Recently I got into vehicle models and filtering in general and immediately faced with the following question.

I have the recorded GPS data from car driving on a highway. However, there is a substantial level of noise present, so I decided to filter this $(x, y)$ data. Currently I am using Kalman filtering (the extended one - bicycle model of the vehicle is assumed) for this purpose, but I somehow have a feeling that Kalman is more suited for online estimation/filtering. I have also tried various other approaches, including median and Savitzky–Golay filters, but they do not take dynamic model into the account which I think is the important information to use while filtering this data.

So, my question is: Is there an alternative to Kalman filter, where model dynamics can be specified, which is more suited for this purpose?

I just once again want to emphasize that I have solely measured time sequence (fixed interval) with $x, y$ coordinates and data needs to be filtered after drive is over (offline usage).

Thank you for your help and I apologize if my question is not stated well - this is my first post:)

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    $\begingroup$ you can start with this refs: robotics.stackexchange.com/questions/11197/… and www-cdr.stanford.edu/dynamic/estimationGPS/avec2002ryu.pdf , if you feel that your question needs re-wording $\endgroup$ – V.V.T Jan 7 at 12:08
  • $\begingroup$ All you have is the GPS lat/lon data? No IMU, odometer, steering, or other data? $\endgroup$ – TimWescott Jan 7 at 15:07
  • $\begingroup$ Yes, that is right. All I have is GPS lat/long data $\endgroup$ – Mark Lumar Jan 7 at 15:47
  • $\begingroup$ Is your data a timed sequence {$x_n, y_n, t_n$} / {$x(t_n), y(t_n)$} or just a set of scattered points {$x_n, y_n$}? If it is a timed sequence, is a time interval fixed or varying? $\endgroup$ – V.V.T Jan 8 at 3:19
  • $\begingroup$ It is timed sequence, time interval is fixed $\endgroup$ – Mark Lumar Jan 8 at 5:37

If you used a commercial GPS receiver to obtain your tracking data, the raw trilateration data from satellites are already processed "using Kalman filtering (more common) or least-squares (less common) estimation algorithms" (see https://insidegnss-com.exactdn.com/wp-content/uploads/2018/01/marapr13-Solutions.pdf). Pay attention also to the counterintuitive statement that the article proves in the section *No Silver Bullet": the differences between least-squares and Kalman are surprisingly minor for the generic application in GPS receivers.

With this in mind, additional post-processing is quite unlikely to improve your data set, but instead your data can deteriorate as a result of this post-processing. It seems you cannot denoise your data any better, but you can analyze your route (whether the highway route passes "canyons", sharp corners or the like) and, knowing the features of your GPS receiver taken from the manufacturer's datasheet, estimate the precision of your tracking data.

The article referenced also gives a partial answer to your highlighted question about an "alternative".


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