1. A target monitoring system comprising: a storage unit; a processing unit; and a display unit, wherein the storage unit stores 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, wherein, when n is an optional natural number equal to or more than 2, the processing unit executes existence probability distribution calculation processing of calculating an existence probability distribution P D of the target at a time t n based on data received from an external sensor, wherein the processing unit executes diffusion existence probability distribution calculation processing of calculating a diffusion existence probability distribution P M (t n ) of the target at the time t n based on an integration target distribution P(t n−1 ) of the target at a time t n−1 previous to the time t n and the physical model of the target, wherein the processing unit executes reliability calculation processing of calculating a reliability p 0 (t n ) of the existence probability distribution P D (t n ) based on at least one of a kind of the external sensor and environment around the external sensor, wherein the processing unit calculates the integration target distribution P(t n ) of the target at the time t 0 based on the following equation (1) 
 P ( t n )= p 0 ( t n )× P D ( t n )+(1 −p 0 ( t n ))× P M ( t n )   (1), wherein the processing unit calculates a wake of the target and a predicted course probability based on the integration target distribution P(t n−1 ), the integration target distribution P(t n ) and the non-physical model of the target, and wherein the display unit displays a combination of the map data, the wake and the predicted course probability.