Extended-Kalman-Filter---Matlab

Easy implementation of the extended Kalman Filter

Extended-Kalman-Filter---Matlab

This repo implements the extended Kalman Filter class which is a multi-purpose EKF to facilitate the implementation and verification of EKFs in Matlab for the post-processing setting.

The user has to define the following functions, and then pass them to the class initializer in order to build an instant of the EKF class:

1. <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$[\pmb{y}_{k|k-1},\pmb{\Phi}_{k-1\rightarrow k}]$</math-renderer> = <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$\text{st\_model}(t_{k-1}, t_{k}, \pmb{y}_{k-1|k-1}, \pmb{P}_{k-1|k-1})$</math-renderer>, which is a propagation function of the state vector. The output of this function must be <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$\pmb{y}_{k|k-1}$</math-renderer>, the predicted value of the state vector, and <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$\pmb{\Phi}_{k-1\rightarrow k}$</math-renderer> where <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$\pmb{\Phi}_{k-1\rightarrow k}$</math-renderer> is the state transition matrix between the two time instants <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$t_{k-1}$</math-renderer> and <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$t_{k}$</math-renderer>
2. <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$\pmb{z}_{k}$</math-renderer> = <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$\text{meas}(t_k)$</math-renderer> which is a function that returns the measurement vector at time <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$t_k$</math-renderer>.
3. <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$[\pmb{H}_k, \pmb{H}_k, \pmb{z}_k]$</math-renderer> = <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$\text{meas\_model}(t_{k}, \pmb{y}_{k|k-1}, \pmb{z}_k)$</math-renderer>: is the measurement model function. The output must be the vector <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$\pmb{H}_k$</math-renderer> of modeled measurements, the matrix <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$\pmb{H}_k = \frac{\partial \pmb{H}_k}{\partial \pmb{y}_k}$</math-renderer>, and optionally the measrement vector after removing outlaiar measuremets.
4. <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$\pmb{Q}_{k}$</math-renderer>, the state model covarience matrix (constant or callable), <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$\pmb{Q}(t_{k}, \pmb{y}_{k|k-1})$</math-renderer>
5. <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$\pmb{R}_{k}$</math-renderer>: measurement covarience matrix (constant or callable), <math-renderer class="js-inline-math" style="display: inline" data-static-url="https://github.githubassets.com/static" data-run-id="84b5bd432c93d3ab9960635ca19df3f2">$\pmb{R}(t_{k}, \pmb{z}_{k})$</math-renderer>

The EKF class has some visualization cababilities, which are illustrated in the example.