Path fitting problem - which approach?
First let me say that this is my first visit to these forums. As such, I apologize if this question is in any way inappropriate (wrong location, etc).
Having said that, I am hoping you will be able to suggest reasonable approaches to a problem that I am currently investigating. Basically, it's a path fitting problem that I will describe in terms of an aircraft:
Data - pairs of observed position/location (coordinates) of the plane as it travels, with the time of the observation. Some characteristics of the data:
a) the data can be dense (many datapoints close together) or sparse (few datapoints widely separated).
b) both position and time have some error associated (unknown magnitude, at least as yet).
c) there may be true outliers with very large errors, at a low rate of occurrence.
Problem - identify a path/trajectory that is consistent with the observed data and multiple constraints (see below), and that is either resistant to the presence of outliers or can identify them and exclude them. With the solution in hand it should be possible to query the position, heading, and velocity of the plane at any time along the path.
Constraints - the observed position/time data, and known 'realistic' velocities, rates of turn, and possibly acceleration for the plane. Obviously due to the fact that the observed data has error, the trajectory shouldn't be constrained to hit each observed datapoint exactly, but it should come close.
Approaches - first let me say I'm way out of my depth mathematically here. I've considered Kalman filters, Lagrangian mechanics, and velocity Verlet integration. I can't find anything that seems exactly suited to what I need, but perhaps my lack of understanding is blinding me to an answer that should be obvious.
Any suggestions and/or comments would be much appreciated!