Objectives:

1.1 To get practical skills in problem solving estimation of random processes with Kalman-Bucy filter (KBF).1.2 To analyze properties of the evaluating procedure for the different modes and different ratios of model and filter parameters.

Methodical instructions to perform the work

Get a variant of the task from a teacher (Table L.2.1).

Table L.2.1 Task variantsVariant Task

1To get realization of signal formula with parameters formula=1, formula=1, formula=1/10; formula=1/100; formula=1/1000.

2To get realization of signal formula with parameters formula=3, formula=1, formula=1/30; formula=1/300; formula=1/3000.

3To get realization of signal formula with parameters formula=2, formula=1, formula=1/10; formula=1/100; formula=1/1000.

4To get realization of signal formula with parameters formula=5, formula=1, formula=1/30, formula=1/700, formula=1/5000.

5To get realization of signal formula with parameters formula=3, formula=1, formula=1/30, formula=1/300, formula=1/3000.

6To get realization of signal formula with parameters formula=1, formula=1, formula=1/10, formula=1/100, formula=1/1000.

7To get realization of signal formula with parameters formula=2, formula=1, formula=1/10, formula=1/100, formula=1/1000.

8To get realization of signal formula with parameters formula=5, formula=1, formula=1/30, formula=1/100, formula=1/700.

To analyze results of KBF modeling. Analyze the influence of the convergence of the algorithm for what plot the a posteriori variance formula depending on the signal-to- (observation noise) ratio and at specified sampling increment formula.

Plot the dependence of estimate error variance to the relative correlation window of the estimated process.

Find the stability boundaries of the KBF for various values of formula and formula.

Make the conclusions.