I have a sensor that gives me a direction of the target in degrees with a certain standard deviation and I use a circular probability density function (PDF) to represent probable locations for the target. For example if the sensor is in [20 20] and the measurement is 45 degrees with 3 degrees of std, I get something like this,
I multiply the PDF of the measurements when sensor is in three or four different locations and I get almost an accurate estimate of the target position. My problem is the calculation of CEP (Circular Error Probability) or even other types of position accuracy measures. Table below has the definition,
As you can see they all have the variance in the direction of x and y but I only have one variance in the form of square degrees. So can I somehow convert this variance? or am I missing some obvious facts?