This paper presents an ambient magnetic field map-based matching (MM) positioning algorithm for smartphones in an indoor environment. To improve the low distinguishability of a magnetic field fingerprint at a single point, a magnetic field sequence (MFS) combined with the measured trajectory contour coming from pedestrian dead-reckoning (PDR) is used for MM. Based on the fast approximation of magnetic field gradient, a Gauss-Newton iterative (GNI) method is used to find a rigid transformation that optimally aligns the measured MFS with a reference MFS coming from the magnetic field map. Then, the position of the reference MFS is used to control the position drift error of the inertial navigation system (INS) based PDR by an extended Kalman filter (EKF) and to further improve the accuracy of the trajectory contour. Finally, we conduct several experiments to evaluate the navigation performance of the proposed MM algorithm. The test results show that the position estimation error of the MM algorithm is 0.64 m (RMS) in an office building environment, 1.87 m (RMS) in a typical lobby environment, and 2.34 m (RMS) in a shopping mall environment.

Accurate multispectral image segmentation is essential in remote sensing research. Traditional fuzzy clustering algorithms used to segment multispectral images have several disadvantages, including: (1) they usually only consider the pixels’ grayscale information and ignore the interaction between pixels; and, (2) they are sensitive to noise and outliers. To overcome these constraints, this study proposes a multispectral image segmentation algorithm based on fuzzy clustering combined with the Tsallis entropy and Gaussian mixture model. The algorithm uses the fuzzy Tsallis entropy as regularization item for fuzzy C-means (FCM) and improves dissimilarity measure using the negative logarithm of the Gaussian Mixture Model (GMM). The Hidden Markov Random Field (HMRF) is introduced to define prior probability of neighborhood relationship, which is used as weights of the Gaussian components. The Lagrange multiplier method is used to solve the segmentation model. To evaluate the proposed segmentation algorithm, simulated and real multispectral images were segmented using the proposed algorithm and two other algorithms for comparison (i.e., Tsallis Fuzzy C-means (TFCM), Kullback–Leibler Gaussian Fuzzy C-means (KLG-FCM)). The study found that the modified algorithm can accelerate the convergence speed, reduce the effect of noise and outliers, and accurately segment simulated images with small gray level differences with an overall accuracy of more than 98.2%. Therefore, the algorithm can be used as a feasible and effective alternative in multispectral image segmentation, particularly for those with small color differences.

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