Abstract:
A target tracking arrangement predicts the state of a target. The predictor may be a Kalman filter. In the presence of a target which is maneuvering, the prediction may be in error. A maneuver detector is coupled to receive residuals representing the difference between the predictions and the target state. The maneuver detector is matched to the predictor or Kalman filter to thereby tend to reduce the undesirable effects of system noise. The matching may be of the frequency response.

Description:
FIELD OF THE INVENTION 
   This invention relates to automatic target tracking, and more particularly to target maneuver detection in automatic tracking systems. 
   BACKGROUND OF THE INVENTION 
   Automatic tracking systems are widely used for various military and nonmilitary purposes. Among the military purposes are the determination of the locations of airborne, undersea, and seaborne vehicles in a region to be controlled, and the automatic control of weapons directed toward such targets. Air traffic and harbor traffic control are among the civilian or peacetime uses of automatic tracking systems. 
     FIG. 1  is a simplified block diagram of a prior-art target tracking system  10 . In  FIG. 1 , a sensor or sensor array designated  12  observes a region  14  in which one or more targets T are maneuvering. An arrow  16  illustrates the instantaneous velocity of target T. Sensor  12  may be a radar, sonar, or lidar system, a staring optical array, an acoustic system, or any sensor which is capable of sensing information relating to the position and velocity state of the target T. Sensor  12  may include a receiver in some cases. 
   State information from sensor  12  of  FIG. 1  is coupled by a path  18  to a tracker designated generally as  20 . Path  18  may be an electrical, optical or acoustic path, and may carry analog, digital, or other signals. Tracker  20  includes a corrector or estimator  24  which receives difference or residual information from a subtractor or difference signal generator (also known as an error detector)  26 , and which processes the signal to produce a better estimate of the state of the target(s). The predicted state of the target is fed back to the inverting (−) input port of subtraction circuit  26  by way of a predictor (into the future) or propagator illustrated as a block  28 . The predicted state of the target applied to the inverting input port of the subtracting circuit is compared with the actual sensed state applied to the noninverting (+) input port to produce the residual which is applied to the corrector  24 . The corrected state produced by corrector  24  is made available for use, as for example by applying the state information to a display unit  30 . The name generally given to a tracker such as  20  of  FIG. 1  is “Kalman filter”. 
   Those skilled in the art know that predictors such as  28  of  FIG. 1 , and the Kalman filter generally, make certain assumptions about the characteristics of the target. For example, a predictor may operate on the assumption that the target&#39;s current velocity is the velocity which it will have in the future. If such a predictor is used in a situation in which the target accelerates, the prediction of the future state may be in error. Put another way, the target may maneuver by varying speed, direction, and the like, and such maneuvers may adversely affect the predicted state. 
   A maneuver detector illustrated as a block  32  is coupled to receive the residual information from error detector  26  of  FIG. 1 . The purpose of maneuver detector  32  is to declare the presence of maneuvering in the presence of deviation from constant velocity. The output of the maneuver detector  32  is coupled to a utilization apparatus. In the particular case illustrated in  FIG. 1 , the declaration from the maneuver detector  32  is applied by way of a threshold  34  to the display  30  (as an alternative viewpoint, threshold  34  is part of maneuver detector  32 ). If the target is not accelerating, the residual is expected to be zero-mean white noise. In the presence of acceleration, the residuals will develop a bias (an average value greater or less than zero) which is indicative of the amount of acceleration. Various types of maneuver detectors have been used in the prior art. Among the prior-art maneuver detectors are those that average the residuals to determine the presence or absence of a bias. Another prior-art scheme uses inverse exponential weighting of residuals, also known as “fading memory.” The maneuver detector  32  of  FIG. 1 , which is coupled to a threshold illustrated as a block  34 , which determines if the bias exceeds a given level, and thus exceeding the threshold is indicative of a maneuver by the target. The output of the maneuver detector  32  and threshold  34 , if any, is coupled to a utilization apparatus, which may be, for example, display  30 , to advise the operator that the indicated track may not be accurate. 
     FIG. 2  illustrates another prior-art system  200  similar to that of  FIG. 1 , in which the maneuver declaration information generated by maneuver detector  32  and tested by threshold  34  is applied not only to display  30 , but also by way of a path  36  to corrector  24 , so that the tracking parameters of the corrector may be adjusted, generally by loosening the bounds, in the presence of a maneuver. 
   Target tracking with improved or alternative maneuver detection is desired. 
   SUMMARY OF THE INVENTION 
   A method for maneuver detection in a target tracking context includes the steps of generating data relating to the state of a target. This data may include position and velocity, velocity and acceleration, or other derivatives or integrals of position and rate of change of position. The method also includes the step of predicting the state of the target at a selected time by use of a predictor having a known response to an instantaneous change in velocity of the target. The state of the target at the selected time is compared with the predicted state, to thereby generate a residual. The residual is detected and filtered with a detector having a response which is ideally identical to, or which is tuned to, impulse (acceleration) response of the residual. In a particularly advantageous mode of the method, the known impulse response includes a low-pass characteristic and is optimal in a theoretical matched filter sense. 

   
     BRIEF DESCRIPTION OF THE DRAWING 
       FIG. 1  is a simplified block diagram of a prior-art tracking arrangement including a maneuver detector; 
       FIG. 2  is a simplified block diagram of a prior-art tracking arrangement similar to that of  FIG. 1 , in which the output of the maneuver detector is coupled to the corrector; 
       FIG. 3  is a simplified block diagram of a portion of the arrangement of either  FIG. 2  or  FIG. 3 , showing by time plots the position of a target undergoing acceleration and nature of the resulting residuals; 
       FIG. 4  is a flow diagram or chart illustrating some of the steps according to an aspect of the invention for matching the maneuver detector to the characteristics of the predictor or Kalman filter; and 
       FIG. 5  is an amplitude/frequency plot illustrating a low-pass frequency characteristic. 
   

   DESCRIPTION OF THE INVENTION 
   The invention is based upon the understanding that the frequency characteristics of the maneuver detector should match the impulse response of the predictor of the Kalman filter tracking system. A maneuver is declared when the value of the output of the matched-filter maneuver detector exceeds a given value or threshold. 
   In general, the assumption is made for purposes of determining the response of the Kalman filter that the target has been flying with a fixed velocity, and at some moment in time undergoes impulse acceleration. Thus, the target is assumed to change velocity instantaneously from the original fixed velocity to a new velocity. This corresponds to an infinite velocity slope, corresponding to an acceleration impulse. This is a convenient mathematical fiction which allows testing or modeling of the residual response of the Kalman filter. The modeling of the residual response characterizes the frequency response of the residual. The maneuver detector in the prior art looked for a bias in the residual. Noise in such prior-art systems can result in a non-zero value in the residual. In order to avoid false declarations of maneuvers, the maneuver detector must ignore such non-zero values caused by noise. Noise tends to have a higher frequency than a bias caused by true target acceleration. Thus, “low-pass filtering” of the residual in the frequency domain tends to reduce the relative magnitude of noise in the maneuver detector response. The impulse response of the residual of the Kalman filter identifies the maximum possible frequency associated with a true maneuvering target. Thus, matching of the frequency response of the maneuver detector to the impulse response of the residual of the Kalman filter makes the maneuver detector, in principle, sensitive to the residual frequencies associated with targets, but not with noise. 
     FIG. 3  illustrates the tracker  20  of  FIG. 1  or  2  with a noise free test signal deemed to represent the position of the target as a function of time. In  FIG. 3 , plot portion  310  represents a progressive change of position as a function of time which represents an original fixed velocity. At a time designated t 2 , an impulse of acceleration is applied to the target, causing a theoretically instantaneous change of velocity to a second velocity, greater than the first. Plot portion  312  of  FIG. 3  plots a change of position with time which is greater than that for plot portion  310 , representing the greater velocity after application of the acceleration impulse at time t 1 . Plot  314  of  FIG. 3  represents the amplitude of the residuals produced by subtracting circuit  26  in response to the input signals represented by plot  310 ,  312 . Plot  314  has a zero value preceding time t 1 , since the velocity represented by plot portion  312  is constant. At time t 1 , plot  314  ramps upward at a rate or slope which is determined by the loop frequency response of the Kalman filter. At some later time, plot  314  reaches a peak value, and then declines toward zero value or amplitude at times much later than t 1 , as the velocity represented by plot portion  312  becomes the new “fixed velocity.” 
   The procedure for determining the impulse response of the Kalman filter is illustrated in the flow diagram of  FIG. 4 . In  FIG. 2 , the logic of the method begins at a START block  410 , and proceeds to a block  412 , representing determination of the impulse response of the Kalman filter. This determination of the impulse response requires a priori determination of the coefficients of the predictor. The first step in determining the coefficients of the predictor in the case of a two-state Kalman filter is to determine the steady-state Kalman gains alpha (a) and beta (i). (Note: Arbitrary values for alpha and beta can also be chosen if an alpha-beta filter is used instead of a Kalman filter.)
 
β=2(2−α)−4√{square root over (1−α)}  (1)
 
α=−⅛( I   2 +8 I− ( I+ 4)√ {square root over (I 2 )}+ 8 I )   (2)
 
where
 
 I=t   2 σ w /σ m ;
 
   σ w  is the process noise uncertainty; 
   σ m  is the measurement uncertainty; and 
   T is the update interval. 
   The second step of the a priori determination of the coefficients of the predictor  24  of  FIG. 1  is to simulate the position and velocity profile of a target undergoing a modeled acceleration for one time interval. This step is illustrated by block  414  of  FIG. 4 . Fundamental kinematic equations such as S=S 0 +V 0 t+½ at 2  are used. In one simulation, the modeled acceleration was selected to be one gravitational unit, 9.8 meters/sec 2 . The time interval, as defined by the number of samples included in the interval, should be selected to be sufficient to not clip the tail of the residual response. 
   The “truth” data is then effectively “run through” the Kalman filter to identify the residual response, as set forth by block  416  of  FIG. 4 . This third step of the a priori determination of coefficients is determination of truth data by the simulation of the processing of the data from the simulated position and velocity with the fixed gain values alpha and beta determined for the filter. Referring to  FIG. 3 , the incoming truth information, in the form of position data versus time, includes a first portion  310  in which the position increases linearly with time at a first rate represented by the slope of portion  310 . At a time designated time t 1 , the velocity instantaneously changes to a new velocity, greater than the first. This new velocity is represented by portion  312 . The change of slope or velocity at time t 1  is instantaneous, corresponding to an acceleration impulse. Since these are simulated values, there should be no noise in the resulting residual. The residual resulting from the truth velocity profile is illustrated as plot  414  of  FIG. 4 . Plot  414  includes a zero-value portion preceding time t 1 , and a generally peaked response following time t 1 , decaying back to zero at times much later than t 1 . The peaked response is an illustration of the limited or low-pass nature of the frequency response of the residuals of the Kalman filter, or in other words the loop response of the Kalman filter. A low-pass frequency characteristic is illustrated as amplitude/frequency plot  510  in  FIG. 5 . This “running through” step includes calculation of 
                   [             x   ^       k   +   1                   v   ^       k   +   1             ]     =       [         1       T           0       1         ]     ⁡     [             x   ^     k                 v   ^     k           ]               (   3   )                 s   k+1   =x   k+1,truth   −{circumflex over (x)}   k+1   (4) 
                   [             x   ^       k   +   1                   v   ^       k   +   1             ]     =       [       α   *     s     k   +   1           β   *       s     k   +   1       T         ]     +       [           1   -     α   *     s     k   +   1               0               -   β     *       s     k   +   1       T           1         ]     ⁡     [             x   ^       k   +   1                   v   ^       k   +   1             ]                 (   5   )               
where:
 
   {tilde over (x)} k  is the corrected (smoothed) position at time k; 
   {tilde over (v)} k  is the corrected velocity at time k; 
   {circumflex over (x)} k+1  is the predicted position at time k+1; 
   {circumflex over (v)} k+1  is the predicted velocity at time k+1; 
   s k+1  is the residual value at time k+1; 
   x k+1,truth  is the true target position at time k+1; and 
   α and β are the steady-state Kalman filter gains. Equations 3, 4, and 5 together simulate the ideal impulse response of the predictor to a unit acceleration impulse. The frequency response of the Kalman filter is implicit in the calculated result. 
   The response of the residual of the Kalman filter, illustrated as  314  in  FIG. 4  and calculated in equations 3, 4, and 5 can now be normalized, if desired. The response of the residual  314  of the Kalman filter, whether or normalized or not, is the desired result. The response of the maneuver detector  32  of  FIG. 1  or  2  is set equal to the response so calculated, as indicated by block  418  of  FIG. 4 . The implementation of the maneuver detector often involves the use of a transversal filter. Such a filter is made to have an impulse response given by 
                   y   i     =       ∑     j   =   1     k_max     ⁢           ⁢       residual     i   -   j       *     s   j                 (   6   )               
where
 
   y i =matched response; and 
   k_max is that value of j for which the tail of the response becomes insignificant, which is merely an implementation choice. 
   A method for maneuver detection in a target tracking context includes the steps of generating data ( 12 ,  18 ) relating to the state ( 16 ) of a target (T). This data ( 12 ,  18 ) may include position and velocity ( 310 ,  312 ), velocity and acceleration, or other derivatives or integrals of position and rate of change of position. The method also includes the step of predicting the state of the target at a selected time by use of a predictor ( 28 ) having a known response ( 314 ) to an instantaneous change in velocity ( 310 , t 1 ,  312 ) of the target (T). The predictor may be part of a Kalman filter. The state ( 16 ) of the target (T) at the selected time is compared with the predicted state, to thereby generate a residual. The residual is detected with a detector ( 32 ) having a response, such as a frequency response, identical to the known response ( 314 ). In a particularly advantageous mode of the method, the known response includes low-pass frequency characteristics ( 510 ).