Using the EKF for estimating a noisy sinewave

[Ultimâ]

Ok, well my understanding of the EKF is based on the following link:

http://www.visio-moralis.com/ekf.pdf

Say we have the following samples entering the EKF:

-0.11941369504011
0.17714531905549308
0.13943940597678897
0.2538148550150054
0.32572405004542754
0.29906083643454207
0.4809146663261077
0.4273129043735685
0.08411661027357817
0.17033115308274613
0.08438199704865516
-0.0026833111833972634
-0.3006184032754452
-0.2748192218103497
-0.20946270399458924
-0.5437491245626156

which is the contaminated version of the real samples:

0.0
0.10815594803123159
0.20572483830236557
0.28315594803123156
0.3328697807033037
0.35
0.33286978070330375
0.28315594803123156
0.20572483830236563
0.10815594803123162
4.286263797015736E-17
-0.10815594803123141
-0.20572483830236554
-0.28315594803123156
-0.3328697807033037
-0.35

How would I setup the filter to work through this? (Something I've been struggling with for sometime-any help would be appeciated)

 

[lippyka]

The EKF is an iterative filter, meaning it works in a loop. The first step would be to set up the filter's state equations and measurement equations. These equations form the basis of the EKF and will define how the filter will work. The state equations describe how the state of the system (in this case, the samples) evolves over time. In our case, this could be a linear equation describing the change in samples as time passes. The measurement equations describe how the filter can use the measurements to update the state of the system. In our case, this could be a linear equation that describes how the measured samples are related to the true samples. Once these equations are set up, the next step is to initialize the filter's internal state variables, such as the state vector, error covariance matrix, and process noise. This is done using the initial samples and their associated measurements. Finally, the filter can be run in a loop. At each iteration, the filter uses the current samples and measurements to update its internal state variables based on the previously defined state and measurement equations. This loop is repeated until the filter converges to a stable state.