How to implement a random natural motion for a single particle?

I have a Drone class implemented as a Thread that is called from a Map class and every X milliseconds the movement() function of the Drone class is called to update the position and show it on the map.

Currently the movement() function looks as follows.

    public void moveDrone() {
        double increment = 0.000007;
//      Straight line movement
        if(this.mode == true)
            p.setX(this.p.getX() + increment);
        if(this.mode == false)
            p.setX(p.getX() - increment);
        if(p.getX()>38.88602||p.getX()<38.88453)
            this.mode = !this.mode;

Which creates a movement in a straight line that looks pretty simple.

I would like to simulate a random motion that looks kind of natural. I've been reading about different implementations like brownian motion and boids but I couldn't find how to implement them for a single particle (drone in this case) that moves randomly inside a bounding box.

Any link or pseudocode will help.