DE19626556A1 - Determining absolute phase between two interferometric images generated by synthetic aperture radar - Google Patents

Abstract

An unfiltered, folded in-phase element is subtracted from an a priori absolute phase element after initialising an iteration. The result is filtered, unfolded and added to the absolute phase. The standard deviation of the difference between the absolute in-phase and priori absolute phase elements is determined and compared with a previous standard deviation to determine whether to proceed with the iteration. The a priori absolute in-phase element is replaced with the last determined value and the old standard deviation is simultaneously replaced with the new value and the process returns to the first step or the iteration is interrupted, when an absolute in-phase element of a first form is achieved, enabling an accurate terrain model to be derived using the flight geometry.

Description

The invention relates to a method for determining an abso luten phase between two interferometric, using radar Images taken with synthetic aperture (SAR).

Radar with a synthetic aperture (SAR) is an active micro wave imaging system operating on moving platforms such as egg an airplane or a satellite. Overflyed ne areas are mapped in two dimensions, namely in Rich the distance and in the direction of flight, the so-called Azi direction. Images obtained in this way have a geometric one Resolution in the distance direction by the bandwidth of the transmission signal and in the azimuth direction by the length of the synthetically constructed antenna aperture is determined. By SAR interferometry can be carried out in addition to two-dimensional Illustration of a very precise terrain model of the recorded Ge determine. This enables the interferometric SAR a three-dimensional image of the area overflown.

The interferometric method is based on the evaluation the phase difference of the backscatter signal two by the Ba sis line of separate radar antennas.

The two antenna backscatter signals can be obtained The following type. In the case of one-pass interferometry, the radar  two antennas; the corresponding radar backscatter signal pair won by an overflight.

With two-pass interferometry, the radar has only one antenna no; the corresponding radar backscatter signal pair is replaced by two Overflights won. Both overflights are spatially ver so that there is a baseline between the two shots that is.

Processing the two backscatter signals into a terrain model determination is carried out as follows:

The backscatter signal from both radar antennas is used for acquisition the distance and azimuth resolution processed separately. This creates two complex, two-dimensional SAR images.

To determine the complex interferogram, one of the Images with the complex conjugate shape of the other image multiplied. Due to the complex conjugate form one of the both images correspond to the phase of the complex interfero the phase difference of the two images. This interfero metric phase is used in the description below Designated in-phase.

The in-phase is determined by an arctangent operation of the complex interferogram. However, the modulus-2π information is lost as a result of the arctangent operation, ie the determined in-phase is always in the range from 0 to 2π or from 0 ° to 360 °. The phases 0 °, 360 °, 720 ° etc. are always displayed as a 0 ° phase. The determined in phase is thus a folded in phase. (See for example the phase curve in Fig. 4b).

The absolute in-phase, d. H. the unfolded in-phase from which he above mentioned, folded in-phase. This phase cancellation is called "phase unwrapping".  

Since the receiving geometry of the radar antennas is basically the height as a function of the distance and determine the azimuth direction from the absolute phase. In order to becomes the third dimension of a SAR image and thus a Ge Get country model.

The step in interferometry processing, which with is the most difficult, however Phase development. For example, when Pha The noise in the phase development is very computationally intensive and radio works poorly.

Here, the phase noise appears regularly from the following Establish:

• 1) The oblique view of the radar recording geometry creates Shadow and overlap (layover) areas. In these Be range, the in-phase is misleading and shows no height formation of the site. This error is therefore called Pha considered noise, the local error in the phase cancellation tung caused.
• 2) The thermal noise of the radar is high, so that the In-phase in turn is additionally affected by phase noise. There Most systems send strong enough is the occurrence of the thermal noise is negligible and will not be here considered.
• 3) There is also a time decorrelation between the two Ra backscatter signals. However, time decorrelation occurs only with two-pass interferometry, since both recordings take place with a time delay. There is a time decorrelation for example, when the weather is different between the two shots. When you take the first shot, the bottom is for example, dry while taking the second shot is wet due to a rain shower. A shower of rain thus makes a strong backscatter difference and causes  thus a decorrelation between the two recordings. The In-phase is therefore faulty and contains high phases rustle.

Time decorrelation is almost always present in forests, since the control properties of the forest change especially in C and X band strong with the movement of leaves by wind to change. For waters, the time decorrelation is for all Ra darfrequenzen highest because a water surface movement and therefore always a complete backscatter change before is there.

The phase noise due to time decorrelation is al len two-pass recordings available and is the main cause of a malfunction of the phase unfolding process or the ma manual intervention to successfully carry out the Pha deployment.

The slope of the phase noise level, i.e. H. the slope of the The amplitude of the phase noise causes the Ko to decrease between the two radar backscatter signals. The Kohä renz is always in the range between 0.0 and 1.0. For the ideal case, d. H. if both radar backscatter signals are fully correct are related, the coherence is 1.0. If both radar backscatter signals are totally decorrelated, the coherence is 0.0.

There are basically two classes of phase unfolding processes drive, namely the residual method (see R.M. Goldstein, HA. Zebker and C. Werner, "Satellite radar interferometry: two-dimensional phase unwrapping ", Radio Sci., 23 (1988, Pp. 713-720) and linear methods (see G. Fornaro, G. France Schetti, R. Lanari, "SAR Phase Unwrapping Using Green's Formu lation ", IEEE Transactions for Geoscience and Remote Sensing, May 1996, Vol. 34, No. 3, pp. 720-727).  

The absolute in-phase becomes the reason for the residual method additionally calculated without errors. This almost always requires one manual intervention, especially in scenes with high time decorations relation or low coherence; with decreasing coherence however, the computing time increases enormously. With shadow, overlap areas (layover) and totally decorrelated areas Absolute phase is not determined and must be done manually be interpolated.

The linear methods require a much shorter Re time than the residual method. The absolute phase is estimated as soon as phase noise is present. Also at a coherence of 0.8, which is for two-pass interferometry is a very good value and is rarely achieved in the linear methods with respect to the absolute phase Feh 30%. This makes a 1000 m higher one, for example Mountain valued at an altitude of 700 m. Also shadow and Overlap areas cause local and global errors the absolute phase estimate. The only big advantage is the linear method compared to the residual method, as stated above, the calculation speed speed, which is often 100 times higher than that of resi process.

So far, no method is known with which the Phase development fast, error-free and without operation in the presence of time decorrelation, shadow and over Lapping areas can be carried out and which can still be used operationally.

So far, there is still no method by which the In-phase with a coherence less than 0.5 is error-free can be tet. So far, the in-phase has been filtered by one maintain higher coherence. When filtering, however, the geometric resolution greatly deteriorated. This leads to, that the terrain model only calculates with a large grid  can be net. Therefore, there are still mistakes in the terrain model available, which are due to the phase unfolding.

The object of the invention is therefore to provide a measured, approx unfolded and folded in-phase so that the actual absolute, in-phase (the so-called absolute actual-in phase) can be determined exactly.

According to the invention, this is the case for methods for determining the absolute phase between two interferometric, using SAR generated recordings by the features in claims 1, 2 and 3 reached.

According to the invention, a deployment of a folded and unfiltered in-phase performed so that the geometric Resolution of the terrain model is not deteriorated. In egg nem first unfolding method according to claim 1, the un filtered and folded in-phase with time decorrelation so processed that an absolute in-phase determined first form that is freed from errors due to time decorrelation is.

In a second deconvolution process according to claim 2 the unfiltered and folded in-phase with shadow and Overlap (layover) areas processed. By means of this second deconvolution method according to the invention is then egg received an absolute in-phase, at which errors due to Shadow and overlap areas are eliminated.

According to the invention is by linking the unfolding Method according to claim 1 and claim 2 achieved that from egg ner unfiltered and folded in-phase in the presence of Time decorrelation and from shadow to overlap rich absolute phase errors with an absolute in-phase is calculated or calculated, which are neither errors due to a  Time decorrelation still errors due to shadow and over has lapping areas.

According to the invention, despite a strong phase roughness or a low coherence of up to 0.2 or less ger despite the presence of a time decorrelation or / and despite the presence of shadow and overlap areas the absolute difference phase very precisely and with only a slight Re expenses determined.

With the help of the method according to the invention and use the two-pass interferometry could, for example, from the SAR data from the European satellite ERS-1 / ERS-2 and al len other satellite-based SAR systems with regard to Height accuracy significantly improved terrain models will create. Since so far no satellite-borne SAR system equipped with two antennas is the invention of great importance for all satellite-based SAR systems tung.

In addition, the invention is also for use in the ope rational one-pass interferometry very useful because the Shadow and overlap areas no longer an obstacle to Ge Represent country model calculation. On top of that, the Er opens finding a new area of application, especially in the two pass-interferometry, since this has not been used operationally could be set.

The invention based on a preferred Aus management form with reference to the accompanying drawings explained in detail. Show it:  

FIG. 1 shows in block diagram form, (1000) a sequence of steps of a deployment process of the invention for a pleated in-phase with time only de-correlation;

Figure 2 in the form of another block diagram (2000) a white tere step sequence of a deployment process of the invention for a pleated in-phase with shadow and overlapping areas.

Fig. 3 is still a further sequence of steps a Entfaltungsver procedure in accordance with the invention for a pleated in-phase with time decorrelation and with shadow and overlapping areas, and

FIGS. 4a to 4f graphs of different phase characteristic shapes depending on the distance.

In order to clarify the problem underlying the invention of unfolding a measured, folded in-phase, the first phase profiles are explained with reference to FIGS . 4a to 4f. FIG. 4a shows an absolute actual in-phase, ie a so-called absolute actual in-phase of a terrain model, which, however, is not measurable in this form. The noise shown in FIG. 4a is due to a time decorrelation and to shadow and overlap areas.

FIG. 4b shows a folded actual-in phase, ie the folded phase shape of the unmeasurable absolute actual-in phase from FIG. 4a. In contrast to FIG. 4a, the folded actual in-phase shape can be measured.

In Fig. 4c to 4e intermediate results are explained in more detail below phase deconvolution method according to the invention shown.

Fig. 4f shows the result of the unfolding process according to the invention, which comes very close to the course of the absolute actual-in phase of Fig. 4a. This course of the absolute phase is proportional to the terrain height.

In the example in Fig. 4a, a mountain with a building to the left of the mountain top was viewed. The beginning of the mountain was at zero distance, the top of the mountain at distance 250 and the end of the mountain at distance 500. The building to the left of the mountain top was at a distance of about 130.

In the flight geometry under consideration, a radian (1rd) corresponds in reality to about 4 m. That means the mountain is about 100 m and the building is about 30 m high. Due to the lighting geometry of the radar, overlap areas appear, which are entered in Fig. 4a on the left side next to the building, and shadow areas, which can be seen in Fig. 4a on the right side next to the building.

In Fig. 1, designated by a block 1000 portion of a deployment method is shown according to the invention in which an unfiltered and folded in-phase ff with time decorrelation of a complex interferogram, the production of which is described in the introduction, is processed.

In the deconvolution method according to the invention, identical linear deconvolution modules 1240 , 2140 and 2240 are used as the basis for a phase deconstruction several times in terms of structure and func- tion, whereby any well-functioning linear deconvolution module can be used. (See, for example, the process by Fornaro et al.

The first method section for determining or calculating an absolute in-phase of the first form is described with reference to FIG. 1. At the input of block 1000 , the unfiltered and folded in-phase ff is present with time decorrelation from a complex interferogram, with ff being the variable of the unfiltered, folded in-phase. At step 1100, an iteration is initialized. Sa is the value of the last calculated standard deviation, which is set to zero. Ref also denotes the value of the last calculated, absolute in-phase; this value is also set to zero in step 1100.

In step 1200, deconvolution is carried out using the variables ff and an a-priori absolute in-phase ref. In a subtractor 1220 , the subtraction (ff-ref) is carried out in the complex plane, so that the value at the output of the subtractor 1220 represents the residual error between ff and ref. Here, the closer the value ref comes to the correct absolute phase, the lower the value at the output of the subtractor 1220 , ie the fewer 2π folds are present. The output signal of the subtractor 1220 is tertpaßgefil tert in a downstream low-pass filter 1210 and then unfolded by a linear deconvolution method (block 1240 ). Here, the subtractor 1220 and the low-pass filter 1210 represent an auxiliary function for the downstream deconvolution process (block 1240 ).

After the unfolding, the a priori information ref is added up again in a summing element 1260 , so that the output signal of the summing element 1260 and thus the signal represents an unfolded in-phase; this unfolded in-phase is closer to the ideal absolute in-phase than the a-priori information ref.

The initial value uff obtained in step 1200 becomes at a step 1300 the standard deviation Sn of (ref-uff) determined. In the next step 1400 it is checked whether the Standard deviation Sn smaller than the previously calculated standard dard deviation is Sa or not.

If the result at step 1400 is yes, this means that the iteration is still converging and the process proceeds to step 1500, in which the a priori absolute in-phase ref is loaded with the last calculated absolute in-phase uff. At the same time, the old standard deviation Sa is loaded with the new standard deviation Sn calculated in block 1300 . Then it goes back to step 1200.

If the result at step 1400 is no, it means that the iteration no longer converges and the process is terminated. The initial value of the first method section 1000 is then the absolute in-phase on _abs , first form that is equivalent to the last calculated unfolded in-phase on.

The calculated absolute in-phase uff _abs is freed from phase errors due to a time decorrelation. Fig. 4c shows an example of the absolute in-phase Uff _abs first mold. This means that the shape of the mountain is well represented. However, due to the shadow and overlap areas, the building is practically completely suppressed. In the case of a phase without shadow and overlapping areas, the result on _abs would be the final absolute in-phase.

If the unfiltered, folded in-phase ff does not contain a time decor relation, but is affected by shadow and overlap areas, the final absolute in-phase is determined and calculated using an deconvolution method, which is explained in detail below with reference to FIG. 2 is tert.

In a section of the method shown in block 2000 shown in dashed lines, two deconvolution modules 2100 and 2200 , which have the same function as the deconvolution module 1200 of the first method section represented by block 1000 , and a Kalman filter 2030 are provided. At the entrance to block 2000 , the unfiltered and folded in-phase ff with shadow and overlap areas from a complex interferogram is applied, which is simultaneously applied to a subtractor 2120 in the deconvolution module 2100 and to a further subtractor 2220 in the deconvolution module 2200 .

In the subtractor 2120 , if an a-priori folded in-phase ref is present, the a-priori absolute phase ref is subtracted from the folded in-phase ff with phases corresponding to shadow and overlapping areas. The sub traction result at the output of the subtractor 2120 is subjected to strong low-pass filtering by a low-pass filter 2130 and is then unfolded using a linear deconvolution method (block 2140 ). The phase developed by the linear unfolding method is added to the a-priori absolute phase ref in an adder 2160 . If there is no a priori absolute phase, ie if ref = 0, the subtraction ( 2120 ) and the addition ( 2160 ) are omitted.

This filters out all global errors that arise due to shadow and overlap areas. The low-pass filter 2130 also simultaneously filters out the high-frequency height information of the in-phase. The signal at the output of the deconvolution module 2100 is applied to an input PL of the Kalman filter 2030 and at the same time to another low-pass filter 2020 .

In Fig. 4d, the above-mentioned properties of the phase are presented. The phase noise is hardly present anymore. Due to the strong low-pass filtering (block 2130 ), the building height is heavily damped.

The absolute in-phase at the output of the deployment module 2100 is now the reference phase for the second deployment module 2200 . In the deconvolution module 2200 , a subtractor 2220 used as a residual error forming unit and a unit 2240 performing the linear deconvolution method are provided.

The absolute in-phase of the second deconvolution module 2200 is the phase at the output of a summing unit 2260 , which has no deterioration in the geometric resolution compared to the original folded in-phase, since it is in the chain formed by a subtractor 2220 and the linear deconvolution method 2240 second deconvolution module 2200 there is no low-pass filtering. Since no low-pass filter is provided in the second deconvolution module 2200 , the absolute phase in turn has a low-frequency error, which leads to an incorrect height calculation.

The absolute in-phase at the output of the summing element 2260 and thus of the deconvolution module 2200 is applied to an input P _{H of} the Kalman filter 2030 . This can also be seen in FIG. 4e. The absolute phase of the mountain has an inclination of about 20 rd, since the mountain starts at about 10 rd on the left and ends at about -10 rd on the right. In Fig. 4e, however, the building profile appears very clearly. The final, absolute unfolded in-phase is then generated in the Kalman filter 2030 , from which an exact terrain model can then be calculated taking into account the flight geometry.

In FIG. 3, an unfiltered and folded in-phase ff with phase errors due to a time decorrelation and due to shadow and overlapping areas is present at the input of block 1000 and at the input of block 2000 . As described in detail with reference to FIG. 1, the unfolded absolute in-phase uff _abs first form is at the output of block 1000 , which is freed from the phase errors due to the time decorrelation, but still contains phase errors caused by shadow and overlapping operations .

The absolute in-phase on _abs first form is low-pass filtered by means of a low-pass filter 3010 and used as a reference value in the deconvolution module 2100 of block 2000 ; a strong low-pass filtering is carried out by the low-pass filter 2130 , as already explained in connection with FIG. 2, before the actual linear deconvolution method (block 4120 ). This filters out all global errors that are due to shadow and overlap areas. However, as already explained in connection with the description of FIG. 2, the low-pass filter 2130 also simultaneously filters out the high-frequency height information of the in-phase.

Thus, the absolute phase at the output of the first deployment module, which has the phase sequence shown in FIG. 4d, has the advantage that the local errors due to the shadow and overlapping areas are no longer present, ie the low-frequency portion of the terrain is exactly in the absolute phase; however, the absolute phase at the output of the first deployment module 2100 has the disadvantage that the high-frequency portion of the terrain is filtered out.

The absolute phase at the output of the second deployment module 2200 , which has the phase profile shown in FIG. 4e, has the advantage that this phase profile accurately reproduces the high-frequency portion of the terrain; however, this phase profile in turn has the disadvantage that it has a low-frequency phase error. (See the slope shown in Fig. 4e in the phase curve).

By using the Kalman filter 2030 , the low-frequency component of the absolute phase at the output of the first deconvolution module 2100 (see phase profile in FIG. 4d) is thus combined with the high-frequency component of the absolute phase at the output of the second deconvolution module 2200 (see phase profile in FIG. 4e) merged. A final absolute in-phase is then obtained at the output of the Kalman filter 2030 , which has the following properties:

There is no influence by a time decorrelation up to a coherence of 0.2. (Effect of the first procedural section; block 1000 ).

There is no influence of the shadow and overlap areas (effect of the unfolding module 2100 ).

The highest possible geometric resolution is achieved (effect of the deployment module 2200 ).

In the case of an unfiltered, folded in-phase, which only has errors based on time decorrelation and no errors due to shadow or overlapping areas, a correct absolute in-phase can only be obtained with those summarized as a block diagram in FIG. 1 in dashed block 1000 and reproduced unfolding procedures.

In the case of an unfiltered and folded in-phase with only phase errors caused by shadow and overlap areas, which thus has no errors due to a time decorrelation, the correct absolute in-phase can only be achieved with the one in FIG. 2 in the broken block Determine 2000 summarized deconvolution processes.

Only in the case of an unfiltered and folded in-phase, which is subject to phase errors which are due to both a time decorrelation as well as to shadow and overlapping surfaces, must the correct absolute in-phase with the help of the two by blocks 1000 and 2000 reproduced process sections are calculated, as shown in Fig. 3.

Further possible uses of the method according to the invention ren are their use in interferometric LIDAR systems as well as holographic and interferometric Forward view radar systems (FLAR).

Claims (31)

1. Procedure for determining the absolute phase between two interferometric, using radar with synthetic aperture (SAR) received recordings, following the steps below be performed: a₁) After initialization of an iteration ( 1100 ), a subtraction ( 1220 ) between an unfiltered, folded in-phase ff with time decorrelation and an a-priori absolute phase ref is carried out in a first step sequence ( 1200 ); b₁) the subtraction result (ff-ref) is unfolded after low-pass filtering ( 1210 ) by means of a linear unfolding method ( 1240 ) and then the unfolded phase, the a-priori absolute phase ref is added again ( 1260 ); c₁) with the help of the determined absolute in-phase uff, a standard deviation Sn with respect to the difference between the absolute in-phase uff and the a-priori absolute phase ref is determined ( 1300 ); d₁) depending on a comparison ( 1400 ) of the standard deviation Sn with a previously calculated standard deviation Sa, the iteration is continued by d₁₁) the a-priori absolute phase ref with the last determined absolute in-phase and at the same time the old standard deviation Sa with the new standard deviation Sn are loaded and then returned to the first sequence of steps ( 1200 ), or d₁₂) the interruption is terminated because an absolute in-phase uff _abs first form is reached, which is equivalent to the last calculated, unfolded in-phase uff, and from which an exact terrain model can then be calculated taking into account the flight geometry. 2. Procedure for determining the absolute phase between two interferometric, using radar with synthetic aperture  (SAR) received recordings, following the steps below be performed: e₂) In a second sequence of steps (in an unfolding module 2100 ), if an a-priori absolute phase ref is present, a subtraction between an unfiltered and folded in-phase ff with shadow and overlap areas and the a-priori absolute phase ref performed ( 2120 );
f₂) the subtraction result (ff-ref) is developed after low-pass filtering ( 2130 ) by means of a linear deconvolution process ( 2140 ); g₂) then the a-priori absolute phase ref is added to the unfolded phase ( 2160 ) and the addition result is applied to a first input (PL) of a Kalman filter ( 2030 ); h₂) at the same time the addition result is subtracted in a third sequence of steps (in a second discharge module 2200 ) after egg low pass filtering ( 2020 ) in a subtractor ( 2220 ) from the unfiltered and folded in-phase ff; i₂) the subtracting result is unfolded again by means of a linear unfolding method ( 2240 ); j₂) the low-pass filtered addition result is then added to the output of the first deconvolution module ( 2100 ) and applied to a second input (P _H ) of the Kalman filter ( 2030 ) in which the final, fully developed Phase is generated, from which an exact terrain model can then be calculated taking into account the flight geometry. 3. The method of claim 2, wherein instead of the step te e₂ to h₂ the following steps are carried out: f₂₁) If there is no a-priori absolute phase ref, the unfiltered and folded in-phase ff with shadow and overlap areas in the low-pass filter ( 2130 ) is strongly low-pass filtered and then unfolded using a linear unfolding method ( 2140 ); g₂₁) the low-pass filtered and unfolded phase is applied to the egg nen input (P _L ) of the Kalman filter ( 2030 ), and h₂₁) is simultaneously subtracted from the unfiltered and folded in-phase ff after a further low-pass filtering ( 2020 ) in the subtractor ( 2220 ). 4. Procedure for determining the absolute phase between two interferometric, using radar with synthetic aperture (SAR) received recordings, following the steps below be performed: a'₁) after initialization of an iteration ( 1100 ) in a first step sequence ( 1200 ) a subtraction ( 1220 ) between an unfiltered, folded in-phase ff with time decorrelation and with shadow and overlap areas and an a-priori absolute phase ref carried out; b₁) the subtraction result (ff-ref) is unfolded after low-pass filtering ( 1210 ) by means of a linear unfolding method ( 1240 ) and then the unfolded phase, the a-priori absolute phase ref is added again ( 1260 ); c₁) with the help of the determined absolute in-phase uff, a standard deviation Sn with respect to the difference between the absolute in-phase uff and the a-priori absolute phase ref is determined ( 1300 ); d₁) depending on a comparison ( 1400 ) of the standard deviation Sn with a previously calculated standard deviation Sa, the iteration is continued by d₁₁) the a-priori absolute phase ref with the last determined absolute in-phase and at the same time the old standard deviation Sa with the new standard deviation Sn are loaded and then returned to the first sequence of steps ( 1200 ), or d₁₂) the iteration is terminated because an absolute in-phase on _abs first form is reached; k) the absolute in-phase on _abs first form is subjected to a further low-pass filtering ( 3010 ); e'₂) in a second sequence of steps (in a first unfolding module 2100 ) a subtraction between an unfiltered, folded in-phase ff with time decorrelation and with shadow and overlap areas and the low-pass filtered absolute in-phase uff _abs ' is carried out; f'₂) the subtraction result (ff-uff _abs ') is unfolded after low-pass filtering ( 2130 ) by means of a linear unfolding process ( 2140 ); g₂) then the low pass filtered absolute in-phase uff _abs ' is added to the unfolded phase ( 2160 ) and the addition result is applied to a first input (PL) of a Kalman filter ( 2030 ); h₂) at the same time, the addition result is subtracted in a third step sequence (in a second discharge module 2200) after egg low pass filtering ( 2020 ) in a subtractor ( 2220 ) from the unfiltered and folded in-phase ff with time dede and with shadow and overlapping areas ; i₂) the subtraction result is unfolded again using a linear unfolding method ( 2240 ); j₂) then the low pass filtered addition result is added to the developed phase at the output of the first unfolding module ( 2100 ) and applied to a second input (PH) of the Kalman filter ( 2030 ), in which the final, fully developed in-phase is generated, from which an exact terrain model can then be calculated taking into account the flight geometry.