Unsupervised Learning in RSS-Based DFLT Using an EM Algorithm

Abstract

Received signal strength (RSS) changes of static wireless nodes can be used for device-free localization and tracking (DFLT). Most RSS-based DFLT systems require access to calibration data, either RSS measurements from a time period when the area was not occupied by people, or measurements while a person stands in known locations. Such calibration periods can be very expensive in terms of time and effort, making system deployment and maintenance challenging. This paper develops an Expectation-Maximization (EM) algorithm based on Gaussian smoothing for estimating the unknown RSS model parameters, liberating the system from supervised training and calibration periods. To fully use the EM algorithm’s potential, a novel localization-and-tracking system is presented to estimate a target’s arbitrary trajectory. To demonstrate the effectiveness of the proposed approach, it is shown that: (i) the system requires no calibration period; (ii) the EM algorithm improves the accuracy of existing DFLT methods; (iii) it is computationally very efficient; and (iv) the system outperforms a state-of-the-art adaptive DFLT system in terms of tracking accuracy.

A Two-Filter Approach for State Estimation Utilizing Quantized Output Data

“…Provided p(x t |y 1:t ) in (33) as a GMM, the state estimator given in (10) and the covariance matrix of the estimation error in ( 12) can be computed as follows:…”

“…1 Input: The PDF of the initial state p(x 1 ), e.g., Compute the state estimation in (10) and the covariance matrix of the estimation error in (12) according to (37) and (38).…”

“…State estimation is a scientific discipline that studies methodologies and algorithms for estimating the state of dynamical systems from input-output measurements [2,3]. There are a variety of applications that use state estimation, such as control [4][5][6][7], parameter identification [8][9][10], power systems [11,12], fault detection [13][14][15][16][17], prognosis [18,19], cyber-physical systems [20], hydrologic and geophysical data assimilation [21,22], maritime tracking [23], consensusbased state estimation using wireless sensor networks [24][25][26], navigation systems [27], and transportation and highway traffic management [28][29][30], to mention a few. Depending on the measurements that are used, two algorithms of state estimation can be distinguished: filtering and smoothing.…”

“…14 Time Update 15 Set M t+1|t = M t|t . 16 for k = 1 to M t+1|t do 17 Compute and store γ k t+1|t , xk t+1|t , and Σ k t+1|t according to Theorem 2. state estimation in(10), the covariance matrix of the estimation error in(12), the filtering PDFs p(x t |y 1:t ), the predictive PDFs p(x t+1 |y 1:t ), and the set {ς τ t , η τ t , µ τ t }, for t = 1, . .…”