Method of processing the sum and difference signals of a radar of the monopulse type for estimating the parasite phase introduced between these signals by the ultrahigh frequency formation circuits of the sum and difference channels

The method of the invention, applied for example to estimating the parasite phase .phi..sub.a between the azimuth sum .SIGMA..sub.a and difference .DELTA..sub.a channels, consists in calculating the expressions S=.SIGMA..sub.a .multidot..SIGMA..sub.e * and D=.DELTA..sub.a .multidot..SIGMA..sub.e * for different successive measurements made by the radar, then in calculating the expressions [S.sub.(k+1) -S.sub.(k-1) ].multidot.D*(k) for different successive times k-1, k, k+1 and in averaging the result of this expression or different times k, it being understood that the radar antenna sweeps in azimuth and that the radar wave emitted is polarized circularly, the single pulse azimuth and elevation receivers receiving respectively only one of the circular polarization types: right hand or left hand.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates generally to the field of radar and concerns 
more particularly a method of processing the signals of a radar of the 
monopulse type, for estimating a parasite phase introduced between these 
signals by the ultrahigh frequency formation circuits of the sum and 
difference channels. 
2. Description of the Prior Art 
It is known that with a radar of the monopulse type the angular location of 
targets may be obtained by processing the different signals received 
simultaneously from these targets and corresponding to different beam 
directivities. 
Thus, as shown very schematically in FIG. 1, by providing two sources 
respectively in the azimuth plane (1a, 2a) and in the elevational plane 
(1e, 2e), at reception there are available for each of these two planes 
two signals of which the sum .SIGMA. and the difference .DELTA. may be 
formed by ultrahigh frequency means (3, 4), which is tantamount to having 
an antenna with a beam corresponding to the .SIGMA. channel and another 
beam corresponding to the .DELTA. channel, and thus allows angular 
location of the targets to be obtained simply. 
It is also known that, with the reradiation of a target being a sum of the 
waves reflected by each of the reflecting elements which form it, the 
signals S and D received respectively in the sum and difference channels, 
in azimuth or in elevation, have as complex representation: 
##EQU1## 
with: s(.theta..sub.i): gain of the sum channel at the angle .theta..sub.i 
; 
d(.theta..sub.i): gain of the difference channel at the angle .theta..sub.i 
; 
a.sub.i : amplitude relative to the ith reflector; 
.phi..sub.i : phase shift introduced by the ith reflector; 
d.sub.i : distance between the radar and the ith reflector; 
.PSI.: parasite phase introduced between the .SIGMA. and .DELTA. channels 
by the ultrahigh frequency formation circuits of the sum and difference 
channels. 
It is also known that, in the particular case of the elevational plane, the 
parasite phase .PSI. between the sum and difference channels may be 
evaluated in the following way: 
let 
##EQU2## 
where D* designates the complex conjugate quantity of D, and where: 
##EQU3## 
If we calculate the mean value of P over different distances divisions of 
the radar, the phase 
##EQU4## 
being considered as random, we have: 
##EQU5## 
where E designates the expectation operator. 
The term "a" is real, but is a priori of unknown sign because of the 
factors d(.theta..sub.i) which may be positive or negative. In fact, 
referring to FIG. 2 which shows the trend of the sum and difference 
diagrams, .SIGMA. and .DELTA., in the azimuth plane or in the elevational 
plane, the sum diagram has the maximum in the direction of the axis of the 
antenna, whereas the difference .DELTA. diagram has on the contrary a 
minimum in this direction and is, on each side of this direction, either 
in phase (.DELTA.+) or in phase opposition (.DELTA.-) with .SIGMA.. 
By averaging P, we can then a priori only estimate the phase .PSI. to with 
in the sign. 
Now, it so happens that in the elevational plane this ambiguity of sign may 
be relatively simply removed for the sign of d(.theta..sub.i) is always 
related to the rank of the range bin considered being negative for the 
closest range bins and positive for the furthest range bins. By averaging 
P over the different range bins, an estimation of the phase .PSI. is 
obtained without ambiguity of sign after correction of the sign as a 
function of the considered range bin. 
SUMMARY OF THE INVENTION 
The present invention relates to a method of estimating the parasite phase 
.PSI. for resolving these ambiguities of sign also in the azimuth plane, 
and whose principle is also applicable to the estimation of the parasite 
phase .PSI. in the elevational plane, as well as to the estimation of the 
differential phase .delta..phi. between the azimuth and elevational 
planes, this latter possibility moreover forming, as will be seen further 
on, the basis of another method of estimating the parasite phase in the 
azimuth plane. 
According to the invention, the method of processing the sum .SIGMA. and 
difference .DELTA. signals, in azimuth: .SIGMA..sub.a, .DELTA..sub.a, and 
in elevation: .SIGMA..sub.e, .DELTA..sub.e, of a radar of the monopulse 
type, for estimating the parasite phase .PSI. introduced between these 
signals by the ultrahigh frequency formation circuits of the sum and 
difference channels consists: 
in calculating for each measurement made by the radar the expressions S and 
D, with 
##EQU6## 
(where the symbol * designates the complex conjugate quantity), depending 
on whether it is desired to estimate the parasite phase .PSI..sub.a in 
azimuth in the first case, or the parasite phase .PSI..sub.e in elevation 
in the second case or the differential parasite phase 
.delta..PSI.=.PSI..sub.a -.PSI..sub.e in the third case, it being 
understood that the radar wave emitted is polarized circularly and that 
the azimuth and elevation monopulse receivers only receive respectively 
one of the circular polarization types: right or left, 
in calculating the expression 
EQU [S(k+1)-S(k-1)]D*(k) 
it being understood that the radar antenna sweeps during time in azimuth in 
the first case and in the third case, in elevation in the second case and 
that k-1, k, k+1 designate three successive times such that the difference 
s.sub.(k+ 1) (.theta.)-s.sub.(k-1) (.theta.) is of the same sign as 
d.sub.(k) (.theta.), where s.sub.(k+1) (.theta.) and s.sub.(k-1) (.theta.) 
designate respectively the gain of the sum channel at the angle .theta., 
in azimuth in the first case and in the third case, in elevation in the 
second case, respectively at times k+1 and k-1, and where d.sub.(k) 
(.theta.) designates the gain of the difference channel at the angle 
.theta. at time k, in azimuth in the first and in the third cases, in 
elevation in the second case; 
in calculating the mean value of the result of the preceding expression for 
several successive times corresponding to several measurements 
successively made by the radar, which allows an expression to be obtained 
of the form e.sup.j.PSI..a, where .PSI. is the parasite phase sought and 
"a" a real number of given absolute value and sign.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
The invention is used in a radar system with circularly polarized coherent 
or non coherent transmission, capable of receiving and discriminating the 
right hand circular polarization and left hand circular polarization. For 
the sake of clarity in what follows, the azimuth channels will receive the 
right hand polarization whereas the elevational channels receive the left 
hand polarization; the reverse would also be possible. 
Thus, referring to an absolute hypothetical phase the sum signals 
.SIGMA..sub.a and .SIGMA..sub.e, respectively in azimuth and in elevation, 
and the difference signals .DELTA..sub.a and .DELTA..sub.e, respectively 
in azimuth and in elevation, are written: 
##EQU7## 
where the indices D and G designate the channels receiving the right hand 
and left hand polarizations, and the indices a and e the angular azimuth 
and elevational dimensions, and where .phi..sub.t designates the non 
coherent phase component which changes from pulse to pulse. 
From the sum and difference signals .SIGMA..sub.a, .SIGMA..sub.e, 
.DELTA..sub.a, .DELTA..sub.e, the following expressions are calculated. 
EQU S=.SIGMA..sub.a .multidot..SIGMA..sub.e * 
EQU D=.DELTA..sub.a .multidot..SIGMA..sub.e * 
With a unit of time fixed sufficiently small for the phase shift between 
channels to be considered as constant, we have at a time k: 
##EQU8## 
It will be noted that calculation of the expressions S and D allows, among 
other things, to be free of the non coherent phase component .phi..sub.t. 
We then calculate the expression: 
EQU [S(k+1)-S(k-1)]D*(k) 
where k-1, k and k+1 designate three successive times. 
We have: 
##EQU9## 
In the expression 
##EQU10## 
the factors b.sub.n are assigned with a phase term .phi..sub.n which, 
since it may be considered as random, will disappear by averaging the 
expression: [S(k+1)-S(k-1)]D*(k) over several successive measurements of 
.SIGMA..sub.a, .DELTA..sub.a, .SIGMA..sub.e, .DELTA..sub.e made by the 
radar and corresponding to several successive times k. 
The notion of measurements made by the radar relates to the notion of range 
bins and pulses. For a given range bin, the averaging is carried out over 
several successive pulses, and averaging is then carried out over several 
distance divisions. Because of the double polarization. the factors to 
which such a phase term has not been assigned are limited to the 
expression "a" for which we have the equality i=l and j=m. All the other 
cases (such as i=j or m=l) are in fact excluded for they would correspond 
to individual reflectors which would reflect the two types of 
polarization: right hand and left hand, that is to say which would be both 
of the dihedron type (even number of successive reflections) and of the 
trihedral type (uneven number of successive reflections). 
The invention allows then any angular information between the signals 
received to be kept, while eliminating the non coherence of the 
transmission, by referencing them to the response to the same pulse of 
different reflectors. This is achieved through the combination of the 
calculation of expressions S and D and the double polarization. 
During the preceding development, the important assumption was made that 
between times k-1 and k+1 the angles of elevation .theta..sub.e (in this 
case .theta..sub.G since we are considering in this example the case where 
the azimuth channels receive the right hand polarization whereas the 
elevational channels receive the left hand polarization) are invariable, 
which allows the common factorization in the expression "a". This 
assumption is reasonable in the case of a fixed radar or of an airborne 
radar if the time unit is sufficiently small so that advance of the 
platform does not change the geometry of the system. 
The invention is moreover used in an azimuth sweep radar system, the 
rotational speed of the antenna (in azimuth) being fixed at a value such 
that the lobes .DELTA.- and .DELTA.+ at time k coincide respectively with 
the lobe .SIGMA. at time k-1 and with the lobe .SIGMA. at time k+1, as 
shown in FIG. 3. 
Under these conditions, the product 
EQU [s.sub.a(k+1) (.theta..sub.Di)-s.sub.a(k-1) (.theta..sub.Di)]d.sub.a(k) 
(.theta..sub.Di) 
is positive for any elementary reflector "i". In fact, if we consider for 
example an elementary reflector which is at time k on lobe .DELTA.+, we 
then have d.sub.a(k) which is positive, s.sub.a(k+1) which is also 
positive and s.sub.a(k-1) which is very small. The product is therefore 
positive; it would be the same for an elementary reflector which at time k 
would be on lobe .DELTA.-. 
The azimuth speed of rotation of the antenna is not critical and could be 
chosen differently. The proposed choice seems however optimum in that it 
gives the largest values of the difference (s.sub.a(k+1) -S.sub.a(k-1). 
The factor "a" is therefore written as the sum of a large number of 
positive definites. On the contrary the factors b.sub.n are assigned with 
a phase term .phi..sub.n which may be considered as random. 
Examination of several successive measurements of [S(k+1)-S(k-1)]D*(k), by 
averaging, allows the phase correction .PSI..sub.1 -.PSI..sub.3 to be 
estimated whose variance will vary inversely with the number of 
measurements made, this number of measurements being fixed a priori or 
adapted to the desired accurancy by software. 
Adaptation of the repetition period of the measurements made by the radar 
(coresponding to the notion of range bins and pulses) and of the 
repetition period of times k, that is to say the sweeping speed of the 
antenna, may be made in different ways, for example by suitably choosing 
the repetition period of the pulses or else by carrying out post 
integration over several pulses. 
In FIG. 5 a diagram has been shown of the product detector used in the 
processing carried out in accordance with the invention for estimating the 
parasite phase between the sum and difference channels in azimuth. 
The signals .SIGMA..sub.a, .DELTA..sub.a and .SIGMA..sub.e are applied to 
the input of this product detector which calculates the expressions: 
EQU S=.SIGMA..sub.a .multidot..SIGMA..sub.e * 
EQU D=.DELTA..sub.a .multidot..DELTA..sub.e * 
by means of two mixers 5 and 6 one of which receives on the one hand the 
signal .SIGMA..sub.e and on the other hand either the signal 
.SIGMA..sub.a, or the signal .DELTA..sub.a, and the other of which 
receives on the one hand the signal .SIGMA..sub.a phase shifted by 
90.degree. by means of a phase shifter 7 and, on the other hand, either 
the signal .SIGMA..sub.a or the signal .DELTA..sub.a. The signals 
.SIGMA..sub.a .multidot..DELTA..sub.a and .SIGMA..sub.e are further 
transformed into medium frequency signals by means of frequency change 
stages 8 and 9. 
It should be noted that S and D are not used at the same times, since only 
the product [S(k+1)-S(k-1)]D*(k) is important. It is then possible to use 
only a single product detector, addressed successively through a switch 10 
by channels .SIGMA..sub.a and .SIGMA..sub.c, then .DELTA..sub.a and 
.SIGMA..sub.c. 
The magnitudes S and D are complex magnitudes which may be written in the 
form I+jQ where I and Q designate respectively their real part and their 
imaginary part; magnitudes I and Q are obtained at two outputs of the 
product detector. 
The other steps of the method may be achieved using adapted software. 
In the foregoing, the invention has been described for estimating the 
parasite phase between the sum and difference channels in azimuth. The 
principle of the invention is nevertheless applicable to estimating the 
parasite phase between the sum and difference channels in elevation. 
In this case, the following expressions would be calculated: 
EQU S=.SIGMA..sub.e .multidot..SIGMA..sub.a * 
EQU D=.DELTA..sub.e .multidot..SIGMA..sub.a * 
The constraint concerning the sweep would then become a constraint 
concerning the elevational sweep, and the assumption that between times 
k-1, k and k+1 the azimuth angles are invariable would also have to be 
made. 
As will now be seen the principle of the invention is also applicable to 
estimating the differential parasite phase .PSI..sub.a -.PSI..sub.e, where 
.PSI..sub.a and .PSI..sub.e designate respectively the parasite phase in 
azimuth and in elevation. Estimation of this differential parasite phase 
may be interesting for the following reasons. 
In the case more especially of a radar carried by a missile whose 
supersonic speed decreases during flight to subsonic values, the high 
temperature differences between the beginning and the end of the mission 
cause a variation of the azimuth and elevation parasite phases. 
Now, the above mentioned antenna sweep constraints mean that estimation of 
a phase correcting factor is not possible during the whole period of use 
and processing of the radar. 
Starting from the fact that the four receivers (two in azimuth and two in 
elevation) are physically close to each other and thermally 
interdependent, so that the variations of .PSI..sub.a and .PSI..sub.e will 
be similar, it is then sufficient to evaluate .PSI..sub.a and .PSI..sub.e 
during a so called calibration phase (previous to any operation in the 
search or tracking mode) and to calculate the difference .PSI..sub.a 
-.PSI..sub.e which will remain constant during the whole flight time. In 
the tracking phase, it is still possible, as recalled in the introduction, 
to calculate .PSI..sub.e by a method of evaluation which offers no antenna 
position or frequency constraint. It is then possible to deduce 
.PSI..sub.a therefrom. 
However, a successive evaluation of .PSI..sub.a and .PSI..sub.e during the 
calibration phase risks inducing an error in .PSI..sub.a -.PSI..sub.e as 
for as the temperature may have changed between the two evaluations. 
Moreover, the calibration phase lasts a considerable time with respect to 
the total time of the mission of a short range missile. 
The method of estimating the parasite phase of the invention allows the 
differential phase .PSI..sub.a -.PSI..sub.e to be calculated directly 
without passing through the successive calculations of .PSI..sub.a and 
.PSI..sub.e, which removes the above mentioned risk of error. 
This method will now be described applied to estimating the differential 
phase .PSI..sub.a -.PSI..sub.e. As before, the signals received by the 
four angle error measurement channels are written: 
##EQU11## 
where the indices D and G designate the channels receiving the right hand 
and left hand polarizations (still assuming that the azimuth channels 
receive the right hand polarization and the elevational channels the left 
hand polarization) and indices a and e the angular azimuth and elevation 
dimensions. 
a.sub.i is the amplitude of the ith individual reflector; 
.phi..sub.i is the phase shift introduced by the ith reflector; 
d.sub.i is the radar-ith reflector distance; 
.phi..sub.t is the non coherent phase component which changes from pulse to 
pulse; 
.PSI..sub.1, .PSI..sub.2, .PSI..sub.3, .PSI..sub.4 are the parasite phases 
introduced in the four reception channels. 
According to the same method as before, a product detector calculates: 
EQU S=.SIGMA..sub.a .multidot..SIGMA..sub.e * 
EQU D=.DELTA..sub.a .multidot..DELTA..sub.e * 
Then 
##EQU12## 
where the phases .phi.n may be considered as random phases and where: 
##EQU13## 
Now, the azimuth rotational speed of the radar has been chosen so that the 
product: [s.sub.a(k+1) (.theta..sub.Di)-s.sub.a(k-1) 
(.theta..sub.Di)]d.sub.a(k) (.theta..sub.Di) is positive for all the 
elementary reflectors. 
Moreover, s.sub.e (.theta..sub.Gj) is positive, a.sup.2.sub.Di 
a.sup.2.sub.Gj is positive and d.sub.e (.theta..sub.Gj) is negative for 
the nearest range bins and is positive for the furthest range bins 
The ambiguity of sign may therefore be removed and corrected so that the 
factor "a" is the sum of a large number of positive real numbers 
Examination of several successive measurements of [S(k+1)-S(k-1)]D*(k) 
allows by averaging to estimate the phase correction .PSI..sub.1 
-.PSI..sub.2 -.PSI..sub.3 +.PSI..sub.4 that is to say .PSI..sub.a 
-.PSI..sub.e. 
The average is calculated for several range bins and several pulses so as 
to obtain the desired accuracy.