How to deal with Extended Kalman Filter in Simulink when my state transition function is given in continuous time form?

I have an EKF with the above state transition function.

where u=[fm omega]

Control Systems Toolkit EKF requires state transition function in the discrete time form:

x(k+1) = f(x(k),w(k),StateTransitionFcnInputs)

However the equation I want to use is in the continuous time with derivative of the state space in LHS. Can I get Simulink EKF to work with such a state transition matrix?

Answer 1

[Bill Tubbs]

Check out the examples in the documentation here:

https://www.mathworks.com/help/control/ref/extendedkalmanfilter.html

The example looks like this:

function x = vdpStateFcn(x) 
% vdpStateFcn Discrete-time approximation to van der Pol ODEs for mu = 1. 
% Sample time is 0.05s.
%
% Example state transition function for discrete-time nonlinear state
% estimators.
%
% xk1 = vdpStateFcn(xk)
%
% Inputs:
%    xk - States x[k]
%
% Outputs:
%    xk1 - Propagated states x[k+1]
%
% See also extendedKalmanFilter, unscentedKalmanFilter

%   Copyright 2016 The MathWorks, Inc.

%#codegen

% The tag %#codegen must be included if you wish to generate code with 
% MATLAB Coder.

% Euler integration of continuous-time dynamics x'=f(x) with sample time dt
dt = 0.05; % [s] Sample time
x = x + vdpStateFcnContinuous(x)*dt;
end

function dxdt = vdpStateFcnContinuous(x)
%vdpStateFcnContinuous Evaluate the van der Pol ODEs for mu = 1
dxdt = [x(2); (1-x(1)^2)*x(2)-x(1)];
end