I'm facing the following simulation problem. A ship is on a lake, the position of which is completely unknown (so it is assumed uniformly distributed over the entire lake). Then given depth measurements from the ship and a topological map of the lake, (that is, the real depth at a certain position in a 200x100 grid) find the position of the ship. This was relatively easy, and I have done it with a simple particle filter. However, the next step is to assume both the location and map is unknown, thus this is a SLAM problem. My understanding is that the EKF SLAM algortihm is unsuited for this task as the grid much too large, and the values at each grid point are continous. So this is not an occupancy grid map, but a map of continous values.
The ship has a compass and speed measurements, so the heading and speed of the ship is known. Given these measurements and the previous location, the new location of the ship is gaussian distributed. Additionally, the error on the depth measurements can be assumed gaussian. Is there a SLAM algorithm capable of handling this problem?