Stochastic State Estimation Có lẽ một phần quan trọng nhất của nghiên cứu một vấn đề trong người máy hay tầm nhìn, cũng như trong hầu hết các khoa học khác, là để xác định một mô hình tốt cho các hiện tượng và các sự kiện có liên quan đến. Ví dụ, nghiên cứu thao tác đòi hỏi phải xác định mô hình cho một cánh tay robot có thể di chuyển như thế nào và làm thế nào nó tương tác với thế giới. Phân tích hình ảnh chuyển động ngụ ý xác định các mô hình. | Chapter 7 Stochastic State Estimation Perhaps the most important part of studying a problem in robotics or vision as well as in most other sciences is to determine a good model for the phenomena and events that are involved. For instance studying manipulation requires defining models for how a robot arm can move and for how it interacts with the world. Analyzing image motion implies defining models for how points move in space and how this motion projects onto the image. When motion is involved as is very often the case models take on frequently the form of dynamic systems. A dynamic system is a mathematical description of a quantity that evolves over time. The theory of dynamic systems is both rich and fascinating. Although in this chapter we will barely scratch its surface we will consider one of its most popular and useful aspects the theory of state estimation in the particular form of Kalman filtering. To this purpose an informal definition of a dynamic system is given in the next section. The definition is then illustrated by setting up the dynamic system equations for a simple but realistic application that of modeling the trajectory of an enemy mortar shell. In sections through we will develop the theory of the Kalman filter and in section we will see that the shell can be shot down before it hits us. As discussed in section Kalman filtering has intimate connections with the theory of algebraic linear systems we have developed in chapters 2 and 3. Dynamic Systems In its most general meaning the term system refers to some physical entity on which some action is performed by means of an input M. The system reacts to this input and produces an output .7 see figure . A dynamic system is a system whose phenomena occur over time. One often says that a system evolves over time. Simple examples of a dynamic system are the following An electric circuit whose input is the current in a given branch and whose output is a voltage across a pair of
