Abstract:
A method and apparatus for directing a pursuing vehicle, such as a torpedo,n an intercept trajectory from a launching vehicle to a target vehicle with evasion capabilities. Models of the pursuing vehicle and evading target provide proposed trajectories based upon various environmental considerations. A guidance system uses estimates of initial operating parameter solutions, such as gyro angle, alertment time and intercept time, to begin a convergent, iterative process that defines final operating parameter solutions from which the guidance parameters are determined and transferred to the pursuing vehicle at launch. These parameters take into account various evasive strategies that a target vehicle might use to avoid being intercepted by the pursuing vehicle.

Description:
STATEMENT OF GOVERNMENT INTEREST 
     The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor. 
    
    
     BACKGROUND OF THE INVENTION 
     (1) Field of the Invention 
     This invention generally relates to trajectory control and more specifically to a method and apparatus for providing guidance parameters at launch that direct a pursuing vehicle from a launching vehicle to a target vehicle capable of evasive maneuvering after the target vehicle becomes alerted to the presence of the pursuing vehicle. 
     (2) Description of the Prior Art 
     The trajectory control of a pursuing vehicle can be classified as post-launch or pre-launch control. In post-launch control, guidance information is sent from the launching vehicle to guide the pursuing vehicle to the target. The following United States Letters Patent disclose such post-launch trajectory control systems: 
     U.S. Pat. No. 3,260,478 (1966) Welti 
     U.S. Pat. No. 3,643,616 (1972) Jones 
     U.S. Pat. No. 3,784,800 (1974) Willoteaux 
     U.S. Pat. No. 5,319,556 (1994) Bessacini 
     The Welti patent discloses the control of a first object in dependence upon a position of a second object for collision or anti-collision purposes. A regulator, that controls the travel and includes a travel control member for the first object, receives positional information of the first and second objects as a pilot magnitude and a reference magnitude. One of the positional informations is delayed in dependence upon a timing interval proportional to the time change of the quotient of the distance information of the two objects. The regulator subsequently supplies an output magnitude to the travel control member that represents the time differentials between the angular co-ordinates of the first and second objects modified by a disturbance magnitude. 
     The Jones patent discloses a method and apparatus for guiding a torpedo along a collision course to a moving target ship. A control system on the launching vehicle sends guidance parameters over a communication cable to maintain a predetermined, substantially constant lead angle with respect to the target ship by adjusting torpedo speed as the torpedo travels toward an anticipated collision. 
     In the Willoteaux patent a trajectory control system calculates the distance between a moving body and other moving or stationary objects by taking account of the speeds and direction of each. The control system simulates a series of hypothetical trajectories diverging on either side of the actual trajectory until a hypothetical trajectory is determined which satisfies various imperatives. The system then instructs the moving body control system to change the linear and or angular speed thereof so that the moving body follows the latter trajectory. 
     The Bessacini patent discloses an adaptive trajectory apparatus and method for providing, after launch, vehicle control commands to steer an underwater vehicle launch from a vessel toward a contact. As commands produced by this system transfer between the launching vessel and the launched vehicle over a communications link. 
     As generally found in prior art post-launch control systems, a pursuing vehicle exits a launching vehicle. Control systems on the launching vehicle monitor the relative positions of the pursuing vehicle and a target and control the pursuing vehicle by the transfer of information between the launching vehicle and the pursuing vehicle over communications link. When the launching vehicle is a submarine and the pursuing vehicle is a torpedo, the communications link typically comprises a communications wire. If the pursuing vehicle is a missile the communications typically occurs over some radio link. In either case, post-launch control systems on the launching vehicle issue guidance parameters to guide the pursuing vehicle along some trajectory into a predetermined relationship with the target. 
     In a pre-launch system, the pursuing vehicle follows a predetermined trajectory after launch that may or may not be programmable prior to launch. However, with either type, the pursuing vehicle leaves the launching vehicle and travels along a known trajectory that may be simple or complicated. With torpedoes, missiles and the like, that may undergo pre-programmed maneuvers, the input guidance parameters may include gyro angles and time lapse signals, such as the time between the launch and the enablement of any instrumentation on the torpedo or missile such as an acoustic seeker on a torpedo. 
     In order to provide the most accurate pre-launch guidance parameters to the pursuing vehicle, it is necessary that the interval between the time a last estimate of target state is made and the time a pursuing vehicle is launched be quite short. It is during this interval that a prior art pre-launch system must produce the guidance parameters, and this interval has constrained the nature of the analysis required to produce such guidance parameters. For example, prior art pre-launch systems generally assume that the target will maintain a constant velocity even after the target becomes alerted to the presence of the pursuing vehicle. In actual practice, however, a target normally takes evasive action. With prior art pre-launch systems two or more pursuing vehicles travel along the calculated course and one or more offsets from that calculated course to take evasive maneuvers into account. 
     SUMMARY OF THE INVENTION 
     Therefore it is an object of this invention to provide a control method and apparatus for producing guidance parameters for use by a pursuing vehicle at launch that take into account potential evasive maneuvers of a target. 
     Another object of this invention is to provide a control method and apparatus for providing guidance parameters to a pursuing vehicle for use at launch that take into account a time at which the target becomes aware of the pursuing vehicle and the effect of any potential evasive maneuvers thereafter. 
     Yet another object of this invention is to provide a control method and apparatus for providing guidance parameters to a pursuing vehicle for use at launch a short interval after a launching vehicle obtains an estimate of target vehicle state for producing an intercepting trajectory to an alerted target taking evasive action. 
     In accordance with this invention guidance parameters are provided for use by a pursuing vehicle at launch to place a pursuing vehicle on an intercept trajectory from a launching vehicle to a target vehicle with evasion capabilities. At the launching vehicle, the control method and apparatus, in response to estimates of current target vehicle state and classification, establishes predetermined target vehicle operating characteristics. The control method and apparatus use a representation of a pursuing vehicle characteristic trajectory derived from a corresponding generic model, a representation of an evading target characteristic trajectory derived from another generic model, and estimates of target vehicle state to produce predetermined operating parameters that characterize a particular trajectory of the pursuing vehicle based upon defined interactions of the representations of the pursuing vehicle and target vehicle trajectories. Iterative processing of functional forms of the trajectories, starting with the initial estimates of the operating parameter solutions, provides successive operating parameters solutions that converge. The pursuing vehicle receives guidance parameters based upon the last target state estimates and the new solutions produced within the update interval of the target estimation process. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The appended claims particularly point out and distinctly claim the subject matter of this invention. The various objects, advantages and novel features of this invention will be more fully apparent from a reading of the following detailed description in conjunction with the accompanying drawings in which like reference numerals refer to like parts, and in which: 
     FIG. 1 depicts particular trajectories or tracks of a target vehicle and pursuing vehicle on an intercept trajectory; 
     FIG. 2 depicts a generic model for a target vehicle trajectory; 
     FIG. 3 represents a generic model for a pursuing vehicle trajectory; 
     FIG. 4 is a block diagram depicting an evading target vehicle intercept unit constructed in accordance with this invention; 
     FIGS. 5A and 5B depict the operation of the evading target vehicle intercept unit in FIG. 4; 
     FIG. 6 depicts the trajectory of a pursuing vehicle generated where the target vehicle undertakes an evasive maneuver after alertment; and 
     FIGS. 7 through 9 depict the values of operating parameters obtained during the pre-launch analysis of the operation shown in FIG. 6. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     FIG. 1 is useful to an understanding of this invention and depicts typical trajectories of a target vehicle 10 that has the capability of maneuvering evasively. It is assumed that at some point in time a launching vehicle 12 detects the presence of a target vehicle 10 and determines current target vehicle state at a point 13. Target vehicle state includes the bearing and range to the target vehicle and its course and speed. After the pursuing vehicle 11 leaves the launching vehicle 12, it travels along a path 14 that is defined by guidance operating parameters supplied just prior to launch. These operating parameters establish the point at which the pursuing vehicle 11 completes a gyro turn onto a intercept trajectory at point 16, the point of the completion of an initial climb or dive at point 17 and the position of the pursuing vehicle at point 18 when the target vehicle becomes aware or is alerted to the presence of the pursuing vehicle. This alertment occurs at point 20 on the track 21 of the target vehicle 10. A short time later, at point 22, the target vehicle begins an evasive maneuver, shown in FIG. 1 as a 45° turn to port. 
     After alertment at point 18, the pursuing vehicle 11 may begin and complete a second dive at points 23 and 24 respectively. If the pursuing vehicle 11 contains some instrumentation, such as an acoustic seeker, that instrumentation activates at point 25. The pursuing vehicle 11 continues along the path 14 to the intercept point 26. 
     In accordance with this invention, generic models that can be customized for particular events define each of the paths 14 and 21. FIG. 2 depicts a generic model for a target vehicle 10. At t=0, the launching vehicle 12 establishes a range vector 30 and a target velocity vector 31 extending at an angle A with respect to the range vector 30. The generic path can be defined by a sum of X and Y coordinates representing various positions of the target vehicle 10 over time and with respect to a coordinate system aligned with the range vector 30, e.g., a rectangular coordinate system with the Y axis on the range vector 30 and the 0,0 point at the point 33. These times correspond to particular events designated as t a , t m , t mc  and t i . The time, t a , corresponds to the time at which the target vehicle 10 detects the pursuing vehicle 11; it is called the alertment time. The time, t m , represents the beginning of an evasive maneuver; the time, t mc , the end of that evasive maneuver; the time, t i , the intercept time. The evasive maneuver can be defined as a fixed radius turn having a radius, r c , and an angle, θ cm . After the target vehicle 10 completes an evasive maneuver, it is assumed that the target vehicle continues along a straight line, S ca , to an intercept time, t i . The distance from the end of the maneuver to the intercept is L m . Thus the change in positions from t o  to t a  along an X axis perpendicular to and across the line of sight represented by the range vector 30 is -S c  t a  sin(A); along the Y axis in the line of sight axis, the change is -S c  t a  cos(A). The position change between the alertment time, t a , and the beginning of the evasive maneuver at t m  can be defined as -S c  (t m  -t a )sin(A) across the line of sight and -S c  (t m  -t a )cos(A) along the line of sight. The evasive maneuver from t m  to t mc  can be defined in terms of the radius, r c , and the angle, θ c , as r c  cos(A)-r c  cos(A-θ c ) across the line of sight and -r c  sin(A)+r c  sin(A-θ c ) along the line of sight. The change in position from the end of the evasive maneuver to the intercept are given by -L m  sin(A-θ c ) and -L m  cos(A-θ c ) respectively across and along the line of sight. 
     Given these incremental definitions, the generic model path 21&#39; in FIG. 2 for a target vehicle 10 is: 
     
         ΣX.sub.c =-S.sub.c t.sub.a sin (A)-S.sub.c (t.sub.m -t.sub.a) sin (A)+r.sub.c cos (A)-r.sub.c cos (A-θ.sub.c)-L.sub.m sin (A-θ.sub.c)                                         (1) 
    
     and 
     
         ΣY.sub.c =-S.sub.c t.sub.a cos (A)-S.sub.c (t.sub.m -t.sub.a) cos (A)-r.sub.c sin (A)+r.sub.c sin (A-θ.sub.c)-L.sub.m cos (A-θ.sub.c)                                         (2) 
    
     where for 
     
         t.sub.i &gt;t.sub.mc :L.sub.m =S.sub.ca (t.sub.i -t.sub.mc) and θ.sub.c =θ.sub.cm 
    
     and where for 
     
         t.sub.i ≦t.sub.mc :L.sub.m =0 and θ.sub.c =θ.sub.cdot (t.sub.i -t.sub.m) 
    
     FIG. 3 depicts a generic trajectory 14&#39; for the pursuing vehicle 11. It depicts point 18 as the alertment time, t a , and point 26 as the time of intercept, t i . Assuming that the axis 32 of the launching vehicle 12 is vertical in FIG. 3, the range vector 30 to the target has a bearing B relative to that axis 32. Point 33 in FIGS. 1 and 3 indicates the position of the launching vehicle 12 at the time of launch. In FIG. 3 the distances P 0  and P n  define offsets to the center of the torpedo from the reference point of the launching vehicle 12. Segment 34 represents the initial trajectory of the pursuing vehicle 11 for a distance, R g , along an angle, B g , relative to the axis of the launching vehicle. These relationships establish initial launch parameters that co-ordinate the position of the pursuing vehicle at the start of the gyro turn at point 15 in FIGS. 1 and 3; the parameters are: (1) P 0  sin(B)-P n  cos(B)+R g  sin(B-Bg) across the line of sight, and (2) P 0  cos(B)+P n  sin(B)+R g  cos(B-Bg) parallel to the line of sight. An analysis of the remainder of the generic path 14&#39; shows that the path can be defined by X p  and Y p  as follows: 
     and ##EQU1## where r p  and θ p  represent the radius and included angle of the gyro turn from point 15 to point 16. In these equations, t d  represents the time at the dive point 23 and t c  the time at the enable point 25. L 0  represents a distance characteristic of a sensory system, such as an acoustic seeker on a torpedo, and L a  represents an acoustic offset distance or guidance distance. D r  represents a drift rate for the torpedo. 
     The target vehicle intercept unit 40 shown in FIG. 4 includes a target vehicle position system 41 that implements position equations (1) and (2) and a pursuing vehicle position system 42 that implements equations (3) and (4). Each system includes equipment, not shown but known in the art, for providing particular parameters, such as the turning radius, r c , evasion angle, θ cm , and rate of turn, θ cdot , shown in FIG. 2. Thus a target vehicle position system 41 generates a representation of an evading target characteristic trajectory based upon the generic model shown in FIG. 2, estimations of the target vehicle state, known characteristics of that target vehicle 10 and estimations of particular maneuvers. Likewise the pursuing vehicle model 44 uses the pursuing vehicle position system 42 to produce a representation of the pursuing vehicle characteristic trajectory based upon known characteristics of the pursuing vehicle 11. 
     The range, R a , between point 18 and point 20 in FIG. 1 at the time of alertment t a  constitutes a target vehicle detection range at alertment. Stored information about the target vehicle typically provides the alertment range to the unit 40. Alternatively, an operator can enter the alertment range. In FIG. 4, the source of that range is an alertment parameter unit 45. 
     This alertment range constrains the computed range between the target vehicle and pursuing vehicle to be equal to the contact detection range at alertment. Using pre-alertment contact target vehicle and pursuing vehicle trajectory components along the line of sight and across the line of sight as defined by the range vector 30, propagate-to-alertment systems 46 and 47 in the target vehicle model 43 and pursuing vehicle model 44, respectively, provide information to a compute-range-at-alertment system 48 that acts in response to: ##EQU2## 
     An error system 50 includes an error unit 51 that, as will become apparent, produces the alertment range error at alertment. 
     Another error unit 52 produces positional errors with respect to the target vehicle and pursuing vehicle positions across and along the line of sight at intercept. These signals are provided by a propagate-to-intercept system 53 in the target vehicle model 43 and a propagate-to-intercept system 54 in the target vehicle model 44. More specifically, the positional errors in the X and Y directions at intercept result from equating target vehicle and pursuing vehicle components as follows: ##EQU3## By inspection of FIGS. 1 through 3 the following relationships exist: 
     
         t.sub.m =t.sub.a +t.sub.st 
    
     
         t.sub.mc =t.sub.a +t.sub.st +r.sub.c (θ.sub.cm)/S.sub.ct 
    
     
         t.sub.pc = R.sub.g +r.sub.p (θ.sub.p)!/S.sub.pt 
    
     
         t.sub.p =R.sub.g /S.sub.pt 
    
     
         t.sub.srch =L.sub.0 /S.sub.ps 
    
     
         t.sub.e -t.sub.d =L.sub.d /S.sub.pd 
    
     
         t.sub.dive =L.sub.d /S.sub.pd 
    
     
         L.sub.xr =P.sub.0 sin (B)-P.sub.n cos (B)+R.sub.g sin (B-Bg) 
    
     
         L.sub.xc =r.sub.c cos (A)-S.sub.c t.sub.st sin (A) 
    
     
         L.sub.yr =P.sub.0 cos (B)+P.sub.n sin (B)+R.sub.g cos (B-Bg) 
    
     
         L.sub.yc =R.sub.c -r.sub.c sin (A)-S.sub.c t.sub.st cos (A) 
    
     
         B.sub.1 =(B-Bg) 
    
     
         B.sub.2 =(L.sub.0 /S.sub.ps +L.sub.d /S.sub.pd) 
    
     t m  =t a  +t st  where t st  represents the reaction time of the target vehicle between alertment and the beginning of an evasive maneuver, 
     t mc  =t a  +t st  +r c  (θ cm )/S ct  where S ct  represents speed of the target vehicle during the evasive turn, 
     t pc  = R g  +r p  (θ p )!/S pt  where S pt  equals the speed of the pursuing vehicle during the gyro turn, 
     t p  =R g  /S pt  where S pt  is also the speed with which the pursuing vehicle 11 leaves the launching vehicle 12, 
     t srch  =L 0  /S ps  where L 0  represents the seeker offset distance and S ps  equals the speed of the pursuing vehicle in a search phase, 
     t dive  =L d  /S pd  where L d  is the distance from point 23 to point 24 in FIG. 1, 
     t e  -t d  =(L d )/S pd  where L d  represents the distance travelled by the pursuing vehicle during a dive phase and S pd  represents the speed of the pursuing vehicle during the dive. 
     Substituting these relationships in equations (6) and (7) yields: ##EQU4## 
     It is possible to define the time, t e , to turn on an acoustic seeker or other instrumentation or feature in two ways, either (1) the time to travel a fixed turn-on distance, L sto , from the launch point or (2) as a time to travel a fixed seeker offset distance, L o . If L sto  is selected, then ##EQU5## 
     Likewise substituting the foregoing relationships in equation (5) yields an alertment range error defined by: ##EQU6## 
     The evading target vehicle intercept unit 40 operates in accordance with equations (8), (9) and (12) to generate control updates required to converge to an intercept solution. As previously indicated, these equations are not readily solved because they are transcendental in nature and do not lend themselves to a solution in a closed form. In accordance with this invention, however, initial estimates of operating parameter solutions that characterize a particular trajectory of the pursuing vehicle based upon defined interactions of the representations of the pursuing vehicle and target vehicle trajectories can be produced. Then iterative processing provides successive operating parameter solutions that converge to provide a set of guidance parameters for the pursuing vehicle. In accordance with this invention, the guidance parameters are generated from the numerical solution that exhibits particularly rapid convergence characteristics and accurate estimates. 
     Expressing equations (8), (9) and (12) as general functions of the problem unknowns and performing a Taylor series expansion yields: ##EQU7## 
     Neglecting the higher order terms, the solution for this linear set of three expressions with three unknowns is: ##EQU8## where e i , f i  and g i  are given by equations (8), (9) and (12) respectively. The partial derivatives in equations (18) through (21) are: ##EQU9## and for t i  &gt;t mc  : L m  =S ca  (t i  -t a  -t st  -r c  (θ cm )/S ct ); ∂L m  /∂t a  =-S ca  and ∂θ c  /∂t a  =0 
     t i  ≦t mc  : L m  =0; ∂L m  /∂t a  =0 and ∂θ c  /∂t a  =-θ c  dot 
     and when 
     L sto  is selected: t e  =(L sto  -L d )/S p  +L d  /S pd  ; ∂t c  /∂t i  =0 
     L sto  not selected: t e  =t i  -L o  /S ps  ; ∂t e  /∂t i  =1 
     FIG. 5 depicts an operation of the evading target vehicle intercept unit 40 shown in FIG. 4 particularly adapted for applications in which both the launching and target vehicles are submarines and the pursuing vehicle is a torpedo. In this application, primary guidance parameters to be transferred to the torpedo prior to launch include an initial gyro angle, and the distance from the torpedo launch point 32 in FIG. 1 and the point 25 at which the acoustic seeker is enabled, commonly the run to enable. The launching vessel determines the range, bearing, course and speed of the target ship and normally can classify the target ship based on prior historical information to obtain estimates of other information such as the alertment range, R a , the typical turn rate, θ cdot , radius, r c , at which the target vessel can turn during an evasive maneuver, and the reaction time, or time delay, between alertment and the beginning of an evasive maneuver. For a given tactical situation it also is possible to define particular parameters of the torpedo itself. Consequently in step 60 of FIG. 5 the evading target vehicle intercept unit 40 of FIG. 4 responds to the foregoing and other parameters to select appropriate position equations from the target vehicle position system 41 and the pursuing vehicle position system 42. 
     The evading target vehicle intercept unit 40 in FIG. 4 then uses the various equations, as previously indicated, to obtain the gyro angle and the run to enable by iteratively processing a series of equations until values of the gyro angle, alertment time and intercept time converge. In FIG. 5 step 61 represents the selection of initial or estimated values of alertment time, t a , intercept time, t i , and initial gyro angle, θ p . In step 62 the unit 40 in FIG. 4 calculates the time for completion of the target ship maneuver, t mc , by summing the maneuver start time, t m , and the time to complete the selected evasive maneuver obtained by dividing the maneuver included angle, θ cm , by the predicted angular turn rate, θ cdot . In step 63 the unit 40 determines whether the intercept will occur after an evasive maneuver is complete. If it will, the unit 40 calculates a value, L m , that is the distance from the end of the target ship maneuver to the intercept point based upon the speed of the target vessel after the maneuver is complete, S ca , the time interval between the termination of the maneuver, t mc , and the time to the intercept point, t i . Specifically in step 64, the process determines a value for L m  as follows: 
     
         L.sub.m =S.sub.ca (t.sub.i -t.sub.mc)                      (33) 
    
     The target ship turn angle, θ c , is also set to the estimated target evasive maneuver angle, θ cm , for the selected evasive maneuver. 
     If, on the other hand, the intercept will occur during the evasive maneuver, the distance from the end of maneuver to the intercept point, L m , must be zero and the actual target maneuver angle, θ c , will depend upon characteristic contact turn rate, θ cdot , for the target over the interval that expires between the beginning of the maneuver, t m , and the intercept point, t i . Specifically, in step 65, as previously stated, for example 
     
         L.sub.m =0                                                 (34) 
    
     
         θ.sub.c =θ.sub.cdot (t.sub.i -t.sub.m)         (35) 
    
     As previously stated, it is often possible to determine the time at which an acoustic seeker turns on by one of two methods. If, in step 66, the unit 40 determines that a fixed run distance from launch to seeker turn on, or that L sto  is not selected, step 66 diverts to step 67 whereupon the unit 40 in FIG. 4 determines the turn on time, t c , as a function of the intercept time minus a search time, t srch , that is one of the input parameters provided in step 60. Specifically: 
     
         t.sub.e =t.sub.i -t.sub.srch                               (36) 
    
     This time is based upon the seeker offset distance of a pursuing vehicle with an acoustic seeker or corresponding parameter of another device. If, on the other hand, it is desired to turn on the acoustic homing device a predetermined distance after launch, step 66 diverts to step 70 that defines the turn-on time as a function of the distance travelled from launch to dive point (L sto  -L d ), the distance travelled by the torpedo during any dive phase, L d , the speed of the torpedo, S p , and the time required for any diving maneuvers, t dive . Specifically: ##EQU10## 
     Next the unit 40 in FIG. 4 executes step 71 thereby to calculate equations (8), (9) and (12) as the general functions of problem unknowns. The unit 40 determines the values of the partials using equations (22) through (32) to solve for the problem unknowns in step 72. Next the unit 40 uses equations (18), (19), (20) and (21) to solve for errors as delta values, Δt a , Δt i  and Δθ p  in step 73. In this particular embodiment there must be coincident convergence for each of the alertment time, intercept time and gyro angle values. If convergence has not been reached, step 75 uses the new estimates of the problem unknowns and operation transfers back to step 62 to begin another iteration. When convergence has been achieved, step 75 diverts to step 76 representing the determination and transfer of guidance parameters to the torpedo, particularly the gyro angle, θ p , and run-to-enable. 
     FIGS. 6 through 9 demonstrate the process in quantitative terms. In this particular example it is assumed that the target vessel will, at a fixed time after alertment, make a 180° turn to port to reverse course. When the corresponding models of the target vessel and torpedo were utilized in accordance with this invention together with appropriate other parameters, the first iteration of the process shown in FIG. 5 used assumed values of -60° for gyro angle, 30 seconds for alertment time, and 200 seconds for intercept time, as shown in FIGS. 7 through 9. At the end of the iteration, however, these numbers changed by decreasing the gyro angle to -88.74°, increasing the alertment time to 157.46 seconds and increasing the intercept time to 299.05 seconds. Convergence was not obtained. During the next iteration, each of the gyro angle, alertment time and intercept time values increased. In a third iteration, each of the values again increased, but at a reduced rate. On the fourth iteration the convergence criteria were reached. Thus it will be apparent that reasonable convergence was reached even after two iterations in this particular example. However even with four or more iterations, the control unit 40 provides the guidance parameters within a very short interval so that any delays do not affect the solution due to any change in relationships while the information is being determined. 
     When the resulting gyro angle and run-to-enable times were included as the guidance parameters for the given torpedo, a plot in FIG. 6 shows that a torpedo is fired along the line 14. Shortly after the alertment time shown at points 18 and 20, the target vessel begins its evasive turning maneuver at point 22. When the torpedo reaches point 25, the acoustic seeker activates to produce the response area 80 that eventually circumscribes the target vessel at the intercept point 26 as shown by the fan-like shape 81. 
     It has been found therefore that the process shown in FIG. 5 as implemented in the evading target vehicle unit 40 in FIG. 4 can reach convergence and can produce valid guidance information for the torpedo in a short interval. This invention also enables the consideration of solutions for a pursuing vehicle that undergoes multiple speed changes, depth changes and drifts and has different sensor activation criteria. More importantly, however, the system also accounts for the responses of a target vehicle to the presence of a pursuing vehicle, such as a torpedo, reaction times and various evasion strategies that might be utilized. Thus the invention allows the generation of initial guidance parameters for transfer to a pursuing vehicle based upon predicted evasive tactics by a target vehicle. This facilitates the effectiveness of firing a torpedo without post-launch guidance. It will also be apparent that, while not disclosed with any specificity, the specific processes for performing the specific operations of this invention could be performed on general purpose computers, or on one or more special purpose computers that could be substituted for each of the systems shown in FIG. 4. Dedicated hardware and software might also be combined to perform the function of each system in FIG. 4. 
     This invention has been disclosed in terms of certain embodiments. It will be apparent that many modifications can be made to the disclosed organization of apparatus and method without departing from the invention. Therefore, it is the intent of the appended claims to cover all such variations and modifications as come within the true spirit and scope of this invention.