Abstract:
A passive system for locating a distant source of radio frequency energy, for example a pulsed radar transmitter, from a portable platform such as a moving aircraft. The disclosed system is non ambiguous in locating ability by way of using time difference of arrival and time difference of arrival-rate processing of signals received from the distant source. This is in contrast with phase-based locating wherein location ambiguities are inherent. The disclosed system is supported by an included recalibration subsystem enabling practical maintenance of time difference of arrival system algorithm accuracy notwithstanding physical component and signal delay changes attributable to thermal or other environment effects. Maintenance of delay measurements accurate into the tens of picosecond range by this recalibration arrangement are employed to obtain usefully precise energy source locations. Mathematical equation-based disclosures of signal delay algorithms and their recalibration are included.

Description:
RIGHTS OF THE GOVERNMENT 
     The invention described herein may be manufactured and used by or for the Government of the United States for all governmental purposes without the payment of any royalty. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates to the field of remote energy-emitting source location through passive received signal processing. 
     Although radio locating has been used since the early days of radio, current military apparatus with its limited output signal durations and the availability of computerized signal processing, faster analog to digital conversion apparatus and a need to accomplish rapid accurate signal locations from a moving vehicle provide opportunity for improvement in this art. 
     Present aircraft based radio frequency emitter locating methods for example require use of two platforms to obtain angle and range data relating to a radio frequency emitting energy source or one platform flying for some seconds to obtain a multiple line of bearings (i.e., multiple angles of arrivals). In both of these cases range is determined by an intersection on multiple line of bearings. In this invention precisely measured time difference of arrival and a single aircraft are used to determine line of bearing to an emitter and time difference of arrival rate at this aircraft is used to determine emitter range. 
     SUMMARY OF THE INVENTION 
     The present invention provides unambiguous locating of a distant source of radio frequency energy from a moving platform, such as an aircraft. The identified location may be relative to the search aircraft or may be a geolocation determined with respect to the earth. The distant emission source may be of a pulsed output nature, such as a radar apparatus, and the achieved location may be accomplished with as little as two successive emission pulses. 
     It is an object of the present invention, therefore, to provide rapid accurate location of a stationary ground emitter, such as a radar transmitter, from a moving platform. 
     It is another object of the invention to provide distant radar location in azimuth, elevation and range through concurrent use of two nominally orthogonal large baseline interferometers. 
     It is another object of the invention to provide a time based unambiguous locating system for a distant radio frequency energy source. 
     It is another object of the invention to provide location of a radar emission which may be random pulse to pulse frequency agile. 
     It is another object of the invention to provide a time based distant radio frequency source locating arrangement in which a calibration sub system maintains usable accuracy notwithstanding presence of environmental-sourced and other inaccuracy influences. 
     It is another object of the invention to provide a time based distant radio frequency source locating arrangement employing a recalibration-correctable locating algorithm. 
     It is another object of the invention to provide a distant radio frequency source locating arrangement embodied in a moving platform, such as an aircraft, and employing platform-peripheral signal collection. 
     It is another object of the invention to provide a distant radio frequency source locating arrangement capable of enhanced location accuracy through use of an input antenna separation-enhancing trailing antenna member. 
     It is another object of the invention to provide a distant radio frequency source locating arrangement supported by a propagation time-based mathematical algorithm. 
     It is another object of the invention to provide a distant radio frequency source locating arrangement supported by a propagation time delay-based array of mathematical equations. 
     It is another object of the invention to provide a time difference of arrival emission source locating arrangement disposable in either of the azimuth or elevation planes, a locating arrangement usable in replication to determine both azimuth and elevation locations of a distant radio frequency source. 
     It is another object of the invention to provide both relative and absolute or geo location of a remote radio frequency emission source. 
     It is another object of the invention to provide rapid location of a remote radio frequency emission source, that is location within the time of a second or less. 
     It is another object of the invention to provide a long baseline interferometer and moving platform digital apparatus for distant emission source location. 
     It is another object of the invention to provide an airborne distant emission source location arrangement in which known aircraft velocity and long baseline interferometer-determined angle of arrival information are used to determine emitter location. 
     Additional objects and features of the invention will be understood from the following description and claims and the accompanying drawings. 
     These and other objects of the invention are achieved by an airborne long baseline interferometer radio frequency signal emitter source locating apparatus comprising the combination of: 
     a signal emitter search aircraft containing first and second radio frequency receivers and input and output signal conveying members connected therewith; 
     said first and second radio frequency receivers being disposed in receipt of signals from said radio frequency signal emitter source by way of first and second antenna members disposed in physically separated portions of said aircraft and said signal conveying members; 
     time difference of arrival signal processing apparatus received in said aircraft in communication with output signals of said first and second radio frequency receivers, said apparatus being responsive to ranges of arrival time difference and arrival time difference rate occurring in signals from said radio frequency signal emitter source output by said first and second radio frequency receivers; 
     selectively operable signal propagation time delay calibration apparatus electively connectable with said signal conveying members in paths interconnecting said first and second antennas with said time difference of arrival signal processing apparatus and generating picosecond-resolved measurement data representing environment-induced changes in signal propagation delay attending signal propagation in said signal conveying members. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 shows a distant radio frequency energy source locating military scene in which the present invention may be used to advantage. 
     FIG. 2 shows a power splitter and bi-directional signal coupler apparatus usable in embodying the present invention. 
     FIG. 3 shows geometric relationships applicable to the radio frequency signals in one arrangement of the present invention. 
     FIG. 4 shows a family of time and angle error curves relating to the FIG. 3 geometric relationships and their attending mathematical equations. 
     FIG. 5 shows geometric relationships applicable to the radio frequency signals in a second arrangement of the present invention. 
     FIG. 6 shows a family of time and angle error curves relating to the FIG. 5 geometric relationships and their attending mathematical equations. 
     FIG. 7 shows one arrangement of a time difference of arrival-responsive locator system according to the present invention. 
     FIG. 8 shows another arrangement of a time difference of arrival-responsive locator system according to the present invention. 
     FIG. 9 shows in FIG. 9 a  and FIG. 9 b  a single channel digital receiver and a single channel digital exciter usable in implementing a portion of the present invention. 
     FIG. 10 shows another arrangement of a time difference of arrival-responsive locator system according to the present invention. 
     FIG. 11 shows a bi-directional digital receiver and exciter according the present invention. 
     FIG. 12 shows another arrangement of a time difference of arrival-responsive locator system according to the present invention. 
    
    
     DETAILED DESCRIPTION 
     FIG. 1 in the drawings shows a military environment distant radio frequency energy source locating scene in which the present invention may be used to advantage. In the FIG. 1 scene a search aircraft  100  is shown to be seeking either the relative or the geolocation of an enemy radar site  102  in order that the tactical aircraft represented  104  and  106  may decommission the radar apparatus using, for example, either the gravity responsive munitions devices represented at  108  or rocket assisted munitions devices from the aircraft-carried pods represented at  110 . The radar site  102  is presumed located distantly from the search aircraft  100 , i.e., at a distance perhaps greater than suggested by the perspective of the FIG. 1 drawing, and is represented to be obscured from visual observation by the camouflage netting  114  or other visual hiding arrangements. The straight line path between the radar site  102  and the search aircraft  100  is represented at  112  in FIG. 1, as indicated by the break symbol  130 , path  112  is usually of greater length than appears in the FIG. 1 drawing perspective. 
     The FIG. 1 search aircraft  100  is represented to have mounted on its peripheral surfaces several omni-directional radio frequency receiving antennas as are indicated by the antenna pairs at  116  and  118  and at  120  and  122  in the drawing. As will become more apparent in later portions of this document these antennas are preferably disposed in such pairs and located at differing extremities of the aircraft  100 . These antennas may include one or more additional antennas located below the aircraft  100  in positions not visible in the FIG. 1 drawing. In addition to these aircraft-disposed antennas the present invention radio frequency energy source locating system may also employ one or more other receiving antennas disposed in a long baseline-removed location with respect to the aircraft  100 , i.e., disposed on a trailing enclosure  126 . The antenna  124  disposed on the enclosure  126  is connected with the aircraft  100  for signal communication purposes by a signal path included in the tether member  128 . The tether member  128  may according to present day practices therefore include an electrical signal or an optical signal communicating path in addition to a tensile force-resistant member such as a stranded steel cable. 
     As will become more apparent in later paragraphs herein the FIG. 1 tether member  128  may be of substantial length with respect to the length of the aircraft  100  in order to obtain a long “baseline” dimension for use in the described time difference of arrival locating system. The tether  128  is, moreover, presumed to be of the type deployed upon command once the aircraft  100  is in flight and may also be of a disposable rather than a retrieved by retraction type. For the present time difference of arrival-based locating of a distant radio frequency energy source a precise knowledge of the signal propagation delay encountered in traversing the tether  128  path is needed and therefore knowledge regarding the effective physical and propagation time length of this path is of great interest. As also discussed below herein the enclosure  126  may contain a radio receiver apparatus or may provide only a passive communication path between the antenna  124  and the aircraft  100 . In the latter passive enclosure instance the tether  128  may include a radio frequency signal conveying member such as a coaxial cable rather than a fiber optic communication path. In a related manner the radio frequency receiver, into which electrical signals generated by the antennas of the present invention are communicated, may take the form of either a single receiver with multiple input ports or a plurality of differing receivers each generating an output signal in response to an antenna input signal. 
     The following additional description of the invention is divided into several “parts”. The first of these parts discloses how a large baseline interferometer (of the present invention time difference of arrival configuration) determines angle and range to an emitter. This is a two-dimensional analysis and represents either the azimuth plane or the elevation plane portion of a three dimensional real world system. The second “part” of this description relates to the implementation of a long baseline interferometer. A long baseline interferometer, however, performs an open loop rather than a closed loop measurement and therefore requires some form of calibration and recalibration to maintain measured time and distance accuracy. For example, to achieve a 10 picosecond time measurement accuracy (or an equivalent 0.003 meters distance accuracy) requires the signal transmission paths between two time difference of arrival antennas and their receivers be known generally to within the same 0.003 meters or 3 millimeters signal propagation path length (assuming signal propagation in air and in a transmission line have the same velocity). (d=Cτ=3×10 8  m/s×10×10 −12 S=30×10 −4 m=3 mm) 
     In practice such 3 millimeter physical dimension accuracy cannot be achieved and maintained in a fixed, non-adjustable system, especially if one of the signal paths involved includes the towline of an aircraft-tethered antenna assembly. Therefore some form of closed loop calibration of an algorithm used to process the time difference of arrival signal data is needed. The third “part” of this description therefore describes the preferred arrangement for such closed loop calibration of a system and its communication paths. For determining geo-location of the unknown source moreover the earth related location of the search platform must be known (and the Global Positioning System may be used for this purpose). If one of the receiver antennas is separated by a tether, then the location of the tethered antenna must also be known. The final “part” of this description, therefore, discloses arrangements by which the tethered antenna can be located and, for example, considers use of an additional long baseline interferometer to locate the tethered antenna. In addition to “parts”, the name “case” is used to identify sub topics in several of the following descriptions. 
     Part I Large Baseline Interferometer Determination of Emitter Angle and Range 
     Two long baseline interferometer arrangements are considered in this part. Arrangement one (case 1) involves a long baseline interferometer oriented orthogonal to its platform velocity and arrangement two (case 2) involves a long baseline interferometer oriented parallel with its platform velocity. 
     Case One—Interferometer Orthogonal to Platform Velocity 
     FIG. 3 in the drawings shows an aircraft-disposed large baseline interferometer system having receiver antennas located orthogonal to the aircraft velocity vector. FIG. 3 conditions occur with wing tip-mounted antennas and emitter source locating accomplished in the azimuth plane. In the FIG. 3 drawing the emitter source is presumed located at the point  300  and the interferometer antennas are located at  302  and  304  on either side of the coordinate axis origin  306 . The straight line paths between each interferometer antenna and the emission source at point  300  are indicated to have lengths R 1  and R 2  in FIG. 3, the distance between antennas is indicated as L and the angle θ between a line R connecting the origin  306  with the emission source  300  is indicated at  308 . Distances along the horizontal and vertical axes in the FIG. 3 drawing are represented by variables X and Y with the aircraft velocity being in the direction of the Y variable and being identified as V y . 
     From the FIG. 3 drawing it is possible to obtain the following mathematical relationships: 
     
       
           X=R  Sin θ  (1)  
       
     
     
       
           Y=R  Cos θ  (2)  
       
     
     
       
         
           
             
               
                 
                   
                     R 
                     1 
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             X 
                             - 
                             
                               L 
                               / 
                               2 
                             
                           
                           ) 
                         
                         2 
                       
                       + 
                       
                         Y 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   
                     R 
                     2 
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             X 
                             + 
                             
                               L 
                               / 
                               2 
                             
                           
                           ) 
                         
                         2 
                       
                       + 
                       
                         Y 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
                 
         
             
         
      
     
     
       
         i TDOA=( R   2   −R   1 )/ c   (5)  
       
     
     where TDOA represents time difference of arrival i.e., the time interval separating arrival of signals from point  300  at antennas located at  302  and  304  and c represents the speed of light or 3*10 8  meters/sec.                TDOA                 rate     =                             t              (       R   2     -     R   1       )     /   c       =         V   y     c          (       Y     R   2       -     Y     R   1         )                 (   6   )                                
     The above equations are exact with respect to the FIG. 3 drawing. An approximate equation for R 2 −R 1  is: 
     
       
           R   2   −R   1   =L  Sin θ.  (7)  
       
     
     This approximation is based on R 1  and R 2  being nearly parallel. From this approximate relationship equations (5) and (6) can be rewritten as follows: 
     
       
           TDOA =( L/c ) Sin θ  (8)  
       
     
     
       
         
           
             
               
                 
                   
                     TDOA 
                      
                     
                         
                     
                      
                     rate 
                   
                    
                   
                       
                   
                   = 
                   
                     
                       τ 
                       ′ 
                     
                     = 
                     
                       
                         - 
                         0.5 
                       
                        
                       
                           
                       
                        
                       
                         ( 
                         
                           L 
                           R 
                         
                         ) 
                       
                        
                       
                           
                       
                        
                       
                         ( 
                         
                           
                             V 
                             y 
                           
                           c 
                         
                         ) 
                       
                        
                       
                           
                       
                        
                       
                         Sin 
                          
                         
                           ( 
                           
                             2 
                              
                             θ 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
                 
         
             
         
      
     
     Note from equation (8), that TDOA is a function of angle of arrival (θ) only. That is TDOA is not a function of range. Therefore equation (7) can be solved for angle of arrival.              θ   =       Sin     -   1            (       TDOA   *   c     L     )               (   10   )                                
     Once the angle of arrival is determined by equation (10) the range to the emission source  300  can be determined by the TDOA rate (τ′).              Range   =     R   =       -   0.5                     (     L     τ   ′       )                     (       V   y     c     )                     Sin        (     2      θ     )                   (   11   )                                
     These equations have been modeled using the software MATLAB (available from The Mathworks, Inc.; see http://mathworks.com) including an error bound on theta (θ) and the TDOA rate (τ′). An example of the results is shown in FIG.  4 . 
     In FIG. 4 a measurement system with no errors may measure a TDOA of 50 nanoseconds and a TDOA rate of  217  picoseconds/second and thereby the emitter would be correctly located at a point  408  in the FIG. 4 drawing (wherein, from FIG. 3, R=50 kilometers and θ=30 degrees.) If, instead, the measurement system incorrectly measured TDOA as 49 nanoseconds it would incorrectly place the emitter angle at line  406  in FIG.  4 . Similarly if the measurement system incorrectly measured TDOA as 51 nanoseconds it would incorrectly place the emitter angle at line  404  in FIG.  4 . The angular wedge bounded by lines  406  and  404  in FIG. 4 therefore represents the location bound of a system with ±1 nanosecond measurement accuracy. Similarly the curved boundaries  402  and  400  represent the error boundaries for measurement accuracies of ±10 picoseconds/second for the TDOA rate. The rectilinear wedge defined by the intersection of lines  404  and  406  and the error contours  400  and  402  in FIG. 4 therefore shows the possible location of the point  408  with measurement errors of ±1 nsec for the TDOA and ±10 psec/sec for the TDOA rate. FIG. 4 is thus an example of results that may be obtained using the present invention. 
     Case Two—Interferometer Parallel to Platform Velocity 
     FIG. 5 in the drawings shows another aircraft-disposed large baseline interferometer, an interferometer having receiver antennas located parallel with the aircraft velocity vector. The FIG. 5 interferometer configuration is relevant to aircraft nose and tail-mounted antennas and emitter source locating accomplished in the azimuth plane. In the FIG. 5 drawing the emitter source is presumed located at the point  500  and the interferometer antennas are located at  502  and  504  above and below the coordinate axis origin  506 . The straight line paths between each interferometer antenna and the emission source at point  500  are indicated to have lengths R 1  and R 2  in FIG. 5, the front to back distance between antennas is identified as L and the angle θ between the line R connecting the origin  506  with the emission source  500  is indicated at  508 . Distances along the horizontal and vertical axes in the FIG. 5 drawing are again represented by variables X and Y with the aircraft velocity being in the direction of the Y variable and being identified as V y . 
     In the manner of the above arrangement 1 analysis, from the FIG. 5 drawing it is possible to verify the following mathematical relationships: 
     
       
           X=R  Sin θ  (12)  
       
     
     
       
           Y=R  Cos θ  (13)  
       
     
                     R   1     =         X   2     +       (     Y   -     L   /   2       )     2                 (   14   )                 R   2     =         X   2     +       (     Y   +     L   /   2       )     2                 (   15   )                                TDOA =( R   2   −R   1 )/ c   (16) 
     Where c=speed of light=3*10 8  meters/sec                TDOA                 rate     =                             t              (       R   2     -     R   1       )     /   c       =         V   y     c          (         Y   +     L   /   2         R   2       -       Y   -     L   /   2         R   1         )                 (   17   )                                
     The above equations are exact. The following equations are approximate assuming R 1  and R 2  are parallel. 
     
       
           R   2   −R   1   =L  Cos θ  (18)  
       
     
     
       
           TDOA =( L/c ) Cos θ  (19)  
       
     
     
       
         
           
             
               
                 
                   
                     TDOA 
                      
                     
                         
                     
                      
                     rate 
                   
                    
                   
                       
                   
                   = 
                   
                     
                       τ 
                       ′ 
                     
                     = 
                     
                       
                         ( 
                         
                           L 
                           R 
                         
                         ) 
                       
                        
                       
                           
                       
                        
                       
                         ( 
                         
                           
                             V 
                             y 
                           
                           c 
                         
                         ) 
                       
                        
                       
                           
                       
                        
                       
                         Sin 
                         2 
                       
                        
                       θ 
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
                 
         
             
         
      
     
     Note from equation (19), that TDOA is a function of angle of arrival (θ) only. That is it is not a function of range. Therefore equation (19) can be solved for angle of arrival.              θ   =       Cos     -   1            (       TDOA   *   c     L     )               (   21   )                                
     Once the angle of arrival is determined by equation (21) the range can be determined by the TDOA rate (τ′).              Range   =     R   =       (     L     τ   ′       )                     (       V   y     c     )                     Sin   2        θ               (   22   )                                
     These equations have also been modeled in MATLAB with an error bound on theta (θ) and the TDOA rate (τ′). An example of the FIG. 4 type for the results of this modeling is shown in FIG.  6 . In the FIG. 6 drawing the angle of the line  604  represents a measurement error of ±1 nanosecond (i.e., a measured value of 168 nanoseconds instead of 167 nanoseconds) and the angle of the line  606  represents a measurement error of −1 nanosecond. Similarly the curved contours  600  and  602  represent τ′ measurement errors of −10 picoseconds and +10 picoseconds respectively. Also for the FIG. 6 example L=100 meters, Range=50 km, Velocity=250 m/sec, and the emitter angle is at 60 degrees. The correct value for the TDOA rate in FIG. 6 is 1250 picoseconds/second and the correct value for TDOA is 167 nanoseconds. FIG. 6 thus shows the error bounds with a TDOA measurement error of ±1 nsec and a TDOA rate measurement error of ±10 picoseconds/sec. 
     In either of the present interferometer parallel or perpendicular to platform velocity settings Equation (10) gives the Azimuth angle if the aircraft is flying straight and level and the elevation angle if the aircraft is rolled 90°. Also note that equation (21) is roll symmetric. 
     Part II Large Baseline Interferometer Implementations 
     Case 1 —Analog Interferometer with Video Receiver 
     FIG. 7 in the drawings shows a diagram of an analog long baseline interferometer for measuring time difference of arrival and time difference of arrival rate using the preceding mathematical relationships. The FIG. 7 measurements are accomplished using a null seeking method. In the FIG. 7 apparatus signals from the long baseline separated antennas  700  and  702  are coupled to the adjustable time delay elements τ 1 , τ 2  at  704  and  708  and thence to the adjustable attenuators α 1 , α 2  at  706 ,  710 . Output from the attenuators α 1 , α 2  is connected to the hybrid at  712  for generation of the Σ and Δ signals applied to the video receiver and processor  714 . The bipolar video in the FIG. 7 sum or Σ channel and delta or Δ channel is sampled in the wide band receiver  714  near the center of the received pulses. Controls signals for selecting values of time delay and attenuation are generated in the receiver and processor  714  and fed back to the time delay and attenuators along the paths  716 ,  718  and  720 ,  722  respectively. These signals are generated in accordance with iterative mathematical equations and adjust attenuators (α 1 , α 2 ) and time delays (τ 1 , τ 2 ) to obtain a null at the Δ port of the hybrid  712 . 
     There are many ambiguities in the value of the FIG. 7 delay τ because there are many radio frequency wavelengths present in a receiver input pulse. There is, however, only one value of τ 2 −τ 1  that will eliminate the ears (i.e., the leading and trailing edge spikes) occurring when two out-of-phase received pulses do not overlap exactly. This value of time difference of arrival=τ 2 −τ 1  can be found by further filtering the signal through a narrow band filter in the video receiver and processor  714  to stretch the ears so they also can be measured. The time delay devices  704  and  708  may be implemented at the frequency of the signal involved using waveguide or coaxial cable. Other implementing approaches include use of a tapped acoustic delay line or use of a switched fiber optic delay line. The following Table 1 shows the number of bits needed and the delay time for each bit for a tapped analog delay line (of these or other types) used in the FIG. 7 apparatus. The delay values are expressed in nanoseconds. As can be seen 14 bits are needed to obtain resolution of a representative 125 picoseconds time difference of arrival interval. 
     
       
         
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
             
             
               
                 Bit value in ns 
                 .125 
                 .25 
                 .5 
                 1 
                 2 
                 4 
                 8 
                 16 
                 32 
                 64 
                 128 
                 256 
                 512 
                 1024 
               
               
                 Bit number 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 9 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
               
               
                   
               
             
          
         
       
     
     The FIG. 7 analog approach to time difference of arrival measurement using this relatively long and tapped delay line becomes somewhat bulky in physical size. Note also that the FIG. 7 implementation is not self-calibrating. To add self-calibration to this system would result in an even more complex and bulky apparatus. An improved approach is disclosed in the Case 2 hybrid analog/digital interferometer arrangement described below. In case 2 a self-calibration arrangement has also been added. 
     Case 2—Hybrid Analog/Digital Interferometer 
     FIG.  8  and FIG. 10 in the drawings each show a combination analog and digital hybrid arrangement of a time difference of arrival interferometer in which the fine grain time delay elements are implemented in analog form and the larger time delays are determined by a radio frequency signal receiver (or receivers) that are digital in nature. The FIGS. 8 and 10 interferometers are useful in the present document for both describing the benefits achieved with a hybrid interferometer and also as examples of a present invention interferometer installed on an aircraft and its calibration. The aircraft and calibration aspects of these FIGS. 8 and 10 interferometers is discussed in the subsequent topics herein; the hybrid interferometer aspects are considered in the immediately following paragraphs below. 
     Using a digital receiver in the FIGS. 8 and 10 interferometers significantly reduces the number of bits required in the analog delay lines from that of the FIG. 7 interferometer because the time interval between receiver signal sampling events is accurately known. In the FIGS. 8 and 10 interferometers the largest delay line bit used need only be of a duration as large as the time between signal samples in the digital receiver. For a sample frequency of 50 MHz, for example, this time between samples is 20 nanoseconds. For a 500 MHz sample frequency the time between samples is 2 nanoseconds. Additionally in the FIGS. 8 and 10 interferometers the smallest bit can be reduced in time significance. The digital samples in the FIGS. 8 and 10 interferometers include both in phase (I) and quadrant (Q) samples. Therefore the phase between the two signals can be calculated. Also the signal frequency can be determined so the phase relationships can be converted to a time delay significance. Therefore analog delay bits below one wavelength are not needed. 
     In the FIGS. 8 and 10 interferometers at 20 GHz one wavelength corresponds to 50 picoseconds of propagation time. The values and number of bits or the analog variable time delay using this 50 MHz sample rate and a maximum radio frequency input of 20 GHz are given in the Table 2 below. The Table 2 bit values are in nanoseconds. The number of bits is not only reduced in Table 2 with respect to Table 1 but the resolution in Table 2 is also increased. The maximum bit length in Table 2 is also reduced from 1024 nanoseconds to 12.8 nanoseconds. 
     
       
         
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
             
             
               
                 bit value 
                 .025 
                 .05 
                 .1 
                 .2 
                 .4 
                 .8 
                 1.6 
                 3.2 
                 6.4 
                 12.8 
               
               
                 index # 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
               
               
                   
               
             
          
         
       
     
     Part III Long Baseline Interferometer Calibration 
     When reduced to the fundamental concepts involved, each of the FIGS. 8 and 10 interferometers (i.e., the interferometers discussed as arrangements 1 and 2 in the present topic of this specification) performs emitter location by way of measuring the time delay between a signal arriving at a first and at a second receiver antenna; that is, the interferometer discerns the difference in signal propagation time to two physically separated points. For such measurements time resolutions quantified into picoseconds of time are needed together with measurement stabilities of comparable or better than this picoseconds resolution. Since maintenance of such measurement accuracy in a fixed reference or an open loop measurement apparatus is difficult at best or bordering the impractical because of system variations encountered, it is desirable in the present invention to use a closed loop or self calibrated measurement algorithm for maintaining needed measurement accuracy under real world conditions. In the case of a long baseline interferometer completely mounted on an aircraft recalibration in this manner is readily accomplished. 
     Long Baseline Interferometer Calibration, Arrangement 1 
     The FIG. 8 interferometer may be considered as an example of an aircraft mounted interferometer emitter locating apparatus, in this FIG. 8 system signals from the distant radio frequency emitter are received at the antennas  800  and  802  and communicated to the digital receiver  826  along the paths  801  and  803 , the paths identified as P 1  and P 2  in the FIG. 8 drawing. Included in the paths  801  and  803  are the signal coupling elements at  804  and  806  which are abbreviated and drawing simplified representations of the structure shown in FIG. 2 of the drawings. 
     In the FIG. 2 drawing the bi-directional power splitter and bi-directional couplers represented at  804 , for example in FIG. 8, are shown to be comprised of one coupling element  204  to couple a received signal from antenna  200  to path P 1 c through path Pc 2  and one coupling element  206  to couple a transmitted signal from path P 1 c to path P 1  through path Pc 3 . Additionally, a signal from antenna  200  is coupled to path P 1  through path Pc 1 . These three coupling paths are needed in order to write the time delay equations (23) through (27) shown below. Since the FIG. 2 coupling arrangement is arranged such that Pc 2  is equal to Pc 3  these two paths can be eliminated in the equations (23) through (27). 
     Returning now to FIG. 8, the signal delays occurring along paths  801  and  803 , and any changes in these delays from temperature influences and the like, are of course inseparable from the genuine time difference of arrival in signals from the energy source being located during signal processing in the receiver  826 . Therefore, adjustment of the time difference of arrival-determining algorithm in the receiver  826 , according to the encountered delays in these paths and their changes, must be accomplished in order to maintain locating accuracy of the FIG. 8 interferometer. Notably the delays at blocks  818  and  824  in the FIG. 8 system are reciprocal in nature and are, therefore, delays requiring more bulky realization apparatus. The clock to clock time interval-resolving delay lines at  820  and  822  in FIG. 8 are helpful in resolving the delay intervals between clock pulses of the FIG. 8 system and thereby increase the accuracy with which time difference of arrival values may be measured. 
     Signal delays occurring in the paths  801  and  803  and delays encountered in the reciprocal calibration signal paths  830  and  831  paralleling the paths  801  and  803  may be considered mathematically by way of the following time delay equations. In the first of these equations, for example, it is considered that an unknown signal S 1 u has been received at the antenna  800  and subsequently the signals S 1 r and S 3 r are received: 
     
       
         S 1 u+Pc 1 +P 1 +τ 1 =S 1 r (note that Pc 1  appears in FIG.  2 )  (23)  
       
     
     
       
         S 1 u+P 1 c+τ 1c =S 3 r  (24)  
       
     
     Subtracting equation 23 from equation 24 gives: 
     
       
         P 1 c−P 1 =S 3 r−S 1 r+Pc 1 +τ 1 −τ 1c   (25)  
       
     
     Note in FIG.  8  and equation (25) that both τ 1  and τ 1c  are adjustment verniers (e.g. tapped analog delay lines of overall time interval equal to the system clock interval) enabling time of arrival determination at S 3 r and S 1 r. These verniers resolve the ambiguities of the multiple wavelengths within the receiver clock steps. 
     Then injecting a signal into path P 1 ,  801  via the reciprocal path P 1 c,  830  gives: 
     
       
         S 3 t+T 1c +P 1 c +P 1 +τ 1 =S 1 r  (26)  
       
     
     which can be rewritten as: 
     
       
         P 1 c+P 1 =S 1 r−S 3 t−τ 1 −τ 1c   (27)  
       
     
     Equations 25 and 27 are independent because the value of their determinant is non zero.                              1         -   1             1       1              =   2                          
     Therefore, these equations can be solved for P 1  and P 1 c. 
     In the other FIG. 8 path, path P 2 ,  831 , P 2  and P 2 c can be calibrated following the same procedure as for path  1 . 
     Long Baseline Interferometer Calibration, Arrangement 2 
     A long baseline interferometer calibration approach requiring no reciprocal variable delay line and only two non-reciprocal analog variable delay lines is shown in FIG. 10 of the drawings. In FIG. 10, P 15  represents the path length from the antenna  1000  phase center to the first coupler  1002  and P 16  represents the path length from the first coupler  1002  to the second coupler  1004 . These P 15  and P 16  path lengths are relatively short, rigid and fixed and therefore may be factory calibrated. These path lengths may, however, vary with temperature, therefore a temperature sensing element such as a thermocouple may be added to this portion of the FIG. 10 apparatus to measure its effective temperature. With such measurement the precise value of P 15  and P 16  delay time can be determined from a temperature versus path length table. The remaining paths associated with the antenna  1000 , the paths P 11 , P 12 , and P 13  are calibrated during operation of the FIG. 10 system. 
     Note that directional couplers  1004  and  1005  in FIG. 10 couple in both directions and are represented by FIG.  2 . For simplification the path Pc 1  is omitted; that is, it is assumed to be zero. The Pc 1  term can, however, be easily added into the equations for the final determinations of the paths if desired. Also Pc 2  and Pc 3  are not included in the equations but since they are equal they are incorporated into FIG. 10 path P 12 . 
     In the FIG. 10 apparatus a signal from the emission source to be located is received at the antennas  1000  and  1008  and communicated through the delay-inclusive paths at P 11  and P 21  to two different inputs of the digital receiver, processor and digital exciter  1010 . In the delay-inclusive paths at P 11  and P 21  the analog delay elements at  1006  and  1007  provide time/emitter-location resolution within the interval defined by two adjacent system clocks; this is accomplished by the steps of table 2. The paths P 13  and P 23  in the FIG. 10 apparatus are bi-directional and reciprocal paths by which calibration signals from the digital exciter portion of the digital receiver, processor and digital exciter  1010  are communicated into the S 1 r and S 2 r receiver input paths by way of the couplers  1002  and  1003  during the calibration portion (i.e., during a transmit or (t) operation of the indicated S 31 r/t signal communication) of a FIG. 10 system operating cycle. During the receive (r) portion of this S 31 r/t signal communication in a system operating cycle the path P 13  provides reception of the S 1 t signal to the S 31 r input. The paths P 12  and P 22  in the FIG. 10 time difference of arrival interferometer and their associated couplers  1004  and  1005  provide a signal to S 1 r and S 2 r respectively. The paths P 12  and P 22  in the FIG. 10 time difference of arrival interferometer and their associated couplers  1004  and  1005  also provide a signal to the S 31 r and S 32 r inputs of the digital receiver, processor and digital exciter  1010 . 
     By inspection of the FIG. 10 long baseline interferometer the following independent time delay equations can be written. For initial calibration τ 1  can be set to zero; therefore τ 1  does not appear in the following equations. 
     
       
         S 1 t+P 12 +P 11 =S 1 r  (28)  
       
     
     
       
         S 1 t+P 12 +P 16 +P 13 =S 31 r  (29)  
       
     
     
       
         S 31 t+P 13 +P 16 +P 11 =S 1 r  (30)  
       
     
     To show that these three equations are independent they can be rewritten in matrix form and the resulting determinant calculated. The matrix equation (equation 31) follows.                  [         1       1       0           0       1       1           1       0       1         ]                [         P11           P12           P13         ]     =     [           S1r   -   S1t               S31r   -   S1t   -   P16               S1r   -   S31t   -   P16           ]             (   31   )                                
     The value of this determinant is 2; therefore the three equations are independent and can be solved. The receive path P 11  has now been calibrated with τ 1  set to zero. 
     The FIG. 10 paths for antenna 2 at  1008 , paths P 21 , P 22  and P 23  can be calibrated following the above same procedure as described for antenna 1. The resolution of the time difference of arrival at the digital receiver is, however, limited by the resolution of the clock steps. The time delays τ 1  and τ 2  can be adjusted to increase this resolution by aligning the envelopes of the two received pulses. 
     Now if path P 15 +P 16 +P 11  is equal to P 25 +P 26 +P 21  the time difference of arrival measured between S 1 r and S 2 r is the same as the time difference of arrival at the antenna A 1  and A 2 . Therefore the emitter is located relative to the two antennas. Since P 11  and P 12  have been calibrated (i.e., their time delay measured) and P 15 , P 16 , P 25 , and P 26  are known, the time difference of arrival measured at the digital receiver can be used to determine the time difference of arrival at the antennas. 
     In FIG. 10 note that A 1  represents an assembly inclusive of antenna 1. That is the two couplers at  1002  and  1004  are built into the antenna assembly in the factory and the whole assembly is calibrated there and delivered with a calibration table. If any part of the A 1  assembly fails the entire assembly is replaced as a unit and the calibration table for the new unit is loaded into the digital processor of the digital receiver, processor and digital exciter  1010 . 
     Digital Receiver, Processor, and Digital Exciter (DRPE) 
     Some discussion of the Digital Receiver, Processor, and Digital Exciter shown, for example, at  1010  in FIG. 10 may be helpful in appreciating the present invention. Of initial interest in this discussion is the reciprocal nature and calibration aspects of the Digital Receiver, Processor, and Digital Exciter  1010 . A truly reciprocal receiver transmitter for the S 31 r/t and S 32 r/t function can be fabricated using an analog approach as depicted in the FIG. 7 drawing herein. Inclusion of the FIG. 7 analog apparatus in the Digital Receiver, Processor, and Digital Exciter  1010 , however, distracts from the overall intent of a digital system. Inclusion of a FIG. 7 analog subsystem in Digital Receiver, Processor, and Digital Exciter  1010  would result in a hybrid analog/digital system and incur the disadvantages described in connection with FIG. 7, for example. An all digital approach is, therefore, shown in FIG. 11 of the drawings. 
     Before discussing the FIG. 11 Digital Receiver, Processor, and Digital Exciter a consideration of the included subsystem apparatus shown in FIG. 9 may also be helpful. The FIG. 9 a  and FIG. 9 b  views in FIG. 9 represent receiver and exciter portions of the Digital Receiver, Processor, and Digital Exciter at  1010  in FIG. 10 respectively. In the FIG. 9 a  receiver a radio frequency signal is input to the mixer  901  which down converts the signal to an intermediate frequency signal. This intermediate frequency signal has two sidebands. Only one sideband passes through the filter  902  and this sideband is converted to digital samples by the analog to digital converter  903 . A single stage of down conversion is shown but multiple stages can be used. As indicated by the signal labels at the input path of mixer  901  in FIG. 9 a , connection and disposition of the FIG. 9 a  receiver within the Digital Receiver, Processor, and Digital Exciter  1010  of FIG. 10 is to receive the delayed analog signals from blocks  1006  and  1007  respectively. The output of the two FIG. 9 a  receivers included in block  1010  is a digitized version of the received S 1 r and S 2 r signals as indicated in FIG. 9 a . 
     In a similar manner in the FIG. 9 b  exciter digital signal samples representing a digital version of one of the signals S 1 t and S 2 t are fed into the digital to analog converter  904  then mixed up to radio frequency by the mixer  906  and finally filtered in the filter  905  to eliminate one of the mixing-produced sidebands. A single state of up-conversion is shown but multiple stages can be used. The output signal from the filter  905  is, as indicated by the labels in FIG. 9 a , the analog signal fed to respective of the signal couplers  1004  and  1005  in the FIG. 10 Digital Receiver, Processor, and Digital Exciter. The FIG. 9 subsystems are believed, therefore, to come within the capability of persons skilled in the electronic art. 
     With this discussion of the FIG. 9 subsystems in mind a consideration of additional portions of the Digital Receiver, Processor, and Digital Exciter  1010  in FIG. 10 is possible. This involves the apparatus and the signals associated with the reciprocal paths characterized by signal delays P 13  and P 23  in the FIG. 10 system; the signals S 31 r/t and S 32 r/t. In order to better appreciate several aspects of this apparatus and these signals the subsystem of FIG.  11  and the separated receive and transmit signal paths P 3 t and P 3 r shown there may be considered as follows. 
     In this discussion it is perhaps helpful to appreciate that an overall consideration in the present invention is to obtain precise knowledge of how the delays P 11  and P 21  in the FIG. 10 behave in the real world environment of a present invention time difference of arrival interferometer. This knowledge is obtained in the present invention by way of calibration signals developed in the Digital Receiver, Processor, and Digital Exciter  1010  of FIG. 10; i.e., by way of inserting these calibration signals into the signal paths characterized by delays P 11  and P 21  in FIG. 10 using the couplers at  1002  and  1003 , for example. In such real world conditions however it must be remembered that the paths conveying these calibration signals to their physical point of insertion in the FIG. 10 system (e.g. the paths characterized by the FIG. 10 delays P 13  and P 23  for example) are also characterized by delays and delay changes which must be considered in the calibration process—and in the time delay equations used herein to describe the system and its calibration. In view of these considerations the following discussion of the FIG. 10 Digital Receiver, Processor, and Digital Exciter and its subsystem shown in FIG. 11 involves a combination of the delay terms P 13 , P 23 , P 11  and P 21  and the equations using these terms. With such calibration accomplished, signal timings measured at a receiver become useful in determining actual signal timing relationships occurring at an antenna or antennas; without such calibration, delays between antenna signals and measured signals make a time difference of arrival interferometer difficult to accomplish. Delay variations of course compound this difficulty. 
     In the FIG.  10 -related equation (29) the delay P 13  includes the delays shown in path P 3 r appearing in the FIG. 11 drawing. Similarly in equation (30) the delay P 13  includes the delays shown in path P 3 t of FIG.  11 . Therefore the delay term P 13  is the same unknown in the two equations (29) and (30) only if delays P 3 t and P 3 r are equal. The delay differences between paths P 3 t and P 3 r in FIG. 11 can be made small during the manufacturing process and may remain small during the subsequent deployment of the present invention interferometer and its Digital Receiver, Processor, and Digital Exciter. For consistency of the calibration it is assumed that short passive paths remain constant or vary in a know manner with temperature. A mixer as shown at  1105  and  1107  in FIG. 11 is, however, not passive. Also the mixing process is usually lossy and is, therefore, followed by an amplifier not shown in FIG. 9 or FIG.  11 . Again such an amplifier is not passive. Therefore, for completeness it is assumed that P 3 t is not equal to P 3 r and the error this produces in paths P 11  and P 21  is determined by the disclosed equations. 
     Long Baseline Interferometer Expanded Calibration, Arrangement 2 
     By inspection of FIG.  10  and FIG. 11 the time delay equations (32) through (34) can be written in the form of: 
     
       
         S 1 t+P 12 +P 11 =S 1 r  (32)  
       
     
     
       
         S 1 t+P 12 +P 16 +P 13 +P 3 r=S 31 r  (33)  
       
     
     
       
         S 31 t+P 3 t+P 13 +P 16 +P 11 =S 1 r  (34)  
       
     
     Note that the P 13  in equations (33) and (34) is not the same P 13  in equations (29) and (30); this is because the P 3 r and P 3 t paths have been assumed non equal and removed from inclusion as part of P 13 . Also for these equations it is assumed that paths  1101  and  1104  in the FIG. 11 subsystem are equal and part of P 13 . Rewriting equations (32) through (34) in matrix form gives.                  [         1       1       0           0       1       1           1       0       1         ]                [         P11           P12           P13         ]     =     [           S1r   -   S1t               S31r   -   S1t   -   P16   -   P3r               S1r   -   S31t   -   P16   -   P3t           ]             (   35   )                                
     Equation (35) can be solved for the terms P 11 , P 12 , P 13 , i.e., for the delays of these paths, assuming P 3 r and P 3 t are known. The result is given below.                [         P11           P12           P13         ]     =       [                    .5         -   .5         .5           .5       .5         -   .5               -   .5         .5       .5                    ]                [         S1r1t             S31r1t   -   P16   -   P3r               S1r31t   -   P16   -   P3t           ]             (   36   )                                
     Where the simplifying notation S 1 r 1 t=S 1 r−S 1 t, S 31 r 1 t=S 31 r−S 1 t, and S 1 r 31 t=S 1 r−S 31 t has been applied. This notation is also applied to emphasize that S 1 r in equation (32) is not the same S 1 r in equation (34) but rather that S 1 r−Slt is a propagation time, or a delay time, around the path P 11 +P 12 . 
     Now expanding equation (36) the time delay of the three paths can be written as 
     
       
         P 11 =0.5 (S 1 r 1 t−S 31 r 1 t+S 1 r 31 t)+0.5 (P 3 r−P 3 t)  (37)  
       
     
     
       
         P 12 =0.5 (S 1 r 1 t+S 31 r 1 t−S 1 r 31 t)−0.5 (P 3 r−P 3 t)  (38)  
       
     
     
       
         P 13 =0.5 (−S 1 r 1 t+S 31 r 1 t+S 1 r 31 t)−P 16 −0.5 (P 3 r+P 3 t)  (39)  
       
     
     At this point it may be observed that if P 3 r=P 3 t it does not matter what values they are in the determination of P 11 . If P 3 r and P 3 t both increase the same amount during system operation and warm up then P 11  is still determined correctly. 
     By symmetry of FIG. 10 
     
       
         P 21 =0.5 (S 2 r 2 t−S 32 r 2 t+S 2 r 32 t)+0.5 (P 3 r−P 3 t)  (40)  
       
     
     and the above observation for P 11  also applies to P 21 . 
     Also it may be observed from FIG. 11 that 
     
       
         S 31 t+P 3 t+P 3 c+P 3 r=S 31 r  (41)  
       
     
     Equation (41) can be solved for P 3 t+P 3 r. 
     The result is: 
     
       
         P 3 t+P 3 r=S 31 r−S 31 t−P 3 c  (42)  
       
     
     Therefore, P 13  in equation (39) can be determined since S 31 r 31 t=S 31 r−S 31 t is a measured time delay and P 3 c is a short passive known delay that can be monitored for temperature. 
     It has been shown that path P 13  and by similarity path P 23  can be determined by calibration. This is true to the extent that P 16  and P 3 c are known. Also referring back to FIG. 2, Pc 1  must also be known. 
     The question then arises can P 11  be determined? An approach to consider this question is to write the following equations: 
     
       
         S 1 U+P 15 +P 13 +P 3 r=S 31 r  (43)  
       
     
     
       
         S 1 U+P 15 +P 16 +P 11 =S 1 r  (44)  
       
     
     where S 1 U is a received signal of unknown time of arrival and P 15  is the path from the antenna to the coupler  1002 . 
     Subtracting equation (43) from (44) gives 
     
       
         P 11 +P 16 −P 13 −P 3 r=S 1 r−S 31 r  (45)  
       
     
     Solving this for P 11  gives 
     
       
         P 11 =S 1 r 31 r−P 16 +P 13 +P 3 r  (46)  
       
     
     It may, therefore, be observed that PI I is not determined unless P 3 r is known exactly. While P 16  and P 13  are known, any error in P 3 r will be an error in determining P 11 . P 3 r is not a passive device. The accuracy of P 11  depends on the accuracy of P 3 r and this may be sufficient for most applications. The additional analysis below shows that any error in P 3 r does not contribute to an error in the determination of TDOA. 
     By analogy with the derivation of equation (46) the following equation can be derived. 
     
       
         P 21 =S 2 r 32 r−P 26 +P 23 +P 3 r  (47)  
       
     
     The same observation for equation (46) applies to equation (47). Note that any error in P 3 r produces an error in P 21 . Further note that any error in P 3 r produces the same error in P 11  and P 21 . 
     Now let a signal arrive at antenna  1000  and  1008 . The signals are respectively S 1 U and S 2 U. The TDOA is S 1 U−S 2 U. The TDOAM at the S 1  and S 2  receiver is (with the “m” subscript indicating “measured” at the receiver): 
     
       
         TDOA m =S 1   m −S 2   m =S 1 U+P 15 +P 16 +P 11 −(S 2 U+P 25 +P 26 +P 21 )  (48a)  
       
     
     
       
         TDOA m =S 1 U−S 2 U+(P 11 −P 21 )+(P 15 −P 25 )+(P 16 −P 26 )  (48b)  
       
     
     
       
         Since P 11 −P 21 =S 1 r 31 r−P 16 +P 13 −P 3 r−(S 2 r 32 r−P 26 +P 23 −P 3 r)  (48c)  
       
     
     the value of P 3 r cancels and P 11 −P 12  is determined since all the other terms are known. That is: 
     
       
         P 11 −P 21 =S 1 r 31 r−S 2 r 32 r−(P 16 −P 26 )+(P 13 −P 23 )  (48d)  
       
     
     Now solving equation (48b) for S 1 −S 2 U which is the desired TDOA gives: 
     
       
         TDOA=S 1 U−S 2 U=TDOA M −(P 11 −P 21 )−(P 15 −P 25 )−(P 16 −P 26 )  (49)  
       
     
     Therefore, TDOA can be correctly determined without knowing whether P 3 r contains an error or not. 
     Part IV Calibration of Tethered Antenna Long Baseline Interferometer 
     If one of the interferometer receiver antennas is located on a tethered antenna assembly in order to achieve the accuracy benefits of a longer baseline, for example, the self-calibration of the interferometer is more complex. The use of fiber optics links between the aircraft and the tethered antenna and the fact that fiber optic links are not reciprocal, i.e., the transducer for converting radio frequency signals into fiber optic signals is usually not a bi-directional signal device, provides one prominent source of this additional complexity. One could make a pseudo reciprocal fiber optic link but for high accuracy this would require a calibration system at each end of the fiber optic link. The present invention eliminates the requirement to have a calibration system (i.e., a processor) at the tethered antenna. This is beneficial because a tethered antenna assembly is often an expendable item (i.e., is cut-loose rather than reeled-in after use) in some military interferometer applications. 
     For the present invention use, therefore, the calibration system is disposed only in the long baseline interferometer aircraft. In this interferometer arrangement calibration involves solving eight independent time delay equations having eight unknowns. One of the unknowns (Pf) is the time delay of a free space path between the aircraft and the tethered antenna assembly. Therefore the calibration process also determines the separation between an antenna on the aircraft and the tethered antenna. FIG. 12 in the drawings provides details of the interferometer and its calibration in this instance. 
     In the FIG. 12 interferometer two signal reception antennas are used to collect signals from the emitter source to be located: these antennas are a forward looking antenna at  1204  and a tethered antenna at  1202 . A third aft looking antenna at  1200  is added for the calibration process herein described. These three antennas are coupled to the digital receiver, processor and digital exciter  1228  by way of six signal communication paths. Two of these FIG. 12 signal communication paths, the paths P 13  and P 23  are reciprocal or bi-directional in nature and two of the paths, the paths at P 21  and P 22  are of appreciable but initially imprecise (but subsequently calibrated) length since they extend between the interferometer aircraft and the tethered antenna assembly  1212 . Each of the FIG. 12 antennas is preferably manufactured as a unit and provided with a calibration table to be loaded into the processor portion of the digital receiver, processor and digital exciter of block  1128  whenever an antenna is replaced. 
     In paths P 11  and P 21  the analog delay element τ 1  and τ 2  are added which again enable greater accuracy of emitter source locations by providing between-clock resolution. 
     In the FIG. 12 interferometer the following eight time delay equations can be written. These equations each start with a transmitted signal and end with a received signal. For example S 1 t is the time of the transmitted signal and S 1 r is the time of the received signal. The units of each equation parameter is time. The equations represent the time delay around the various loops which may be defined in the FIG. 12 interferometer. The eight equations enable solutions for each of the eight unknowns of P 11 , P 12 , P 21 , P 22 , P 13 , P 23 , Pf, and P 5 . The remaining paths in the FIG. 12 interferometer are assumed to be known from a factory calibration event. For example, P 22  is the path from the digital exciter portion of the digital receiver, processor and digital exciter  1228  to the coupler  1222  in the tethered antenna assembly. This path includes the fiber optic link from the aircraft to the tethered antenna. Path P 10  is the path from the coupler  1222  to free space. This path P 10  is assumed to be known. The eight equations relating to FIG. 12 are: 
     
       
         S 1 t+P 12 +P 11 =S 1 r  (50)  
       
     
     
       
         S 1 t+P 12 +P 76 +P 13 +P 3 r=S 31 r (note P 3 r is from FIG.  11 )  (51)  
       
     
     
       
         S 2 t+P 22 +P 10 +P 9 +Pf+P 23 +P 3 r=S 32 r  (52)  
       
     
     
       
         S 2 t+P 22 +P 21 =S 2 r  (53)  
       
     
     
       
         S 31 t+P 3 t+P 13 +P 67 +P 11 =S 1 r (note P 3 t is from FIG.  11 )  (54)  
       
     
     
       
         S 32 t+P 3 t+P 23 +P 9 +Pf+P 10 +P 21 =S 2 r  (55)  
       
     
     
       
         S 32 t+P 3 t+P 23 +P 5 +P 7 +P 11 =S 1 r  (56)  
       
     
     
       
         S 1 t+P 12 +P 7 +P 5 +P 9 +Pf+P 10 +P 21 =S 2 r  (57)  
       
     
     These equations represent eight equations having eight unknowns. The equations can be solved if they are independent. To determine if they are independent the equations may be rewritten in matrix form and the value of the determinant calculated.                  [                    1       1       0       0       0       0       0       0           0       1       0       0       1       0       0       0           0       0       0       1       0       1       1       0           0       0       1       1       0       0       0       0           1       0       0       0       1       0       0       0           0       0       1       0       0       1       1       0           1       0       0       0       0       1       0       1           0       1       1       0       0       0       1       1                    ]                [                    P11           P12           P21           P22           P13           P23           Pf           P5                    ]     =     [                      S1r   -   S1t               S31r   -   S1t   -   P76   -   P3r               S32r   -   S2t   -   P9   -   P10   -   P3r               S2r   -   S2t               S1r   -   S31t   -   P67   -   P3t               S2r   -   S32t   -   P9   -   P10   -   P3t               S1r   -   S32t   -   P7   -   P3t               S2r   -   S1t   -   P9   -   P10   -   P7                      ]             (   58   )                                
     Determinant Value=8 
     Since the value of the determinant is non zero the equations have a solution. 
     The matrix equation (58) can be solved for the P 11  through P 5 . The solution is                             [                    P11           P12           P21           P22           P13           P23           Pf           P5                    ]     =       [                                 0.5           -   0.5           0                      0                                 0.5           0                      0                      0                                     0.5                      0.5           0                      0                      -   0.5           0                      0                      0                          0                      0                      -   0.5                      0.5           0                                 0.5           0                      0                          0                      0                                 0.5                      0.5           0                      -   0.5           0                      0                          -   0.5                      0.5           0                      0                                 0.5           0                      0                      0                        0                    0.5           0                      0                      -   0.5                      0.5                      0.5           -   0.5             0         -   0.5                      0.5           -   0.5                      .5           0                      -   0.5                      0.5               -   0.5           0                      0                    0         0                      -   0.5                      0.5                      0.5                      ]                [                    S1r1t             S31r1t   -   P76   -   P3r               S32r2t   -   P9   -   P10   -   P3r             S2r2t             S1r31t   -   P67   -   P3t               S2r32t   -   P9   -   P10   -   P3t               S1r32t   -   P7   -   P3t               S2r1t   -   P9   -   P10   -   P7                      ]               (   59   )                                
     Note the notation change S 1 r 1 t=S 1 r−S 1 t, S 31 r 1 t=S 31 r−S 1 t, etc. 
     Applying the matrix multiplication and simplifying results in the solution for the eight paths. 
     
       
         P 11 =0.5 (S 1 r 1 t−S 31 r 1 t+S 1 r 31 t)+0.5 (P 3 r−P 3 t)  (60)  
       
     
     Since S 1 r 1 t, S 31 r 1 t, and S 1 r 31 t are measured values and P 3 r and P 3 t are assumed known from factory calibration P 11  has now been determined (i.e. calibrated). If P 3 r or P 3 t has changed from the factory calibration then P 11  has been determined but determined with an error. An error analysis will be included later to assess the impact of any error. 
     
       
         P 21 =0.5 (S 2 r 2 t−S 32 r 2 t+S 2 r 32 t)+0.5 (P 3 r−P 3 t)  (61)  
       
     
     
       
         Pf=0.5 (−S 31 r 1 t+S 32 r 2 t−S 2 r 2 t+S 1 r 31 t−S 1 r 32 t+S 2 r 1 t)−(P 9 +P 10 )  (62)  
       
     
     The three paths P 11 , P 21 , and Pf are the only three paths that need to be known for the function of the invention. Observe that Pf is correctly calibrated even if P 3 r and P 3 t change from the factory calibrated values since P 3 t and P 3 r do not appear in equation (62). P 11  and P 21  allow the measurements at S 1 r and S 2 r to determine the time of arrival (TOA) and Pf provides the range between antennas  1206  and  1202  to provide one dimension in the location of the tethered antenna  1202  with respect to the aircraft. 
     It is also observed that if the values of P 3 r and P 3 t change from their factory calibrated values, and this change is unknown, the change does not result in an error in determination of TDOA. The reason for this is that both P 11  and P 21  are calibrated with the exact same error. That is they are both wrong by the same amount. Therefore, while the time of arrival (TOA) at S 1 r and S 2 r will be measured in error the time difference of arrival (TDOA) will be measured correctly. 
     While the other paths do not have to be determined for the function of the invention they are included here for completeness. 
     
       
         P 13 =0.5 (−S 1 r 1 t+S 31 r 1 t+S 1 r3 1 t) −P 76 −0.5 (P 3 r+P 3 t)  (63)  
       
     
     
       
         P 23 =0.5 (S 31 r 1 t−S 1 r 31 t+S 2 r 32 t+S 1 rt−S 2 r 1 t)−0.5 (P 3 r+P 3 t)  (64)  
       
     
     
       
         P 12 =0.5 (S 1 r 1 t+S 31 r 1 t−S 1 r 31 t)−0.5 (P 3 r−P 3 t)  (65)  
       
     
     
       
         P 22 =0.5 (S 32 r 2 t−S 2 r 2 t+S 2 r 32 t)−0.5 (P 3 r−P 3 t)  (66)  
       
     
     
       
         P 5 =0.5 (−S 1 r 1 t−S 2 r 32 t+S 1 r 32 t+S 2 r 1 t)−P 7   (67)  
       
     
     Now returning to equations (60) and (61) and paths P 11  and P 21 . A signal SU arrives at antenna A 1  and A 3  with TOA 1 =SU 1  and TOA 3 =SU 3 . 
     The TDOA is then equal to 
     
       
         TDOA=SU 1 −SU 3   (68)  
       
     
     This is the actual TDOA of the two signals at the receive antenna. The measured time of arrival at S 1 r and S 2 r is 
     
       
         TOA 1 m=SU 1 +P 8 +P 67 +P 11   (69)  
       
     
     
       
         TOA2m=SU 3 +P 10 +P 21   (70)  
       
     
     The measured time difference of arrival (TDOAm) is then 
     
       
         TDOAm=TOA 1 m−TOA 2 m  (71)  
       
     
     
       
         TDOAm=(SU 1 −SU 3 )+P 8 +P 67 −P 10 +(P 11 −P 21 )  (72)  
       
     
     The actual TDOA at the antenna is then 
     
       
         TDOA=TDOAm−P 8 −P 67 +P 10 −(P 11 −P 21 )  (73)  
       
     
     The time difference of arrival (TDOA) at the antenna has now been determined because all the values to the right of the equal sign in equation (73) are known. That is 
     1. P 8 , P 67  and P 10  are known from factory calibration. 
     2. TDOAm is a measured value and 
     
       
         3. P 11 −P 21 =0.5 [(S 1 r 1 t−S 2 r 2 t)+(S 32 r 2 t−S 31 r 1 t)+(S 1 r 31 t−S 2 r 32 t)]  (74)  
       
     
     and all the Sirjt terms in (74) above are measured during the calibration process. Observe that P 3 r and P 3 t do not appear in equation (74) so even if they drift from their factory calibration values TDOA is determined correctly. 
     In FIG. 12 only paths P 11  and P 21  include the between-clock pulse analog delay line usable to eliminate clock interval ambiguity in the time difference of arrival of the received emitter signal. The other paths do not need an analog delay line because, for the calibration signals, a chirp waveform can be used. There is no ambiguity in a chirp waveform because its frequency changes with time. (In contrast, for a constant frequency signal, each succeeding cycle is the same as the previous cycle, hence, ambiguity prevails.) For the initial calibration τ 1  and T 2  can be set to zero. Then they can also be calibrated to verify that each command state change is as expected. 
     In FIG. 12 paths P 6 , P 7 , P 8 , P 9 , and P 10  are not calibrated in real time but are calibrated in the factory. To minimize errors, antenna Al can incorporate paths P 6 , P 7 , and P 8  and be replaced as a unit including transfer to a new factory calibration table. Note that paths P 6 , P 7 , and P 8  are very short rigid paths and are again amenable to thermocouple temperature measurement and a calibration table disclosing time delay as a function of temperature. Again both A 2  and A 3  are small and very rigid. In FIG. 12, the main path requiring calibration is the path P 21  time delay from the tethered antenna  1212  to the receiver  1228 . This path length, because of each tethered antenna assembly possibly having a different towline, can be of different length for each use of the invention. 
     An important path in the FIG. 12 interferometer is the atmospheric path P f  between aircraft antenna  1206  and tethered antenna  1202 . This path P f  is useful in determining L, the long baseline interferometer length in the calibration equations for the tethered antenna embodiment of the invention. For geo-location of the radio frequency signal emission source (i.e., for source location with respect to the earth) the angle of the tethered antenna assembly, with respect to the aircraft, must also be known. One straightforward approach to locating the tethered antenna assembly in angle is by way of an additional large baseline interferometer, of the type disclosed herein or some other type, disposed on the emitter-locating search aircraft. One set of antennas for such an additional interferometer may for example be located on the wing tips of the search aircraft. Another pair of such interferometer antennas may additionally be located at the top of the vertical tail and at the aircraft bottom. A limitation of this latter vertical long baseline interferometer is, of course, the length of the vertical tail. Other approaches to determining the tethered antenna location with respect to the search aircraft may employ an on board laser system as is known in the art to track the tethered antenna from the search aircraft. Such a laser may also be used to provide an independent measure of tethered antenna range. A third arrangement for locating the tethered antenna may employ a differential global positioning system receiver disposed at the tethered receive antenna. 
     Advantages and Features 
     The present interferometer arrangements employs two platforms to obtain angle and range or alternately one platform flying for a few seconds to obtain multiple line of bearing data (i.e., angles of arrivals) with respect to a distant source of emission. In both of these cases range is determined by the intersection of multiple lines of bearings. In this invention therefore, time difference of arrival is used to determine line of bearing to the emission source and time difference of arrival rate is used to determine range. Using time difference of arrival and time difference of arrival rate algorithms, especially algorithms allowing resolution intermediate system clock pulses, from a large baseline interferometer is one aspect of this invention. Use of a tethered antenna as one source of long baseline interferometer signal is another aspect of the present invention. Calibration of initially undetermined long baseline lengths both at the outset of system operation and during use of the interferometer and especially in the instance of a towline tethered antenna is another aspect of the invention. 
     While the apparatus and method herein described constitute a preferred embodiment of the invention, it is to be understood that the invention is not limited to this precise form of apparatus or method and that changes may be made therein without departing from the scope of the invention which is defined in the appended claims.