debrief / curveslicer Goto Github PK

I had a think about how the algorithm could work yesterday.

When I approached the problem a couple of years ago, I followed the advice from the PDF document:

• work through the data, slice the data into two at each step. At the time of the curve-change, the two halves (before + after) will have the best fit.

But, this fails when there are more than two straight legs, since our optimal slice will minimise the errors across the 3+ legs, rather than the minimal error between two legs, and the optimal slice will probably occur part way through the central leg.

Here's another thought:

• work through the continuous period of data
  • find the five-minute period with the lowest delta bearing rate [see note below]
  • if none found, this leg is complete
  • if a matching five minute period is found, treat this as the centre of a straight leg.
  • fit the curve to this period
  • add a point to the right of the curve, fit it again.
  • continue expanding right until we have xx consecutive points above (or below) the curve [see note below]
  • mark the point previous to these "outside" points as the end time of the straight leg
  • continue expanding left until we have xx consecutive points above/below the curve
  • mark the point previous to these "outside" points as the start time of the straight leg
  • add this straight leg to the results list, and remove the data from the overall dataset
  • we now have periods before/after this leg. Treat each one as a continuous period of data, adding them to the list of legs to be processed.

Lowest delta bearing rate

We're trying to find periods of steady state. During the periods the bearing curve takes an ArcTan function. At opposite ends of this curve the shape is convex or concave (see below). This means that at some point in the curve there must be zero degress / min change of rate of bearing. So, we don't look for the lowest bearing rate, we look for the lowest delta bearing rate.

If we were looking for the lowest bearing rate, we'd find the flat horizontal sections near the start/end of the following curve. But, since our plan is to work our way out from the centre of the curve we're more interested in the centre of the curve, where the rate goes from positive to negative:

Above/below the line

When we've got a good curve fit, consecutive data points will generally appear above/below our fitted curve. This good fit will grow as the period we're inspecting continues to represent two vehicle in steady motion (course and speed).

Where the shape of the data moves away from the curve, we will start to get consecutive data points on the same side (above/below) the curve. The error between each point and that predicted by the curve will steadily grow.

Good fit, matching either side:

Bearings moving away from curve, suggesting one vehicle has changed state:

I've found a new training set, it appears to contain more noise than the existing simulated data we're using.
Bearing Course Speed data.txt