Page 109 - Introduction to Autonomous Mobile Robots

Chapter 4
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Cross-sensitivity is the technical term for sensitivity to environmental parameters that
are orthogonal to the target parameters for the sensor. For example, a flux-gate compass can
demonstrate high sensitivity to magnetic north and is therefore of use for mobile robot nav-
igation. However, the compass will also demonstrate high sensitivity to ferrous building
materials, so much so that its cross-sensitivity often makes the sensor useless in some
indoor environments. High cross-sensitivity of a sensor is generally undesirable, especially
when it cannot be modeled.
Error of a sensor is defined as the difference between the sensor’s output measurements
and the true values being measured, within some specific operating context. Given a true
value v and a measured value m, we can define error as error = m – v .
Accuracy is defined as the degree of conformity between the sensor’s measurement and
the true value, and is often expressed as a proportion of the true value (e.g., 97.5% accu-
racy). Thus small error corresponds to high accuracy and vice versa:

 ---------------- - 
error
 accuracy = 1 – v  (4.3)

v
Of course, obtaining the ground truth, , can be difficult or impossible, and so establish-
ing a confident characterization of sensor accuracy can be problematic. Further, it is impor-
tant to distinguish between two different sources of error:
Systematic errors are caused by factors or processes that can in theory be modeled.
These errors are, therefore, deterministic (i.e., predictable). Poor calibration of a laser
rangefinder, an unmodeled slope of a hallway floor, and a bent stereo camera head due to
an earlier collision are all possible causes of systematic sensor errors.
Random errors cannot be predicted using a sophisticated model nor can they be miti-
gated by more precise sensor machinery. These errors can only be described in probabilistic
terms (i.e., stochastically). Hue instability in a color camera, spurious rangefinding errors,
and black level noise in a camera are all examples of random errors.
Precision is often confused with accuracy, and now we have the tools to clearly distin-
guish these two terms. Intuitively, high precision relates to reproducibility of the sensor
results. For example, one sensor taking multiple readings of the same environmental state
has high precision if it produces the same output. In another example, multiple copies of
this sensor taking readings of the same environmental state have high precision if their out-
puts agree. Precision does not, however, have any bearing on the accuracy of the sensor’s
output with respect to the true value being measured. Suppose that the random error of a
µ
σ
sensor is characterized by some mean value and a standard deviation . The formal def-
inition of precision is the ratio of the sensor’s output range to the standard deviation: