CODEWITHSUNDEEP
filtergpstrackingcoordinate-systemskalman-filter
computador7
computador7

Reputation: 170

Kalman filtering for movement in long lat coordinates

I am trying to implement a simple kalman filter that will be used for filtering/predicting the movement of a vehicle in long/loat coordinates.

There are no measurements from vehicle sensors, just a new update on an observed long/lat position, so basically the state that I will be trying to predict and correct is the longitude and latitude of the vehicle at any given time.

As far as I understand the model is non linear as there may be random accelerations change of direction etc, but I think this can be largely ignored as long as I keep track of the bearing as well in my state. My problem is that I do not know how to model this system in terms of the state and prediction matrices and on top of this it seems that it is necessary to convert/project the long/lat coordinates into some cartesian xy system so that the two become independent, but I am not exactly sure how to go about this.

It seems that converting back to wgs84 from xy is not that trivial and potentially a bit intense computationally. Can anyone shed some light into this?

Upvotes: 3

Views: 2087

Answers (1)

Chris Ogden
Chris Ogden

Reputation: 46

It looks like your state variable would be a vector [lat, long], and your measurement variable would be [lat, long, bearing]. You will need to figure out appropriate f and h functions, based on these vectors, for the process and measurement models, respectively. Since this is a non-linear problem, you will probably need to use a nonlinear filter, such as the EKF, UKF or CKF (cubature Kalman filter).

When using a Kalman-type filter to deal with modular values such as angles, latitudes, or longitudes, there is a big problem whenever your state or your measurements are near the discontinuous modular boundary. For example, if your bearing is an angle from 0 to 360 degrees, the filter will have problems if you are measuring at 1 degree or 359 degrees. Also, you could have problems if your longitude is around plus or minus 180 degrees longitude, or your latitude is at one of the poles (which might be remote possibilities that you could ignore).

One example of how to deal with angles in the state or measurement variables is presented in David Frederic Crouse, "Cubature/ Unscented/ Sigma Point Kalman Filtering with Angular Measurement Models," 18th Int'l Conf. on Information Fusion (Wash., D.C. July 6-9, 2015), https://ieeexplore.ieee.org/document/7266741. Based on Crouse's approach, to use bearing as a measurement variable you would need to add a wrapping function to a couple of locations in the standard unscented or cubature filter equations. If you want to deal with the discontinuities in latitude and longitude (which you might not), you would need to transform the coordinates to and from Euclidean space while calculating the covariance matrices.

Upvotes: 1

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