• October 31, 2024
• in Note, Sense
• 4 min read

Bayes Filter

We can use such a graph to understand the meaning of Bayes Filter. For a certain moment \(t\), we apply a control \(u_t\) to the system, drive the system's state from \(x_{t-1}\) to \(x_t\). And at this particular moment, we can only obtain the measurement \(z_t\) rather than directly get \(x_t\). So attemp to estimate the state of the system for given input and measurement is the purpose of Bayes Filter.

graph LR
    L("x(0)") --> J(...)
    J--> B
    A("u(t-1)") --> B("x(t-1)")
    B --> C("z(t-1)")
    B --> E
    D("u(t)") --> E("x(t)")
    E --> F("z(t)")
    E --> H
    G("u(t+1)") --> H("x(t+1)")
    H --> I("z(t+1)")
    H --> K(...)