电子科技大学：《现代数字信号处理理论与算法 Modern theory and algorithm of digital signal processing》课程教学资源（课件讲稿）05 卡尔曼滤波器 Kalman Filter

Contents o S1.Introduction o S2.Conventional Kalman filter o S3.Example o S4.RLS and Kalman filtering o S5.Square-root information filter o S6.Square-root covariance filter Better numerical properties than the conventional one The square-root RLS algorithms are special cases 6

6 Contents  S1. Introduction  S2. Conventional Kalman filter  S3. Example  S4. RLS and Kalman filtering  S5. Square-root information filter  S6. Square-root covariance filter  Better numerical properties than the conventional one  The square-root RLS algorithms are special cases

S1.Introduction o MMSE Estimation o Innovation Process o Iterative MMSE Estimation 7

7 S1. Introduction  MMSE Estimation  Innovation Process  Iterative MMSE Estimation

MMSE Estimation o Orthogonal Principle y1=[y(n-)y(n-2）…y(] a(n)=yn)-(nlyn1)） E(a'(n)y)=0 8

8 MMSE Estimation  Orthogonal Principle       1 ˆ |   n  n y n y n y y y n y n y n1       1 2 1          * E( ) 0 n 1  n y  

Innovation Process(1) o Equality an=tn-tnly,i）=n)-∑atn-k) 1 0 0… 0 y() 1 0 0 三 -0m-1,n-1 -an-ln-2 9

9 Innovation Process (1)  Equality n yn yn y  yn a yn k  n k   n   n k      1 1 1 1,  ˆ |                                                               y n y y a a a n n n n n       2 1 1 1 0 0 1 0 0 0 2 1 1, 1 1, 2 1,1   

Innovation Process( (2) o Orthogonality E(a(n)a(k)》=0 k=1,2,…,n-1 10

10 Innovation Process (2)  Orthogonality      0 * E  n  k  k 1,2,  ,n 1