Presentation_SensorsCalibration

Offset Correction & Sensors Calibration for High-Deployable Low-Cost Devices

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{error\ [dBm]}

\mathrm{Asymmetric\ error\ before\ and\ after\ the\ offset\ correction}

\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

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)

\mathcal{N}(0,\sigma^2)

Collecting a series of measurements (from t to t+T)

Y = HX + w\mathbb{1}^T + E

Y = HX + w\mathbb{1}^T + E

Then,

\min_{X,w} \| w \| + \| Y - HX - w\mathbb{1}^T\|_R

\min_{X,w} \| w \| + \| Y - HX - w\mathbb{1}^T\|_R

s.t.\ \ AX = B

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