# Tracking a moving target

The process of matching frames, based on features that are preserved under certain transformations, as it was described in the previous chapter, works well for stellar objects; detected stars form the same pattern on each frame. Mismatch between any two frames is change in spatial offset, scale and rotation, in some cases also a mirror operation applies. The task of matching a set of frames is about finding a set of equations (matrix) that transforms coordinates of any vector (point) on one frame to a vector in a reference coordinate system.

In case of moving targets, such as minor Solar System bodies, in additional to the mismatch desribed above, another source of mismatch is introduced - an object of interest, having its own radial movement, changes its position with respect to surrounding stars between the frames (in time). Therefore, if a pattern used for the frame matching would include such an object, it would not match. The challange in reduction of an observation of minor bodies is in founding an image of the object of interest on each source frame. Fortunately, it can be reasonably expected, that such an object does not move randomly, but follows a simple trajectory that can be fitted using a simple polynomial function or spline.

The C-Munipack software approaches this task with help of a user. He picks up a small set of frames, called key frames, and on each frame he indicates an object that corresponds to the target. As in the frame matching for stellar objects, a user also chooses one frame to be a reference frame. The rest of the process does not require any further interaction.

The key frames are processed first. The object indicated by the user as the target is left out from the reference frame and the key frame. Then, the same frame matching process as in case of a stellar object is applied to those two frames. This is repeated for each key frame and the equations that transforms frame coordinates into reference coordinates are preserved.

The software keeps an observation time and position of the target object from each key frame and transforms those positions into the reference coordinate system. Then, using linear least squares method, the transformed positions are interpolated using two second order polynomial function of time t:

(1)x(t) = A_x + B_x . t + C_x . t^2

and

(2)y(t) = A_y + B_y . t + C_y . t^2

Using the functions x(t) and y(t) a position of the target in the reference coordinate system can be determined an any given time t.

Subsequently, the matching process continues with processing all other frames. The software reads an observation time t of a frame and using the functions x(t) and y(t), determines the position of the target in reference coordinate system in time t. Then, the target object’s position on the reference frame is changed to values x(t) and y(t) and a standard frame matching process is applied. If the fit is correct, an object close to the expected position of the target is found, the pattern of objects on the reference frame and the pattern on source frame match and an identification of the target object is found as a result of the standard frame matching process.