Table 1 Nomenclature used for “Methods for detecting and quantifying errors in sensor data”,“Methods for correcting errors in sensor data” and “Methods for detecting and correcting errors in sensor data” sections
Symbol | Description |
|---|---|
\(x_i(t_j)\) | Measured data value \(x_i\) of sensor i at a specific point in time \(t_j\) |
\({\hat{x}}\) | Estimated sensor data value |
\(\vec {x}\) | Sensor data vector, where \(\vec {x} = \left( x_1,\ldots ,x_i,\ldots ,x_V\right)\) is a row vector obtained at the same point in time |
t | Time in sensor data stream, e.g \(x_t\) is the observed sensor data value at time t |
i | Column index \(i=1,\ldots ,V\) |
j | Row index \(j=1,\ldots ,N\) |
f | Feature |
q | Size of moving window |
N | Number of samples |
V | Number of variables e.g. temperature, humidity, voltage |
M | Number of sensor unit |
F | Number of features |
\(\mathbf{Z }\) | Sensor data stream in the form of a time series, \(\mathbf{Z } = \left( \dots ,\vec {x}_{t-1},\vec {x}_{t},\vec {x}_{t+1},\dots \right)\) |
\(\mathbf{X }\) | Sensor data matrix where \(\mathbf{X } \in {\mathbb {R}}^{N\times V}\), \(\mathbf{X } = \left( \vec {x}_{1}, \ldots ,\vec {x}_{j},\dots ,\vec {x}_{N}\right)\) |