In this letter, we propose a new distance estimation method based on statistical models of a Received Signal Strength (RSS) at the receiver. The conventional distance estimator estimates the distance between the transmitter and the receiver based on the statistical average of the RSS when the receiver obtains instantaneous RSS and an estimate of the hyperparameters which consists of the path loss exponent and so on. However, it is well-known that instantaneous RSS does not always correspond to the average RSS because the RSS varies in accordance with a statistical model. Although the statistical model has been introduced for the hyperparameters estimation and the localization system, the conventional distance estimator has not yet utilized it. We introduce the statistical model to the distance estimator whose expected value of the estimate corresponds to true distance. Our theoretical analysis establishes that the proposed distance estimator is preferable to the conventional one in order to improve accuracy in the expected value of the distance estimate. Moreover, we evaluate the Mean Square Error (MSE) between true distance and the estimate. We provide evidence that the MSE is always proportional to the square of the distance if the estimate of the hyperparameters is ideally obtained.

In this paper, we propose an error-correction low-pass filter (EC-LPF) algorithm for estimating the wireless distance between devices. To measure this distance, the received signal strength indication (RSSI) is a popularly used method because the RSSI of a wireless signal, such as Wi-Fi and Bluetooth, can be measured easily without the need for additional hardware. However, estimating the wireless distance using an RSSI is known to be difficult owing to the occurrence of inaccuracies. To examine the inaccuracy characteristics of Bluetooth RSSI, we conduct a preliminary test to discover the relationship between the actual distance and Bluetooth RSSI under several different environments. The test results verify that the main reason for inaccuracy is the existence of measurement errors in the raw Bluetooth RSSI data. In this paper, the EC-LPF algorithm is proposed to reduce measurement errors by alleviating fluctuations in a Bluetooth signal with responsiveness for real-time applications. To evaluate the effectiveness of the EC-LPF algorithm, distance accuracies of different filtering algorithms are compared, namely, a low-pass filer (LPF), a Kalman filter, a particle filter, and the EC-LPF algorithm under two different environments: an electromagnetic compatibility (EMC) chamber and an indoor hall. The EC-LPF algorithm achieves the best performance in both environments in terms of the coefficient of determination, standard deviation, measurement range, and response time. In addition, we also implemented a meeting room application to verify the feasibility of the EC-LPF algorithm. The results prove that the EC-LPF algorithm distinguishes the inside and outside areas of a meeting room without error.

In the received signal strength-based ranging algorithms, distance is estimated from a path loss model, in which the path loss exponent is considered a key parameter. The conventional RSS-based algorithms generally assume that the path loss exponent is known a priori. However, this assumption is not acceptable in the real world because the channel condition depends on the current wireless environment. In this paper, we propose an accurate estimation method of the path loss exponent that results in minimizing distance estimation errors in varying environments. Each anchor node estimates the path loss exponent for its transmission coverage by the sequential rearrangement of the received signal strengths of all sensor nodes within its coverage. Simulation results show that the proposed method can accurately estimate the actual path loss exponent without any prior knowledge and provides low distance estimation error.

In the research field of microwave radar, a range finding method based on standing wave is known to be effective for measuring short distances. In this paper, we focus our attention on audible sound and fundamentally examine the distance estimation method in which acoustical standing wave is used.