Page 294 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

COMPUTATIONAL ISSUES 283

Algorithm 8.1: Sequential update

1. Initialization:

def
. xði; 0Þ¼ xðiji 1Þ
def
. Cði; 0Þ¼ Cðiji 1Þ
2. Sequential update:

For n ¼ 0, 1, 2, ... , N 1:
T
. sði; nÞ¼ h n Cði; nÞh þ 2 n (innovation variance)
n
Cði; nÞh T
. k n ¼ n (Kalman gain vector)
sði; nÞ
. xði;nþ1Þ¼ xði;nÞþk n ðz n ðiÞ h n xði;nÞÞ(update of the estimate)
T
Cði;nÞh h n Cði;nÞ
n
. Cði;nþ1Þ¼ Cði;nÞ (update of the covariance)
sði;nÞ
3. Closure:

. xðijiÞ¼ xði; nÞ

. CðijiÞ¼ Cði; nÞ

2
The number of required operations is about 2M N þ 2MN. It outper-
forms the conventional Kalman filter. However, the subtraction that is
needed to get C(i, n þ 1) can introduce negative eigenvalues. Conse-
quently, the algorithm is still sensitive to round-off errors.

Example 8.12 Sequential processing
The results obtained by the application of sequential processing of the
measurements to the problem from Example 8.10 is shown in
Figure 8.9. Negative eigenvalues are not prevented, and the filter does
not behave correctly.

8.3.3 The information filter

In the conventional Kalman filter it is difficult to represent a situation in
which no knowledge is available about (a subspace of) the state. It would