Patent Publication Number: US-8115148-B1

Title: Method for targeting a preferred object within a group of decoys

Description:
BACKGROUND OF THE INVENTION 
     Current threats in the art of hostile ballistic missiles include the deployment of decoys to make it difficult to identify the preferred object (the object targeted for intercept). The decoy objects for the most part travel in a ballistic manner along paths similar to those of the preferred object. The deployment method may result in mutual separation of the decoy objects from each other and from the preferred object, possibly with high speed. The decoy objects may include booster housing(s), ejected shrouds, metal-surfaced balloons inflated after reaching ballistic operation, including large balloons enclosing the preferred object, a booster of boosters, an attitude control module (acm) and various other objects. “Busing” is used with some missiles, whereby a single boost vehicle carries multiple preferred objects, in which case each preferred object may be viewed as being a decoy as to the other preferred object. 
     Defense against ballistic missiles includes the use of interceptor missiles fitted with explosive warheads or with kinetic kill vehicles. Targeting is accomplished by guiding the interceptor toward the spatially derived guidance point of the group or cluster of ballistic objects, including both the decoy(s) and the preferred object. A determination is made of which of the objects of the cluster is the preferred object, and the guidance system of the interceptor is then activated, and guides the interceptor toward the preferred object. Ideally, the guidance of the interceptor toward a spatially derived guidance point (a point chosen based on the relative geometry between the objects in the group) of the projected group of objects makes it possible for engagement of the preferred object by diversion of the interceptor during a final stage of guidance. That is, the spatially derived guidance point of the projected group is deemed to be the best location from which to divert when the interceptor final guidance is initiated. 
     Improved targeting is desired. 
     SUMMARY OF THE INVENTION 
     A method according to an aspect of the invention is for targeting, with an interceptor, a preferred object from among a plurality of ballistic objects in an associated group of objects. The method comprises the step of sensing a group of potential target objects which includes a preferred object and an associated group of non-preferred objects, to thereby produce position and velocity vectors for each potential target object of the group. From the position and velocity vectors for each potential target object of the group, at least one of specific energy and specific angular momentum is computed for each of the potential target objects, to thereby produce constants of orbital motion. From the constants of orbital motion, the three target objects exhibiting the specific energy or specific angular momentum above a threshold value are identified, to thereby identify a group of three most likely target objects. The threshold value is a user-defined design parameter, chosen so that three of the target objects have specific energy or specific angular momentum above the threshold. The spatially derived guidance point is calculated of the group of three most likely target objects. The spatial rate of change of the constants of orbital motion is calculated, to thereby produce a guidance direction increment. The spatially derived guidance point is combined with the guidance direction increment, to thereby produce a target or guide point. The target or guide point is expected to be closer to the location of the preferred object than is the spatially derived guidance point. The thrust of the interceptor is controlled to guide the interceptor vehicle toward the target or guide point. 
     In a particular mode of the method, after the step of controlling the thrust of the interceptor toward the target point, a determination is made of which of the potential target objects is the preferred object, and control of the interceptor is transitioned to guidance toward the preferred object. 
     An engagement system according to an aspect of the invention is for targeting and engaging a preferred object among a group of non-preferred objects. The system comprises at least one sensor ( 312 ) for sensing a group of potential target objects (preferred object, acm, B,  315 ) which includes a preferred object and an associated group of non-preferred objects, to thereby produce position and velocity vectors for each potential target object. The system also comprises a computer arrangement, which may be a single computer or a distributed computer, and which may include modules for performing specific tasks or an integrated software entity for performing multiple specific tasks. The computer includes at least an aspect for computing, from the position and velocity vectors, at least one of specific energy and specific angular momentum for each of the potential target objects, to thereby produce constants of orbital motion. A computer or ranking aspect thereof ranks the constants of orbital motion for each of the potential target objects, and deems the three target objects having values above a threshold (of the one of the specific energy and specific angular momentum) as identifying a group of the three most likely target objects. A computer or spatially derived guidance point aspect thereof calculates the spatially derived guidance point of the group of three most likely target objects, and calculates the spatial rate of change of the constants of orbital motion, to thereby produce a guidance direction increment. A computer or combining aspect thereof combines the spatially derived guidance point with the guidance direction increment, to thereby produce an interceptor vehicle target point which is closer to the location of the preferred object than is the spatially derived guidance point. A controllable thrust controller is coupled to receive the interceptor vehicle target point, and is also coupled to the interceptor vehicle, for controlling the thrust of the interceptor vehicle to guide the interceptor vehicle toward the target point. In a particularly advantageous aspect of the system, a computer or identification aspect thereof is coupled for receiving at least the constants of orbital motion, for determining which of the potential target objects is the preferred object, and for generating a command for a transition from guidance toward the target point to guidance toward the preferred object. A computer or aspect thereof is coupled to the interceptor vehicle and to receive the command for transition from guidance toward the target point to guidance toward the preferred object, and effectuates the transition from guidance toward the target point to guidance toward the preferred object. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
         FIG. 1  illustrates an orbit and various vectors to aid in explanation of constants of orbital motion; 
         FIG. 2A  represents a scenario in which a multipartite hostile missile is launched, illustrating various portions of the orbits of the parts,  FIG. 2B  illustrates an ellipse for defining terms, and  FIG. 2C  illustrates the orbital trajectories underlying  FIG. 2A ; 
         FIG. 3  illustrates additional aspects of the scenario of  FIG. 2A , and in which the interceptor missile is guided toward the spatially derived guidance point of a triangle defined by the three principal separated components of the hostile missile, and which also illustrates a specific energy derived guidance point; 
         FIG. 4  illustrates a scenario similar to that of  FIG. 3 , with additional vectors explaining aspects of the invention; 
         FIG. 5  represents a three-dimensional C coordinate frame or space defined by C 1 , C 2 , and C 3  dimensions, in which the preferred object, the attitude control module, and the booster lie in the C 1 -C 2  plane, and further showing a specific energy space; 
         FIG. 6  illustrates a specific energy gradient about the spatially derived guidance point to aid in shifting the interceptor aim point; 
         FIG. 7  illustrates geometry associated with  FIG. 6  for aiding in determining the new aim or guide point prior to final guidance of the interceptor toward the target; and 
         FIG. 8  is a simplified logic or control flow chart or diagram illustrating the method of the invention. 
     
    
    
     DESCRIPTION OF THE INVENTION 
     The “guide” point toward which the interceptor is guided is chosen so as to contain the preferred object (po) within the divert capability of the interceptor. This can be important because the objects of the ballistic group or cluster may diverge at a rate which does not allow all of them to be contained using the prior-art spatially derived guidance point method. It should be noted that the spatially derived guidance point lies in a plane which contains those three objects of a group having specific energy or specific angular momentum above a threshold value. According to an aspect of the invention, the interceptor aim, guide, or target point before terminal guidance begins is shifted or deviated away from the spatially derived guidance point and toward the preferred object. This allows containment of those objects likely to be the preferred object within the interceptor divert capability. The shifting or deviation of the guide or target point is based on orbital parameters of the objects. The specific orbital parameter which can be used is one of (a) specific energy and (b) specific angular momentum. 
     It has been found that specific energy derived guidance point is slightly closer to the preferred object than the spatially derived guidance point of the three objects having specific energy or angular momentum above a threshold value. The specific energy gradient within the plane formed by the objects of the group is in the form of a vector. The vector points in a direction close to the preferred object, or in other words points generally “at” or “toward” the preferred object from the spatially derived guidance point. Shifting of the guide point of the interceptor in the direction indicated by the gradient vector tends to allow containment of the preferred object and other probable objects within the divert capability for a longer period of time than when a simple spatially derived guidance point is used. This additional time allows more time in which to perform the sensing and computations to identify the preferred object. 
       FIG. 1  illustrates constants of orbital motion. The constants of orbital motion can be used to differentiate among objects based on their motion. In  FIG. 1 , the gravitational center  12  of the Earth  10  is centered on X and Y coordinates. The radius R e  of the Earth is indicated. An object, in the form of a hostile missile  14 , is illustrated as having followed a boost and ballistic path illustrated by a dash line  16 , and currently lies at a radius {right arrow over (r)}. A local horizon orthogonal to radius {right arrow over (r)} {right arrow over (r)} is a plane indicated as line  18 . The velocity vector of the missile  14  is identified as {right arrow over (V)}, and is at an angle φ relative to local horizon  18 . The specific energy E of the object  14  of  FIG. 1  can be expressed as 
                   E   =         v   2     2     -       μ   e     r               (   1   )               
where μ e =3.986×10 14 .
 
               m   3       s   2           
The angular momentum H of the object  14  can be expressed as
 
 H=|{right arrow over (r)}×{right arrow over (V)}|=rV  cos φ  (2)
 
In general, E and H determine the properties of a ballistic trajectory including maximum orbital radius and orbital distance normal to the major axis of the orbital ellipse.
 
       FIG. 2A  is a simplified representation of trajectories of missile  14 , its deployed preferred object po and some “decoy” objects, together defining a group or cluster  208  of objects. Elements of  FIG. 2A  corresponding to those of  FIG. 1  are designated by like alphanumerics. The decoy objects which are illustrated in  FIG. 2A  are the attitude control module (acm) and the booster B. Group  208  of objects may include other objects, but only the three objects having specific energy or angular momentum above a threshold value are considered. The specific energy of each object is calculated according to equation (1), and the three objects having specific energy (or angular momentum) above a threshold value are considered. Consideration of the three objects having specific energy above a threshold value is accomplished by ranking the values of specific energy of the objects. This method allows for targeting of the object most likely to be the preferred object, but also allows the possibility of targeting another object, which has some probability of being the preferred object. In  FIG. 2A , the horizon is illustrated as  210 , and a body of water as  212 . A first land mass  214  represents the location from which the hostile missile  14  is launched, as suggested by dash line portion  218 . The ultimate target of hostile missile  14  is a friendly land mass designated  216 . As illustrated at position  1  in  FIG. 2A , missile  14  includes a preferred object, an attitude control module acm, and a booster B. 
       FIG. 2B  illustrates an orbital ellipse  206 . In  FIG. 2B , F 1  and F 2  represent first and second focal points lying on the major axis  204  at distance c from the center  212  of the ellipse  206 . The semi-major axis is designated a, so the major axis has dimension  2   a . The semi-minor axis is designated b, so the minor axis has dimension  2   b . An object  14  is illustrated as orbiting along ellipse  206  at a radius R from F 1 , which radius makes an angle τ with the major axis.  FIG. 2C  represents the orbits of the various objects of  FIG. 2A , namely the booster B, the attitude control module (acm), and the preferred object po as superposed on the Earth  10 . In  FIG. 2C , the Earth&#39;s center is designated  12  and also as F 1 . The booster trajectory is designated  220 , the preferred object trajectory is designated  224 , and the acm trajectory is designated  226 . The hostile missile or target  14  launch point is designated  203 . The largest orbital radius from the center of the Earth reached by the booster along trajectory  220  is designated R max  booster and is measured from the focal point F 1 . The largest orbital radius reached by the acm along trajectory  226  is designated R max  acm and is also measured from the focal point F 1 . The largest orbital radius reached by the preferred object po along trajectory  224  is designated R max  po and is also measured from the focal point F 1 . 
     At a time after launch of missile  14  of  FIG. 1 , the booster B separates from the preferred object and attitude control module acm, and follows a path illustrated as dash line segment  220  in  FIG. 2A , while the conjoined preferred object/acm follows a path suggested by solid-line segment  222 . At a position illustrated as  2  in  FIG. 2A , the preferred object po separates from the acm. The preferred object follows solid-line segment  224  toward its destination, while the acm follows a dash line segment  226 . There may be some atmosphere at ballistic missile orbital altitudes, and the differences between or among the paths of the objects is attributable at least in part to frictional or retarding effects of this atmosphere. 
     In  FIG. 2A , the gravitational center of the Earth  12  is also designated F 1 , representing the first focus of the elliptical paths taken by the preferred object, the attitude control module acm, and the booster B. The second focus of the elliptical path taken by the booster B is designated F 2  booster. The major axis of the orbital ellipse for the booster B lies along the line extending between F 1  and F 2 B. The second focus of the elliptical path taken by attitude control module acm is designated F 2  acm, and the major axis of the orbital ellipse for the acm lies along the line extending between F 1  and F 2  acm. The second focus of the elliptical path taken by the preferred object is designated F 2 po, and the major axis of the orbital ellipse for the preferred object lies along the line extending between F 1  and F 2 po. 
     The maximum orbital radius R max  of an orbiting object travelling on an elliptical trajectory is given by
 
 R   M   =a (1+ε)  (3)
 
where:
 
     a is the semi-major axis of the ellipse; and 
     ε is the eccentricity of the ellipse. 
     The semi-major axis a of the ellipse is given by 
                   a   =       -     μ   e         2   ⁢   E               (   4   )               
where:
 
     μ e  is the Earth&#39;s gravitational constant (equal to) 
             3.986   ×     10   14     ⁢       Meters   3       Second   2             
; and
 
     E is the specific energy. 
     The eccentricity ε of the ellipse is given by 
                   ɛ   =         1   +     2   ⁢     EH   2           μ   e   2                 (   5   )               
Equation (3), as it applies to  FIG. 2A , shows that the maximum orbital radius, or the maximum height above the Earth&#39;s surface achieved by an orbiting object depends on the specific energy of the object.
 
     The orbital distance normal to the major axis at second focus F 2  of an orbital ellipse is known as the semilatus rectum and is designated p. The semilatus rectum is illustrated in  FIG. 2B  and represents the distance traveled by the object normal to the major axis of the orbital ellipse. The semilatus rectum of the booster in  FIGS. 2A and 2C  is designated p booster or pB, the semilatus rectum of the attitude control module in  FIGS. 2A and 2C  is designated p acm, and the semilatus rectum of the preferred object in  FIGS. 2A and 2C  is designated p_po. The value of p can be calculated as 
                   p   =       H   2       μ   e               (   6   )               
where:
 
     H is the specific angular momentum of the object as calculated in Equation (2); and 
     μ e  is the Earth&#39;s gravitational constant as described above. 
       FIG. 3  is a representation of various geometrical relationships which are found in a scenario  300  in which a hostile missile  14  is launched from a location  305  and which conceals the identity of the preferred object with an attitude control module (acm) and spent booster (B), and in which the interceptor missile is guided toward a spatially derived guidance point  322 . Elements of  FIG. 3  corresponding to those of  FIG. 2  are designated by like alphanumerics.  FIG. 3  also illustrates a ship  310  which senses the missile  14  in the boost phase, as suggested by “lightning bolt” symbol  312 . In  FIG. 3 , the hostile missile  14  boosts along path  218 , and the boosting results in a cloud of debris designated  314 . Ultimately, the booster takes a path  220 , and at a given time arrives at a location illustrated by a booster circle  303 . In the same manner, the acm follows a path  226  and arrives at the given time at a location illustrated as an acm circle  302 . The group of objects including the preferred object po, the acm, and the booster, together with other debris  314 , is designated  315 . The preferred object po follows path  224  and at the given time arrives at a preferred object location illustrated as  301 . Locations  301 ,  302 , and  303  define the vertices or corners of a triangle designated generally as  320  and defined by sides  320   1 ,  320   2 , and  320   3 . Side  320   1  of the triangle  320  extends from the location  301  of preferred object po to the location  302  of attitude control module acm. Side  320   2  of triangle  320  extends from the preferred object location  301  to the location  303  of booster B, and side  320   3  extends from acm location  302  to the booster location  303 . The range from the ship  310  to booster location  303  is designated {right arrow over (r)} b , the range to acm location  302  is designated {right arrow over (r)} acm , and the range to preferred object location  301  is designated {right arrow over (r)} po . 
     An interceptor missile  330  of  FIG. 3  launched as a counter to a hostile ballistic missile such as  14  must be guided, either remotely or locally, toward its target along a path such as path  332  until such time as the preferred object is identified from among the various decoy objects in the group. The guidance of the interceptor missile may often be remote until the autonomous seeker “locks onto” the preferred object object, which by that time is known. In the prior art, the interceptor missile was guided toward the spatially derived guidance point of the group of three principal objects until the preferred object was identified. A representative spatially derived guidance point location is designated  322  in  FIG. 3 . This method of guidance was not without faults, as, in order to effect an intercept of the preferred object, the interceptor missile would ordinarily have to be able to divert its path. In some cases, by the time the preferred object was identified from among the other objects, insufficient divert capability was available for intercepting the preferred object. 
     The spatially derived guidance point  322  of triangle  320  of  FIG. 3  is designated {right arrow over (r)} c  and given by 
                       r   -&gt;     c     =       1   N     ⁢       ∑     i   =   1     N     ⁢           ⁢       r   -&gt;     i                 (   7   )               
where:
 
     N represents the number of objects; 
     {right arrow over (r)} a position vector of the i th  object; and 
     i is an index representing the i th  object. 
     The specific energy of a ballistic object is designated as E and defined in equation (1). The specific energy of a group of N objects is defined by 
                   E   =       ∑     i   =   1     N     ⁢           ⁢     E   i               (   8   )               
and the specific energy derived guidance point is given by
 
                       r   →     E     =       1   E     ⁢       ∑     i   =   1     N     ⁢           ⁢         r   →     i     ⁢     E   i                   (   9   )               
A representative specific energy derived guidance point {right arrow over (r)} E  is designated  324  in  FIG. 3 . The specific energy derived guidance point is closer to the location of the preferred object than the spatially derived guidance point. It has been found, however, that this difference in guidance point location is not a sensitive indicator of the actual preferred object location, and it was found that targeting the specific energy derived guidance point with the interceptor missile before final guidance gave little improvement.
 
       FIG. 3  illustrates as an arrow  360  the specific energy gradient associated with triangle  320 . It has been found that the gradient of the specific energy points generally in the direction of the preferred object. That being so, targeting the interceptor missile toward the spatially (or specific energy) derived guidance point modified by the gradient of the specific energy provides improved performance, in that the targeting point tends to be closer to the location of the preferred object than the unmodified spatially (or specific energy) derived guidance point  322  (or  324 ). Since the targeting point as modified by the gradient of the specific energy ends up closer to the actual location of the preferred object, there is a greater likelihood that the divert capability of the interceptor missile will be adequate to intercept the hostile missile. 
       FIG. 4  is generally similar to  FIG. 3 , but shows additional geometric information useful in understanding aspects of the invention. Elements of  FIG. 4  corresponding to those of  FIG. 3  are designated by like reference alphanumerics. In  FIG. 4 , the coordinate frame is based at the spatially derived guidance point  322 . A vector extending between the Earth&#39;s center of gravity  12  and the location  301  of preferred object is designated {right arrow over (r)} po , a vector extending from center  12  to the location  302  of attitude control module acm is designated {right arrow over (r)} ACM , and a vector extending from center  12  to the location  303  of booster B is designated {right arrow over (r)} B . A vector extending between the Earth&#39;s center  12  and the location of the spatially derived guidance point  322  is designated {right arrow over (r)} sp    
     The three objects having specific energy above a threshold value (namely the preferred object, the acm, and booster B) are resolved into a coordinate frame defined by the plane containing the three objects, which plane is suggested by triangle  320  of  FIG. 4 . The coordinate frame is formed based on the position vectors of the three objects and the spatially derived guidance point  322 , defined in the ECEF (Earth-Centered-Earth-Fixed) coordinate frame. Vector ŝ 1  is a unit vector (a vector with a magnitude of one) pointing from the spatially derived guidance point  322  toward one of the objects (illustrated as being the preferred object in the case of  FIG. 4 ), where ŝ 1  is given by 
                       s   ^     1     =           r   →     po     -       r   →     sp                  r   →     po     -       r   →     sp                      (   10   )               
Vector ŝ 2  is a unit vector pointing from the spatially derived guidance point  322  to another object, illustrated as being the booster.
 
     
       
         
           
             
               
                 
                   
                     
                       s 
                       ^ 
                     
                     2 
                   
                   = 
                   
                     
                       
                         
                           r 
                           → 
                         
                         b 
                       
                       - 
                       
                         
                           r 
                           → 
                         
                         sp 
                       
                     
                     
                        
                       
                         
                           
                             r 
                             → 
                           
                           b 
                         
                         - 
                         
                           
                             r 
                             → 
                           
                           sp 
                         
                       
                        
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     The basis vectors defining the coordinate frame are then formed as follows:
 
 û   1   =ŝ   1   (12)
 
     
       
         
           
             
               
                 
                   
                     
                       u 
                       ^ 
                     
                     3 
                   
                   = 
                   
                     
                       
                         
                           u 
                           ^ 
                         
                         1 
                       
                       × 
                       
                         
                           s 
                           ^ 
                         
                         2 
                       
                     
                     
                        
                       
                         
                           
                             u 
                             ^ 
                           
                           1 
                         
                         × 
                         
                           
                             s 
                             ^ 
                           
                           2 
                         
                       
                        
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       u 
                       ^ 
                     
                     2 
                   
                   = 
                   
                     
                       
                         
                           u 
                           ^ 
                         
                         3 
                       
                       × 
                       
                         
                           u 
                           ^ 
                         
                         1 
                       
                     
                     
                        
                       
                         
                           
                             u 
                             ^ 
                           
                           3 
                         
                         × 
                         
                           
                             u 
                             ^ 
                           
                           1 
                         
                       
                        
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     In  FIG. 4 , basis vectors û 1  and û 2  lie in the plane with the three principal objects (that is, in the plane including triangle  320 ), and basis vector û 3  is normal to the plane. 
       FIG. 5  illustrates a new C coordinate frame with mutually orthogonal axes or dimensions C 1 , C 2 , and C 3 . The C 1  and C 2  axes may be viewed as representing position, and the C 3  axis may be viewed as representing specific energy. The three objects, namely the preferred object po, the attitude control module acm, and the booster B, lie in the C 1 -C 2  plane. The spatially derived guidance point is designated sp. The rotation matrix R ECEF   C  from the ECEF coordinate frame to the new coordinate frame C is:
 
 R   ECEF   C   [û   1   û   2   û   3 ] T   (15)
 
A vector representing each object can now be expressed in a specific energy space defined by the object&#39;s position vector in the C frame and the object&#39;s specific energy. The specific energy space is illustrated in  FIG. 5  by the specific energy plane defined by vectors {right arrow over (q)} 1 , {right arrow over (q)} 2 , and the specific energy space defined by vector {right arrow over (n)}, normal or orthogonal to the specific energy plane. Vectors {right arrow over (q)} 1  and {right arrow over (q)} 2  connect the three objects in the specific energy plane, and vector {right arrow over (n)} is normal or orthogonal to the specific energy plane. Vectors connecting the objects in specific energy space are defined as follows:
 
 {right arrow over (q)}   1   ={right arrow over (x)}   po   C   −{right arrow over (x)}   b   C   (16)
 
 {right arrow over (q)}   2   ={right arrow over (x)}   ACM   C   −{right arrow over (x)}   b   C   (17)
 
The specific energy plane is defined by a vector normal to that plane, calculated as:
 
 {right arrow over (n)}={right arrow over (q)}   1   ×{right arrow over (q)}   2   (18)
 
all of which are illustrated in  FIG. 5 .
 
     Let vector {right arrow over (r)} i   C  be the position vector of the i th  object represented in the C coordinate frame. The vector of the i th  object defined in specific energy space is formed by setting the third element of the position vector, {right arrow over (r)} i   C , equal to the object&#39;s specific energy: 
     
       
         
           
             
               
                 
                   
                     
                       x 
                       → 
                     
                     i 
                     C 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             
                               
                                 r 
                                 → 
                               
                               i 
                               C 
                             
                             ⁡ 
                             
                               ( 
                               1 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 r 
                                 → 
                               
                               i 
                               C 
                             
                             ⁡ 
                             
                               ( 
                               2 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             E 
                             i 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     The specific energy plane can also be expressed in the form:
 
 ax+by+cz+d= 0  (20)
 
Solving for z gives an expression for the specific energy at any point (x,y):
 
                     E   ⁡     (     x   ,   y     )       =     z   =         -   ax     -   by   -   d     c               (   21   )               
The gradient at a point (x,y) gives the direction of the maximum spatial rate of increase of the specific energy. The gradient is calculated as:
 
                       ∇   →     E     ⁢     =           ∂     E   ⁡     (     x   ,   y     )           ∂   x       ⁢     i   ^       +         ∂     E   ⁡     (     x   ,   y     )           ∂   y       ⁢     j   ^                   (   22   )               
A unit vector in the direction of the gradient is given by:
 
                     u   ^     =         ∇   →     E              ∇   →     E                    (   23   )               
where ∥ ∥ denotes the norm of the vector contained within. Evaluation of the specific energy gradient at the spatially derived guidance point gives the direction to shift the aimpoint.
 
     In  FIG. 6 , the triangle  320  in the plane including the preferred object po, the attitude control module acm, and the booster illustrates the spatially derived guidance point  322  and a plurality of arrows indicating the specific energy gradient. A vector {right arrow over (∇)}E indicates the magnitude and direction of the specific energy gradient. 
     The aim point should be shifted from the spatially derived guidance point along the specific energy gradient so as to keep the objects most likely to be the preferred object within the divert capability of the missile. 
       FIG. 7  is a simplified illustration of geometrical considerations which may be used to determine the shifted aim or new guide point  722  from the spatially derived guidance point and vector {right arrow over (∇)}E. In  FIG. 7 , a dotted-line circle  710  represents the divert capability of the interceptor missile centered on the spatially derived guidance point  322 . In this hypothetical situation, it can be seen that the preferred object lies just outside of the divert limit circle  710 . This means that, were the spatially derived guidance point  322  to be used as a guide point before acquisition of the preferred object and final guidance to the target, the interceptor could not “hit” the target. On the other hand, with the center of the divert circle  712  shifted to new guide point  722 , the preferred object lies well within the bounds of the circle  712 , meaning that there the interceptor missile is capable of reaching the target missile. 
       FIG. 8  is a simplified logic or control flow diagram or chart illustrating a method according to an aspect of the invention. In  FIG. 8 , the logic  800  begins at a START block  810 , and flows to a block  812 , which represents detection and tracking of a hostile target. From block  812 , the logic flows to a block  814 , representing the initiation of an engagement, which involves launching an intercepting missile. Upon threat separation (separation of the preferred object from the decoys), the logic flows to block  816 , which represents collecting sensor information relating to the targets, such as target tracks of the various objects. From block  816 , the logic  800  of  FIG. 8  flows to a block  818 , which represents calculation of the specific energy (or angular momentum) of each object in track, as described in conjunction with equations 1 and 2. From block  818 , the logic  800  of  FIG. 8  flows to a block  820 , representing identification of the three most significant objects in the track, which are the three objects having specific energy above a threshold value. The identification is made using equations (1) or (2). From block  820 , the logic flows to a block  822 , which represents the calculation of the spatially derived guidance point, as detailed in conjunction with the description of equation 7. From block  822 , the logic flows to block  824 , which represents calculation of the specific energy gradient {right arrow over (∇)}E, described in conjunction with equations (22) and (23). From block  824 , the logic flows to block  826 , representing the selection of the aim or shifted guide point, which is performed as described in conjunction with  FIGS. 6 and 7 . The guide point is shifted from the spatially derived guidance point, in (parallel to) the direction of the specific energy gradient, until it intersects the line connecting the two objects of specific energy above another threshold value, taken in this case as being the dash line joining the preferred object with the acm. The point labeled “new guide point,” will be the point toward which to guide the intercepting missile. This is illustrated in  FIG. 7  and calculated in Equations 24 and 25: 
                     x   g     =           -     y   1       ⁢     x   2       +       x   1     ⁢     y   2             -     y   1       +     y   2     +     m   ⁡     (       x   1     -     x   2       )                   (   24   )                 y   g   =mx   g   (25)
 
     Where, m is the slope of the specific energy gradient. 
     
       
         
           
             
               
                 
                   m 
                   = 
                   
                     
                       ∇ 
                       
                         E 
                         ⁡ 
                         
                           ( 
                           2 
                           ) 
                         
                       
                     
                     
                       ∇ 
                       
                         E 
                         ⁡ 
                         
                           ( 
                           1 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
     From block  826 , the logic flows to a block  828 , which represents guidance of the interceptor missile toward the shifted aim point. At some time, the preferred object will be identified by known means. The identity of the preferred object will be made known either to the interceptor missile, as by remote identification together with transmission to the interceptor of the identifying information, or by an autonomous seeker in the interceptor missile. At the time the preferred object is identified by or to the interceptor missile, control is transitioned away from guidance of the interceptor missile toward the shifted guide point and to guidance toward the preferred object, as suggested by block  830  of  FIG. 8 . The guidance toward the preferred object after the preferred object has been identified is well known in the art, and requires no further explanation. The logic  800  ends at an END block  832 , and may occur when the interceptor missile hits the target, or may result from determination that a miss has occurred, in which case the warhead, if any, may be disarmed. 
     A method ( 800 ) according to an aspect of the invention is for targeting, with an interceptor ( 330 ), a preferred object from among a plurality of ballistic objects (preferred object, acm, booster,  314 ) in an associated group ( 315 ) of objects. The method comprises the step of sensing ( 312 ,  812 ,  816 ) a group ( 315 ) of potential target objects which includes a preferred object and an associated group of non-preferred objects (acm, B,  314 ), to thereby produce position and velocity vectors for each potential target object of the group. From the position and velocity vectors for each potential target object of the group, at least one of specific energy and specific angular momentum is computed ( 818 ) for each of the potential target objects, to thereby produce constants of orbital motion. From the constants of orbital motion, the three target objects having values of one of the specific energy and specific angular momentum above a threshold value are identified ( 820 ), to thereby identify a group of the three most likely target objects. The spatially derived guidance point ( 322 ) is calculated ( 822 ) of the group of three most likely target objects, using equation (7). The spatial rate of change or gradient ({right arrow over (∇)}E) of the constants of orbital motion is calculated ( 824 ), as described in conjunction with equations (22) and (23). A guidance direction increment (x g ,y g ) is generated ( 826 ), and the spatially derived guidance point ( 322 ) is combined ( 826 ) with the guidance direction increment (x g ,y g ) to thereby produce ( 826 ) a target or guide point ( 722 ) which is closer to the location of the preferred object than is the spatially derived guidance point ( 322 ). The thrust of the interceptor ( 330 ) is controlled to guide the interceptor vehicle toward the target or guide point ( 722 ). In a particular mode of the method, after the step ( 828 ) of controlling the thrust of the interceptor ( 330 ) toward the target or guide point ( 722 ), a determination is made of which of the potential target objects is the preferred object, and control of the interceptor ( 340 ) is transitioned ( 829 ) to guidance ( 830 ) toward the preferred object. 
     An engagement system ( 300 ) according to an aspect of the invention is for targeting and engaging a preferred object among a group of non-preferred objects ( 315 ). The system ( 300 ) comprises at least one sensor ( 312 ) for sensing a group of potential target objects (preferred object, acm, B,  315 ) which includes a preferred object and an associated group ( 314 ) of non-preferred objects, to thereby produce position and velocity vectors for each potential target object. The system ( 300 ) also comprises a computer arrangement ( 399 ), which may be a single computer or a distributed computer, and which may include modules for performing specific tasks or an integrated software entity for performing multiple specific tasks. The computer ( 399 ) includes at least an aspect for computing ( 818 ), from the position and velocity vectors, at least one of specific energy and specific angular momentum for each of the potential target objects, to thereby produce constants of orbital motion. A computer or ranking aspect thereof ( 820 ) ranks the constants of orbital motion for each of the potential target objects, and deems the three target objects having values (of the one of the specific energy and specific angular momentum) above a threshold as identifying a group of the three most likely target objects. A computer or spatially derived guidance point aspect ( 822 ) thereof calculates the spatially derived guidance point of the group of three most likely target objects, and calculates ( 824 ) the spatial rate of change of the constants of orbital motion, to thereby produce ( 826 ) a guidance direction increment. A computer or combining aspect ( 826 ) thereof combines the spatially derived guidance point with the guidance direction increment, to thereby produce an interceptor vehicle target point which is closer to the location of the preferred object than is the spatially derived guidance point. A controllable thrust controller ( 828 ) is coupled to receive the interceptor vehicle target point, and is also coupled to the interceptor vehicle, for controlling the thrust of the interceptor vehicle to guide the interceptor vehicle toward the target point. 
     The combining aspect of the method may include the identification of a particular line extending between the two objects having the values of the constant of orbital motion above a threshold, and identifies the interceptor vehicle target point as the intersection of the particular line with the projection of the spatially derived guidance point parallel with the guidance direction increment. 
     In a particularly advantageous aspect of the system ( 300 ), a computer ( 399 ) or identification aspect thereof is coupled for receiving at least the constants of orbital motion, for determining which of the potential target objects is the preferred object, and for generating a command for a transition ( 829 ) from guidance toward the target point to guidance toward the preferred object ( 830 ). A computer or aspect thereof ( 398 ) is coupled to the interceptor vehicle ( 330 ) and to receive the command for transition from guidance toward the target point to guidance toward the preferred object, and effectuates the transition from guidance toward the target point to guidance toward the preferred object.