From Equation (1), we can obtain the estimated distance D:D=D0��1

From Equation (1), we can obtain the estimated distance D:D=D0��10((P(D0)?P(D)?Xr)/10n)(2)However, in real systems, there are uncertainties in the arriving signal strength due to the influence of environmental factors such as reflection, refraction, multi-path transmission, antenna gain, and many other obstacles [12]. Moreover, under different environments or at different communication distances, the level of uncertainty in RSSI values will also be different (if uncertainty is represented by the statistical variance, the higher the variance, the greater the uncertainty is). Generally in an open air environment the level of uncertainty in RSSI values is lower than that of an environment which has obstacles, such as walls. Therefore, the relationship between RSSI and D can hardly fulfill Equation (2).

There is no longer a linear relationship between the RSSI value and lg(D) in these scenarios.If we directly apply the above-mentioned empirical model-based linear or curve fitting method to RSSI-D estimation, the communication distance estimation relative error could be 50% or worse [13]. To solve this problem, scholars have performed many studies on the subject and have proposed various methods. Some researchers have proposed particle swarm optimization (PSO) [10], extended Kalman filter (EKF) [14,15], particle filter (PF) [16] and methodology to filter out the errors in the RSSI. However, with these filters, the system model must be accurately described and moreover, the computation complexity is high, and timing requirements in real-time processing are difficult to meet for many WSN applications.

Although real RSSI values exhibit a significant level of uncertainty, their distributions still share some statistical properties in terms of uncertainties. Carfilzomib Specifically, RSSI values with the same communication distance tend to constitute a cluster. The objective of this paper is to find a more effective way to overcome the uncertainty of RSSI values and achieve better RSSI-D estimation results.To improve distance estimation accuracy, we have proposed a RSSI-D estimation method using interval data clustering, called Distance Estimation using Uncertain Data Clustering (DEUDC). As shown in Figure 1, the framework of DEUDC is comprised of an off-line environment measurement module and an on-line distance estimation module.Figure 1.The framework of DEUDC.Off-line environment measurement: We first perform RSSI sample measurements at different communication points in the wireless communication environment. We then submit the RSSI data for statistical computation and model the RSSI distribution characteristic in terms of RSSI uncertainties.

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