1. A state estimation apparatus for tracking a plurality of objects, the apparatus comprising: observation obtaining circuitry configured to obtain, at each predetermined time interval, an observation image that is observation data obtained from an observable event, and obtain an extracted-feature image representing a predetermined feature quantity extracted from the obtained observation image; labeling circuitry configured to extract a closed image area from the observation image obtained by the observation obtaining circuitry, and add a label number to the extracted closed image area to generate a label image; object information management circuitry configured to add an object number to each target object to be tracked, and manage the object number added to each target object; prediction circuitry configured to perform, for each object that is to be tracked at a current time t, prediction using posterior probability distribution data, and generate predictive probability distribution data for each object that is to be tracked at the current time t, the posterior probability distribution data indicating a probability distribution of an internal state of the object at a preceding time t−1, the predictive probability distribution data indicating a probability distribution of an internal state of the object at the current time t; likelihood obtaining circuitry configured to: (A) obtain, for each object determined as being tracked at the preceding time t−1, particles based on the predictive probability distribution data, and determine an area to be erased from the extracted-feature image based on the obtained particles to generate an object erased image for tracking or for a new object detection, the object-erased image for tracking being an image from which an area corresponding to an object other than a processing target object selected from the objects that are to be tracked at the current time t has been erased; the object-erased image for new object detection being an image from which an area corresponding to each of the objects that are to be tracked at the current time t has been erased, (B) generate particles for the new object detection, use the particles for the new object detection to process the object-erased image to obtain a new object candidate area, and determine whether the new object candidate area corresponds to a new object that is to be a new tracking target at the current time t based on the obtained new object candidate area and the label image to determine a target object to be tracked at the time t, and (C) calculate a final likelihood based on a likelihood that is calculated for each object determined to be a tracking target object at the time t by using the particles generated based on the predictive probability distribution data to process the object-erased image, and update the predictive probability distribution data obtained by the prediction circuitry based on the calculated final likelihood to generate updated probability distribution data; posterior probability distribution estimation circuitry configured to estimate, for each object determined to be a tracking target object at the time t, posterior probability distribution data for a state of the event from the updated probability distribution data and the final likelihood obtained by the likelihood obtaining circuitry; and prior probability distribution output circuitry configured to output probability distribution data based on the posterior probability distribution data estimated by the posterior probability distribution estimation circuitry as prior probability distribution data at a next time t+1.