## 2 Overview of Time-Series RSS Observation Outlier Detection Methods
### Density-Based Method  
This method uses a density function to calculate the likelihood of a data point being an outlier. Data points that have a low likelihood of being part of the data distribution are considered outliers. The local outlier factor (LOF) is a common density-based method for outlier detection. The LOF computes an RSS observation's density in relation to its neighbours and uses this information to identify outliers. Using the RSS observation in Equation (1), the LOF of an RSS observation, \(\mathit{rss}(n)\) is calculated as follows [26; 27]:  
1. For each RSS observation, \(\mathit{rss}(n)\), find the \"\(k\)\" nearest neighbours using a distance metric such as Euclidean distance.
2. Calculate the reachability distance for each RSS observation, \(\mathit{rss}(w)\) in the \"\(k\)\" nearest neighbours of, \(\mathit{rss}(n)\), which is the maximum of the Euclidean distance between \(\mathit{rss}(n)\) and \(\mathit{rss}(w)\) and the distance between \(\mathit{rss}(n)\) and its \"\(k-th\)\" nearest neighbour.
3. Calculate the local reachability density (LRD) of each RSS observations in the \"\(k\)\" nearest neighbours of \(\mathit{rss}(n)\), which is the inverse of the average reachability distance of \(\mathit{rss}(w)\) to its \"\(k\)\" nearest neighbours.
4. Calculate the LOF of each RSS observation, \(\mathit{rss}(n)\) as the ratio of the average LRD of its \"\(k\)\" nearest neighbours to its own LRD. Mathematically, the LOF is: \[LOF(\mathit{rss}(n))=\frac{1}{k}sum\left(\frac{LRD(\mathit{rss}(l))}{LRD( \mathit{rss}(n))}\right)\] (4)
5. Assign a threshold value to the LOF, typically 1, above which an RSS observation is considered an outlier.  
The LOF measures how unusual an RSS observation is in comparison to its neighbours. A high LOF value indicates that the RSS observation is an outlier due to its low local reachability density in comparison to its neighbours [27].  
As mentioned earlier, there is no best outlier detection technique for any univariant time-series observation. It depends on several factors, including the size and distribution of observations. However, when dealing with a small observation sample size, outlier detection using the modified Z-score method based on the median absolute deviation (MAD)scale estimator is considered to be the fastest, simplest, and most effective method [29]. As a result, the focus of this paper will be on the application of the modified Z-score method to the detection of outliers in time-series RSS observations.  
Several research works have used Z-score based on the MAD scale estimator to detect outliers [30; 31; 32]. However, this method is only effective for symmetrically distributed univariant time-series observations. Experimental analyses have shown that time-series RSS observations measured at a fixed reference location do not always follow a normal distribution [33; 34; 35]. The distribution of RSS observations over time can be affected by a variety of factors. These factors include the environment, transmit power, receiver sensitivity, and the distance between the transmitter and receiver, among others. The time-series RSS observations may have a Gaussian distribution if the environment is relatively stable and there are no significant obstacles or changes in the environment. Also, it may not have a non-Gaussian distribution if the environment is dynamic and there are significant changes in the environment. Such changes could include the presence of obstacles, the movement of people or vehicles, or changes in weather conditions. This demonstrates that the modified Z-score method based on the MAD scale estimator will not be efficient in detecting outliers in time-series RSS observations. A robust scale estimator to be used with the Z-score method as an alternative to the MAD is proposed and presented in the next section. This scale estimator is highly efficient for both normally and skewedly distributed time-series RSS observations.