{\text{w}}{\text{]}}^{\mathit{\text{T}}}$$

is then for a radiating cell C _i and after phase shift by the latter:

a _i being a weighting coefficient with which the signal of the radiating cell C _i is added to the signals of the other radiating cells to generate the overall signal of the antenna.

de sorte que le signal global de l'antenne vaut :

Assuming that the errors Δv and Δw are small, that is to say that the beam is little depointed from the target, the field received from a radiating cell C _i can be written:

so that the global signal of the antenna is worth:

The values adopted for the weighting coefficient a _i are different depending on whether one seeks to make a sum channel, a circular difference deviation path or an elevation difference deviation path.

To make a sum channel, we choose the weighting coefficients a _i so that we have: $$\text{Σ}{\mathit{\text{at}}}_{\text{i}}{\mathit{\text{y}}}_{\text{i}}\text{= Σ}{\mathit{\text{at}}}_{\text{i}}{\mathit{\text{z}}}_{\text{i}}\text{= 0}$$

indépendant des erreurs de pointage Δv, Δw tant que celles-ci sont faibles.This can be done by giving identical values to the weighting coefficients of two radiating cells arranged in the antenna symmetrically with respect to the axis of pitch Oy _a and of yaw Oz _a . We then obtain a global signal level: $$\text{Σ}{\mathit{\text{at}}}_{\text{i}}$$

independent of pointing errors Δv, Δw as long as these are low.

To make a circular difference deviation path, the weighting coefficients a _i are chosen so that: $$\text{Σ}{\mathit{\text{at}}}_{\text{i}}\text{= Σ}{\mathit{\text{at}}}_{\text{i}}{\mathit{\text{z}}}_{\text{i}}\text{= 0}$$

qui est proportionnel à l'erreur Δv.This can be done by giving identical values to the weighting coefficients of two radiating cells arranged in the antenna symmetrically with respect to the pitch axis Oy _a and by giving opposite values to the weighting coefficients of two radiating cells arranged in the antenna symmetrically with respect to the yaw axis Oz _a . We then obtain an alobal signal level:

which is proportional to the error Δv.

To make an elevation difference deviation path, the weighting coefficients a _i are chosen so that: $$\text{Σ}{\mathit{\text{at}}}_{\text{i}}\text{= Σ}{\mathit{\text{at}}}_{\text{i}}{\mathit{\text{y}}}_{\text{i}}\text{= 0}$$

qui est proportionnel à l'erreur Δw.This can be done by giving values opposite to the weighting coefficients of two radiating cells arranged in the antenna symmetrically with respect to the pitch axis Oy _a and by giving identical values to the weighting coefficients of two radiating cells arranged in the antenna symmetrically with respect to the yaw axis Oz _a . We then obtain an alobal signal level:

which is proportional to the error Δw.

The deviation device of an electronic scanning antenna therefore provides two pointing error signals, one proportional to an error Δv on the direction cosine v, along the pitch axis, of the pointing direction of the beam. , and the other proportional to an error Δw on the director cosine w, along the yaw axis, of the beam pointing direction.

It is therefore possible, in order to obtain a target tracking device, to use, instead of the deflection control circuit 4, a deviation circuit 11, as shown in FIG. 3. This deviation circuit 11, the coupling of which with the electronic scanning antenna 1 is recalled by a dotted line provides, as a component of the deflection modification setpoint along the pitch axis, a component proportional to the error Δv on the director cosine v of the pointing direction of the beam, and, as a component of deflection modification setpoint along the yaw axis, a component proportional to the error Δw on the director cosine w of the beam pointing direction. These two instructions are applied to two independent prosecutions without mutual coupling.

As in all tracking systems, there are on the path of the components Δv, Δw, loop filters 12, 13 whose transfer characteristic, of low-pass type, is traditionally called H (s).

A variant of this scheme exploits all modern filtering methods, in particular Kalman filtering, which include an explicit estimate of the angular velocity. In this case, H (s) must be replaced by the estimator which delivers y 'or z' from the pointing error Δy or Δz.

The target tracking device by the beam of an electronic scanning antenna carried by a mobile according to FIG. 2 can be completed with a guidance device for proportional navigation tending to allow the mobile to catch the target on which is pointed the beam of its electronic scanning antenna because there are the cosines guiding the line of sight which are those of the direction of pointing of the beam and variations in time y ', z' of the rotation of this line of sight with respect to the inertial coordinate system according to the axes of pitch and yaw of the frame of reference linked to the mobile.

Figure 4 is a vector diagram illustrating the principle of proportional navigation. There is a mobile M animated with a speed V _M approaching a target B animated with a speed V _B. Axes M x _m y _m z _m constitute a direct orthogonal trihedron linked to the mobile M referencing by the plane M y _m z _m the plane of the control surfaces of the mobile. The axis M x _m is a roll axis collinear with the speed vector V _M of the mobile. The axis M z _m is a yaw axis perpendicular to the line of sight connecting the mobile M to the target B. Axes M x _s , y _s , z _s constitute another direct orthogonal trihedron linked to the mobile with an axis Mx _s collinear with the line of sight MB, and an axis M z _s coincides with the axis M z _m .

peut se décomposer de deux façons différentes :

• soit selon une composante V_t dans le plan M y_s, z_s perpendiculaire à la lignée de visée qui est une composante transverse et selon une composante V_r le long de la ligne de visée qui est une composante de vitesse radiale $${\mathit{\text{V}}}_{\mathit{\text{R}}}\text{=}{\mathit{\text{V}}}_{\mathit{\text{t}}}\text{+}{\mathit{\text{V}}}_{\mathit{\text{r}}}{\mathit{\text{V}}}_{\mathit{\text{t}}}\text{et}{\mathit{\text{V}}}_{\mathit{\text{r}}}\text{orthogonaux}$$
  
• soit selon une composante V_g dans le plan M y_mz_m des gouvernes résultant d'une projection parallèle à la ligne de visée et selon une composante V_l le long de la ligne de visée non représentée sur la figure $${\mathit{\text{V}}}_{\mathit{\text{R}}}\text{=}{\mathit{\text{V}}}_{\mathit{\text{g}}}\text{+}{\mathit{\text{V}}}_{\mathit{\text{l}}}{\mathit{\text{V}}}_{\mathit{\text{g}}}\text{et}{\mathit{\text{V}}}_{\mathit{\text{l}}}\text{non orthogonaux}$$
  

Soit Us le vecteur unitaire de la ligne de visée et r la longueur MB. Le vecteur rotation Ω de la ligne de visée vaut par définition : $$\text{Ω=}\mathit{\text{U}}\mathit{\text{s}}\text{∧}\mathit{\text{V}}\mathit{\text{r}}\text{/}\mathit{\text{r}}\text{=}\mathit{\text{U}}\mathit{\text{s}}\text{∧}\mathit{\text{V}}\mathit{\text{t}}\text{/}\mathit{\text{r}}\text{=}\mathit{\text{U}}\mathit{\text{s}}\text{∧}\mathit{\text{V}}\mathit{\text{g}}\text{/}\mathit{\text{r}}$$

The relative speed of the target compared to the mobile which is expressed by the vector relation: $${\mathit{\text{V}}}_{\mathit{\text{R}}}\text{=}{\mathit{\text{V}}}_{\mathit{\text{B}}}\text{-}{\mathit{\text{V}}}_{\mathit{\text{M}}}$$

can be broken down in two different ways:

• either according to a component V _t in the plane M y _s , z _s perpendicular to the line of sight which is a transverse component and according to a component V _r along the line of sight which is a component of radial speed $${\mathit{\text{V}}}_{\mathit{\text{R}}}\text{=}{\mathit{\text{V}}}_{\mathit{\text{t}}}\text{+}{\mathit{\text{V}}}_{\mathit{\text{r}}}{\mathit{\text{V}}}_{\mathit{\text{t}}}\text{and}{\mathit{\text{V}}}_{\mathit{\text{r}}}\text{orthogonal}$$
  
• either according to a component V _g in the plane M y _m z _m of the control surfaces resulting from a projection parallel to the line of sight and according to a component V _l along the line of sight not shown in the figure $${\mathit{\text{V}}}_{\mathit{\text{R}}}\text{=}{\mathit{\text{V}}}_{\mathit{\text{g}}}\text{+}{\mathit{\text{V}}}_{\mathit{\text{l}}}{\mathit{\text{V}}}_{\mathit{\text{g}}}\text{and}{\mathit{\text{V}}}_{\mathit{\text{l}}}\text{non orthogonal}$$
  

Let Us be the unit vector of the line of sight and r the length MB. The rotation vector Ω of the line of sight is by definition valid: $$\text{Ω =}\mathit{\text{U}}\mathit{\text{s}}\text{∧}\mathit{\text{V}}\mathit{\text{r}}\text{/}\mathit{\text{r}}\text{=}\mathit{\text{U}}\mathit{\text{s}}\text{∧}\mathit{\text{V}}\mathit{\text{t}}\text{/}\mathit{\text{r}}\text{=}\mathit{\text{U}}\mathit{\text{s}}\text{∧}\mathit{\text{V}}\mathit{\text{g}}\text{/}\mathit{\text{r}}$$

A étant une constante. Il vient :

La formule du double produit vectoriel donne :

soit :

en tenant compte du fait que : $${\mathit{\text{V}}}_{\mathit{\text{g}}}{\mathit{\text{.V}}}_{\mathit{\text{M}}}\text{= 0}$$

par construction.The principle of proportional navigation is to try to get the direction of the line of sight to end up being constant. This is achieved by applying lateral acceleration to the mobile $$\text{γ =}\mathit{\text{AT}}\text{Ω∧}{\mathit{\text{V}}}_{\mathit{\text{M}}}$$

A being a constant. He comes :

The formula of the double vector product gives:

is :

taking into account that: $${\mathit{\text{V}}}_{\mathit{\text{g}}}{\mathit{\text{.V}}}_{\mathit{\text{M}}}\text{= 0}$$

by construction.

γ is therefore collinear with V _g that it tends to cancel which also tends to cancel V _t and justifies the law of navigation.

que l'homme de l'art cherche généralement à maintenir constant pour des raisons de stabilité.In the vector relation (15) there appears a term A (U _S .V _M ) which is also found in the expression of the reduced gain:

which those skilled in the art generally seek to maintain constant for reasons of stability.

Il faut donc estimer V_g. Cela peut se faire au moyen de la vitesse transverse V_t qui vaut par définition : $${\mathit{\text{V}}}_{\mathit{\text{t}}}\text{=}\mathit{\text{r}}\frac{\mathit{\text{dUs}}}{\mathit{\text{dt}}}$$

In summary, to guide a mobile in pursuit of a target by proportional navigation, it is necessary to apply an acceleration to it:

We must therefore estimate V _g . This can be done by means of the transverse speed V _t which is by definition worth: $${\mathit{\text{V}}}_{\mathit{\text{t}}}\text{=}\mathit{\text{r}}\frac{\mathit{\text{of}}}{\mathit{\text{dt}}}$$

k étant un scalaire. D'où : $${\mathit{\text{V}}}_{\mathit{\text{g}}}\mathit{\text{/r}}\text{=}\frac{{\mathit{\text{dU}}}_{\mathit{\text{s}}}}{\mathit{\text{dt}}}\text{-}{\mathit{\text{kU}}}_{\mathit{\text{s}}}$$

The vector V _g / r which is the projection into the plane of the control surfaces M y _m z _m of the vector V _t / r parallel to the line of sight can be written: $${\mathit{\text{V}}}_{\mathit{\text{g}}}\mathit{\text{/ r}}\text{=}{\mathit{\text{V}}}_{\mathit{\text{t}}}\mathit{\text{/ r}}\text{-}{\mathit{\text{kU}}}_{\mathit{\text{s}}}$$

k being a scalar. From where : $${\mathit{\text{V}}}_{\mathit{\text{g}}}\mathit{\text{/ r}}\text{=}\frac{{\mathit{\text{of}}}_{\mathit{\text{s}}}}{\mathit{\text{dt}}}\text{-}{\mathit{\text{kU}}}_{\mathit{\text{s}}}$$

d'où :

The unit vector U _s of the line of sight corresponds to the unit vector U of the direction of the antenna beam since the latter illuminates the target and the frame of reference Mx _s y _s z _s is the frame of reference linked to the mobile considered above so that we have in this benchmark:

from where :

D'où :

Sachant que l'on a, d'après la relation (5) $$\mathit{\text{ux}}\text{'+}\mathit{\text{vy}}\text{'+}\mathit{\text{wz}}\text{'=0}$$

On peut exprimer x' en fonction de y' et z'. Il vient :

ce qui s'écrit sous forme d'un produit de matrices :

On en déduit les ordres de guidage :

The first component x'-ku is zero since, by definition V _g is in the plane of the control surfaces M y _m z _m $$\mathit{\text{x}}\text{'-}\mathit{\text{ku}}\text{= 0}$$

From where :

Knowing that we have, according to relation (5) $$\mathit{\text{ux}}\text{'+}\mathit{\text{vy}}\text{'+}\mathit{\text{wz}}\text{'= 0}$$

We can express x 'as a function of y' and z '. He comes :

which is written in the form of a product of matrices:

We deduce the guidance orders:

The components y 'and z' with respect to the axes of pitch and yaw of the frame of reference linked to the mobile, of the derivative with respect to time of the unit vector of the line of sight Us relative to an inertial frame of reference are none other than the inputs of the summers 7 and 9 devoted to the tracking terms upstream of the integrators which supply v and w, the other inputs receiving the stabilization terms. We therefore have, with the target tracking device of FIG. 3, all the parameters, with the exception of the module for the target moving closer speed V _r , making it possible to develop lateral acceleration instructions for the moving object. γ _y , γ _z in pitch and yaw constituting guidance orders in proportional navigation.

To make a guidance device, it is therefore sufficient to add to the target tracking device, as shown in FIG. 3, a means for estimating the target moving approach speed 15 and an acceleration control circuit. 14.

The means for estimating the target moving approach speed 15 may be a Doppler cinemometer coupled to the electronic scanning antenna or an estimator exploiting the results of a distance tracking telemetry carried out by a seeker equipping the mobile, or any other means of estimation.

et une consigne d'accélération en lacet γ_z par mise en oeuvre de la relation :

ces deux relations se déduisant de la relation matricielle (16).The acceleration control circuit 14 receives the signals y 'and z', along the pitch and yaw axes of the mobile, for correcting the direction of pointing of the beam of the electronically scanned antenna delivered by the circuit of deviation 11 after processing in the loop filters 12, 13, the values of the directing cosines u, v, w, according to the roll axes, pitch and yaw of the mobile, of the pointing direction of the antenna beam and an estimate or a measurement of the target moving approach speed, and calculates a pitch acceleration setpoint γ _y by implementing the relation:

and a yaw acceleration setpoint γ _z by implementing the relation:

these two relations deducing from the matrix relation (16).

In the above description, all the relationships between variables have been written in continuous form. However, this does not exclude that they can be implemented by digital processing of sampled variables as is the case when using microprocessor circuits.

Claims (6)

Device for stabilizing the pointing of an electronic scanning antenna (1) rigidly fixed on a mobile, equipped with a pointer (3) operating on the basis of an orientation control made up of the cosine directors v and w of the direction of the antenna beam (1) according to axes of pitch and yaw of a direct orthogonal reference frame linked to the mobile, the roll axis of which is collinear with the direction of orientation of the antenna (1), and controlled by a beam deflection control circuit (4) delivering components, along the pitch and yaw axes of the frame of reference linked to the mobile, of a modification instruction for deflection of the beam independent of the rotation speed of the mobile, said mobile being equipped with an inertial unit (2) giving the components p, q and r, along the roll, pitch and yaw axes of the frame of reference linked to the mobile, of its own speed of rotation, said stabilization device being characterized e n what it includes: - an overlap circuit (5) which determines the director cosine u, along the roll axis of the frame of reference linked to the mobile, of the beam direction from the two other director cosines v and w, according to the axes of pitch and of yaw of the frame of reference linked to the mobile, of the direction of the beam applied to the pointer (3) by implementing the relation: $$\text{u =}\sqrt{\text{1-}\mathit{\text{v}}\text{²-}\mathit{\text{w}}\text{²}}$$

- a stabilization circuit (6) receiving the components p, q and r of the natural speed of rotation of the mobile delivered by the inertial unit (2), the direction cosines v and w applied to the pointer (3) and the direction cosine u delivered by the covering circuit (5), and delivering a first stabilization component pw-ru along the pitch axis of the frame of reference linked to the mobile and a second stabilization component qu-pv along the yaw axis of the linked frame of reference mobile, - a first summing integrator circuit (7, 8, 7 ', 8a, 8b) adding and integrating with respect to time the component along the pitch axis of the frame of reference linked to the mobile, of the deflection modification instruction delivered by the circuit deflection control (4), and the first stabilization component, along the pitch axis of the frame of reference linked to the mobile, delivered by the stabilization circuit (6) to obtain the cosine director v, along the pitch axis of the frame of reference linked to the mobile, of the direction of the beam, and - a second summing integrator circuit (9, 10, 9 ', 10a, 10b) adding and integrating with respect to time the component along the yaw axis of the frame of reference linked to the mobile, of the deflection modification instruction delivered by the circuit deflection control (4), and the second stabilization component, along the yaw axis of the frame of reference linked to the mobile, delivered by the stabilization circuit (6) to obtain the director cosine w, along the yaw axis of the frame of reference linked to the moving beam direction. Device according to claim 1, characterized in that said beam deflection control circuit (4) is a scanning control circuit supplying the components, along the axes of pitch and yaw of the frame of reference linked to the mobile, of a speed setpoint scanning independent of the mobile rotation speed. Device according to claim 1, characterized in that said beam deflection control circuit is a deviation circuit (11) associated with the electronic scanning antenna (1) and delivering, from the signals received by the latter, errors Δ v , Δ w between the director cosines v, w, along the pitch and yaw axes of the frame of reference linked to the mobile, of the direction of the beam and the director cosines of the direction of a target being pursued. Device according to claim 3, characterized in that it further comprises loop filters (12, 13) interposed between the outputs of the deviation circuit (11) and the inputs of the summing integrator circuits. Guidance device, by proportional navigation, of a mobile equipped with an electronic scanning antenna radar (1) oriented along its roll axis, equipped with a pointer (3) operating from an orientation control consisting of the cosine directors v and w, along the axes of pitch and yaw of the mobile, of the direction of the antenna beam (1) and controlled by a deviation circuit (11) which is associated with it and delivers the components error y ', z' between the director cosines v, w, along the axes of pitch and yaw of the mobile, of the direction of the antenna beam (1) and the cosines directing the direction of a target being pursued, said mobile being equipped with an inertial unit (2) giving the components p, q and r of the natural speed of rotation of the mobile with respect to its roll, pitch and yaw axes, said guide device being characterized in that it comprises: - an overlap circuit (5) which determines the directing cosine u, along the roll axis of the mobile, of the direction of the beam from the two other directing cosines v and w, along the pitch and yaw axes of the mobile , of the direction of the beam applied to the pointer (3) by implementing the relation: $$\text{u =}\sqrt{\text{1-}\mathit{\text{v}}\text{²-}\mathit{\text{w}}\text{²}}$$

- a stabilization circuit (6) receiving the components p, q and r of the natural speed of rotation of the mobile delivered by the inertial unit (2), the direction cosines v and w applied to the pointer (3) and the direction cosine u delivered by the covering circuit (5), and delivering a first stabilization component pw-ru along the pitch axis of the mobile and a second stabilization component qu-pv along the yaw axis of the mobile, - a first summing integrator circuit (7, 8) adding and integrating with respect to time the error y 'on the director cosine v, along the pitch axis of the mobile, of the beam direction provided by the deviation circuit (11) and the first stabilization component, along the pitch axis of the mobile, delivered by the stabilization circuit (6) to obtain the direction cosine v, along the pitch axis of the mobile, of the beam direction, - a second summing integrator circuit (9, 10) adding and integrating with respect to time the error z ′ on the director cosine w, along the yaw axis of the mobile, of the direction of the beam provided by the deviation circuit (11) and the second stabilization component, along the yaw axis of the mobile, delivered by the stabilization circuit (6) to obtain the director cosine w, along the yaw axis of the mobile, of the beam direction, a means (15) of estimating the speed of mobile-target approximation pursued

and, - an acceleration control circuit (14) receiving the errors y ', z' on the director cosines v and w, along the pitch and yaw axes of the mobile, of the beam pointing direction delivered by the circuit d deviation measurement (11), the values of the directing cosines v and w, according to the axes of pitch and yaw of the mobile, of the direction of the beam delivered by the summing integrator circuits (7, 8, 9, 10), the value of director cosine u, along the roll axis of the mobile, of the direction of the beam delivered by the covering circuit (5) and an estimate

of the speed of approached mobile-target pursued delivered by the estimation means (15), and delivering a first acceleration setpoint γ _y along the pitch axis of the mobile by implementing the relation:

and a second acceleration setpoint γ _z along the yaw axis of the mobile by implementing the relationship:

a being a constant called reduced gain. Device according to claim 5, characterized in that it further comprises loop filters (12, 13) interposed between the outputs of the deviation circuit (11) and the inputs of the summing circuits (7, 9) and of the circuit acceleration control (14).

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