# 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

SymbolDescription
$$x_i(t_j)$$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
tTime in sensor data stream, e.g $$x_t$$ is the observed sensor data value at time t
iColumn index $$i=1,\ldots ,V$$
jRow index $$j=1,\ldots ,N$$
fFeature
qSize of moving window
NNumber of samples
VNumber of variables e.g. temperature, humidity, voltage
MNumber of sensor unit
FNumber 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 $$\mathbf{X } \in {\mathbb {R}}^{N\times V}$$, $$\mathbf{X } = \left( \vec {x}_{1}, \ldots ,\vec {x}_{j},\dots ,\vec {x}_{N}\right)$$
1. Depending on how the samples are obtained, the variables in sensor data vector $$\vec {x}$$ might be produced by more than one sensor. For example, in environmental monitoring, the data may be produced by several sensors, each measuring one variable e.g. temperature and humidity. On the other hand, some variables are produced by one sensor alone, such as an accelerometer which produces readings for three variables i.e. the acceleration in the direction x, y, and z