1. Field of the Invention
The present invention relates to a method for estimating the true trajectory of a rocket, a method for predicting the future position of the rocket, a method for identifying the rocket, and a method for detecting the situation of the rocket, using a tracking system installed on the ground or mounted on various platforms such as aircraft, ships and other vehicles.
2. Description of the Prior Art
Estimation of a rocket trajectory is an effective technique for predicting the flight position of a rocket at an arbitrary time. The outline of typical estimation of the rocket trajectory using a passive ranging sensory system will be described. As shown in FIG. 1, a tracking system 1 is a passive ranging sensor system to acquire information on GLOS (Geometric Line of Sight) angles (elevation angle (EL) and azimuth angle (AZ)) as observation information by tracking a flying rocket 2. The positional relationship between the tracking system 1 and the rocket 2 is shown in FIG. 2. The rocket 2 flies from the left side to the right side in FIG. 2, i.e., from a launch point 3 shown by ".DELTA." to a drop point 4 shown by ".largecircle.". It is defined that the radius vector of the tracking system 1 from the geocentric of the earth is a vector (R), and the radius vector of the rocket 2 is a vector (r). In addition, it is defined that the range between the tracking system 1 and the rocket 2 is a slant range (.rho.). The trajectory of the rocket 2 is shown by the locus of the radius vector (r) of the rocket 2, i.e., an elliptical orbit 5 in FIG. 2. If the trajectory 5 is estimated, the position of the rocket 2 at an arbitrary time can be estimated. FIGS. 1 and 2 show the case where the tracking system 1 is mounted on an aircraft. When the tracking system 1 is settled on the ground, the aircraft is replaced with a building or the like on the ground.
As described above, the tracking system 1 mounted on the aircraft can obtain information on the GLOS angles (EL, AZ) as observation information by tracking the rocket 2. On this information, noises and biases are added as observation errors. When the tracking system 1 is mounted on the aircraft, positional information (R) of the tracking system 1 can be obtained from a navigation system or the like. Therefore, the flow of algorithm for estimating the trajectory of the rocket 2 is as shown in FIG. 3.
First, in a geocentric equatorial-plane-based inertial coordinate system shown in FIG. 4, a GLOS vector (L), which is a matrix in a radial direction of the rocket 2 viewed from the tracking system 1, is derived from observation information (EL, AZ) as shown by the following formula (1) (step 101). It is herein assumed that EL=.alpha. and AZ=.beta.. ##EQU1##
Then, the radius vector (r) of the rocket 2 is derived as a solution of 8th order algebraic polynomials, which are simultaneous equations of geometric equations and Keplerian orbital equations, which are shown by the following formula (2) (step 102). It is herein assumed that the velocity and acceleration of the tracking system 1 are "0" for simplification. EQU r(k)=.rho.(k)L(k)+R R(k).ident.R(k).ident.0 (2) EQU r(k)=-.mu..sub.e r(k)/r(k).sup.3
.mu..sub.e : gravitational constant
Then, the radius vector (r) of the rocket 2 is substituted to derive a slant range (.rho.) by the following formula (3) (step 103). EQU L(k).rho.(k)+2L(k).rho.(k)+(L(k)+.mu..sub.e L(k)/r(k).sup.3).rho.(k)=-.mu..sub.e R/r(k).sup.3 (3)
Finally, these are used to calculate orbital elements to estimate the trajectory of the rocket 2 (step 104).
An example of simulation analysis for the accuracy of the above described trajectory estimation of the rocket 2 will be described with respect to supposed long range and intermediate range rockets, which fly along trajectories I and II, respectively, from the left side to the right side as shown in FIG. 5.
It is assumed that the flight range of the supposed long range rocket is S.sub.1 km, and the maximum altitude thereof is H.sub.1 km. It is also assumed that the flight range of the supposed intermediate range rocket is S.sub.2 km, and the maximum altitude thereof is H.sub.2 km. In addition, it is assumed that the tracking system 1 mounted on the aircraft is located at A kilometers forward from the drop point in order to detect the rocket in an early phase. Moreover, it is assumed that the accuracy of estimation is analyzed 150 s before the drop of the long range rocket after the rocket flies in the vicinity of the maximum altitude, and 150 s before the drop of the intermediate range rocket after the burnout thereof.
Then, using a lateral range of the tracking system 1 (a horizontal distance from a rocket trajectory plane) (D) as a parameter, simulation analysis is conducted. FIG. 6 shows the condition of analyses in the case that the tracking system 1 has tracked the intermediate range rocket 2. In FIG. 6, the axis of ordinates denotes the accuracy (E) of trajectory estimation, and the axis of abscissas denotes a period of time (T) until the rocket reaches the drop point. Furthermore, FIG. 6 also shows the trajectory of the intermediate range rocket 2 in order to facilitate better understanding of the results of analysis of the accuracy (E) of trajectory estimation.
The intermediate range rocket 2 flies along the elliptical orbit 5 from the left side to the right side. The tracking system 1 is located at A kilometers forward from the drop point and a lateral range (D) from the rocket trajectory plane 6, and tracks the intermediate range rocket 2. Assuming that the position of the rocket at a certain time is a position shown in FIG. 6, the accuracy of estimation at that time is plotted at a position of ".star." in FIG. 6. Since the intermediate range rocket 2 flies along the elliptical orbit 5, the results at the times are sequentially plotted on a broken line B.
FIG. 7 shows the results of the estimation analyses in the range of from D.sub.1 km to D.sub.2 km using the lateral range (D) as a parameter. In FIG. 7, the accuracy of trajectory estimation is distinguished by color. The colorless portion means that the accuracy is less than 2 km. The sprinkled portion means that the accuracy is 2 km or more. It can be seen from FIG. 7 that there are many portions having the accuracy of trajectory estimation of 2 km or more, so that the accuracy is not so good under the influence of observation errors.
FIG. 8 shows the condition of analyses in the case that the tracking system 1 has tracked the long range rocket 2. In FIG. 8, the axis of ordinates denotes the accuracy (E) of trajectory estimation, and the axis of abscissas denotes a period of time (T) until the rocket reaches the drop point. Furthermore, FIG. 8 also shows the trajectory of the long range rocket 2 in order to facilitate better understanding of the results of analysis of the accuracy (E) of trajectory estimation.
The long range rocket 2 flies along the elliptical orbit 5 from the left side to the right side. The tracking system 1 is located at A kilometers forward from the drop point and a lateral range (D) from the rocket trajectory plane 6, and tracks the long range rocket 2. Assuming that the position of the rocket at a certain time is a position shown in FIG. 8, the accuracy of estimation at that time is plotted at a position of ".star." in FIG. 8. Since the long range rocket 2 flies along the elliptical orbit 5, the results at the times are sequentially plotted on a broken line B.
FIG. 9 shows the results of the estimation analyses in the range of from D.sub.3 km to D.sub.4 km using the lateral range (D) as a parameter. In FIG. 9, the accuracy of trajectory estimation is distinguished by color. The colorless portion means that the accuracy is less than 2 km. The sprinkled portion means that the accuracy is 2 km or more. It can be seen from FIG. 9 that most of portions have the accuracy of trajectory estimation of 2 km or more, so that the whole accuracy is bad under the strong influence of observation errors.
As described above, in the typical rocket trajectory estimating algorithm, the accuracy of trajectory estimation of a rocket deteriorates under the influence of observation errors of the tracking system mounted on the aircraft. In addition, the accuracy of prediction of the future position of the rocket, and the accuracy of prediction of the drop time at the future position are not sufficient. Moreover, it is not possible to precisely estimate the true trajectory of the rocket, so that there is a problem in that it is difficult to identify the rocket by the comparison between trajectories. Therefore, in order to measure the slant range (.rho.) between the aircraft and the rocket, the aircraft must have a very large laser range finder.