Can Kalman Filter be used to track Randomly Moving Target?

i want to track random moving object with a camera using kalman filter...i have the following questions...

1. Randomly moving target means $Corelation(t) = E[ x(T)x(T+t) ]$ is very low...where $x(T)$ is the position of the target at time = $T$ along an axis say $x$ axis..eg...moving hand...moving bird..moving ant..what will be my state transition matrix $F(k)$ in $x(k+1) = F(k)x(k) + w(k)$ because i cannot describe it randomness...

2. is there any standard model to represent any random moving target?

any suggestion is welcome....i am aware that any object can be determined in a given image frame using its characteristics by image processing techniques and hence tracked....but is it possible to use Kalman Filter?

You should define a linear $F$ to use Kalman filtering recursions. However, I think, random movements can not be described very well with linear models (an object which is tied to certain and linear physical rules can be tracked by the Kalman filter). Therefore, your state space model will not be linear.
Then, your question about $F$ is critical. Because, in many times, the art of Bayesian modeling is to write appropriate models for underlying physical structure. Therefore, if you write a certain motion model, you can use particle filtering (Also for nonlinear models it would not be $Fx$, it will become $f(x)$ where $f$ is a nonlinear function). And, I do not know, you may write a piecewise linear model for a bird or ant, in that case, you can use the Kalman filter but you have to estimate switching variable.