Abstract:
The tracking of moving vehicles over long distances without emitting illumination signals is accomplished with a narrowband passive differential tracking system. Instead of Providing especially designed radar transmitters in a bistatic radar system, illuminators of opportunity (which may include UHF and VHF television station) are selected by their geographic locations so that they are in proximity to a moving target. The Doppler-shifted target reflected signals from the illuminators of opportunity are converted into digital data and combined with the independently derived initial target location and used to update the target&#39;s position and velocity by correlating the Doppler-shift with geographic coordinates. The correlation can be accomplished with a tracking algorithm which was designed for use in data processing of the signal processing system of the narrowband passive position tracking system.

Description:
STATEMENT OF GOVERNMENT INTEREST 
     The invention described herein may be manufactured and used by or for the Government for governmental purposes without the payment of any royalty thereon. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates generally to bistatic passive differential tracking systems, which is not radar, and specifically, to a process for passively tracking moving vehicles over long distances once their initial position has been established without emitting illumination signals based upon bistatic doppler only target echo return signals engendered by illuminators of opportunity. 
     The determination of the location of a passive target aircraft can be done with RADAR, which uses a dedicated transmitted waveform from one or more transmitting stations. RADAR requires an active transmission of a specific signal. Alternately, the determination of the location of a passive target aircraft can be done by passive coherent location (PCL) methods, where there is no specific transmission of an electromagnetic waveform required. This has the advantage of being covert, jam-proof, survivable, low cost and reliable. The invention herein is based on PCL methods and is not RADAR. 
     The term “location”, as used herein, means the identification of a previously unknown locus. The term “tracking”, as used herein, is the activity of following the: motion of a target whose location was previously known. The invention herein deals with tracking only, and requires a prior knowledge of the target&#39;s location. The term “passive differential tracking” is the term used to describe the action of the invention herein, which is the measurement of time-sequential displacement of the instantaneous position of a target with respect to a previously known, independently derived target location. In a bistatic passive tracking system, the illuminating transmitters and receiver are located at different locations. 
     When used in military applications, monostatic or bistatic radar has the disadvantage that the transmitter cab be detected at long range (hundreds of miles) by the electromagnetic pulses it emits. This allows the enemy to detect the presence of a radar system and also to determine its location. To get around this disadvantage, Passive Coherent Locations (PCL) was developed. PCL does not have a transmitter, but rather has a receiver system that utilizes the radiating emitted by separately located illuminators of opportunity in its reception area. In contrast the transmitter of a radar system which is being used by a monostatic or bistatic radar receive station is specific in waveform, frequency and other parameters. 
     The task of providing a bistatic radar receiver is alleviated, to some degree by the prior art techniques disclosed in the following U.S. Patents; 
     U.S. Pat. No. 3,487,462 issued to Holmberg; 
     U.S. Pat. No. 3,812,493 issued to Afendykiw et al; 
     U.S. Pat. No. 4,246,580 issued to Caputi Jr.; 
     U.S. Pat. No. 4,325,065 issued to Caputi, Jr.; and 
     U.S. Pat. No. 4,370,656 issued to Frazier et al. 
     All of the patents listed above, disclose bistatic synthetic aperture radar systems, and are incorporated herein by reference. Both of the Caputi patents, as well as that of Frazier et al, disclose Airborne bistatic radar systems entailing a first aircraft possessing a long range radar transmitter, and a second aircraft with a receiver. The distance between the two aircraft,is determined when the second aircraft receives direct path signals, which are received directly from the transmitter on the first aircraft. 
     The task of tracking targets with a passive bistatic radar tracking system is alleviated by the prior art techniques of the following U.S. Patents, which are incorporated herein by reference: 
     U.S. Pat. No. 2,940,076 issued to Bissett on Jun. 7, 1960; 
     U.S. Pat. No. 2,968,034 issued to Cafarelli on Jan. 10, 1961; 
     U.S. Pat. No. 2,972,742 issued to Ross on Feb. 21, 1961; 
     U.S. Pat. No. 3,863,257 issued to Kang on Jan. 28, 1965; 
     U.S. Pat. No. 4,281,327 issued to Frazier on Jul. 28, 1981; 
     U.S. Pat. No. 4,350,984 issued to Fisher on Sep. 21, 1982; 
     U.S. Pat. No. 4,442,4,32 issued to Quigley on Apr. 10, 1984; and 
     U.S. Pat. No. 4,477,812 issued to Frisbee on Oct. 16, 1984. 
     The designs of most prior art bistatic radar systems entail a building of one or more cooperative radar transmitters to serve as illuminators for an especially designed radar receiver. The narrowband passive differential tracking system of the present invention utilizes a receiving system which uses non-cooperative transmitters of opportunity as independent illumination sources and tracks the target with a tracking algorithm which updates the target&#39;s state with respect to a independently known initial position using Doppler-shifted signals reflected from a target. 
     SUMMARY OF THE INVENTION 
     The process of the present invention is an algorithm which can provide differential tracking of targets based upon a known initial position of the target and the bistatic Doppler target return information. The procedure requires the knowledge of the position of two illuminators or transmitters and the known target initial position. When a target passes through a region illuminated by the transmitters, the present invention can continuously update the target&#39;s new location, based on average speed, course and distance traveled computed from the Doppler shifted target reflected signal history, if the invention is initially given the position coordinates of both illuminators, the receiver and the initial target location. 
     The process begins by the selection of two illuminators of opportunity, which are two independent electromagnetic signal transmitters which serve as transmitters of uncooperative and independent signals. In the embodiment which was tested, the two illuminators of opportunity were the narrowband video carrier of two television stations: channel 15 of Lancaster, Pa., and channel 16 of Salisbury, Md. 
     Since most illuminators of opportunity are stationary radio frequency radio frequency (RF) signal sources, their latitudes and longitudes are well established and available. Similarly, the latitude and longitude of the PCL receiver is established. Next, the PCL receiver is monitored until a target vehicle reflects signals to the receiver. At this point, this known initial target position and the subject algorithm are used to establish the change in the target&#39;s state (its position and velocity). This involves using the given latitude and longitude of the two illuminators, the receiver and the target. The present invention uses an interactive narrowband passive coherent location (PCL) two-Doppler tracking program, which continuously accepts new Doppler data as an input for updating the target&#39;s state (position and velocity). 
     The two-Doppler tracking program of the present invention is an algorithm written in BASIC. This algorithm converts all latitude and longitude values to an x-y grid and correlates the Doppler shifted signals from the two illuminators to an expression of distance in wavelengths which, in turn, can be expressed in more convenient units such as nautical miles. The target position is then updated and reconverted into latitude and longitude, while the change in distance of target location over the time interval provides the vehicle ground speed. 
     It is a principal object of the present invention to provide a narrowband passive differential tracking system which uses independent sources of electromagnetic emission as illuminators. 
     It is another object of the present invention to provide a target tracking algorithm which continuously updates a target&#39;s state using Doppler-shifted target echo return signals. 
     These objects together with other objects, features advantages of the invention will become more readily apparent from the following detailed description when taken in conjunction with the accompanying drawing wherein like elements are given like reference numerals throughout. 
    
    
     DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic of the passive radar system of the present invention; 
     FIG. 2 is a chart of a United States TV spectrum envelope; 
     FIG. 3 is a chart of a typical United States TV spectrum near the carrier; and 
     FIG. 4 is an illustration of the geographic coordinate system. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The present invention is a narrowband passive position tracking system for differential position tracking of moving vehicles over long distances without emitting illumination signals. Continuous target tracking is accomplished using Doppler-shifted target echo return signals engendered by illuminators of opportunity. 
     The reader&#39;s attention is now directed towards FIG. 1, which is a schematic of the passive system of the present invention. This passive system includes a receiving antenna  100 , at least one receiver  110 , a signal processing system  120 , and a display  130 ; all of which work in combination with two illuminators of opportunity  150  and  160  to track a target  190 . 
     In the present invention the illuminators of opportunity  150  and  160  are not limited to radar transmitters which have been designed to act cooperatively with a co-designed bistatic radar receiver. These illuminators of opportunity include selected independent electromagnetic signal transmitters (such as television station transmitters) which act as uncooperative RF signal sources are used in the present invention to to track a target&#39;s state (position and velocity). 
     If television station&#39;s transmitters are used as the illuminators of opportunity, the following needs to be considered. The TV picture carrier is typically less than 1 Hz in bandwidth, picture carrier for a US TV signal is shown in FIG.  2 . 
     The part of the TV spectrum of interest to passive coherent local (PCL) is that near the carrier. FIG. 2 shows a typical US TV spectrum near the video carrier. This spectrum is dominated by the carrier and the spectral lines which occur at multiples of 60 Hz away from it. The video picture data is contained in the energy that occurs between the lines. However, the picture data spectrum level is generally quite low. That is A(w)/A(0) 2 ≦10 −7  for w≠2π N60. The only exception to this occurs when the scene in the TV picture changes. Then, the gap between the lines fill in somewhat. 
     TV transmitters operate at predefined frequencies in the VHF and UHF frequency bands. To some extent, the frequencies allocated to each TV channel vary from country to country. However, most of the transmitters currently in use operate in one of 3 frequency ranges. They are 50-90 MHz (channels 2-6), 164-230 MHz (channels 7-13), and 470-890 (channels 14-83). 
     Generally, a guideline to the sources and frequencies of United States illuminators is as depicted below in Table 1. These illuminators are generally available 100% of the time, although, the user of the present invention would be presumed to know the operating hours (as well as the latitudes and longitudes) of stations before selecting them as illuminators of opportunity. 
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Sources and Frequencies of U.S. Illuminators 
               
             
          
           
               
                   
                 Sources 
                 Narrowband 
               
               
                   
                   
               
               
                   
                 UHF TV (Video) 
                 470-906 MHZ 
               
               
                   
                 Low VHF TV (Video) 
                  54-88 MHZ 
               
               
                   
                 High VHF TV (Video) 
                 174-216 MHZ 
               
               
                   
                   
               
             
          
         
       
     
     The Transmitter parameters of illuminators of interest those presented in Table 1 are summarized Table 2. 
     
       
         
               
             
               
               
             
               
               
               
               
             
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Transmitter Parameters 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1) 
                 Video Carrier ERP (P T G T ) 
               
             
          
           
               
                   
                 Typical 
                 Maximum 
                 Frequency Band 
               
               
                   
                 100 kW 
                 100 kW 
                  50-90 MHz 
               
               
                   
                 200 kW 
                 316 kW 
                 164-230 MHz 
               
               
                   
                 500 kW 
                 5000 
                 470-890 MHz 
               
             
          
           
               
                 2) 
                 Transmitter Antenna Azimuth Beamwidth-Generally 360° 
               
               
                 3) 
                 Polarization-Generally Horizontal 
               
               
                   
               
             
          
         
       
     
     The radio receiver antenna  100  of FIG. 1 is, therefore, designed to receive signals engendered in response to target signals which are reflections of one of the illuminator picture carriers with characteristics from Table 1. 
     The narrowband passive position tracking system of the present invention is designed to continuously generate a target&#39;s updated location, average speed, course and distance traveled from Doppler-shifted target return signals, when given the latitude of: two illuminators, the receiver, and the initial target location. The process begins by the selection of two illuminators of opportunity In a test of the present invention, the two illuminators selected were: Channel 15 of Lancaster, Pa. and Channel 16 of Salisbury, Md. When the two illuminators are selected their latitudes, longitudes, videocarrier frequencies and maximum delta in their frequencies should be identified for algorithm of the present invention. This algorithm is presented below in the form of Table 3. 
     The selection of the two illuminators of opportunity might be made based upon their: geographic location, availability (not all stations broadcast continuously over a 24 hour period), frequencies and power output. 
     
       
         
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
             
             
               
                 1 
                 TWO ILLUMINATOR NARROW-BAND TRACKING PROGRAM 
               
               
                 2 
                 This program performs the 2 illuminator narrow-band tracking algorithm 
               
               
                   
                 This program can artificially error the input dopplers in Gaussian fashion 
               
               
                 9 
                 ‘ FNDMS and FNDMSI convert points on an x-y grid to lat-long and back again. 
               
               
                 10 
                 DEF FNDMS(X)=INT(X)+(INT(X$100+1/120)-INT(X)$100)/60 + 
               
               
                   
                    (X$10000-INT(X$100+1/120)$100)/3600 
               
               
                 20 
                 DEF FNDMSI(X)=SGN(X)$(ABS(INT(X))+ABS(INT((X-INT(X))$60+1/70)/10000)) 
               
               
                   
                    ABS(INT((X$60-INT (X$60+1/70))$60+1/70)/10000)) 
               
               
                 21 
                 N=VAL(RIGHT$(TIME$,2)) 
               
               
                 22 
                 RANDOMIZE N 
               
               
                 25 
                 LPRINT CHR$(27)+CHR$(69):LPRINT DATE$:LPRINT 
               
               
                 30 
                 INPUT″LOC OF RECEIVER IN LAT,LONG(dd.mmss)″;LA(0),LO(0) 
               
               
                 40 
                 LPRINT″LOC OF RECEIVER IN LAT,LONG(dd.mmss)″LA(0),LO(0) 
               
               
                 50 
                 INPUT″LOC OF ILLUMINATOR 1 IN LAT,LONG(dd.mmss)″;LA(1),LO(1) 
               
               
                 60 
                 LPRINT″LOC OF ILLUMINATOR 1 IN LAT,LONG(dd.mmss)″;LA(1),LO(1) 
               
               
                 70 
                 INPUT″LOC OF ILLUMINATOR 2 IN LAT,LONG(dd.mmss)″;LA(2),LO(2) 
               
               
                 80 
                 LPRINT″LOC OF ILLUMINATOR 2 IN LAT,LONG(dd.mmss)″LA(2),LO(2) 
               
               
                 90 
                 INPUT″INPUT CARRIER F AND ASSOCIATED DELTA F FOR ILLU. 1″;CAR(1),DOP(1) 
               
               
                 100 
                 LPRINT″INPUT CARRIER F AND ASSOCIATED DELTA F FOR ILLU. 1″CAR(1),DOP(1) 
               
               
                 110 
                 INPUT″INPUT CARRIER F AND ASSOCIATED DELTA F FOR ILLU. 2″;CAR(2),DOP(2) 
               
               
                 120 
                 LPRINT″INPUT CARRIER F AND ASSOCIATED DELTA F FOR ILLU. 2″CAR(2),DOP(2) 
               
               
                 130 
                 INPUT″INPUT TIME FROM LAST MEASUREMENT (IN SECONDS)″;T 
               
               
                 140 
                 LPRINT″INPUT TIME FROM LAST MEASUREMENT (IN SECONDS)″T 
               
               
                 149 
                 COUNT=0 
               
               
                 150 
                 INPUT″INITIAL LOC OF TARGET IN LAT,LONG(dd.mmss)″;LA(3),LO(3) 
               
               
                 160 
                 LFPRINT″INITIAL LOC OF TARGET IN LAT,LONG(dd.mmss)″LA(3),LO(3) 
               
               
                 170 
                 FOR I=1 TO 2 
               
             
          
           
               
                 171 
                 XX=0 
               
               
                 172 
                 FOR J=1 TO 20;XX=XX+RND:NEXT 
               
               
                 173 
                 XX=(XX-10)$.7745967 
               
               
                 174 
                 DOP(I)=DOP(I) + DOP(I)$.002$XX 
               
               
                 175 
                 PRINT DOP(I) 
               
               
                 176 
                 NEXT 
               
             
          
           
               
                 177 
                 FOR A=0 TO 3 ‘convert lat-long values to an x-y grid 
               
             
          
           
               
                 180 
                 LAA(A)=FNDMS(LA(A)) 
               
               
                 190 
                 LOO(A)=FNDMS(LO(A)) 
               
               
                 200 
                 X(A)=60$(LOG(0)-LOO(A))$COS(LAA(0)$3.14159/180) 
               
               
                 210 
                 Y(A)=60$(LAA(A)-LAA(0)) 
               
               
                 220 
                 NEXT 
               
             
          
           
               
                 230 
                 FOR A=1 TO 2 ‘calculate range sum difference 
               
             
          
           
               
                 240 
                 RSD(A)=-(162000!)$DOP(A)$T/CAR(A) 
               
               
                 250 
                 NEXT 
               
             
          
           
               
                 260 
                 XG=X(3):YG=Y(3) 
               
               
                 270 
                 FOR A=1 TO 2 ‘calculate values af simultaneous equations 
               
             
          
           
               
                 280 
                 RR(A)=RDS(A)+SQR((XG-X(0)){circumflex over ( )}2)+(YG-Y(0)){circumflex over ( )}2)+SQR((XG-X(A)){circumflex over ( )}2+(YG-Y(A)){circumflex over ( )}2) 
               
               
                 290 
                 RRG(A)=RR(A)-RSD(A) 
               
               
                 300 
                 NEXT 
               
             
          
           
               
                 310 
                 WHILE SQR((RR(1)-RRG(1)){circumflex over ( )}2+(RR(2)-RRG(2)){circumflex over ( )}2) &gt;.001 ‘window of convergence 
               
             
          
           
               
                 320 
                 COUNT=COUNT+1 
               
               
                 330 
                 IF COUNT=50 THEN PRINT″DIVERGENCE″:GOTO 800 
               
               
                 340 
                 FOR A=0 TO 2 ‘calculate values of Jacobian 
               
             
          
           
               
                 350 
                 DRDX(A)=((XG-X(A)){circumflex over ( )}2+(YG-Y(A)){circumflex over (&lt;)}2){circumflex over ( )}(−.5)$(XG-X(A)) 
               
               
                 360 
                 DRDX(A)=((XG-X(A)){circumflex over ( )}2+(YG-Y(A)){circumflex over (&lt;)}2){circumflex over ( )}(−.5)$(XG-X(A)) 
               
               
                 370 
                 NEXT 
               
             
          
           
               
                 380 
                 J(1,1)=DRDX(0)+DRDX(1) 
               
               
                 390 
                 J(1,2)=DRDV(0)+DRDY(1) 
               
               
                 400 
                 J(2,1)=DRDX(0)+DRDX((2) 
               
               
                 410 
                 J(2,2)=DRDV(0)+DRDV(2) 
               
               
                 420 
                 D=J(1,1)$J(2,2)-J(1,2)$J(2,1) ‘determinant of Jacobian 
               
               
                 430 
                 IF D=0 THEN PRINT″J IS SINGULAR″:GOTO 800 
               
               
                 440 
                 IN(1,1)=(1/D)$J(2,2) ‘calculate inverse of Jacobian 
               
               
                 450 
                 IN(1,2)=(1/D)$J(1,2) 
               
             
          
           
               
                 460 
                 IN(2,1)=-(1/D)*J(2,1) 
               
             
          
           
               
                 470 
                 IN(2,2)-(1/D)$J(1,1) 
               
               
                 480 
                 XG=XG+(IN(1,1)$(RR(1)-RRG(1))+IN(1,2)$(RR(2)-RRG(2))) ‘next guesses of 
               
               
                 490 
                 YG=VG+(IN(2,1)$(RR(1)-RRG(1))+IN(2,2)$(RR(2)-RRG(2))) ‘next location 
               
               
                 500 
                 FOR A=1 TO 2 
               
             
          
           
               
                 510 
                 RRG(A)=SQR((XG-X(0)){circumflex over ( )}2+(YG-Y(0)){circumflex over ( )}2)+SQR((XG-X(A)){circumflex over (&lt;)}2+(YG-Y(A)){circumflex over ( )}2) 
               
               
                 520 
                 NEXT 
               
             
          
           
               
                 530 
                 PRINT XG,YG 
               
               
                 540 
                 WEND 
               
             
          
           
               
                 550 
                 LAT=LAA(0)+VG/60 
               
               
                 560 
                 LOT=LOO(0)-XG/(60$COS(LAA(O)$3.14159/180)) 
               
               
                 570 
                 LAT=FNDMSI(LAT) ‘convert beck to lat-long 
               
               
                 580 
                 LOT=FNDMSI(LOT) 
               
               
                 590 
                 PRINT″NEW LOC IS″LAT,″LAT,″LOT″LONG″ 
               
               
                 600 
                 LPRINT″NEW LOC IS″LAT″LAT,″LOT″LONG″ 
               
               
                 610 
                 PRINT″AVERAGE SPEED IS″3600$SQR((X(3)-XG){circumflex over ( )}2+(Y(3)-YG){circumflex over ( )}2)/T″KNOTS″ 
               
               
                 620 
                 LPRINT″AVERAGE SPEED IS″3600*SQR((X(3)-XG,{circumflex over ( )}2+(Y(3)-YG){circumflex over ( )}2)/T″KNOTS″ 
               
               
                 625 
                 IF XG-X(3)=0 THEN Z=1 
               
               
                 630 
                 IF Z=1 THEN IF YG-Y(3) &gt;0 THEN HE=0 ELSE HE=180 ELSE 
               
               
                   
                    HE=ATN((VG-V(3))/(XG-X(3)))$180/3.14159 
               
               
                 640 
                 IF XG-X(3) &gt;0 THEN HE=90-HE 
               
               
                 650 
                 IF XG-X(3) &lt;0 THEN HE=270-HE 
               
               
                 660 
                 PRINT″THE COURSE IS″HE″DEGREES″ 
               
               
                 670 
                 LPRINT″THE COURSE IS″HE″DEGREES″ 
               
               
                 680 
                 PRINT″DISTANCE TRAVELED IS″SQR(X(3)-XG){circumflex over ( )}2+(Y(3)-YG){circumflex over ( )}2)″NAUT. MILES 
               
               
                 690 
                 LPRINT″DISTANCE TRAVELED IS″SQR((X(3)-XG){circumflex over ( )}2+(Y(3)-YG){circumflex over ( )}2)″NAUT. MILES″:LPRINT 
               
               
                 700 
                 INPUT″INPUT A NEW SET OF DOPPLERS (1=YES,0=NO)″;N 
               
               
                 710 
                 LPRINT″INPUT A NEW SET OF DOPPLERS (1=YES,0=NO)″N 
               
               
                 720 
                 IF N=0 THEN GOTO 800 
               
               
                 730 
                 INPUT″NEXT DOPPLER FOR ILL. 1″;DOP(1) 
               
               
                 740 
                 LPRINT″NEXT DOPPLER FOR ILL. 1:″DOP(1) 
               
               
                 750 
                 INPUT″NEXT DOPPLER FOR ILL. 2″;DOP(2) 
               
               
                 760 
                 LPRINT″NEXT DOPPLER FOR ILL. 2:″DOP(2) 
               
               
                 761 
                 INPUT″INPUT NEW INITIAL LOC (1=YES,0=N0)″;G 
               
               
                 762 
                 IF G=1 THEN GOTO 149 
               
               
                 770 
                 LA(3)=LAT:LO(3)=LOT 
               
               
                 780 
                 COUNT=0 
               
               
                 790 
                 GOTO 170 
               
               
                 800 
                 STOP 
               
               
                   
               
             
          
         
       
     
     The initial target location is identified in terms of the latitude and longitude. The target location may be obtained in a number of ways. For example, the target position might be initially known for some reason. In a test of the present invention, Doppler data was collected on Northwest flight 90 after a takeoff run north along the Potomac River from Washington National Airport. The initial target location was: latitude 38°,51′50″ and longitude 77°.02′20″; just beyond the end of the north runway. The Doppler track data generated is presented below in the form of Table 4. 
     
       
         
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
             
             
               
                 KK-29-1983 
                   
               
               
                 LOC OF RECEIVER IN LAT.LONG(dd.mmss) 39.09 
                 77.13 
               
               
                 LOC OF ILLUMINATOR 1 IN LAT,LONG(dd.mmss) 40.1545 
                 74.2753 
               
               
                 LOC OF ILLUMINATOR 2 IN LAT,LONG (dd.mmss) 38.2415 
                 75.3445 
               
               
                 INPUT CARRIER F AND ASSOCIATED DELTA F FOR ILLU. 1 4.778+08 
                 235 
               
               
                 INPUT CARRIER F AND ASSOCIATED DELTA F FOR ILLU. 2 4.526+08 
                 23 
               
               
                 INPUT TIME FROM LAST MEASUREMENT (IN SECONDS) 10 
               
               
                 INITIAL LOC OF TARGET IN LAT,LONG(dd.mmss) 38.515 
                 77.022 
               
               
                 NEW LOC IS 38.5214 LAT. 77.0239 LONG 
               
               
                 AVERATE SPEED IS 173.4565 KNOTS 
               
               
                 THE COURSE IS 328.4937 DEGREES 
               
               
                 DISTANCE TRAVELED IS .4823792 NAUT. MILES 
               
               
                 INPUT A NEW SET OF DOPPLERS (1=YES,0=NO) 1 
               
               
                 NEXT DOPPLER FOR ILL. 1: 233 
               
               
                 NEXT DOPPLER FOR ILL. 2: 27 
               
               
                 NEW LOC IS 38.5238 LAT. 77.0236 LONG 
               
               
                 AVERAGE SPEED IS 175.866 KNOTS 
               
               
                 THE COURSE IS 328.5874 DEGREES 
               
               
                 DISTANCE TRAVELED IS .4829611 NAUT. MILES 
               
               
                 INPUT A NEW SET OF DOPPLERS (1=YES,0=NO) 1 
               
               
                 NEXT DOPPLER FOR ILL. 1: 233 
               
               
                 NEXT DOPPLER FOR ILL. 2: 18 
               
               
                 NEW LOC IS 38.3302 LAT. 77.0321 LONG 
               
               
                 AVERAGE SPEED IS 185.0642 KNOTS 
               
               
                 THE COURSE IS 323.1027 DEGREES 
               
               
                 DISTANCE TRAVELED IS .5140672 NAUT. MILES 
               
               
                 INPUT A NEW SET OF DOPPLERS (1=YES,0=NO) 1 
               
               
                 NEXT DOPPLER FOR ILL. 1: 230 
               
               
                 NEXT DOPPLER FOR ILL. 2: 0 
               
               
                 NEW LOC IS 38.5335 LAT. 77.0332 LONG 
               
               
                 AVERAGE SPEED IS 206.9362 KNOTS 
               
               
                 THE COURSE IS 314.0168 DEGREES 
               
               
                 DISTANCE TRAVELED IS .5748227 NAUT. MILES 
               
               
                 INPUT A NEW SET OF DOPPLERS (1=YES,0=NO) 1 
               
               
                 NEXT DOPPLER FOR ILL. 1: 220 
               
               
                 NEXT DOPPLER FOR ILL. 2: −12 
               
               
                 NEW LOC IS 30.3347 LAT. 77.0428 LONG 
               
               
                 AVERAGE SPEED IS 216.6511 KNOTS 
               
               
                 THE COURSE IS 309.2495 DEGREES 
               
               
                 DISTANCE TRAVELED IS .6019065 NAUT. MILES 
               
               
                 INPUT A NEW SET OF DOPPLERS (1=YES,0=NO) 1 
               
               
                 NEXT DOPPLER FOR ILL. 1: 220 
               
               
                 NEXT DOPPLER FOR ILL. 2: −12 
               
               
                 NEW LOC IS 38.541 LAT. 77.0503 LONG 
               
               
                 AVERAGE SPEED IS 217.0049 KNOTS 
               
               
                 THE COURSE IS 309.8834 DEGREES 
               
               
                 DISTANCE TRAVELED IS .6027913 NAUT. MILES 
               
               
                 INPUT A NEW SET OF DOPPLERS (1=YES,0=NO) 1 
               
               
                 NEXT DOPPLER FOR ILL. 1: 230 
               
               
                 NEXT DOPPLER FOR ILL. 2: −10 
               
               
                 NEW LOC IS 38.5434 LAT. 77.0538 LONG 
               
               
                 AVERAGE SPEED IS 222.126 KNOTS 
               
               
                 THE COURSE IS 311.4585 DEGREES 
               
               
                 DISTANCE TRAVELED IS .6170167 NAUT. MILES 
               
               
                 INPUT A NEW SET OF DOPPLERS (1=YES,0=NO) 1 
               
               
                 NEXT DOPPLER FOR ILL. 1: 238 
               
               
                 NEXT DOPPLER FOR ILL. 2: −6 
               
               
                 NEW LOC IS 38.5501 LAT. 77.0612 LONG 
               
               
                 AVERAGE SPEED IS 221.7166 KNOTS 
               
               
                 THE COURSE IS 313.6958 DEGREES 
               
               
                 DISTANCE TRAVELED IS .6158795 NAUT. MILES 
               
               
                 INPUT A NEW SET OF DOPPLERS (1=YES,0=NO) 1 
               
               
                 NEXT DOPPLER FOR ILL. 1: 240 
               
               
                 NEXT DOPPLER FOR ILL. 2: 0 
               
               
                 NEW LOC IS 38.5527 LAT. 77.0643 LONG 
               
               
                 AVERAGE SPEED IS 215.3022 KNOTS 
               
               
                 THE COURSE IS 316.6644 DEGREES 
               
               
                 DISTANCE TRAVELED IS .5980615 NAUT. MILES 
               
               
                 INPUT A NEW SET OF DOPPLERS (1=YES,0=NO) 1 
               
               
                 NEXT DOPPLER FOR ILL. 1: 245 
               
               
                 NEXT DOPPLER FOR ILL. 2: 1 
               
               
                 NEW LOC IS 38.5554 LAT. 77.0714 LONG 
               
               
                 AVERAGE SPEED IS 219.2406 KNOTS 
               
               
                 THE COURSE IS 317.6068 DEGREES 
               
               
                 DISTANCE TRAVELED IS .6090018 NAUT. MILES 
               
               
                 INPUT A NEW SET OF DOPPLERS (1=YES,0=NO) 1 
               
               
                 NEXT DOPPLER FOR ILL. 1: 245 
               
               
                 NEXT DOPPLER FOR ILL. 2: 3 
               
               
                 NEW LOC IS 38.5621 LAT. 77.0744 LONG 
               
               
                 AVERAGE SPEED IS 215.5667 KNOTS 
               
               
                 THE COURSE IS 318.9585 DEGREES 
               
               
                 DISTANCE TRAVELED IS .5987964 NAUT. MILES 
               
               
                 INPUT A NEW SET OF DOPPLERS (1=YES,0=NO) 1 
               
               
                 NEXT DOPPLER FOR ILL. 1: 245 
               
               
                 NEXT DOPPLER FOR ILL. 2: 3 
               
               
                 NEW LOC IS 38.5648 LAT. 77.08141 LONG 
               
               
                 AVERAGE SPEED IS 215.156 KNOTS 
               
               
                 THE COURSE IS 319.5273 DEGREES 
               
               
                 DISTANCE TRAVELED IS .5976001 NAUT. MILES 
               
               
                 INPUT A NEW SET OF DOPPLERS (1=YES,0=NO) 1 
               
               
                 NEXT DOPPLER FOR ILL. 1: 248 
               
               
                 NEXT DOPPLER FOR ILL. 2: 0 
               
               
                 NEW LOC IS 38.5715 LAT. 77.0845 LONG 
               
               
                 AVERAGE SPEED IS 222.2685 KNOTS 
               
               
                 THE COURSE IS 319.0021 DEGREES 
               
               
                 DISTANCE TRAVELED IS .6174126 NAUT. MILES 
               
               
                 INPUT A NEW SET OF DOPPLERS (1=YES,0=NO) 1 
               
               
                 NEXT DOPPLER FOR ILL. 1: 252 
               
               
                 NEXT DOPPLER FOR ILL. 2: −3 
               
               
                 NEW LOC IS 38.5745 LAT. 77.0917 LONG 
               
               
                 AVERAGE SPEED IS 229.2261 KNOTS 
               
               
                 THE COURSE IS 318.6627 DEGREES 
               
               
                 DISTANCE TRAVELED IS .6367392 NAUT. MILES 
               
               
                   
               
             
          
         
       
     
     The algorithm of Table 3 used by the coop signal processing system  120  of FIG. 1 is written in BASIC. This algorithm converts all latitude and longitude values to an x-y grid, and correlates the Doppler shifted signals from the two illuminators to an expression of distance in wavelengths which, in turn, can be expressed in more convenient units such as nautical miles or kilometers. 
     Conversion is a difficult process because the functional relationship between Doppler frequencies and geographic coordinates is very nonlinear. Therefore, to determine velocity and position coordinates from Doppler frequencies, an iterative approach must be used. Secondly, the functional relationship is not single valued, that is, for a given association of doppler frequencies, more than one set of position and velocity component can exist. Third, since relatively large changes in position coordinates generally produce relatively small changes in Doppler frequencies, position components computed from measured Doppler frequencies are very sensitive to the inherent uncertainty of those measurements. Relatively large position errors can result from relatively small errors in Doppler frequency measurements. Methods of solving for position and velocity components are below. 
     FIG. 4 is an illustration of the geographic coordinate system used. Before proceeding further, it is necessary to derive the equations that relate the position and velocity coordinates of a body to the Doppler frequency shift of electromagnetic radiation reflected from that body. The following definitions will be used: 
     c is the velocity of electromagnetic propagation in the atmosphere (2.998×10 8  meters/sec or 5.8726×10 8  knots/sec) 
     f n  is the carrier frequency of the n th  transmitter measured in Hertz 
     f′ n  is the carrier frequency of the n th  transmitter seen by a moving body measured in Hertz 
     f″ n  is the carrier frequency of the n th  transmitter reflected from a moving body as seen by the receiver 
     d n  is the carrier frequency n th  transmitter as seen at the receiver, and is equal to (f n −f″ n )/f n    
     r n  is the shortest distance from the n th  transmitter to the moving body (n=1,2 k) or from the receiver to the moving body n=0), measured in nautical miles (nm) 
     r n  is dr n /dt measured in knots 
     x,y are the instantaneous position coordinates of the moving body along orthogonal geographic axes, measured in nm 
     u,v are the instantaneous velocity components of the moving body along orthogonal geographical axes, measured knots (u=dx/dt,v=dy/dt) 
     x n ,Y n  are the position coordinates of the n th  transmitter n=1,2, . . . k) or the receiver (n=0), measured in nm 
     x′ i ,Y, i u′ i  are the i th  estimate of the position and velocity components of the moving body, measured in nm and knots, respectively 
     Using the receiver and the n th  transmitter, the relativistic Doppler formula is 
     
       
         f″ n ≈f′ n (l−r o /(l−c 2 /r 2l/2   
       
     
     and 
     
       
         f′ n =f′ n (l−r n /(l−c 2 /r 2l/2   
       
     
     Because ŕ n  and ŕ o  are much less than c, terms of magnitude r 2 /c 2  or smaller will be ignored. Therefore: 
     
       
         f′ n =f n (l−ŕ o /(c−ŕ n /c) 
       
     
     and the normalized Doppler frequency is: 
     
       
         d n =l.f″ n /f n (ŕ o +ŕ n )/C 
       
     
     In terms of transmitter and receiver coordinates, 
     
       
         r n =[(x−x n )2+(y−y a )2]½ 
       
     
     
       
         r n =[(x−x n )u+(y−Y n )v]/r n =P n   u +q n   v   
       
     
     Note that for a given x an y, d n  is a linear function of u and v, since P n  and q n  are functions of x n , Y n , x, and y only. This relationship will prove useful in simplifying the association process. 
     The algorithm of Table 3 presumes a set of two Doppler-shifted signals from two illuminators of opportunity, although a pair of cooperative transmitters could also be used as illuminators. The receiving system is time multiplexed between the two signals. With two sets of Doppler measurements, this algorithm solves for two unknowns by solving simultaneous equations. Given the location (in latitude and longitude) of the two selected illuminators, their frequencies and the last known location of the target and an estimate of the target speed. The Doppler shift on signals reflected from the target can be predicted from this queing information. 
     The detected signals are then examined for the existence of signals in the anticipated frequency regions. 
     When the illumination source and the receiver are defined as the foci of an infinite set of elliposoids, and the target position is known, the range from illuminator to target to receiver is constant for a single element of the set of ellpsoids, (i.e., the sum of the ranges is constant for all points on the elliposoid.) When the geometry is large (e.g., 50 miles between illuminator, target and receiver), the ellipsoid can be approximated in two dimensions as an ellipse (i.e., the intersection of the ellipsoid with x,y plane is and eclipse. The Doppler shift produced by the vehicle motion can be expressed as distance in wavelengths and converted to convenient units such as kilometers, nautical miles etc., per unit of time. The distance derived above is a change in the sum of the ranges of illuminator to target and target to receiver. A change in the range sum implies target motion to another ellipse of constant range sums. When two illuminators are employed, the distance and direction of the target vehicle motion can be derived and a new position recorded at the end of the time interval that the Doppler measurements were made. The change in distance over the time interval provides the vehicle ground speed. The Dopplers in the above example were taken every 10 seconds to generate the target&#39;s flight path, but the process of the present invention may select any one of a variety of intervals to determine the location, speed and heading of a target from measured Doppler history. 
     While the invention has been described in its presently preferred embodiment it is understood that the words which have been used are words of description rather than words of limitation and that changes within the purview of the appended claims may be made without departing from the scope and spirit of the invention in its broader aspects.