IL119704A

IL119704A - Synthetic aperture doppler radar

Info

Publication number: IL119704A
Application number: IL11970496A
Authority: IL
Original assignee: Aerospatiale
Priority date: 1995-12-08
Filing date: 1996-11-27
Publication date: 2001-04-30
Also published as: ES2171633T3; DE69618328D1; FR2742233B1; EP0778471B1; DE69618328T2; FR2742233A1; EP0778471A1; IL119704A0

Abstract

Detection method, using a synthetic aperture radar (1) on board an aircraft (A) and observing an overflown territory (T), wherein the following operations are effected: electromagnetic radiation (S1) is transmitted towards said overflown territory (T); a signal (S2) corresponding to said electromagnetic radiation reflected by said overflown territory is detected; a distance determination processing operation is carried out on said detected signal; a focusing processing operation is carried out to correct an unwanted phase-shift in said detected signal and due notably to the displacement of said synthetic aperture radar, in order to obtain a corrected signal; a frequency determination processing operation is carried out on said corrected signal; and a transposition processing operation is carried out in order to transpose, into a reference frame of reference (OXYZ) tied to said observed territory, the results obtained from the previous operations and defined in a distance and frequency frame of reference (R) tied to the radar, in order to form a radar image defined in said reference frame of reference tied to the observed territory, characterised in that: using data obtained exclusively from at least one of the preceding operations, a Doppler gradient is determined that is representative of said unwanted phase-shift in the detected signal; and the Doppler gradient determined in this way is used: on the one hand, during said focusing processing operation, to correct said unwanted phase-shift of the detected signal; and on the other hand, during said transposition processing operation, to determine an auxiliary frame of reference (Rref) enabling the transposition from said distance and frequency frame of reference (R) to said reference frame of reference by way of said auxiliary frame of reference. 76 ז' באייר התשס" א - April 30, 2001

Description

SYNTHETIC APERTURE DOPPLER RADAR Eitan, Pearl, Latzer & Cohen Zedek Advocates, Patent Attorneys & Notaries P-67419-IL ABSTRACT The present invention concerns a synthetic aperture radar including: . means (2) for transmitting and detecting electromagnetic radiation; . means (5) for correcting an unwanted phase-shift in the detected signal; and . means (9) for transposing into a reference frame of reference the results obtained in a distance and frequency frame of reference.

In accordance with the invention, said radar (1) further includes means (11) for determining, exclusively from data received from the radar, a Doppler gradient that is representative of said unwanted phase-shift and that is transmitted to the correction means (5) and to the transposition means ( 9 ) . 1 The present invention concerns a detection method using synthetic aperture radar and synthetic aperture radar for implementing this method.

Synthetic aperture radar, usually carried on board an aircraft, is particularly suitable for Earth observation.

Moreover, radar of this kind has many advantages that explain the research and development effort expended on and the great benefits of this type of radar, in particular: - it can be used in any weather; - it is compact in size; and - the processing it performs is little dependent on the observation distance.

As is well known, synthetic aperture radar includes means for carrying out the following successive operations : - transmitting electromagnetic radiation towards an observed territory overflown by the aircraft carrying said radar; - detecting a signal corresponding to said electromagnetic radiation reflected by said overflown and observed territory; - carrying out a distance determination processing operation on said detected signal; - carrying out a focusing processing operation to correct an unwanted phase-shift in said detected signal due in particular to the displacement of said synthetic aperture radar, in order to produce a corrected signal; - carrying out a frequency determination processing operation on said corrected signal, said focusing and frequency determination operations optionally being carried out simultaneously using "correlation processing" (synthetic aperture radar in "sliding mode" ) ; and 2 - carrying out a transposition processing operation to transpose into a frame of reference tied to said observed territory the results obtained from the previous operations and defined in a distance and frequency frame of reference tied to the radar, so as to form a radar image defined in said frame of reference tied to the observed territory.

However, a synthetic aperture radar of this kind has the drawback that some of the operations mentioned above, notably the focusing and transposition processing operations, require navigation data relating to the aircraft carrying said radar.

This navigation data is determined by auxiliary sensors, generally incorporated into an inertial navigation system mounted on board said aircraft.

Operation of the synthetic aperture radar is therefore dependent on external means, and its measured values can consequently be falsified by measurement errors and/or malfunctions of such external means.

Moreover, the use of an inertial navigation system has many disadvantages, in particular: - high cost, - large overall size, and - in some instances, limited reliability.

One object of the present invention is to remedy these drawbacks. It concerns a detection method using synthetic aperture radar that can be employed without using navigation data relating to the aircraft carrying said radar, and therefore in a- manner that is completely independent of auxiliary sensors and, where applicable, an inertial navigation system.

To this end, in accordance with the invention, said method including the aforementioned successive operations, is noteworthy in that: - using data obtained exclusively from at least one of 3 the preceding operations, a Doppler gradient is determined that is representative of said unwanted phase-shift in the detected signal; and - the Doppler gradient determined in this way is used: . on the one hand, during said focusing processing operation, to correct said unwanted phase-shift of the detected signal; and . on the other hand, during said transposition processing operation, to determine an auxiliary frame of reference enabling . the transposition from said distance and frequency frame of reference to said reference frame of reference by way of said auxiliary frame of reference.

Thus the processing operations that usually require navigation data, namely the focusing and the transposition processing operations, are carried out in accordance with the invention using data determined directly by said radar.

Consequently, the synthetic aperture radar using the method of the invention is completely independent of external means, notably an inertial navigation system, which eliminates the disadvantages previously mentioned.

In the context of the present invention, said Doppler gradient can be determined in various ways.

In a first embodiment, in order to determine said Doppler gradient, the following operations are carried out on a detected signal subjected to a distance determination processing operation: - for a plurality of successive different theoretical gradient values chosen arbitrarily: . a focusing processing operation is carried out using the chosen theoretical gradient; . a frequency determination processing operation is carried out; and 4 . the contrast is measured on a radar image obtained from the previous processing operations, said contrast corresponding to the mean standard deviation of the amplitudes of the detected signal over said radar image ; - the various contrasts measured in this way are compared; and - the chosen Doppler gradient is the theoretical gradient for which the contrast is the highest.

In a second embodiment, in order to determine said Doppler gradient μ, the following operations are carried out : - two signals are detected at two different times separated by a time ΔΤ; - for each of said signals previously subjected to a distance processing operation, a frequency ^ determination processing operation is carried out; - the frequency shift AFd between the two radar images obtained from the previous processing operations is calculated; and - the Doppler gradient μ is calculated from the expression: μ ΔΤ Moreover, in accordance with the invention, during said transposition processing operation, in order to transpose from the distance and frequency frame of reference to the reference frame of reference by way of said auxiliary frame of reference, the following operations are carried out: - for each point of said distance and frequency frame of reference, having a frequency F and a distance D, the associated point having a frequency Fref and a distance Dref of said auxiliary frame of reference is determined from the following equation: 5 ( Fref = F - \ U(t)dt 1 Jtref ( Dref = D + μ(τ) dtdt in which: . i{t) represents the Doppler gradient determined and varying with ime t.; . tref represents the time between said predetermined reference time and the time at which the distance and frequency frame of reference corresponds to the auxiliary frame of reference; . tl represents the time between said reference time and the detection time; and . λ represents the wavelength of the electromagnetic radiation transmitted; and - for each point having a frequency Fref and a distance Dref determined in this way of said auxiliary frame of reference, the associated point with coordinates X, Y and Z of said reference frame of reference is determined from the following equations : iX = (λ. Dref .Fref ) / (2.Vnom) γ _ 7Dref2 - hnom2 - X2 Z = -hnom in which: . Vnom is the nominal speed of the aircraft; and . hnom is the nominal altitude of the aircraft.

Note that the nominal speed of the aircraft is used, which is known, rather than its actual speed, which must be measured by appropriate sensors.

The transposition mode described previously is particularly advantageous because: - it is completely independent of navigation data; - it can be implemented quickly and easily; and - it requires only a double transposition of frames of reference, unlike the usual methods which generally 6 employ three successive transpositions.

The present invention also makes it possible to estimate the time At between two successive radar images so that a radar map can be produced by juxtaposition of a plurality of successive radar images.

In accordance with a first embodiment of the invention, by assuming that the trajectory of the aircraft carrying the radar is parabolic between two successive radar images, said time At is calculated from the simplified expression: At = Β/|μ| in which: - μ is the Doppler gradient determined; and - B is the width of the frequency band processed to obtain a radar image .

Furthermore, in a second embodiment of the invention, by assuming any trajectory of the aircraft, said time At is calculated from the expression: ft2 +At B = Fmoy (t2+At) - Fmoy (t2) + μ(ί^ in which, additionally: - Fmoy represents the mean Doppler frequency of the radar image considered; - μ^) represents the Doppler gradient determined and varying with time t.; and - t2 represents a reference time relating to the time of detection of the first of said two radar images considered.

Moreover, the method of the invention also enables the speed of a mobile target moving over the observed territory to be calculated.

To this end, in accordance with the invention: - the radial speed Vr of said mobile target is determined from the expression: Vr = Vnom.cosccc - {λ/2) .Fc in which: 7 . Vnom is the nominal speed of the aircraft; . λ is the wavelength of the electromagnetic radiation transmitted; . ac is the azimuth of the mobile target relative to the aircraft; and . Fc is the Doppler frequency obtained from the electromagnetic radiation reflected by said mobile target; and - the transverse speed Vt of said mobile target is determined from the expression: Vt = Vnom.sinac - V^nom2-sinac2>+ (λ.ά.Δμ)/2 in which: . d is the distance between the mobile target and the radar; and . Δμ is the difference between the Doppler gradient associated with the mobile target and that associated with any fixed point of the observed territory.

The present invention also concerns a synthetic aperture radar including the means mentioned hereinabove and adapted to implement the aforementioned method.

To this end, in accordance with the invention, said synthetic aperture radar is noteworthy in that it further includes calculation means for determining, exclusively from data received from the preceding means, a Doppler gradient that is representative of said unwanted phase-shift in the detected signal, said calculation means transmitting the Doppler gradient determined to said focusing means and to said transposition means for processing .

Furthermore, said radar advantageously includes means for determining the speed of a mobile target moving across the observed territory using the previously specified speed determination method.

Moreover, in one particularly advantageous 8 embodiment of the invention, said radar further comprises means, preferably of the type disclosed in French patent application 95 07199 filed 16 June, 1995 by this applicant, for determining the mean Doppler frequency and the mean analysis distance of the analysis window of said synthetic aperture radar.

The advantages of the above means include: - it enables the mean Doppler frequency to be determined, notably in order to perform centring about said mean Doppler frequency, without using navigation data, unlike the methods generally used; and - it enables centring of the analysis window of the radar to obtain optimal measurements, used notably by said calculation means, which increases the accuracy of the processing operations carried out in accordance with the invention.

The figures of the accompanying drawings show how the invention may be put into effect. In the figures, the same reference numbers designates similar components . Figure 1 is the block diagram of a synthetic aperture radar of the invention.

Figure 2 shows the illumination of a territory by a radar on board an aircraft overflying said territory.

Figure 3 is the block diagram of calculation means used in the radar of the invention.

Figure 4 shows the transposition of data from a distance and frequency frame of reference to an auxiliary frame of reference.

Figure 5 shows the position and the speed of a mobile target relative to the radar of the invention.

The synthetic aperture radar 1 of the invention shown diagrammatically in figure 1 is mounted on an aircraft A and is used to observe a territory T overflown → by said aircraft A (moving . at a speed V ) , as shown in figure 2. 9 In a manner that is known in itself, said synthetic aperture radar 1 includes : - means 2 for transmitting electromagnetic radiation SI towards the overflown territory T so as to illuminate an area ZI of said territory T, as shown in figure 2 ; - means 2 for detecting a signal S2 corresponding to said electromagnetic radiation reflected by said illuminated area ZI . Said transmit and receive means 2 are preferably implemented in the form of an electronic system 2A including a transmit-receive antenna 2B; - means 3 connected by a connection 4 to said means 2 and adapted to carry out a distance determination processing operation using said detected signal S2; - means 5 connected by a connection 6 to said means 3 and adapted to carry out a focusing processing operation to correct an unwanted phase-shift in said detected signal S2 , due notably to the displacement of said synthetic aperture radar 1 on board the aircraft A, in order to obtain a corrected signal Sc; - means 7 connected by a connection 8 to said means 5 and adapted to carry out a frequency determination processing operation using said corrected signal Sc; and - means 9 connected by a connection 10 to said means 7 and adapted to carry out a transposition processing operation to transpose into a frame of reference OXYZ tied to said territory T and shown in figure 2 the results obtained from the above operations and defined in a distance and frequency frame of reference R tied to the radar as shown in figure 4, in order to form a radar image defined in said reference frame of reference OXYZ tied to the observed territory T.

Existing synthetic aperture radars use navigation data from the aircraft A carrying the radar to carry out certain processing operations, including the processing 10 operations carried out by said means 5 and 9.

In the known manner, the navigation data is determined by auxiliary means external to the radar and part of the equipment of said aircraft A.

This has the major disadvantage that existing radars are dependent on these auxiliary means and the results of the detection can therefore by falsified by measurement errors and/or malfunctions of the auxiliary means .

The synthetic aperture radar 1 of the invention remedies these drawbacks .

To this end, in accordance with the invention, said radar 1 further includes calculation means 11 for determining, entirely from data received from at least some of the previous means, for example the means 3 in a particular embodiment described hereinafter, a Doppler gradient that is representative of said unwanted phase-shift in said detected signal S2 , said calculation means 11 being connected, respectively by a connection 12 and by a branch 13A of a connection 13, to said means 5 and 9 to transmit to them the Doppler gradient determined. In accordance with the invention, said means 5 and 9 are adapted to carry out the necessary processing operations entirely on the basis of said Doppler gradient and not on the basis of navigation data, in the manner described hereinafter .

In one particularly advantageous embodiment of the invention, in order to determine said Doppler gradient μ the calculation means 11 carry out the following successive operations: - they detect two signals S2 at two different times separated by a time ΔΤ; - for each of said signals previously subjected to a distance processing operation, they carry out a frequency determination processing operation; 11 - they calculate the frequency shift. AFd between the two radar images obtained from the preceding processing operations; and - they calculate the Doppler gradient μ from the expression: μ = AFd / ΔΤ.

In another advantageous embodiment of the invention, said calculation means 11 include, as shown in figure 3 : - a calculation unit 14 that is connected by a branch 15A of a connection 15 to the connection 6, i.e. to the output of the means 3, and which, on the basis of information received from said means 3 , carries out focusing processing operations specified hereinafter, using each time one of a plurality of different theoretical gradient values chosen arbitrarily and received via a connection 16. Said calculation unit 14 may correspond to the aforementioned means 5 or it may constitute a separate calculation unit, operating in accordance with the same principle of said means 5; - a calculation unit 17 connected by a connection 18 to the calculation unit 14 and carrying out frequency determination processing operations. Similarly, said calculation unit 17 may correspond to the aforementioned means 7 or may constitute an independent calculation unit, operating in accordance with the same principle as said means 7 ; - a calculation unit 19 connected by a connection 20 to the calculation unit 17 and determining the contrast in an image formed and transmitted by the calculation unit 17, said contrast corresponding to the mean standard deviation of the amplitude of the detected signal over said image; - a comparator 21 comparing the contrast determined by the calculation unit 19 and transmitted via a connection 22 with a contrast stored in a memory 23 and 12 received via a connection 24; and - said memory 23 : . which stores each time the highest contrast value of the values compared by the comparator 21, received via a connection 25, and the corresponding theoretical gradient; and . which transmits the contrast value stored in this way to the comparator 21 over the connection 24, for the next comparison.

When the processing operations defined above have been carried out for all the theoretical gradients chosen arbitrarily, the memory 23 transmits the theoretical gradient for which the contrast is the highest via the connection 12 and/or the connection 13. This constitutes the Doppler gradient used in subsequent processing operations .

The means 5 and 9 use the Doppler gradient determined in this way in the processing operations that they carry out, as explained hereinafter.

To this end, it must be remembered, firstly, that for the transmitted electromagnetic radiation SI the radar detects a signal S2 of phase (|>(t) such that (|)(t) = φο + 2.7t.F.t + π.μ-t2, in which: - φο is the phase of the signal at a detection reference time; - F is the Doppler frequency characteristic of the angular position of a corresponding point P of the observed territory T relative to the radar 1; and - μ is the Doppler gradient that generates an unwanted phase shift π.μ-t2 due to the displacement of said radar 1 relative to said point P.

To correct this unwanted phase-shift, which blurs the image obtained, among other things, the means 5 determine a corrected signal Sc(t) during the focusing processing operation, using the expression: 13 Sc(t) = S2 (t) .exp(-j .π.μ. 2) where : - S2(t) is the signal picked up and received from the means 3 ; and - μ is the Doppler gradient determined by the calculation means 11, as previously explained.

Note that existing synthetic aperture radars carry out this focusing, i.e. the correction of said unwanted phase-shift, using navigation data, generally the speed and the radial acceleration of the aircraft carrying the radar, which is not the case in the present invention.

As to the aforementioned transposition processing operation, it is carried out in existing radars by using navigation data to perform three successive transpositions, not shown, namely: - firstly from said distance and frequency frame of reference tied to the radar to a local orthogonal frame of reference, using in particular the speed of the aircraft; - then, from said local orthogonal frame of reference to a local geographical frame of reference; and - finally, from said local geographical frame of reference to said reference frame of reference tied to the overflown territory.

In accordance with the invention, the means 9 carry out said transposition processing operation in a simplified manner and without using navigation data.

To this end, said means 9: - first carry out a transposition from the distance and frequency frame of reference R shown in figure 4 to an auxiliary frame of reference Rref also shown in figure 4; and - then carry out a transposition from said auxiliary frame of reference Rref to said reference frame of reference OXYZ tied to a point 0 of said territory T, 14 as shown in figure 2.

In accordance with the invention, said auxiliary frame of reference Rref corresponds to the distance and frequency frame of reference at a time tref (defined relative to a reference time) and is defined according to the position of the aircraft A on its trajectory C at this time tref.

To explain how the invention is put into effect, any distance and frequency frame of reference R relative to a position Al of the aircraft A on the trajectory C at a time tl can be used (tl is also defined relative to said reference time) .

In accordance with the invention, in order to carry out the first of the aforementioned two transpositions, for each point P having a distance D and a frequency F in the frame of reference R, the corresponding coordinates (distance Dref and frequency Fref) of said point P in the frame of reference Rref are determined using the following equations: (Fref = F — l μ( (^ ) Jtref # λ λ ftl ft (Dref = D + —.Fref .(tl-tref ) + —.1 \ μ(τ) dtdt 2 2 Jtref Jtref in which: - ^) represents the Doppler gradient determined and varying with time t.; and - λ represents the wavelength of the electromagnetic radiation SI transmitted.

Then, in order to transpose from said frame of reference Rref to the reference frame of OXYZ , the means 9 determine, for each point P (distance Dref and frequency Fref) thus characterised its coordinates X, Y and Z in said reference frame of reference OXYZ, using the following equations: 15 .Vnom) in which: - Vnom is the nominal speed of the aircraft A; and - hnom is the nominal altitude of the aircraft A.

As previously indicated, said means 9 form in this way a radar image of a part of the overflown territory.

In a manner that is known in itself, in order to produce a radar map by juxtaposing a plurality of such radar images, generally produced in the form of strip images, it is necessary to know the real time At between two successive radar images, in order to be able to effect an accurate juxtaposition.

In accordance with the invention, the radar 1 includes means 26 connected to the means 11 by a branch 13B of the connection 13 and adapted to calculate said time At without using navigation data, unlike existing radars, and transmitting said time At to the means 2 via a connection 31 in order to produce the next radar image.

To this end, said means 26 determines said time At: - in a first embodiment, by assuming that the trajectory C of the aircraft A is parabolic between the two successive radar images considered, using the simplified expression At = Β/|μ| in which: . μ is the Doppler gradient determined; and . B is the width of the band of frequencies processed to obtain a radar image; and - in a second embodiment, for any trajectory C of the aircraft A, by using the expression: ft2+At B= Fmoy (t2+At) - Fmoy (t2) + μ(ί:)(^ in which: - Fmoy represents a mean Doppler frequency of the radar 16 image considered, which is determined by the means 27 described hereinafter and transmitted to the means 26 via a connection 28; - μ^) represents the Doppler gradient determined and varying with time t; and - t2 represents a reference time relative to the time of detection of the first of said two radar images.

The radar 1 further includes means 29 that receive the radar images from the means 9 via a connection 30 and which determine a radar' map that they can transmit to a user device, not shown, via a connection 32.

In one advantageous embodiment of the invention, said means 27 are adapted to determine, in addition to the mean Doppler frequency previously mentioned, the mean analysis distance of the analysis window of the radar 1, which enables said analysis window to be centred in order to obtain optimal measurements, notably measurements that can be transmitted to the calculation means 11 (via a connection 33). This embodiment therefore increases the accuracy of the processing operations carried out.

Said means 27 are preferably of the type disclosed in the previously mentioned French patent application 95 07199.

The radar 1 further includes means 34 connected to a branch 15C of the connection 15 and adapted to determine the speed VCM > of a mobile target CM moving across the observed territory T.

Said speech VCM ' is formed of a transverse speed Vt > and a radial speed Vr ' , as shown in figure 5 which is a plan view corresponding to the orthogonal projection of the various vectors into the plane of the ground (with the nominal speed Vnom ' as the speed of the aircraft) .

In accordance with the invention, the means 34 determine: 17 - said radial speed Vr, from the expression: Vr = Vnom.cosac - (λ/2) .Fc in which: . λ is the wavelength of the electromagnetic radiation SI transmitted by the antenna 2B; . ccc is the azimuth of the mobile target CM relative to said radar 1; and . Fc is the Doppler frequency obtained from the electromagnetic radiation S2 reflected by said mobile target CM; and - said transverse speed Vt, from the expression: Vt = Vnom.sinac in which: . d is the distance between the mobile target CM and the radar 1 (or the aircraft A) ; and . Δμ is the difference between the Doppler gradient associated with the mobile target CM and that associated with any fixed point of the observed territory, for example the point P at azimuth a in figure 1.

Said means 34 can transmit the speeds determined in this way (for example after transposing them into the frame of reference OXYZ) to a user device, not shown, over a connection 35. 18

Claims

1. Detection method, using a synthetic aperture radar (1) on board an aircraft (A) and observing an overflown territory (T) , wherein the following operations are effected: - electromagnetic radiation (SI) is transmitted towards said overflown territory (T) ; . - a signal (S2) corresponding to said electromagnetic radiation reflected by said overflown territory is detected; - a distance determination processing operation is carried out on said detected signal (S2) ; - a focusing processing operation is carried out to correct an unwanted phase-shift in said detected signal and due notably to the displacement of said synthetic aperture radar, in order to obtain a corrected signal; - a frequency determination processing operation is carried out on said corrected signal; and - a transposition processing operation is carried out in order to transpose, into a reference frame of reference (OXYZ) tied to said observed territory, the results obtained from the previous operations and defined in a distance and frequency frame of reference (R) tied to the radar (1) , in order to form a radar image defined in said reference frame of reference (OXYZ) tied to the observed territory, characterised in that: - using data obtained exclusively from at least one of the preceding operations, a Doppler gradient is determined that is representative of said unwanted phase-shift in the detected signal; and - the Doppler gradient determined in this way is used: . on' the one hand, during said focusing processing operation, to correct said unwanted phase-shift of the detected signal (S2); and 19 . on the other hand, during said transposition processing operation, to determine an auxiliary frame of reference (Rref) enabling the transposition from said distance and frequency frame of reference (R) to said reference frame of reference (OXYZ) by way of said auxiliary frame of reference (Rref) .

2. Method according to claim 1, characterised in that, in order to determine said Doppler gradient, the following operations are carried out on a detected signal subjected to a distance determination processing operation: - for a plurality of successive different theoretical gradient values chosen arbitrarily: . a focusing processing operation is carried out using the chosen theoretical gradient; . a frequency determination processing operation is carried out; and . the contrast is measured on a radar image obtained from the previous processing operations, said contrast corresponding to the mean standard deviation of the amplitudes of the detected signal over said radar image ; - the various contrasts measured in this way are compared; and - the Doppler gradient chosen is the theoretical gradient for which the contrast is the highest.

3. Method according to claim 1, characterised in that, in order to determine said Doppler gradient μ, the following operations are carried out: - two signals (S2) are detected at two different times separated by a time ΔΤ; - for each of said signals previously subjected to a distance processing operation, a frequency determination processing operation is carried out; - the frequency shift AFd between the two radar images 20 obtained from the previous processing operations is calculated; and - the Doppler gradient μ is calculated from the expression:

4. Method according to any one of claims 1 to 3 , characterised in that, during said transposition processing operation, in order to transpose from the distance and frequency . frame of reference (R) to the reference frame of reference (OXYZ) by way of said auxiliary frame of reference (Rref ) , the following operations are carried out: - for each point (P) of said distance and frequency frame of reference (R) , having a frequency F and a distance D, the associated point having a frequency Fref and a distance Dref of said auxiliary frame of reference (Rref tion: μ(τ) dtdt ef in which: . μ^) represents the Doppler gradient determined and varying with time t.; . tref represents the time between a predetermined reference time and the time at which the distance and frequency frame of reference corresponds to the auxiliary frame of reference; . tl represents the time between said reference time and the detection time; and . λ represents the wavelength of the electromagnetic radiation (SI) transmitted; and - for each point having a frequency Fref and a distance Dref determined in this way of said auxiliary frame of reference (Rref) , the associated point with coordinates 21 X, Y and Ζ of said reference frame of reference (OXYZ) is determined from the following equations : X = (λ-Dref .Fref) / (2.Vnom) ^Dref2 - hnom2 - X2 Z = -hnom in which: . Vnom is the nominal speed of the aircraft (A) ; and . hnom is the nominal altitude of the aircraft (A) .

5. Method according to any one of the preceding . claims for estimating the time At between two successive radar images in order to be able to form a radar map by juxtaposing a plurality of successive radar images , characterised in that said time At is calculated from the simplified expression: At = Β/|μ| in which: - μ is the Doppler gradient determined as explained above ; and - B is the width of the frequency band processed to obtain a radar image.

6. Method according to any one of claims 1 to 4, for estimating the time At between two successive radar images, in order to be able to form a radar map by juxtaposing a plurality of successive radar images, characterised in that said time At is calculated from the expression : in which B represents the width of the band of frequencies processed to obtain a radar image; Fmoy represents the mean Doppler frequency of the radar image considered; μ(ί) represents the Doppler gradient determined and varying with time t.; and 22 - t2 represents a reference time relating to the time of detection of the first of said two radar images considered.

7. Method according to any one of the preceding claims, enabling additional calculation of the speed of a mobile target (CM) moving over said observed territory, characterised in that: - the radial speed Vr of said mobile target (CM) is determined from the expression: Vr = Vnom.cosac - (λ/2) . Fc in which: . Vnom is the nominal speed of the aircraft (A) ; . λ is the wavelength of the electromagnetic radiation (SI) transmitted; . ac is the azimuth of the mobile target (CM) relative to the aircraft (A) ; and . Fc is the Doppler frequency obtained from the electromagnetic radiation (S2) reflected by said mobile target (CM) ; and - the transverse speed Vt of said mobile target (CM) is determined from the expression: Vt = Vnom.sinac - (Vnom2-sinac2) + (λ.ά.Δμ)/2 in which: . d is the distance between the mobile target (CM) and the radar; and . Δμ is the difference between the Doppler gradient associated with the mobile target and that associated with any fixed point of the observed territory.

8. Synthetic aperture radar for implementing the method specified in any one of claims 1 through 7, including : - means (2) for transmitting electromagnetic radiation (SI) towards a territory (T) overflown by the aircraft (A) carrying said radar; 23 - means (2) for detecting a signal (S2) corresponding to said electromagnetic radiation reflected by said overflown and observed territory; - means (3) for carrying out a distance determination processing operation using said detected signal (S2); - means (5) for carrying out a focusing processing operation to correct an unwanted phase-shift in said detected signal (S2) and due notably to the displacement of said synthetic aperture radar, in order to obtain a corrected signal; - means (7) for carrying out a frequency determination processing operation on said corrected signal; and - means (9) for carrying out a transposition processing operation in order to transpose into a reference frame of reference (OXYZ) tied to said observed territory (T) the results obtained from the previous operations and defined in a distance and frequency frame of reference (R) tied to the radar, in order to form a radar image defined in the frame of reference (OXYZ) tied to the observed territory, characterised in that it further includes calculation means (11) for determining, exclusively from data received from the preceding means, a Doppler gradient that is representative of said unwanted phase-shift in the detected signal (S2), said calculation means (11) transmitting the Doppler gradient determined to. said focusing means (5) and to said transposition means (9) for processing.

9. Synthetic aperture radar according to claim 8, characterised in that it includes means (34) for determining the speed of a mobile target (CM) moving across the observed territory using the method specified in claim 7.

10. Said synthetic aperture radar according to claim 8 or claim 9, 24 characterised in that it includes means (27) for determining the mean Doppler frequency and the mean analysis distance of the analysis window of said synthetic aperture radar (1) .