Offset Correction & Sensors Calibration for High-Deployable Low-Cost Devices
New Energetic Scenario
New Energetic Scenario
New challenges
High renewables penetration
High uncertainty
Stability issues
Need for sensing
Need for control
Deployment of a large number of low cost sensors
2. Possible issues...
-
Low accuracy
-
Low precision
3. Due to...
-
Systematic error
-
Synchronization error
-
Sensors gain
Large deployment of low cost sensors
1. Used for...
- State estimation
- Monitoring and (successive) control
Possible Solution: Sensor calibration
Sensors calibration improves the performance*
* from Bolognani, Del Favero, Schenato, Varagnolo, Distributed sensor calibration and least–square parameter identification in WSNs using consensus algorithms, Allerton 2008.
\mathrm{error\ [dBm]}
\mathrm{Asymmetric\ error\ before\ and\ after\ the\ offset\ correction}
Effect of systematic errors when estimating distances
Problem Formulation
Measurement model (at time instant t)
y = Hx + w + e
where
- y, measurement
- x, state
- H, meas. matrix
- w, offset error (constant over time)
- e, random noise ~
\mathcal{N}(0,\sigma^2)
Collecting a series of measurements (from t to t+T)
Y = HX + w\mathbb{1}^T + E
Then,
\min_{X,w} \| w \| + \| Y - HX - w\mathbb{1}^T\|_R
s.t.\ \ AX = B
(linearized power flow constraints)
What do we need?
A concrete and consistent measurement model
the closer the model to the reality the better and reliable the calibration
Real data to test the algorithm with
validate the effectiveness of the algorithm for its practical implementation
Algorithm Structure
Collect data
Data cleaning and processing
Offset estimation
Error model
Go to
state estimation
&
control
Sensors Calibration
Logs & statistical report
Presentation_SensorsCalibration
By marco todescato
Presentation_SensorsCalibration
Presentation to briefly present issues and approach to sensor calibration
