DE3531681A1 - FLIGHT TRACK DETERMINATION WITH OPTO-ELECTRONIC LINE CAMERA - Google Patents

Abstract

The process as described serves to determine the trajectory of a missile by means of observation stations which are quasi-stationary or move above the surface of the earth. For this purpose, multiline, opto-electronic or opto-mechanical scanning cameras are used. The passages of the lines of the missile image are recorded as a function of time and of the image co-ordinates. Co-linearity equation pairs are established which contain the known orientation parameters of the observation station, as well as the possibly approximate data for the trajectory of the missile, and from these, the image co-ordinates are calculated. On the basis of the latter and the measured image co-ordinates, error equations are prepared. A compensation method and an iterative process enable the most probable values to be obtained for the missile trajectory parameters sought.

Description

1 Task

It is the task of determining the trajectory of ballistic missiles in the Start phase and the subsequent free flight phase of observation To determine satellites.

2. Solution principle

It is suggested to start the region (s) with one or more dates to fly over successive satellites, each one wear multi-line opto-electronic scanning camera. Such a camera is already from the German patent DE 29 40 871 C 2 ("Photogrammetric Procedures for aircraft and spacecraft. . .") and DE 30 43 577 C 2 (additional application) and application P 32 19 032.8 ("Stereophotogrammetric recording and evaluation method...") Known.

Fig. 1 shows forms of training of such a camera, which works according to the known push broom principle. Here, in the image plane of a camera whose lens is always open, there are three ( A, B, C ) or more ( N ) linear semiconductor sensors (usually so-called CCD sensors with several thousand discrete sensor elements) transverse to the flight direction arranged.

In another embodiment, the sensor lines are arranged in the image planes of several lenses, the optical axes of which are inclined towards one another (see Fig. 1.b). In Fig. 1.b, one sensor line is drawn in the image plane of the lens, several sensor lines can be arranged per lens to increase the number of observations.

These linear sensors scan the object overflown, for example the terrain, synchronously and line by line and in this way create an image strip of the same object with each linear sensor, but from a different perspective ( Fig. 2 and Fig. 3).

According to the above Patents and applications are therefore possible:
a. the orientation parameters (PositionsX _t ,Y _t ,Z _t , and inclinationsω _t ,ϕ _t , _t ) the camera at any timet along the trajectory and
b. the coordinatesX _i ,Y _i ,Z _i  any terrain pointsP _i
to determine.

The prerequisite for the determination of the object points P _i is that their pixels in the linear sensors A, B, C. . . N generated image strips are identified by correlation and their image coordinates are determined. Furthermore, it was previously assumed that these object points P _i are unchangeable in the common coordinate system.

This elementary requirement does not apply to the task at hand, since the ascending rocket changes its position as a function of time. The situation is shown in Fig. 4. At the path points R _A , R _B , R _{C of} the rocket, it is detected by the linear sensors A, B, C of the observation satellite, which at positions T _A , T _B , T _C, positions P _A , P _B and P _C takes. Fig. 4 shows the target acquisition with three sensors A, B, C , but there can also be more ( N ) sensor lines to increase the observation density.

The missile is continuously imaged into the image plane of the scanning camera via the lens and the image crosses at times t _A , t _B , t _C , owing to the relative movement between the satellite and the missile. . . t _N the sensors A, B, C,. . . N in the pixels m _A , m _B , m _C,. . . m _N whose image coordinates x _A , y _A , x _B , y _B , x _C , y _C,. . . x _N , y _{N can be} determined (see Fig. 5).

The identification of these transit points is easily possible since the light or heat radiation from the rocket causes a clear, detectable signal on the sensor and its time t is exactly determined by the synchronous sampling clock of the sensors.

If there is only one missile to be detected, which generates a clearly detectable signal when passing through the sensor line, no problems arise since the missile image crosses each sensor line only once. However, if several missiles can be detected, difficulties arise in assigning the signals to the missiles in question. However, since the image tracks of the rockets are also continuous due to the continuous relative movement between the satellite and the rocket, this results in a specific, at least a narrowed assignment. The more sensor rows there are, the clearer this assignment is. The passage points of a rocket through the sensor lines A, B, C ,. . . N must inevitably lie on a continuous, smooth curve. This problem can also be solved by using a certain curve function and by means of a compensation calculation.

A collinearity equation pair, which represents a straight line, is now set up for each such sensor passage point
- the instantaneous positions R _A , R _B , R _C,. . . R _{N of} the rocket with the respective coordinates X _r , Y _r , Z _r
- the instantaneous positions P _A , P _B , P _C,. . . P _{N of} the satellite or camera with the respective coordinates X _t , Y _t , Z _t
- And contains the image coordinates x and y of the passage point.

These equations are:

In itc _k  the focal length (chamber constant) of the camera and the coefficients a ₁₁ . . .a ₃₃ are the coefficients of the camera's rotation matrix that Functions of their inclination componentsω,ϕ and  at the timet are.

a ₁₁ = cosϕ · Cos
a ₁₂ = - cosϕ · are (3)
a ₁₃ = sinϕ
 a _21st = cosω · Sin  + sinω · Sinϕ · Cos
a ₂₂ = cosω · Cos  - sinω · areϕ · Sin
a ₂₃ = - sinω · Cosϕ
a ₃₁ = sinω · Sin  - cosω · Sinϕ · Cos (3)
a ₃₂ = areω · Cos  + cosω · Sinϕ · Sin
a ₃₃ = cosω · Cosϕ

It is now assumed that the position and inclination parameters of the camera at time t are exactly known in the collinearity equations (1) and (2). Their knowledge is based on the determination by the method mentioned at the beginning and described in the patents, which is referred to here and in the literature as the DPS method (see also O. Hofmann, P. Nav´, H. Ebner: DPS - A Digital Photogrammetric System for Producing Digital Elevation Models and Orthophotos by Means of Linear Array Scanner Imagery, Photogrammetric Engineering and Remote Sensing, Vol. 50, No. 8, August 1984, pp. 1135-1142) and can be assumed to be known.

The determination of the position and inclination of the satellite or camera the DPS procedure is not absolutely necessary here, others could also Procedures are used for this. But the use of the DPS procedure is obvious here, both for this orientation and path data determination of the satellite and the orbit determination of the missile to be observed the same means are used and all calculations in one uniform coordinate system and take place in a homogeneous process can.  

The orbital data of the rocket are unknown and sought. You can be general with the following functions:

X _R = F _x ( X _s , Y _s , Z _s , α , β , b , t )
Y _R = F _y ( X _s , Y _s , Z _s , α , β , b, t ) (4)
Z _R = F _z ( X _s , Y _s , Z _s , α , β , b, t )

Where:
X _s , Y _s , Z _s launch coordinates of the rocket
α azimuth angle of launch
β elevation angle of the launch direction
b acceleration
t time

The starting coordinates X _s , Y _s , Z _{s of} the launch ramp can be assumed to be known. They are determined by preliminary clarification and can be recorded directly with the same system.

The time t is also known (time of passage of the rocket through the linear sensor, see above).

Acceleration b of the rocket in the launch phase is probably approximately known, we can also introduce it as an unknown. In the free flight phase, b = 0. Certainly additional correction parameters are added, but these are more or less known and are not taken into account here for the simple illustration.

The azimuth direction α and the elevation angle β of the missile launch direction are unknown and have to be determined.

However, it is sufficient to first introduce rough approximate values α ₀ , β ₀ , b ₀ etc. for these unknowns. It is probably sufficient to assume a vertical start with the azimuth α = 0 ° and the elevation angle β = 90 °.

With these known and approximated data, it follows from Eq. (4) approximate position dataX _r ,Y _r ,Z _r  the missile at the timest. If you put these in equations (1) and (2), you get the calculated image coordinates  and . As a result of the approximations introduced for the launch directionsα andβ and accelerationb and possibly other unknown but approximate flight parameters give way to these calculated ones Image coordinates  and  from the measured image coordinatesx andy from.

It results from the measured and the calculated image coordinates following errors or observation equations:

v _x  =  -x =f _x  (X _r ,Y _r ,Z _r ) -x(5)
v _y  =  -y =f _y  (X _r ,Y _r ,Z _r ) -y

For each measured passage of the rocket through a linear sensor can such a pair of error equations are established, and the more passes d. H. the more sensor lines there are, the more precise it becomes Determination. It is irrelevant whether these passage observations are in one Camera done or from different cameras in successive Satellites are observed, provided that all measurements are in a uniform time and coordinate system.

All observations are now subjected to an adjustment according to the known least squares method, so that the sum of the squares of all errors v (Eq. 5) becomes a minimum:

[ vv ] → min (6)

with the result that the unknown, initially approximated parameters the assume the most likely value.

The above observation equations (5) are non-linear functions of the unknowns α, β , b etc., they have to be linearized according to Taylor:

In matrix notation results

v = M dX - H (8)

In itM the coefficient matrix of the partial derivativesδ x andδ y to the unknownα, β,bwhose correctionsd α,d β,db as a vectordX summarized are.H is the absolute vector of the limbs (  -x) and (  -y), the are calculated with the approximate values. This correction vectordX becomes through formation and dissolution of the normal equation system

( M ^T GM ) dX = M ^T GH (9)

determined in a known manner. G is the weight matrix, which represents the accuracy of the observations.

With the calculated correction values dX ( d α , d β , db ) the approximated output values α ₀ , β ₀ , b ₀ etc. are improved. A new run is calculated with the improved values. This iteration process continues until a certain residual error limit falls below the error v .

Since only a few observations can be processed in the present case and only a few unknowns can be determined, the computing time is very short.

In order to make the rocket orbit parameters determinable, there must always be at least as many observations as there are unknown parameters to be determined, but more if possible. Each sensor line pass provides two observations x and y .

This mathematical model allows the so-called weight determination balanced unknowns in a simple way a reliable accuracy statement for the results.

A surface camera can also be used for data acquisition. this only increases the number of lines and the number of measuring points, the evaluation principle remains the same.  

3. Advantages of the procedure

3.1 The procedure is simple and homogeneous. It enables seamless and accurate detection and trajectory determination of foreign missiles after a simple Scheme.

3.2 With a single system that is completely self-sufficient, without special external aids works, are both the own positions and orientation data the observation satellites as well as the orbital parameters of foreign missiles and any number of soil points can be determined.

3.3 The use of linear sensors enables the Coverage of a wide observation area. The use of area cameras, Tracking technologies and moving mechanical parts are eliminated.

3.4 The use of IR sensors makes the system all-weather capable.

3.5 Instead of a push-broom scanner, an optically mechanical scanner with multiple scanning directions can be used (see German Patent Application No. P 35 17 671.7).

3.6 An opto-electronic or an optically mechanical area scan camera can be used.

Claims (2)

1. Method and device for determining the trajectory of a rocket one or more observation satellites,characterized,
a. that the observation of the rocket (s) with a known multi-line opto-electronic or optically mechanical scanning camera takes place, the passages of the missile image through the linear sensors detected and their timingt as well as the image coordinatesx  andy this point of passage can be determined and registered;
b. that for each passage observation there is a collinearity (straight line) - Equation pair between the observation satellite and the rocket is established that the known orientation parameters of the Satellite and the known and unknown but approximated data the rocket orbit at the timet contains and calculated image coordinates  and  surrender;
c. that from these calculated coordinates, and the measured Coordinatesx andy the error equations (differences)v _x  =  -x  andv _y  =  -y be formed and that
d. by known adjustment methods using the smallest method Squares the minimum of the least squares sum [vv] → Min and in one iterative process the most likely values of the trajectory parameters sought the rocket (s) can be found. 2. The method according to claim 1, characterized in that several satellites with appropriate multi-line scanning cameras the missile or the line passes watch this rocket and in a uniform time and Coordinate system the calculation of the rocket orbit parameters takes place.