# How to calculate moving average speed from GPS?

I'm developing an android application using GPS. I'd like to implement a feature that displays the users average speed over the 1/5/15 minute. Something like the CPU load on unix. I can calculate average easily by cumulating the distance traveled second by second and divide it by the elapsed time, but I can't think of a smart way of calculating the moving average.

Obviously I can get id done by putting the distance between the last and the current position in an array every second while deleting the oldest value.

I'm looking for a neat way of doing this.

You will need to store all the values for the whole time span, as you already suggested. The reason is that you somehow need to "forget" the contributions of the old values to the moving average. You can't do that exactly if you don't know what these values where (i.e. if you do not store them).

In your case, 1 value each second for 15 minutes amounts to 15 * 60 = 900 data points, that should be OK.

Note that you do not need to perform a sum over the whole array each time you update: You can calculate the new moving average from the number of data points, the new value and the value you are "forgetting" at that moment:

```new_average = (n * old_average - x_forget + x_new)
```

Here, n is the number of data points (900 in your case), x_forget is the value you are "forgetting" and x_new is the latest value. You then drop x_forget from the front of your array and store x_new at the end. Instead of an array you might want to use a queue implemented via a linked list.

Heres one way to go about it that is pretty straight forward:

If you are sampling position every second keep 901 samples in a queue, thats 15 mins worth (and 1 extra). Position 0 is the most recent measurement, effectively your current position.

For an average speed over the last X minutes:

```s = X * 60;
point1 = postion_queue[0]; // this is your current position
point2 = postion_queue[s]; // this is your position s seconds ago
d = distance_between_points(point1, point2);
speed = d / s;
```

speed is now distance units per second, convert to mph, or kph or whatever units you need. Different values of X can be used for any average between 1 and 15 minutes.