## 1 Introduction  
Currently, GPS (Global Positioning System) location estimation is used outdoors, and while indoors, signal attenuation and refraction problems make GPS errors even greater [1]. Currently, the use of smartphones, which have a high penetration rate, is often considered for indoor position estimation.Frequently, wireless signals such as Wi-Fi (Wireless Fidelity) [2], Bluetooth, and ZigBee [3] are often used, all of which use a transmitting terminal to measure the RSSI (Received Signal Strength Indication) of the signal. With the launch of Bluetooth 4.0 technology, low-cost power technology is incorporated into Bluetooth 4.0, and location estimation methods based on BLE (Bluetooth Low Energy) [4] have more advantages. There have been some related studies on BLE channel separation [5], or the combination of BLE and the dead reckoning method [6]. Indoor location estimation methods can be divided into two main categories: by distance and by position fingerprints. The distance-based estimation method is based on triangulation [7]. The triangulation method calculates the distance by observing the RSSI values of multiple APs (Access Points). Its accuracy is insufficient due to the propagation loss of RSSI caused by indoor walls and obstructions [8]. The position fingerprinting method [9; 10] is a position estimation method that uses the distribution pattern of RSSI in the indoor environment. RSSI measurements are taken in advance at several locations and used as position fingerprints (a collection of RSSI values for each location). Localization is performed by comparing the similarity of the position fingerprint RSSI with the actual measured RSSI. Several methods have been proposed for indoor location estimation using fingerprint positioning method, including fingerprinting using CNN (Convolutional Neural Network) [11; 12; 13], k-NN (k-Nearest Neighbor) [14; 15; 16], and SVM (Support Vector Machine) [17]. In the CNN-based method, the RSSI value is transformed into an image that becomes a location fingerprint. By learning the pixel values of the image, the location estimation can be calculated. The method using CNN provides high accuracy in simulations but requires a large amount of data for training, which makes it costly in practical experiments. In the method using k-NN, k fingerprints near the observation point are selected based on the measured RSSI values, and the location is estimated by calculating the average value. In the k-NN-based method, the estimation accuracy is greatly affected by the distribution of RSSI noise. In the method using SVM, the RSSI values of the reference points are learned and transformed into a classification problem by a kernel function for position estimation. The choices of the kernel function and parameters greatly affect the accuracy of the estimation. On the other hand, particle filters [18], which can deal with non-linear cases, have also been widely applied to position estimation for object tracking [19], post-processing, and other purposes using statistical models. The computational complexity of traditional methods using particle filters is also high when the number of particles is large, and therefore methods that can reduce the complexity are considered [20; 21; 22]. Related studies have shown that general particle filtering allows for filtering and improving the accuracy of the predicted positions of machine learning algorithms [22]. In [22], the weight function used in the particle filter considers distance. However, there have been few discussions on the suitable weight functions used in the particle filter used in the fingerprinting method. This study proposes a fingerprint positioning method based on k-NN and improved particle filters, whose weight functions consider the coordinates. The proposed system first estimates the position using k-NN, and then corrects the estimated position using a particle filter with improved likelihood functions to reduce the error of k-NN caused by noise.