应用：运动，信号系统
本质：自回归（auto regression），线性算子（Linear operator）, 离散， 随机系统
该系统由如下方程表示（Controlled by a Linear stochastic difference equation）:
(大写为矩阵，小写为一维变量）
真实过程为线性：
\(w_{k-1}" title="x_k = Ax_{k-1} + B u_{k-1} + w_{k-1} \)
discrete time, linear, dynamic, state space, vector difference equation
State: smallest vector to summarize the past of the system.
Prediction: in the absence of the noise.
State equation:
\( x(k+1) = F(k) x(k) +G(k)u(k) + v(k)
\)
\( x(k) \) is the \(n_x\) dimensional state vector
\( v(k) \) is the white noise with covariance \( Q(k)\)
Measurement equation:
\( z(k) = x(k) + w(k)
\)
\( w(k) \) is the white noise with covariance \( R(k)\)
测量系统也为线性：
$z_k = H x_k +v_k.$
$w_{k-1}$与$v_k$为噪音。