On Sunday, June 3, 2012 8:54:50 AM UTC-7, David Holstius wrote:
....
Once the offset is established, and assuming it's stationary, then
obviously (as you know) the question is the gain. The potential
density of a deployed network based on devices like AQE suggests a
different problem than one-at-a-time factory calibration. Balzano (of
CENS) and Nowak call this "blind calibration" of sensor networks. Some
theoretical and simulated results are here:
http://sunbeam.ece.wisc.edu/publications/bcbook.pdf
Hello David
Fascinating. Blind Calibration.
I read it as possibly solving problems as associated with drift in sensors in the field, they differentiate between uncalibrated sensors (with manufacturing offsets applied) and raw sensors measurements
They identify conditions which if raw sensor output meet could apply more generally
Some excerpts with an attempt at translating it to a gas sensor..
blind calibration - a novel automatic sensor calibration procedure that requires solving a linear system of constraints involving routine sensor measurements. By “routine” we mean that actual signal measured by the sensor network is uncontrolled and unknown.
"sensors slightly oversample the signals of interest," - seems to imply that a physical array of sensors all measuring "over sample" the same gas "signal of interest"
"nor a dense deployment is required" - they suggest a matrix of 8 x 8 sensors, but later use 9 temperature sensors which have been linearized, though the general case is "from n sensors lie in a subspace of n-dimensional Euclidean space"
so my maths gets a bit rusty.
"We assume a linear model for the sensor calibration functions. This means that the sensor readings are calibrated up to an unknown gain and
offset (bias) for each sensor, possibly after applying a suitable and fixed transformation to the raw sensor readings, e.g., taking the logarithm or
applying the original factory calibration transformation." - most sensors are not linear across their range of interest, but maybe there are linear relationships that can be determined from knowledge of the materials (!!) - however drift can be linear, as it applies to all parts of the sensor (?).
"The Nyquist theorem dictates a minimum spacing between sensors in order to adequately sample a bandlimited signal.
If sensors are spaced more closely than the minimum requirement, then we are “oversampling” the signal."
That seems to suggest if the spacing (mechanical design) between the sensors is sufficient to so the measurement error (gasseous distribution and electronics measurement noise) is less that a pre-determined minimum - then the ppb in the gas signal can be determined to be oversampled
(mental note - some needs to understand how close the gas sensors need to be and what level of measurement signal is needed)
Moving into more detail
We can summarize this for all n sensors using the vector notation
x = Y a + b (1)
where Y = diag (y) - the oversample measurements from 'n' sensors.
The blind calibration problem entails the recovery of 'a' and 'b' from routine uncalibrated sensor readings such as y.
now fast forward to sect 6.2.1 Calibration Dataset
"the conclusion was drawn that after the factory-supplied calibration was applied to the raw sensor measurements,
the sensors differed from the reference thermocouple linearly i.e. by only a gain and offset."
and they use 9 temperature sensors for the calibration dataset.
After that they apply it to 26 distributed temperature sensors
and then I'm afraid I can't follow how they are using the data. Plus I'm running out of time.
Sect 8 Extensions and Future Work
"There are many issues in blind calibration that could be explored further.
The two main areas ripe for study are the choice of the subspace P and the implementation of blind calibration.
..
How to choose the subspace when faced with a sensor deployment where the true signals are unknown is an extremely important question for blind
calibration.
and
9 Conclusions
The problem of sensor calibration is central to the practical use of sensor networks.
..
We have demonstrated a working implementation on simulated and real data, which uncovered interesting relationships between implementation and blind calibration performance.
Overall, we have demonstrated that blind calibration has great potential to be possible in practice, and we feel that the proposed formulation merits further investigation.
Gotta leave it at that .. but be interested as to what other people make of it, and I'm wondering why they don't use the raw sensor data from a temperature probe - and temperature after all is the most measured physical parameters and one of the most easily to relate to, and one of the most desirable to get a good accuracy on.