Abstract:
A system and a method of generating a three-dimensional terrain model using one-dimensional interferometry of a rotating radar unit is provided herein. Height information is evaluated from phase differences between two echoes by applying a Kalman filter in relation to a phase confidence map that is generated from phase forward projections relating to formerly analyzed phase data. The radar system starts from a flat earth model and gathers height information of the actual terrain as the platform approaches it. Height ambiguities are corrected by removing redundant 2π multiples from the unwrapped phase difference between the echoes.

Description:
BACKGROUND 
       [0001]    1. Technical Field 
         [0002]    The present invention relates to the field of radar, and more particularly, to interferometric methods using same. 
         [0003]    2. Discussion of Related Art 
         [0004]    Using radar for three-dimensional (3D) mapping is advantageous in many applications in poor visibility conditions, such as harsh weather, limited light, underwater environments and the like. For example, there is a need for a Helicopter Flight and Landing Radar (Heli-FLR) to assist pilots in avoiding potential hazards for helicopter safety during flight phase (such as terrain, antennas, trees and power transmission wires), in various weather conditions during day and night, and, furthermore to provide near-real time information of the landing area (such as obstacles, inclined terrain, holes) during the landing phase. A similar need exists in neighboring applications such as mapping obstacles for submarines and remotely piloted aircrafts (RPA). 
       BRIEF SUMMARY 
       [0005]    Embodiments of the present invention provide a radar system comprising a radar unit arranged to rotate around a rotation axis in respect to a moving platform and a processor connected to the receiver antennas. The radar unit comprises a transmitter antenna arranged to transmit, cyclically around the rotation axis and sequentially such as to cover a 360° azimuth angle around the rotation axis, a plurality of radar signals, each having a spatial angle comprising a range of off-axis angles and a range of azimuth angles; and a first and a second receiver antennas separated along the rotation axis, and arranged to receive, for substantially each radar signal a first and a second echo, respectively. The processor is arranged to: co-register the second echo in relation to positional data of the platform; generate an interferogram of the first echo and the co-registered second echo; apply a Kalman filter to the interferogram in relation to a phase confidence map such as to calculate an unwrapped phase difference between the first and the second echo; calculate an off-axis angle from the unwrapped phase; derive, from the calculated off-axis angle, height information associated with the corresponding spatial angle of the radar signal; calculate, from the off-axis angle, a phase forward projection; and update the phase confidence map with the phase forward projection. The processor is arranged to initially generate the phase confidence map for each spatial angle from a specified surface model, and sequentially update the phase confidence map every cycle in relation to the current cycle phase forward projection and to phase forward projections of former cycles, relating to the radar signals of each spatial angle, and considering the platform movement from cycle to cycle. 
         [0006]    These, additional, and/or other aspects and/or advantages of the present invention are: set forth in the detailed description which follows; possibly inferable from the detailed description; and/or learnable by practice of the present invention. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0007]    The present invention will be more readily understood from the detailed description of embodiments thereof made in conjunction with the accompanying drawings of which: 
           [0008]      FIG. 1  is a high level schematic illustration of a radar sensor, according to some embodiments of the invention; 
           [0009]      FIG. 2  is a high level flowchart illustrating the logical flow of the interferometry algorithm, according to some embodiments of the invention; 
           [0010]      FIG. 3  is a high level schematic illustration of the maximum allowed phase differences from one range cell to the other due to changes in topography, according to some embodiments of the invention; 
           [0011]      FIG. 4  is a high level flowchart illustrating the logical flow of the Kalman filter, according to some embodiments of the invention; 
           [0012]      FIG. 5  is a high level flowchart illustrating the logical flow of the Kalman filtering step of the algorithm, according to some embodiments of the invention; 
           [0013]      FIG. 6  is a high level schematic illustration of the geometry for phase forward projection, according to some embodiments of the invention; and 
           [0014]      FIGS. 7A and 7B  are flowcharts illustrating the method, according to some embodiments of the invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0015]    Before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not limited in its application to the details of construction and the arrangement of the components set forth in the following description or illustrated in the drawings. The invention is applicable to other embodiments or of being practiced or carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein is for the purpose of description and should not be regarded as limiting. 
         [0016]    For a better understanding of the invention, the usages of the following terms in the present disclosure are defined in a non-limiting manner: 
         [0017]    The term “nadir” as used herein in this application, is defined as the direction pointing directly below a particular location; that is, the direction opposite to the zenith. 
         [0018]    The term “off-nadir” as used herein in this application, is defined as the angle a line to a certain point forms to the nadir. 
         [0019]      FIG. 1  is a high level schematic illustration of a radar sensor  100 , according to some embodiments of the invention. Radar sensor  100  may comprise a radar electronics unit  110  mounted below a flying platform (not shown, e.g., a helicopter) rotating around the Z axis. Three antennas are attached to electronics unit  110 . A transmitter  120  is arranged to transmit a signal  125  to ground and the other two—a first receiver sensor  130  and a second receiver sensor  140 , separated vertically in different height positions, are arranged to receive echoes  135 ,  145  (respectively) from the ground. These two receiving channels are processed interferometrically for evaluation of the elevation angle of the incoming echoes and hence determination of the position of the reflection point on ground. The rotation time may comprise about 2 seconds allowing a highly dynamic update of the three dimensional terrain model. 
         [0020]    In embodiments, a one dimensional (1D) interferometric Radar algorithm for generating a three dimensional (3D) model of the landscape beneath a flying platform (e.g., a Helicopter) is provided. Radar  100  comprises transmitter antenna  120  and two receiver antennas  130 ,  140  that are separated in height, along the rotation axis (e.g., vertically when the rotation axis is the z axis). All antennas  120 ,  130 ,  140  are looking down at an angle to the ground and are rotating 360° around the z axis, at a specified speed selected to cover the entire area beneath the platform within a specified short time. Antennas  120 ,  130 ,  140  may comprise fan beams with small beams, e.g. smaller than 5 degrees in azimuth and wide beams, e.g., larger than 50 degrees in elevation, for covering a large area during each rotational scan. Radar signals  125  are transmitted towards the ground, reflected from landscape and obstacles ( 135 ,  145 ) and are received in parallel by both receiver antennas  130 ,  140 . The phases of the two received signal chains  135 ,  145  are processed by interferometric methods in order to derive the vertical (off-nadir) angle to a reflector on ground allowing to estimate its height. The distance of the reflector to radar  100  is measured by the round trip delay time and the azimuth position according to the pointing direction of antennas  120 ,  130 ,  140 . 
         [0021]    Radar sensor  100  may be housed in a RADOM  150  (a radar-transparent covering dome), e.g., having a half spherical form. 
         [0022]    Radar sensor  100  may comprise a transmit-receive switch (e.g., a circulator) connecting one of receiving antennas  130 ,  140  with transmitter antenna  120  for routing transmitted pulse  125  to transmitter antenna  120  and the corresponding one of received echoes  135 ,  145  from the corresponding one of receiving antennas  130 ,  140 . 
         [0023]    Transmitter antenna  120  may be positioned between receiver antennas  130 ,  140  as illustrated in  FIG. 1 , or aside from receiver antennas  130 ,  140 , to minimize a separation distance between the first and the second receiver antennas. Transmitter antenna  120  may be a long transmitter antenna with a small azimuth beamwidth and may be located close to the upper end (mounting point of the flying platform). For example, transmitter antenna  120  may be 1.5 to 2 times longer and with a smaller azimuth beamwidth in respect to receiver antennas  130 ,  140 . Receiver antennas  130 ,  140  may be smaller with a larger azimuth beamwidth. One of receiver antennas  130 ,  140  may be located at the lower position of the rotating sensor  100  such as to minimize the volume of the required spherical RADOM  150 . The azimuth resolution may result from the two-way beamwidth of the combined transmitter  120  and receiver  130 ,  140  antennas. 
         [0024]      FIG. 2  is a high level flowchart illustrating the logical flow of the interferometry algorithm, according to some embodiments of the invention. 
         [0025]    In a first step, the radar data of both sensors are pulse compressed  203 ,  204 . Then, the pulse-compressed data of second sensor  140  is co-registrated  205  to the data of first sensor  130 . Because of the geometry, the resolution and the small baseline, difference between both data sets is very limited. Nevertheless, co-registration  205  is performed in order to reduce phase errors and is realized by multiplying second signal  145  with a phase shift: 
         [0000]      φ= e   −2πj·Δƒ·t     shift     Equation 1
   in frequency domain, where t shift  represents the time difference between both received data with respect to sensor positions and flat earth geometry.   
 
         [0027]    After co registration, multiplying first signal  135  with the complex conjugated of second signal  145  is used to generate the interferogram (stage  210 ). 
         [0028]    In a pre-processing step, phase gradients are estimated out of the interferogram and serve as driving model for the Kalman filter process (stage  230 ). For single pass interferometry the height error σ z  depends on the phase noise σ 100  , wavelength λ, distance R, look angle Θ and the perpendicular baseline length B perp  according to: 
         [0000]    
       
         
           
             
               
                 
                   
                     σ 
                     z 
                   
                   = 
                   
                     
                       
                         
                           λ 
                           · 
                           R 
                           · 
                           sin 
                         
                          
                         
                             
                         
                          
                         
                           ( 
                           Θ 
                           ) 
                         
                       
                       
                         2 
                         · 
                         π 
                         · 
                         
                           B 
                           perp 
                         
                       
                     
                     · 
                     
                       σ 
                       φ 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   2 
                 
               
             
           
         
       
     
         [0029]    The maximum detectable height difference (Height of Ambiguity) can be calculated from equation 2 by setting σ φ =2π. After sampling of the Radar signals, the maximum allowed phase differences from one range cell to the other due to changes in topography ( FIG. 3 ) can be expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       Δφ 
                       A 
                     
                     = 
                     
                       2 
                       · 
                       π 
                       · 
                       
                         
                           
                             R 
                             
                               A 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           - 
                           
                             R 
                             
                               A 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                         λ 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       Δφ 
                       B 
                     
                     = 
                     
                       2 
                       · 
                       π 
                       · 
                       
                         
                           
                             R 
                             
                               B 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           - 
                           
                             R 
                             
                               B 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                         λ 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                        
                       
                         
                           Δφ 
                           A 
                         
                         - 
                         
                           Δφ 
                           B 
                         
                       
                        
                     
                     &lt; 
                     π 
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   3 
                 
               
             
           
         
       
     
         [0030]    The Tx path is identical (one separate Tx antenna  120 ). R A1  and R A2  are the distances from a point A to the receiving antennas Rx 1   130  and Rx 2   140 . R B1  and R B2  are the distances from a point B that is located in an adjacent range cell. To be able to unwrap the phases unambiguous, the magnitude of the phase difference introduced by the topography has to be less than it. Due to the extreme near field geometry, high and steep objects lead to height-ambiguity problems (2π jumps). To overcome this problem a phase confidence map is generated (stage  225 ) by forward projection (stage  220 ) of old measured data and current platform-position, velocity and attitude data. This phase confidence map ( 225 ) is used as an input of the Kalman filtering ( 230 ). 
         [0031]    The result of the Kalman filtering  230  is the unwrapped phases  240 . Finally, off-nadir angles  250  can be calculated. On one hand, they are used to estimate the appropriate height information ( 255 ), and on the other hand, they serve as input to the phase forward projection ( 220 ) to compute the phase confidence map ( 225 ). 
         [0032]    The distance between the receiver antennas  130 ,  140  may be selected according to a relation between expected motion characteristics of the moving platform and an expected topographical variability of the height information. For example, the distance may be adapted to a scenario of an helicopter flying above an urban landscape, with the corresponding flight characteristics (e.g. flight height) and topographical characteristics of the landscape (e.g. height and spacing between the buildings). 
         [0033]      FIG. 4  is a high level flowchart illustrating the logical flow of the Kalman filter, according to some embodiments of the invention. The interferometry processing algorithm is based on the Unscented Kalman filter to unwrap the interferometric phases. The Kalman filter and all its derivates employ a prediction/correction structure based on a state-space model  310  and an observation model  320  to estimate the true state ( 340 ) of the measured variable (the interferometric phase in this case). It also incorporates noise into the state-space model as well as the observation model. By this, the data are treated as measurements of a hidden random process of a state variable. 
         [0034]    The function ƒ describes state-space model  310  in terms of:
   t i : i th  time step, i=0, . . . ,n-1.   x i =x(t i ): State of the i th  time step to be estimated.   u i =u(t i ): known input of the i th  time step.   ω i =ω(t i ): driving error covariance of the i th  time step.   
 
         [0000]      x i =ƒ(x i-1 ,u i-1 , ω i-1 )  Equation 4
 
         [0039]    The function h describes observation model  320  in terms of:
   z i =z(t i ): given measurements of the i th  time step   v i =v(t i ): driving error covariance of the i th  time step   
 
         [0000]      z i =h(z i ,v i )  Equation 5
 
         [0042]    The original Kalman filter assumes that the state-space model and the observation model are linear and the noise is Gaussian with zero mean. 
         [0043]    In the Unscented Kalman filter, these assumptions are relaxed and it allows nonlinear functions f and h. The predicted error covariance is approximated as a Gaussian density by a set of deterministically chosen sample points. These are projected forward ( 330 ) by state-space model  310  and describe the estimated mean and covariance. 
         [0044]    For our case, the state to be estimated is the unwrapped interferometric phase. The observations of this state are the two parts of the complex interferogram, the real and the imaginary part. Observation model  320 : 
         [0000]      z i =cos(x i ),sin(x i ))  Equation 6
 
         [0045]    The state-space model  310  is the linearization of the phase, so the “known” inputs are the phase gradients. State-space model  310 : 
         [0000]        x   i   =x   i-1   +u   i-1   u   i-1   ={dot over (x)}   i-1   Equation 7
 
         [0046]    The gradients of the true phase are not known exactly. They are estimated out of the noisy measured data. 
         [0047]    Mode extraction ( 350 ,  FIG. 5 ). The phase gradients can be observed as frequency shift of the autocorrelation function of the interferogram ( 370 ,  FIG. 5 ). For a time interval of length T=t i -t i-1  the interferogram s is: s(t)=α(t)·exp(− 2 iπ·φ(t)), with a phase function φ and an amplitude function α. 
         [0048]    This can be rewritten as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           s 
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
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                             · 
                             exp 
                           
                            
                           
                             { 
                             
                               
                                 - 
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                                   ( 
                                   
                                     
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                                         ( 
                                         
                                           t 
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                                     + 
                                     
                                       
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                                        
                                       
                                         
                                           
                                             ϕ 
                                             . 
                                           
                                            
                                           
                                             ( 
                                             τ 
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                                   ) 
                                 
                               
                             
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                         = 
                           
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                         = 
                         
                           : 
                           
                             
                                 
                             
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                                 y 
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                   Equation 
                    
                   
                       
                   
                    
                   8 
                 
               
             
           
         
       
     
         [0049]    The integral part is a dynamic frequency variation. The linear part describes the mean phase slope with a constant frequency ƒ 0 . 
         [0050]    Autocorrelating the signal gives: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             corr 
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                                 yy 
                               
                               · 
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                   Equation 
                    
                   
                       
                   
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                   9 
                 
               
             
           
         
       
     
         [0051]    The power spectral density of the signal therefore can be seen as a time shifted version of the power spectral density of the function γ. If the power spectral density is unimodal and approximately symmetric, the frequency ƒ 0  can be extracted as the mode of the power spectral density. 
         [0052]    With the normalized power spectral density, we can also extract the spectral bandwidth σ ƒ of the signal as the second central moment, which relates to the driving error covariance via ω=( 2 π·T) 2 ·σ ƒ   2 . 
         [0053]      FIG. 5  is a high level flowchart illustrating the logical flow of the Kalman filtering step of the algorithm, according to some embodiments of the invention. 
         [0054]    The extracted modes  350  are bound by the bandwidth of the system. If the spectral bandwidth, and thus the driving error covariance are too high, extracted modes  350  are not reliable, due to wrap around effects of the Fast Fourier Transform (FFT). 
         [0055]    In this case, the phase gradients would be replaced by the local slope  355  of the true interferometric phases corresponding to the flat earth signal. These can be pre-generated out of the current position and antenna pointing information of the flying platform (e.g., a helicopter). 
         [0056]    As modes  350  are extracted from the noisy data, the real phase gradients are only estimated by modes  350 . Wrong modes can lead the filter to insert wrong 2π-phase jumps into the estimated phase, which must be corrected. 
         [0057]    Out of the previously computed flat earth true interferometric phases and the forward projected known phases, a map of offsets is generated which give the integer multiple of π of the phase corresponding to every time step. This is called the phase confidence map  360 . If the integer multiple of it of the estimated interferometric phase deviates more than 2π off offset map  260  corresponding to the flat earth signal and the projected phases, the difference between the two will be added (correction  375 ). By this, we can bind the estimated interferometric phase to a realistic height profile. 
         [0058]      FIG. 6  is a high level schematic illustration of the geometry for phase forward projection, according to some embodiments of the invention. In the near field geometry, high and steep objects lead to height-ambiguity problems (2π jumps) whereas the phase of the same object in far range can be unwrapped without problems. To make use of this behavior the phase forward projection was introduced. 
         [0059]    As an initializing step the flat earth phase is used. 
         [0060]    Descending angle β and distance R Platform  are known from platform movement. Off-nadir angles Θ meas  are calculated from unwrapped phases, using the following formula: 
         [0000]    
       
         
           
             
               
                 
                   
                     Θ 
                     meas 
                   
                   = 
                   
                     
                       a 
                        
                       
                           
                       
                        
                       
                         sin 
                          
                         
                           [ 
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       R 
                                       i 
                                     
                                     - 
                                     
                                       
                                         
                                           ϕ 
                                           unwrapped 
                                         
                                         · 
                                         λ 
                                       
                                       
                                         2 
                                         · 
                                         π 
                                       
                                     
                                   
                                   ) 
                                 
                                 2 
                               
                               - 
                               
                                 R 
                                 i 
                                 2 
                               
                               - 
                               
                                 B 
                                 2 
                               
                             
                             
                               
                                 - 
                                 2 
                               
                               · 
                               
                                 R 
                                 i 
                               
                               · 
                               B 
                             
                           
                           ] 
                         
                       
                     
                     + 
                     ζ 
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   10 
                 
               
             
           
         
       
       
         where: 
         Θ meas  is the measured off-nadir angles; φ unwrapped  is the unwrapped phase; λ is the wavelength; ξ is the angle of baseline from horizon; R i  is the slant range sampling; and B is the baseline length. 
       
     
         [0063]    The forward projected range can be calculated by: 
         [0000]    
       
         
           
             
               
                 
                   
                     R 
                     proj 
                   
                   = 
                   
                     
                       
                         R 
                         Platform 
                         2 
                       
                       + 
                       
                         R 
                         i 
                         2 
                       
                       - 
                       
                         
                           2 
                           · 
                           
                             R 
                             Platform 
                           
                           · 
                           
                             R 
                             i 
                           
                           · 
                           cos 
                         
                          
                         
                             
                         
                          
                         
                           ( 
                           
                             
                               90 
                                
                               ° 
                             
                             - 
                             β 
                             - 
                             
                               Θ 
                               meas 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   11 
                 
               
             
           
         
       
       
         and then the forward projected off-nadir angles by: 
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     Θ 
                     proj 
                   
                   = 
                   
                     
                       a 
                        
                       
                           
                       
                        
                       
                         cos 
                          
                         
                           [ 
                           
                             
                               
                                 R 
                                 i 
                                 2 
                               
                               - 
                               
                                 R 
                                 Platform 
                                 2 
                               
                               - 
                               
                                 R 
                                 proj 
                                 2 
                               
                             
                             
                               
                                 - 
                                 2 
                               
                               · 
                               
                                 R 
                                 Platform 
                               
                               · 
                               
                                 R 
                                 proj 
                               
                             
                           
                           ] 
                         
                       
                     
                     - 
                     β 
                     - 
                     
                       90 
                       ∘ 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   12 
                 
               
             
           
         
       
     
         [0065]    By solving Equation 10 for the unwrapped phases φ and replacing Θ mea s and Ri with Θ proj  and R proj  we get the forward projected phases that have to be resampled and interpolated to the current slant range sampling. 
         [0066]    Using the forward projected phases, phase confidence map  360  can be calculated by: 
         [0000]    
       
         
           
             
               
                 
                   
                     Phase 
                      
                     
                         
                     
                      
                     Confidence 
                      
                     
                         
                     
                      
                     Map 
                   
                   = 
                   
                     
                       
                         
                           ϕ 
                           proj 
                         
                         
                           abs 
                            
                           
                             ( 
                             
                               ϕ 
                               proj 
                             
                             ) 
                           
                         
                       
                       · 
                       round 
                     
                      
                     
                         
                     
                      
                     
                       ( 
                       
                         
                           abs 
                            
                           
                             ( 
                             
                               ϕ 
                               proj 
                             
                             ) 
                           
                         
                         π 
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   13 
                 
               
             
           
         
       
     
         [0067]    This phase confidence map  360  then is used during Kalman filtering to track phase jumps introduced by the topography or objects. 
         [0068]    To summarize, the objective of the algorithm is to derive a 3D model of a scene under a Radar  100  rotating around a vertical axis transmitting with one antenna  120  and receiving the echoes with two antennas  130 ,  140  located at different height positions. The two antennas  130 ,  140  receive the echoes of the terrain and process a 3D model out of them based on a one dimensional interferometric principle. 
         [0069]    The new algorithm for this processing makes use of known procedures from two dimensional interferometric processing and applies it to the one dimensional case that is often mentioned in the literature as reference for the two dimensional case, but was never realized in its original form. The one dimensional interferometric processing suffers from effects (ambiguities, phase unwrapping uncertainties, etc.) which can easily be solved in the two dimensional case, but need new procedures to be solved in the one dimensional one. 
         [0070]    The method takes the complex echoes  135 ,  145  in digital form. After preprocessing of the single echoes for reduction of noise and statistical fluctuations (speckle), an appropriate filtering allows the evaluation of the height of each reflection point on ground from the phase difference in the echo data. The problem of phase confidence is solved by Kalman filtering and applying a feedback loop for phase forward projection and generation of a phase confidence map for further use in the Kalman filtering process. 
         [0071]    The algorithm uses a Kalman filter for phase unwrapping. The platform&#39;s position, velocity and attitude are used for estimating phase signals of the illuminated scene after each radar cycle. A phase forward projection  330  for each new (t k ) phase signal is estimated in respect to the position, velocity and attitude of the platform at the current (t k ) and at the former (t k-1 ) radar cycle. Phase confidence map  360  is generated using the phase forward projection  330 . Phase confidence map  360  is further used to solve ambiguity effects and uncertainties created by noise in the signals. The estimated phases from previous scans are used to update and correct the results of phase unwrapping during the Kalman filter process. The corrected phases are used together to generate a three dimensional position determination of radar reflections from the surface leading to the three dimensional terrain model. 
         [0072]      FIGS. 7A and 7B  are flowcharts illustrating the method, according to some embodiments of the invention. The method comprises the following stages: defining a rotation axis in respect to a moving platform, a range of off-axis angles in respect to the rotation axis, and a range of azimuth angles, in respect to the rotation axis (stage  400 ); transmitting, cyclically around the rotation axis and sequentially such as to cover a 360° azimuth angle around the rotation axis, a plurality of radar signals, each having a spatial angle comprising the range of off-axis angles and the range of azimuth angles (stage  405 ). For substantially each radar signal: receiving a first and a second echo (stage  410 ); co-registering the second echo in relation to positional data of the platform (stage  415 ); generating an interferogram of the first echo and the co-registered second echo (stage  420 ); applying a Kalman filter to the interferogram in relation to a phase confidence map such as to calculate an unwrapped phase difference between the first and the second echo (stage  425 ); calculating an off-axis angle from the unwrapped phase difference (stage  430 ); deriving, from the calculated off-axis angle, height information associated with the corresponding spatial angle of the radar signal (stage  435 ) (e.g., derivation may be completed during a single cycle of the transmitter antenna); calculating, from the off-axis angle, a phase forward projection (stage  440 ); and updating the phase confidence map with the phase forward projection (stage  445 ). 
         [0073]    The phase confidence map is initially generated for each spatial angle from a specified surface model, and sequentially updated every cycle in relation to the current cycle phase forward projection and to phase forward projections of former cycles, relating to the radar signals of each spatial angle, and considering the platform movement from cycle to cycle. In embodiments, the method may further comprise, for substantially each radar signal, the following stages: estimating a distance to a source of the echoes by measuring a round trip delay time of the radar signal (stage  450 ); estimating an azimuth of the source from the spatial angle of the radar signal (stage  455 ); and deriving a three dimensional (3D) model from the height information, the distances and the azimuths (stage  460 ). 
         [0074]    The transmitter antenna and the first and second receiver antennas may be aligned such that the interferogram is one dimensional (1D). 
         [0075]    The moving platform may be a flying platform, the rotation axis is a nadir axis, and the derived 3D model is of a landscape below the flying platform. 
         [0076]    In embodiments, the method may further comprise positioning the transmitter antenna between the receiver antennas such as to maximize a separation distance between the first and the second receiver antennas (stage  465 ) and/or positioning the transmitter antenna and the receiver antennas such as to maximize a separation distance between the receiver antennas and to maximize a length of the transmitter antenna under specified RADOM size and form limitations (stage  470 ). 
         [0077]    In embodiments, the method may further comprise selecting a distance between the first and the second receiver (receiving the first and the second echo  410  being carried out by a first and a second receiver antenna respectively) according to a relation between expected motion characteristics of the moving platform and an expected topographical variability of the height information stage  407 , see  FIG. 3 ). 
         [0078]    In embodiments, the method may further comprise generating alerts relating to the height information (stage  475 ), e.g., alerts from nearing objects. The method may further comprise visualizing the 3D model (stage  480 ). 
         [0079]    In embodiments, the method may further comprise preprocessing the first and the second echoes after receiving them to reduce noise and statistical fluctuations (stage  490 ), and co-registering the first echo as well as the second echo and wherein the interferogram is generated from the co-registered first and second echo (stage  485 ). 
         [0080]    The procedure compensates for movements of the flying platform by using information from a navigation unit measuring the speed vector and the attitude of the platform. This new method allows generating a terrain model within one cycle of the antenna assembly azimuth rotation and improves the accuracy of this model with every new rotation cycle lasting in the order of a few seconds, for example. 
         [0081]    Advantageously, in some embodiments, the invention satisfies the need for a Helicopter Flight and Landing Radar (Heli-FLR) to assist pilots in avoiding potential hazards for helicopter safety during flight phase (such as terrain, antennas, trees and even wires), in various weather conditions during day and night, and furthermore, to provide near-real time information of the landing area (such as obstacles, inclined terrain, holes) during the landing phase. The invention uses an advanced one dimensional innovative interferometric method and intuitive visualization. Landing and flight modes may be combined into a light weight and low cost radar-based system. This new system may prevent accidents and casualties and improve the service of helicopter operation companies by increasing the flight capabilities in difficult conditions and the availability of the helicopters. 
         [0082]    In embodiments, the system is able to detect obstacles such as terrain, trees, antennas, wires, etc., in flight mode up to 2000 m thus providing the pilot 30 seconds alert prior to the collision (even in degraded weather conditions, the system may still provide and alert at least 10 seconds ahead). In landing mode, the system may be effective from 500 feet (150 meters), detect obstacles and holes with a resolution of 30 cm during the approach as well as measuring the slope angle in the landing area. The angular coverage of detecting obstacles in the landing area may be 360 degrees with a refresh rate lower than 2 seconds. The information may be presented to the pilot on a multi-function display in an intuitive human factors concept to allow a reduction of pilot workload and enhancing situational awareness. Vocal alerts may inform the pilot in case of danger. 
         [0083]    During landing mode, the radar system may realize a 360° mapping of the terrain below the helicopter. High elevation beamwidth of the antennas may guarantee coverage of large areas. The inventors have discovered that the 3D-mapping is exceptionally well realized by transmitting a 36 GHz signal through one antenna  120  and receiving the return from two different other antennas  130 ,  140 . This frequency allows using the interferometric methods with minimal hardware component size. A one dimensional interferometric data-processing may then permit to retrieve the information from the signals  135 ,  145 . 
         [0084]    The 3D-mapping may be realized in quasi real-time, during the rotation of the system. A full rotation and therefore the complete landing zone may be covered in less than 2 seconds. 
         [0085]    Data-base modeling integrating real-time and pre-loaded information: In traditional data-base systems, the algorithms and the display are based on pre-loaded information which does not allow pilots to view real-time information (such as a new obstacle) on the same system. Innovative algorithms that are implemented in the system allow integration of pre-loaded data (such as Digital Terrain Elevation Data and obstacles) and real-time data. The design concept is based on comparison of each new detected obstacle with the data base and updating it if needed. The integration of the real-time and pre-loaded data shall increase the level of confidence in the real-time data and enhance the situational awareness of the pilots, allowing them to view all the relevant information on the same display. 
         [0086]    In recent years, systems became more sophisticated and the amount of information needed to be displayed has become enormous. In order to reduce the pilot workload, to enhance situational awareness and to shorten training time, a display combining intuitive symbology, terrain and relevant obstacles information may be implemented based on techniques such as color coding, display complexity reduction and data fusion. 
         [0087]    In the above description, an embodiment is an example or implementation of the inventions. The various appearances of “one embodiment”, “an embodiment” or “some embodiments” do not necessarily all refer to the same embodiments. 
         [0088]    Although various features of the invention may be described in the context of a single embodiment, the features may also be provided separately or in any suitable combination. Conversely, although the invention may be described herein in the context of separate embodiments for clarity, the invention may also be implemented in a single embodiment. Reference in the specification to “some embodiments”, “an embodiment”, “one embodiment” or “other embodiments” means that a particular feature, structure, or characteristic described in connection with the embodiments is included in at least some embodiments, but not necessarily all embodiments, of the inventions. 
         [0089]    It is to be understood that the phraseology and terminology employed herein is not to be construed as limiting and are for descriptive purpose only. 
         [0090]    The principles and uses of the teachings of the present invention may be better understood with reference to the accompanying description, figures and examples. 
         [0091]    It is to be understood that the details set forth herein do not construe a limitation to an application of the invention. 
         [0092]    Furthermore, it is to be understood that the invention can be carried out or practiced in various ways and that the invention can be implemented in embodiments other than the ones outlined in the description above. 
         [0093]    It is to be understood that the terms “including”, “comprising”, “consisting” and grammatical variants thereof do not preclude the addition of one or more components, features, steps, or integers or groups thereof and that the terms are to be construed as specifying components, features, steps or integers. 
         [0094]    If the specification or claims refer to “an additional” element, that does not preclude there being more than one of the additional element. 
         [0095]    It is to be understood that where the claims or specification refer to “a” or “an” element, such reference is not to be construed that there is only one of that element. 
         [0096]    It is to be understood that where the specification states that a component, feature, structure, or characteristic “may”, “might”, “can” or “could” be included, that particular component, feature, structure, or characteristic is not required to be included. 
         [0097]    Where applicable, although state diagrams, flow diagrams or both may be used to describe embodiments, the invention is not limited to those diagrams or to the corresponding descriptions. For example, flow need not move through each illustrated box or state, or in exactly the same order as illustrated and described. 
         [0098]    Methods of the present invention may be implemented by performing or completing manually, automatically, or a combination thereof, selected steps or tasks. 
         [0099]    The term “method” may refer to manners, means, techniques and procedures for accomplishing a given task including, but not limited to, those manners, means, techniques and procedures either known to, or readily developed from known manners, means, techniques and procedures by practitioners of the art to which the invention belongs. 
         [0100]    The descriptions, examples, methods and materials presented in the claims and the specification are not to be construed as limiting but rather as illustrative only. 
         [0101]    Meanings of technical and scientific terms used herein are to be commonly understood as by one of ordinary skill in the art to which the invention belongs, unless otherwise defined. 
         [0102]    The present invention may be implemented in the testing or practice with methods and materials equivalent or similar to those described herein. 
         [0103]    Any publications, including patents, patent applications and articles, referenced or mentioned in this specification are herein incorporated in their entirety into the specification, to the same extent as if each individual publication was specifically and individually indicated to be incorporated herein. In addition, citation or identification of any reference in the description of some embodiments of the invention shall not be construed as an admission that such reference is available as prior art to the present invention.