How do I optimize the inputs to a function?

I have a measured pressure-signal (much like the one in the image below) and a function, which when solved by an ode-solver, roughly generates the same dataset.

How do I fine-tune the parameters for the match to improve even further?

My idea of a "plan-of-attack" is as follows:

% Load in raw data.
% Set up initial attempt at finding parameters manually
% 
% Run ode23 to generate a dataset using the assigned parameters.
% Subtract the modelled dataset from the raw one - best-fit being achieved when the value is low. 
%
% Set up new parameters (Monte-Carlo or based on findings, I'm not picky), 
% and redo the process above for e.g. 50 iterations while storing the parameters yielding a best-fit solution.

I have virtually all toolboxes available to me, so this should not be an obstacle if your solution requires one :)

Best Regards,

Answer 1

[Star Strider]

See Solving Coupled Differential Equations (link), Parameter Estimation for a System of Differential Equations (link), Monod kinetics and curve fitting (link) and others.

Answer 2

[Marcus Wikstol]

I was not able to adopt the approach to my particular problem so I designed my own Monte-Carlo method for it. Thanks for trying to help anyways :)

[Star Strider]

My pleasure.

Answer 3

[Paul Sutton]

Do you mind sharing how you achieved this?