Abstract:
A monopulse radar operating at low angles of elevation (LOE) receives returns from a target by a direct path and by a path including a reflection from that portion of the Earth&#39;s surface lying between the radar and the target. The surface-reflected signal tends to cause errors in the estimate of the elevation of the target. A radar system directs at least upper and lower overlapping beams at LOE toward the target for receiving returns. The upper and lower beams may be sequential or simultaneous. Real and imaginary portions of the sum (Σ) and difference (Δ) signals are generated for each beam. The monopulse estimates of elevation ê derived from the real portion of the Σ and Δ signals are processed to produce correction signals for upper and lower beams. Each correction signal is weighted and summed to correct the estimate of elevation.

Description:
This invention relates to method and apparatus for improved estimates of the altitude of a target using conventional or phase monopulse radars when the target is at a low angle of elevation or near the horizon. 
   Monopulse radar systems achieve relatively high accuracy in determining the position of a target, even though the antenna pattern may be relatively broad, by processing sum (Σ) and difference (Δ) signals. For example, the 3 dB beamwidth of a radar antenna main lobe may be on the order of 2°. A conventional radar system which depends exclusively upon a narrow beam to determine direction might, with such a beamwidth, be able to estimate the direction of the target within ±1°. By the use of monopulse signal processing techniques, accuracy improvements are possible. 
     FIG. 1  illustrates in simplified form a prior art conventional monopulse radar system in which an antenna illustrated as  10  directs a beam, illustrated by a contour  12 , which is centered along an axis  14  inclined at an exemplary elevation angle of 0.9° relative to the horizontal. As illustrated, contour  12  defines an antenna beam having a 3 dB beamwidth of about 2° in elevation.  FIG. 1  is described further below. 
   Those skilled in the art know that antennas are reciprocal or passive devices, in which the beamwidth and gain are identical in both the transmitting and receiving modes of operation. Either transmission or reception terms are commonly used, with the reciprocal function being understood. 
     FIG. 2  represents geometric considerations having importance in the estimation of elevation angle by monopulse methods. In  FIG. 2 , the earth&#39;s surface is represented by circle  210  and the Earth&#39;s radius by a. In  FIG. 1  the Earth is assumed flat but in  FIG. 2  the curvature is illustrated. A monopulse radar antenna is located at a point  212  located at a distance H above the Earth&#39;s surface, as by mounting on a mast. A target illustrated as a point  214  is located at an altitude Z above the Earth&#39;s surface. Once the target  214  has been illuminated by a pulse transmitted from antenna  212 , the return signal can travel back to the radar antenna along a direct path  216  and by a further path represented by dotted lines  218   a  and  218   b  which reflects from the Earth&#39;s surface at a specular point  220 . The magnitude of the reflected signal which arrives at radar antenna  212  depends in part upon the reflectivity of the Earth&#39;s surface at point  220 . At low elevation angles, the length of path  216  and the total length of paths  218   a  and  218   b  will be nearly the same. Small differences in path length will result in relative phase shifts between the two paths which may result in constructive or destructive interference of the received signal. For low angles of elevation, both direct return path  216  and two-part return path  218   b  will lie somewhere near the peak of the beam of the main lobe of the antenna (see  FIG. 1 ). Consequently, the antenna beamwidth cannot be relied upon to separate the direct and reflected signals. As a result, both the direct and reflected signals contribute to the generation of the Σ and Δ signals and to the remainder of the signal processing. 
     FIGS. 3 and 4  represent the estimated elevation angle versus the true elevation angle for targets at 2- and 30-mile ranges, respectively, using conventional monopulse estimation procedures. These plots are computer-generated, and are based upon the assumption of a perfectly reflecting flat surface at specular point  220  of  FIG. 2 . As illustrated, plot  312  of  FIG. 3  appears to be a roughly periodic function of the true elevation angle. Ideally, the estimated elevation along the ordinate in  FIG. 3  would correspond to the true elevation angle of the target along the abscissa, and so plot  312  should ideally lie along a straight line  314 , which represents zero error. Lines  316  and  318  above and below line  314 , respectively, represent a range of errors of ±¼° relative to the ideal represented by line  314 . Plot  312  of  FIG. 3  makes excursions substantially above line  316 , especially at lower elevation angles. The greatest excursions occur at about ±0.1° true elevation, with errors on the order of 1°. Such large errors at short range might be very important to a vehicle attempting to direct countermeasures toward an approaching threat. Such a threat might be, for example, a cruise missile approaching a ship. Such a cruise missile might be at a small but positive elevation angle when at a distance and might be at a negative elevation angle (a depression angle) when near the ship. Also in  FIG. 3 , it can be seen that the deviation of the estimated elevation angle away from the true elevation angle becomes less than ±¼° at true elevation angles greater than about 1°, as indicated by the fact that plot  312  lies between lines  316  and  318 . 
     FIG. 4  illustrates generally similar deviations of the estimated elevation angle versus true elevation angle when the target is at a range of 30 miles. In  FIG. 4 , plot  412  representing the estimate lies between the lines  416  and  418  representing ±¼° error for most true elevation angles greater than about 1.3°, and the errors appear to be decreasing asymptotically with increasing actual elevation angle. At a 30 mile range, errors of ¼° correspond to about 800 feet in altitude. Errors of magnitude greater than ¼° at 30 mile range may be of significance for air traffic control purposes, and such errors occur for true elevation angles of less than about 1.3°. 
   It is desirable to minimize errors in estimating elevation angles at low angles of elevation. 
   SUMMARY OF THE INVENTION 
   A method for determining the elevation of a target includes the steps of transmitting electromagnetic energy towards the target. First and second antenna beams are directed towards the target for reception of reflections of the transmitted electromagnetic energy. The first and second beams are angularly spaced in the vertical plane to produce an upper beam and a lower beam. The angular spacing of the upper and lower beams in the vertical plane is about one third of the 3 dB beamwidth of one of the upper and lower antenna beams. The method combines the sum and difference signals from the upper beam with the sum and difference signals from the lower beam to form an estimate of the true elevation of the target. In one embodiment of the invention, the first and second antenna beams are directed toward the target concurrently, and the steps of forming the upper and lower monopulse estimates are performed concurrently. In another embodiment of the invention, the first (upper or lower) beam is directed toward the target for receiving returns therefrom before the second (lower or upper) beam is formed. The upper monopulse estimate is then generated from the upper return signal and the lower monopulse estimate is formed from the lower return signal. 

   
     DESCRIPTION OF THE DRAWING 
       FIG. 1  is a simplified block diagram of a prior art conventional monopulse radar system directing a beam at a low elevation angle for forming an estimate of the elevation of a target; 
       FIG. 2  is a diagram illustrating geometrical considerations relating to the generation of specular reflections from a target; 
       FIGS. 3 and 4  are computer-generated plots of estimated elevation angle in degrees versus true elevation angle in degrees, where the estimated angle is produced by the conventional monopulse radar system of  FIG. 1  with 3 dB beamwidth of 2°, directed at an elevation angle of +0.9° for targets at 2 and 30-mile ranges, respectively, assuming a flat, perfectly reflective specular reflection point; 
       FIGS. 5 ,  6  and  7  are computer-generated plots of estimated elevation angle in degrees versus true elevation angle in degrees, where the estimated angle is produced by the conventional monopulse radar system of  FIG. 1  with 3 dB beamwidth of 2° directed at an elevation angle of +0.9° at a target at a range of 30 miles over seas with wave heights of ¼, 1 and 2 feet, respectively; 
       FIG. 8  is a simplified block diagram of a monopulse radar system including control and signal processing elements for processing signals from sequential antenna beams directed at different elevation angles in accordance with the invention; 
       FIGS. 9 ,  10  and  11  are computer-generated plots of estimated elevation angle in degrees versus true elevation angle, where the estimated angle is produced by the monopulse radar arrangement of  FIG. 8  with plural beams, each having 2° 3 dB beamwidth, the upper beam being directed at a 1.4° elevation angle and the lower beam being directed at a 0.7° elevation angles, for wave heights of ¼ foot at ranges of 10, 20 and 30 miles, respectively; 
       FIGS. 12 ,  13  and  14  are computer-generated plots of estimated elevation angle versus true elevation angle, similar to the plots of  FIGS. 9 ,  10  and  11 , for wave heights of 1 foot and ranges of 10, 20 and 30 miles, respectively; 
       FIGS. 15 ,  16  and  17  are computer-generated plots of estimated elevation angle versus true elevation angle similar to  FIGS. 9 ,  10  and  11 , for wave heights of 2 feet and ranges of 10, 20 and 30 miles, respectively; 
       FIG. 18  is a simplified block diagram of a monopulse radar system in accordance with the invention in which processing of the signals from simultaneous antenna beams is performed; 
       FIG. 19  is a simplified block diagram of another embodiment of the invention; and 
       FIG. 20  is a simplified block diagram of an addition to or modification of the arrangement of  FIG. 19  to provide improved accuracy over a wider range of conditions; and 
       FIG. 21  is a plot of estimated elevation versus time elevation for the arrangement of  FIGS. 19 and 20  for a flat sea at 30-mile range. 
   

   DESCRIPTION OF THE INVENTION 
   In  FIG. 1 , the direction in which the main beam  12  (or plural main beams, not illustrated) of array antenna  10  is directed is controlled by beam steering arrangements illustrated together as a block  20 . Such beam steering arrangements control phase shifters (not illustrated) associated with antenna  10  in a predetermined manner, and are well known in the art. A transmitter illustrated as a block  22  is connected with antenna  10  by one or more paths illustrated together as a path  24  for coupling signals to antenna  10 , which in turn transmits the signals in the form of electromagnetic radiation. The signals produced by transmit block  22  may be simple, constant-frequency pulses, as described for example in the text Principles of Radar, by Reintjes &amp; Coate, published by McGraw-Hill, 1952. As an alternative, frequency-jumped pulses may be used, as described in U.S. patent application Ser. No. 266,757 filed Nov. 3, 1988, or continuous-wave signals of varying frequency may be used. 
   The transmitted signal is directed at an angle above the horizon (an elevation angle) of approximately one-half of the 3 dB beamwidth, as described above. In  FIG. 1 , the 3 dB antenna beamwidth is 2° and the elevation angle is 0.9°. Some of the transmitted energy is intercepted by and is reflected from the target, which may be above or below the center line of beam  12 , as illustrated by targets  26  and  28 , respectively, of  FIG. 1 . The reflected energy is received by antenna  10  after a delay, and the received signals are coupled over a path or paths illustrated together as  30  to signal processing circuits illustrated as a block  32 . Processing block  32  generates the real and imaginary parts of the sum (Σ) and difference (Δ) signals. The four signals produced by block  32  on conductors  34   a ,  34   b ,  34   c  and  34   d  are the real part of the difference signal (Δ I ), the imaginary part of the difference signal (Δ Q ), the real part of the sum signal (Σ I ) and the imaginary part of the sum signal (Σ Q ), respectively. The four outputs of block  32  are connected to a bank  33  of four corresponding analog-to-digital converters (ADCs)  33   a ,  33   b ,  33   c  and  33   d.    
   In response to timing signals from a controller  50 , the bank of ADCs  33  simultaneously converts the amplitude of each of the four signals into four separate binary (digital) values. In a typical system, bank of ADCs  33  may provide each amplitude in the form of a seven bit magnitude and a sign bit. The resulting eight-bit outputs can range in value from minus 128 to plus 128. Each time the controller activates the ADCs, each of these converters provides a new value at its output and as a group these ADCs together provide a new set of these four values. The set of four digital values is provided to a further processing block  38  in which {circumflex over (ρ)}, which is termed the conventional “monopulse”, is calculated as the real part of the quotient of Δ/Σ, 
                   ρ   ^     =       Re   (     Δ   /   Σ     ⁢           )     =           Δ   Q     ⁢     Σ   I       -       Δ   I     ⁢     Σ   Q             Σ   I   2     +     Σ   Q   2                   (   1   )               
The resulting {circumflex over (ρ)} digital value is applied over a path  40  to a further processing block  42  in which the corrected monopulse elevation angle estimate ê is calculated
   ê=f ({circumflex over (ρ)},β)  (2) 
where f is a known calibration function and β is the beam steering angle. The corrected monopulse elevation estimate ê is applied over a path  44  to a display  46 , together with range and bearing information, not illustrated.
 
     FIG. 5  includes a plot of estimated elevation angle ê in degrees versus true elevation angle in degrees. Plot  510  of  FIG. 5  is calculated assuming a conventional monopulse system similar to that of  FIG. 1  using frequency diversity, with a 3 dB antenna beamwidth of 2°, the center of which is located at 0.9° above the horizon at a frequency of 3 gigahertz (GHz) for wave heights of ¼ foot and with the target at a range of 30 miles.  FIG. 6  is similar to  FIG. 5  but for wave heights of 1 foot, and  FIG. 7  is similar to  FIG. 5  for wave heights of 2 feet. It should be noted that the simplifying assumption has been made in generating these plots that the wave structure is static over a period of time equivalent to about 10 milliseconds. Reference to  FIG. 7  shows that at a range of 30 miles, with wave heights of 2 feet, the errors are generally less than ±¼°. However, for calmer seas, the errors may be substantially greater. Since wave height cannot be predicted in advance, reduced errors for all wave heights are desired. 
     FIG. 8  is generally similar to  FIG. 1 , and elements of  FIG. 8  corresponding to those of  FIG. 1  are designated by the same reference numerals. In  FIG. 8 , the four digital values from the four analog-to-digital converters  33   a - 33   d  which are provided to processing block  38  are also provided to a further signal processing block  80  which calculates {circumflex over (λ)} as: 
                   λ   ^     =       Im   (     Δ   /   Σ     ⁢           )     =           Δ   I     ⁢     Σ   I       -       Δ   Q     ⁢     Σ   Q             Σ   I   2     +     Σ   Q   2                   (   3   )               
The resulting {circumflex over (λ)} digital value is applied to a further signal processing block  64 . Signal processing block  64  is a digital multiplier which multiplies the {circumflex over (λ)} received from signal processing block  80  by itself to produce a digital value {circumflex over (λ)} 2  which is the square of the digital value {circumflex over (λ)}. The {circumflex over (λ)} 2  produced by signal processing block  64  is further applied to another digital multiplier illustrated as a block  68 . Controller  50  controls the operation of signal processing block  68  by sending control signals over control lines  51  or  52  but not over both simultaneously. When controller  50  sends a control signal over control line  51 , signal processing block  68  responds by multiplying the digital value {circumflex over (λ)} 2  from processing block  64  by a first predetermined constant K 3 . When controller  50  sends a control signal over control line  52 , signal processing block  68  multiplies the digital value {circumflex over (λ)} 2  by a second predetermined constant K 4 .
 
   Also in  FIG. 8 , the ê produced by signal processing block  42  is applied to a signal processing block  56 . Controller  50  controls the operation of signal processing block  56  by sending control signals over a control line  54  or over a control line  55 , but not over both simultaneously. When signal processing block  56  receives a control signal from controller  50  over control line  54 , signal processing block  56  multiplies ê by constant K 1 . When signal processing block  56  receives a control signal from controller  50  over control line  55 , signal processing block  56  multiplies ê by constant K 2 . 
   Controller  50  also controls the operation of a digital accumulator illustrated as  76 . The digital accumulator stores a digital value. Upon command by the controller, it adds the stored digital value to the value of a selectable one of the digital inputs of accumulator  76 . When the addition is complete, accumulator  76  once again stores the resultant sum. Controller  50  controls signal processing block  76  by sending control signals over control lines  70  and  72  and over reset control line  74 . When accumulator  76  receives a control signal over control line  74 , accumulator  76  resets its stored digital value to zero. When accumulator  76  receives a control signal over control line  70 , it adds the digital value (either K 1 ê or K 2 ê) from signal processing block  56  to the digital value already stored in the accumulator and again stores the resultant sum by overwriting the previously stored sum. When accumulator  76  receives a control signal over control line  72  it adds the digital value from signal processing block  68  (either K 3 {circumflex over (λ)} 1   2  or K 4 {circumflex over (λ)} 2   2 ) to the value already stored in the accumulator and stores the resultant sum. 
   In operation, controller  50  of  FIG. 8  controls the beam steering circuit  20  to cause antenna  10  to direct a received beam  12 , for example first at a 1.4° (upper) angle as illustrated by dotted outline  12   a  in  FIG. 8 , and then at the 0.7° (lower) angle. During that time when antenna  10  is directed at the upper 1.4° angle, controller  50  causes a transmitter pulse to be transmitted which is ultimately reflected from the target (not illustrated in  FIG. 8 ). Signals received from the target pass through antenna  10  by way of the upper beam to receiver processor  32  for producing Δ I , Δ Q , Σ I  and Σ Q  signals. The digitized Δ I , Δ Q , Σ I  and Σ Q  signals are processed by conventional monopulse processors  38  and  42  to produce a first ê digital value designated ê 1 . The Δ and Σ signals are also processed by signal processing blocks  80  and  64  to produce a first {circumflex over (λ)} 2  digital value designated {circumflex over (λ)} 1   2 . Controller  50  sends a control signal over line  74  which resets the value in accumulator  76  to zero. Controller  50  then sends a control signal over control line  54  to signal processing block  56  which causes ê 1 , from signal processing block  42  to be multiplied by K 1 . At the same time, controller  50  sends a control signal over line  51  to signal processing block  68 , which causes {circumflex over (λ)} 1   2  from processing block  64  to be multiplied by K 3 . Controller  50  then sends a control signal over control line  70  to accumulator  76  which causes the value K 1 ê 1  from signal processing block  56  to be stored in the accumulator. Controller  50  then sends a control signal over control line  72  to accumulator  76  which causes the value K 3 {circumflex over (λ)} 1   2  to be added to the current stored value K 1 ê 1 , and to cause the accumulated value K 1 ê 1 +K 3 {circumflex over (λ)} 1   2  to be stored in the accumulator. 
   Controller  50  then directs beam steering circuit  20  to cause antenna  10  to direct its beam at the lower 0.7° elevation angle, and causes a transmitter pulse. This may occur following the processing of signals related to the upper, 1.4° position of the beam produced by antenna  10 . Signals are received by antenna  10  from the target (not illustrated in  FIG. 8 ) and Σ and Δ signals are again produced on conductor set  34  by receiver processing circuit  32 . Conventional monopulse processing blocks  38  and  42  calculate a new value of ê which is designated ê 2 , and signal processing blocks  80  and  64  calculate a new value for {circumflex over (λ)} 2  which is designated {circumflex over (λ)} 2   2 . Controller  50  then sends control signals over control lines  52  and  55  to signal processing blocks  56  and  68 , respectively, which causes ê 2  from processing block  42  to be multiplied by K 2 , and which also causes {circumflex over (λ)} 2   2  from processing block  64  to be multiplied by K 4 . Controller  50  then sends a control signal over control line  70  to accumulator  76  which causes K 2  ê 2  from processing block  56  to be added to the sum K 1  ê 1 +K 3  {circumflex over (λ)} 1   2  already stored in the accumulator and causes the resultant sum K 1  ê 1 +K 2  ê 2 +K 3  {circumflex over (λ)} 1   2  to be stored in the accumulator. Controller  50  then sends a control signal over control line  72  to accumulator  76  which causes K 4 {circumflex over (λ)} 2   2  from processing block  68  to be added to the accumulator which produces a corrected elevation angle estimate:
 
 ē=K 1 ē   1   +K 2 ê   2   +K 3{circumflex over (λ)} 1   2   +K 4{circumflex over (λ)} 2   2  
 
which is applied to display  46 . A particularly advantageous set of constants for a particular application has been found to be K 1 =2.2, K 2 =−1.2, K 3 =−0.75, and K 4 =0.
 
     FIGS. 9 ,  10  and  11  illustrate plots of estimated elevation error ē versus actual elevation using frequency-diversity pulses at ranges of 10, 20 and 30 miles, respectively, for wave heights of ¼ foot, calculated for the system of  FIG. 8  operated as described. Comparison of  FIG. 11  with  FIG. 5  shows a marked improvement in the accuracy of the estimated elevation using the system of  FIG. 8  by comparison with the prior art system of  FIG. 1 .  FIGS. 12 ,  13  and  14 , are similar to  FIGS. 9 ,  10  and  11 , respectively, except that the wave height is 1 foot. Comparison of  FIG. 14  with  FIG. 6  shows that the improvement in accuracy achieved by use of the arrangement of  FIG. 8  is substantial.  FIGS. 15 ,  16  and  17  are the same as  FIGS. 9 ,  10  and  11 , respectively, except that the wave height is 2 feet. Comparison of the plot of  FIG. 17  with  FIG. 7  shows that a considerable improvement in accuracy results from the use of the arrangement of  FIG. 8  and the described operating method. 
   Sophisticated prior art array antennas are capable of producing a single main beam or lobe, and are also capable of being operated in a mode in which several independently controllable beams or lobes can be generated simultaneously. Such antennas are associated with receive signal processors ( 32  of  FIG. 8 ) which produce Σ and Δ signals for each of the beams produced by the antenna.  FIG. 18  illustrates a monopulse radar system according to the invention which simultaneously produces pairs of antenna beams. Elements of  FIG. 18  corresponding to those of  FIG. 8  are designated by the same reference numerals. 
   In  FIG. 18 , antenna  10  directs two simultaneous beams  12   a ,  12   b  toward a target (not illustrated). The upper beam has a 2° 3 dB beamwidth and is directed at an elevation angle of +1.4°. The lower beam also has 2° 3 dB beamwidth and is directed at an elevation angle of 0.7°. Both are directed in the same azimuthal direction. A transmitter pulse may be emitted by one beam or by both. Receive signal processing block  32  produces Σ U  and Δ U  signals for upper beam  12   a , and Σ L  and Δ L  for lower beam  12   b . The Σ U , Δ U , Σ L  and Δ L  signals are sent to a bank of eight A-to-D converters illustrated together as a block  33 . The first four A-to-D converters (not separately illustrated) convert the real and imaginary parts of Σ U  and Δ U  to digital values and the second four convert the real and imaginary parts of Σ L  and Δ L  to digital values. 
   The digital values for Σ U  and Δ U  are provided to processing block  1838  for calculating {circumflex over (ρ)}=R e (Δ U /Σ U ). The digital values for Σ L  and Δ L  are provided to processing blocks  38  and  80  for calculating {circumflex over (ρ)} 2 =R e (Δ L /Σ L ) and {circumflex over (λ)}=I m (Δ L /Σ L ), respectively. The {circumflex over (ρ)} 1  signal from block  1838  is applied to a multiplier illustrated as  56  for multiplication by a constant K 1 . Similarly, the {circumflex over (ρ)} 2  signal from block  38  is applied to a multiplier illustrated as a block  60  for multiplication by a constant K 2 . The {circumflex over (λ)} signal from block  80  is applied to a squaring processor illustrated as a block  64  to produce {circumflex over (λ)} 2 , and thence to a multiplier  68  for multiplication by K 3  to produce K 3 {circumflex over (λ)} 2 . A summer  76  receives K 1 {circumflex over (ρ)} 1  from multiplier  56  by way of a data path  70 , K 2 {circumflex over (ρ)} 2  from multiplier  60  by way of data path  72 , and K 3 {circumflex over (λ)} 2   2  from multiplier  68  by way of data path  74 , for adding them together and producing a sum on a data path  78  for application to display  46 . For the exemplary values of K 1 =2.2, K 2 =1.2, K 3 =−0.75 and K 4 =0, the sum estimate produced by summer  76  is
 
 ē= 2.2{circumflex over (ρ)} 1 −1.2{circumflex over (ρ)} 2 −0.75{circumflex over (λ)} 2   2  
 
which is the same as the estimate ē produced by the sequential-beam arrangement of  FIG. 8 . It should be noted that delays may be required at various points in the block diagrams to compensate for differences in the times required for the various computations in the various signal paths, so that corresponding signals arrive at summer  76  simultaneously. Such delays are so well known as to be notorious in the art.
 
   The specific values for the constants K 1 , K 2 , K 3  and K 4  depend upon judgements relating to the optimum parameters such as desired range coverage and environment, and other values may be selected based upon other judgements. A given phase monopulse radar could be exposed both to environments where little electromagnetic energy is reflected from the earth&#39;s surface and consequently the reflected signal interferes little with the signal from the direct path, and to previously described environments where the interference from the reflected signal interferes strongly with the signal from the direct path. The embodiment of the invention which is illustrated in  FIG. 19  calculates estimates of the elevation angle of a target which are accurate in environments in which the reflected signal is weak, as well as environments where the reflected signal interferes strongly. 
     FIG. 19  is generally similar to  FIG. 8 , and elements of  FIG. 19  corresponding to those of  FIG. 8  are designated by the same reference numerals. In  FIG. 19 , processing proceeds in the same manner as that described for the arrangement of  FIG. 8  through the processing performed by blocks  42  and  64 , which sequentially generate ê and {circumflex over (λ)} 2  samples for the upper and lower beams. The {circumflex over (λ)} 2  signals from block  64  are applied to a multiplier  68  at the next level of processing, for multiplication by either K 3  or K 4  under control of controller  50  by way of consideration  51  or  52 , just as in the arrangement of  FIG. 8 . The sequential ê 1  and ê 2  signals produced by block  42 , however, are applied to a further processing block illustrated as  57 , as well as to multiplier  56 , which multiplies by either K 1  or K 2  under control of control block  50  by way of conductors  54  or  55 , also as described above. 
   In  FIG. 19 , controller  50  controls the operation of signal processing block  57  by sending control signals over control lines  58  or  59 , but not over both simultaneously. When controller  50  sends a control signal over control line  58 , signal processing block  57  responds by storing the digital value ê 1  or ê 2  received from signal processing block  42 . When controller  50  sends a control signal over control line  59 , signal processing block  57  responds by first subtracting the digital value ê 1  or ê 2  currently received from signal processing block  42  from any digital value previously stored in processing block  57 , and second, if the digital value resulting from the subtraction is less than zero, reversing the sign of said digital value to form the digital value |ê 1 −ê 2 |, the absolute value of the difference between the digital value currently received from processing block  42  and the digital value previously stored in processing block  57 . The memory of block  57  is also reset to zero following each completed calculation. 
   The absolute value produced by signal processing block  57  is applied to a multiplier illustrated as a block  90 . Block  90  is enabled by controller  50  over a conductor  91 , for multiplying the received absolute value by a constant K 5  to produce K 5 |ê 1 −ê 2 |, which is made available to accumulator  76 . 
   In operation of the embodiment of  FIG. 19 , accumulator  76  accumulates K 1 ê 1 +K 3 {circumflex over (λ)} 2 , during a first portion of a cycle of operation, as described in conjunction with  FIG. 8 . Also during this first portion of the cycle, block  57  is controlled over control line  58  to store the current value of ê 1 . During the second portion of the cycle, multiplier  56  produces K 2 ê 2  and multiplier  68  produces K 4 {circumflex over (λ)} 2   2 , as previously described in relation to  FIG. 8 . While accumulator  76  begins to accumulate K 2 ê 2  from block  56  and K 4 {circumflex over (λ)} 2   2  from block  68 , block  57  is controlled over conductor  59  to subtract ê 2  from ê 1 , and invert as necessary, and block  90  is controlled over conductor  91  to produce K 5 |ê 1 −ê 2 |. When the output from multiplier  90  is available, accumulator  76  is controlled over conductor  71  to perform the final accumulation of type cycle to produce an elevation estimate
 
 ē=K 1ê 1   +K 2 ê   2   +K 3{circumflex over (λ)} 2   1   +K 4{circumflex over (λ)} 2   2   +K 5| ê   1   −ê   2 |
 
and is reset in readiness for another cycle.
 
   The estimate ē is made available to display  46  by way of a path  206 . 
   The accuracy of the elevation estimate produced in  FIG. 19  is limited in some environments, such as a smooth sea surface where the reflection interferes very strongly with the direct path, because the exact functional relation between the true target elevation e, and the measurements ê 1 , ê 2 , {circumflex over (λ)} 2   2  and {circumflex over (λ)} 2   2  is nonlinear. A more precise estimate of the true elevation e is made by the embodiment of the invention illustrated in  FIG. 20 . 
   The arrangement of  FIG. 20  constitutes an embodiment of the invention which may be viewed as an addition or modification of the arrangement of  FIG. 19 . In particular, the processing arrangement of  FIG. 20  receives certain inputs by way of data paths  200 ,  202  and  204  of  FIG. 19 , and also receives the processed ē signal from accumulator  76  of  FIG. 19 , add further corrections to the processed ē signal received from accumulator  76  of  FIG. 19  to generate a refined elevation estimate designated ē 1 , which is made available to display  46  of  FIG. 19 . 
   In  FIG. 20 , signals from controller  50  ( FIG. 19 ) applied over control lines  101 ,  102 ,  103  and  104  of data bus  200  control the operation of memory locations  100   a ,  100   b ,  100   c  and  100   d , respectively, of a memory designated generally as  100 . Signals ê 1  and ê 2  become available from processing block  42  ( FIG. 19 ) by way of data path  202 . Memory locations  100   a  and  100   b  are sequentially enabled to store ê 1  and ê 2 , respectively, during the first and second halves, respectively, of the cycle described in conjunction with  FIG. 19 . Similarly, memory locations  100   c  and  100   d  are coupled to a data path  204 , by which signals {circumflex over (λ)} 2   1  and {circumflex over (λ)} 2   2  are received from processing block  64  ( FIG. 19 ). Memory locations  100   c  and  100   d  are sequentially enabled by enabling signals applied from controller  50  over control lines  103  and  104 , respectively, for storing {circumflex over (λ)} 2   1  in memory location  100   c  and {circumflex over (λ)} 2   2  in memory location  100   d . The signals stored in the memory locations of memory  100  are made available to a register  110 . 
   Register  110  of  FIG. 20  is controlled by signals applied over control lines  111 ,  112 ,  113  and  114  of data bus  200  from controller  50  ( FIG. 19 ). When a signal is applied over control line  111 , register  110  stores the signal currently stored in memory location  100   a  of memory  100 . Similarly, register  110  stores one of the signals from memory location  100   b, c  or  d  in response to signals applied over control lines  112 ,  113  or  114 , respectively. A further register  120  is coupled to register  110  and is controlled by way of a control line  121  for storing the contents of register  110 . The signals stored by both registers  110  and  120  are made available to a multiplier illustrated as a block  130 . Upon a command applied over a control line  131  of data bus  200  from controller  50  ( FIG. 19 ), multiplier  130  multiplies the value received from register  110  by the value received from register  120  to form a product. The product is applied to a further multiplier illustrated as a block  140 , which is controlled by a plurality of control lines  146 ,  147  . . .  155 , for, in response to the control signal configuration, multiplying the product received from multiplier  130  by one of a like plurality of predetermined constants. For example, when control line  146  is activated, multiplier  140  multiplies the product received from multiplier  130  by a constant K 6 . Likewise, when any one of the control lines  147  . . .  155  is activated, multiplier  140  multiplies by one of predetermined constants K 7  through K 15 , respectively. The product produced by multiplier  140  is applied to an accumulator  176 , which also receives signal ē from accumulator  76  of  FIG. 19  by way of data path  206 . 
   Accumulator  176  of  FIG. 20  is controlled by a pair of control lines  170  and  172 , and by a reset line  174 . Before the beginning of each cycle of operation, control line  174  is activated by controller  50  ( FIG. 19 ) to reset the accumulator to zero. When accumulator  176  receives a control signal over control line  170 , it adds the digital value of ê received by way of data path  206  to the digital value already stored in accumulator  176 . When accumulator  176  receives a control signal over control line  172 , it adds the digital value from multiplier  140  to the digital value already stored in accumulator  176 . 
   In operation of the arrangement of  FIGS. 19 and 20 , the operation of  FIG. 19  may be assumed to proceed as described above. When signal ê 1  is generated by processing block  42  of  FIG. 19 , controller  501  in addition to enabling processing block  57  for storing ê 1 , also enables memory location  100   a  ( FIG. 20 ) for storage of ê 1 . During that time in which {circumflex over (λ)} 2   1  is produced by processing block  64  of  FIG. 19 , controller  50  also enables memory location  10   c  ( FIG. 20 ) for storage of {circumflex over (λ)} 2   1 . Also, controller  50  controls memory locations  100   b  and  100   d  during the second half of each operating cycle to store ê 2  and {circumflex over (λ)} 2   2 , respectively. 
   Preferably during the period in which the arrangement of  FIG. 19  is processing to produce the estimate ē at the output of accumulator  76 , the arrangement of  FIG. 20  processes signals through registers  110 ,  120 ,  130  and  140 . For ease of explanation, assume that accumulator  76  of  FIG. 1  produces its output
 
 ē=K 1 ê   1   +K 2ê 2   +K 3{circumflex over (λ)} 2   1   +K 4{circumflex over (λ)} 2   2   +K 5|ê 1   −ê   2 |
 
before processing begins in the arrangement of  FIG. 20 . With this assumption, accumulator  176 , after being reset, responds to a control signal on line  170  to accumulate the current digital value of ē.
 
   Register  110  responds to a control signal on control line  111  by storing the value of ê 1  from memory location  100   a , and a control signal on control line  121  causes register  120  to store ê 1  from register  110 . Multiplier  130  is activated by a control signal on control line  131  to multiply ê 1  from register  110  by ê 1  from register  120  to produce ê 2   1 . Multiplier  140  is then activated over control line  146  to cause multiplication of the value of ê 2   1  by K 6  to produce K 6  ê 2   1 , which is made available to accumulator  176 . A control signal on control line  172  causes accumulator  176  to add K 6  ê 2   1  to the previously stored value of ē, thereby producing a partial sum represented by the expansion
 
K1ê 1 +K2ê 2 +K3{circumflex over (λ)} 2   1 +K4{circumflex over (λ)} 2   2 +K5|ê 1 −ê 2 |+K6ê 2   1  
 
   Register  110  is then activated by a control signal on line  113  for storing the {circumflex over (λ)} 2   1  signal from memory location  100   c , and register  120  responds to a control signal on control line  121  for storing {circumflex over (λ)} 2   1 . Multiplier  130  is enabled over control line  131  for causing multiplication of {circumflex over (λ)} 2   1  from register  110  by {circumflex over (λ)} 2   1  in register  120  to produce {circumflex over (λ)} 4   1 , following which multiplier  140  responds to control line  147  for multiplying {circumflex over (λ)} 4   1  by a predetermined constant K 7 . Accumulator  176  accumulates the value of K 7 {circumflex over (λ)} 4   1  with the already-summed value ē+K 6 ê 2   1  to produce ē+K 6 ê 2   1 +K 7 {circumflex over (λ)} 4   1 . 
   Register  110  is enabled by control line  112  for storing ê 2 . The value of ê 2  is transferred to register  120  in a fashion generally as described above, and the square ê 2   2  is generated in multiplier  130 . A product K 7 ê 2   2  is generated by multiplier  140 , which product is accumulated to produce
 
ē+K6ê 2   1 +K7{circumflex over (λ)} 4   1 +K8ê 2   2  
 
   During the next step, {circumflex over (λ)} 2   2  stored in memory location  100   d  is stored in register  110  and  120 , multiplier  130  produces {circumflex over (λ)} 4   2 , and multiplier  140  multiplies by a predetermined constant K 9  to produce K 9 {circumflex over (λ)} 4   2 , which accumulator  176  accumulates to produce
 
ē+K6ê 2   1 +K7{circumflex over (λ)} 4   1 +K8ê 2   2 +K9{circumflex over (λ)} 4   2 ,
 
   Register  110  is enabled over control line  111  to cause storage of ê 1  from memory location  10   a , which is transferred to register  120 . Instead of multiplying immediately, register  110  is enabled over control line  112  to cause ê 2  to be loaded from memory location  100   b . Multiplication then occurs in multiplier  130  to produce the product ê 1 ê 2 . Multiplier  140  multiplies product ê 1 ê 2  by a predetermined constant K 10 , to produce K 10 ê 1 ê 2 . Accumulator  176  then accumulates to produce
 
ē+K6ê 1 +K7{circumflex over (λ)} 4   1 +K8ê 2   2 +K9{circumflex over (λ)} 4   2 +K10ê 1 ê 2  
 
   In generally similar manner, any other cross products among ê 1 , ê 2 , {circumflex over (λ)} 2   1  and {circumflex over (λ)} 2   2  may be produced, multiplied by constants, and accumulated. The final corrected altitude estimate is
 
 ē   1   =ē+K 6ê 2   1   +K 7{circumflex over (λ)} 4   1   +K 8 ê   2   2   +K 9{circumflex over (λ)} 4   2   +K 10 ê   1   ê   2   +K 11 ê   1 {circumflex over (λ)} 2   1   +K 12 ê   1 {circumflex over (λ)} 2   2   +K 13{circumflex over (λ)} 2   1 {circumflex over (λ)} 2   2   +K 14 ê   2 {circumflex over (λ)} 2   2   +K 15ê 2 {circumflex over (λ)} 2   1  
 
The following set of constants
 
                                                   K1 = +1.3713   K2 = −0.3713   K3 = +0.1204           K4 = −0.7371   K5 = +1.3418   K6 = −6.0468           K7 = −2.1348   K8 = −6.0468   K9 = −0.0190           K10 = +12.0936   K11 = +5.3358   K12 = +0.4529           K13 = 0   K14 = −0.4529   K15 = −5.3358                        
provides the results illustrated in  FIG. 2  for a range of 30 miles and a wave height of zero.
 
   Altitude estimate ē 1 , is applied to display  46  instead of estimate ē. 
   Other embodiments of the invention will be apparent to those skilled in the art. For example, while the embodiments of  FIGS. 1 and 8  use the same antenna  10  for both transmission and reception, the invention is not so dependent, and the transmission may be made by a different antenna in a different location than antenna  10 , which in that case is used solely for reception.