1. A target monitoring system comprising: a database which stores a program, a physical model of a target, a non-physical model of the target and map data, wherein the physical model shows physical constraints of the target and the non-physical model shows a behavior pattern of the target: a display: and a controller which executes the program to perform: an existence probability distribution calculating function of calculating an existence probability distribution PD(tn) of the target at a time tn based on data received from an external sensor, a diffusion existence probability distribution calculating function of calculating a diffusion existence probability distribution PM(tn) of the target at the time tn based on an integration target distribution P(tn−i) of the target at a time tn−i previous to the time tn and the physical model of the target, a reliability calculating function of calculating a reliability po(tn) of the existence probability distribution PD(tn) based on at least one of a kind of the external sensor and environment around the external sensor, a calculation function of calculating the integration target distribution P(tn) of the target at the time tn based on the following equation (1) 
 P ( tn )= po ( tn )× PD ( tn )+( I−po ( tn ))× PM ( tn )  (1), a calculating function calculating a wake of the target and a predicted course probability based on the integration target distribution P(tn−i), the integration target distribution P(tn) and the non-physical model of the target, and a control function of controlling the display to display a combination of the map data, the wake, and the predicted course probability of a position of the target, where n is an optional natural number equal to or more than 2.