The problem of distributed fusion of Gaussian mixture models (GMMs) provided by the local multiple model (MM) estimators is addressed in this paper. Taking GMMs instead of combined Gaussian assumed probability density functions (pdfs) as the output of local MM estimators can retain more detailed (or internal) information of local estimations, but the accompanying challenge is how to perform the fusion of GMMs. For this problem, a distributed fusion framework of GMMs under the minimum forward Kullback-Leibler (KL) divergence sum criterion is proposed first. Then because the KL divergence between GMMs is not analytically tractable, two suboptimal distributed fusion algorithms are further developed within this framework. These two fusion algorithms all have closed forms. Numerical examples verify their effectiveness in both computational efficiency and estimation accuracy.

We revisit the problem of modeling of the over-the-horizon radar (OTHR) target tracking. The accuracy of target kinematic and measurement models are critical factors affecting tracking performance. In most of the existing literature, a flat Earth OTHR measurement model is used. This has two obvious drawbacks: (1) a state vector with components of ground range, range-rate, bearing, and bearing-rate cannot be used directly in common kinematic models such as the nearly constant velocity (NCV), nearly constant acceleration (NCA), nearly constant turn (NCT), and a combination of these. (2) The curvature of Earth is ignored, which affects the measurement accuracy of the OTHR. We develop a spherical Earth based measurement model. First, the target kinematic state is modeled in a two-dimensional tracker coordinate frame (T frame), which is suitable for the common kinematic models. Second, the measurement modeling is completed using the spherical Earth model, which fully considers the curvature of Earth among the receiver, transmitter, and target. Furthermore, the inverse mapping for track initiation is derived. Finally, the effectiveness of the developed model is demonstrated by a non-maneuvering target moving with the NCV motion and a maneuvering target moving with a sequence of NCV, NCT, and NCV motions. The interacting multiple model (IMM) algorithm is used for state estimation of the maneuvering target. The unscented Kalman filter (UKF), cubature Kalman filter (CKF), and quadrature Kalman filter (QKF) are compared for state estimation.

The problem of two-dimensional bearings-only multisensor-multitarget tracking is addressed in this work. For this type of target tracking problem, the multidimensional assignment (MDA) is crucial for identifying measurements originating from the same targets. However, the computation of the assignment cost of all possible associations is extremely high. To reduce the computational complexity of MDA, a new coarse gating strategy is proposed. This is realized by comparing the Mahalanobis distance between the current estimate and initial estimate in an iterative process for the maximum likelihood estimation of the target position with a certain threshold to eliminate potential infeasible associations. When the Mahalanobis distance is less than the threshold, the iteration will exit in advance so as to avoid the expensive computational costs caused by invalid iteration. Furthermore, the proposed strategy is combined with the two-stage multiple hypothesis tracking framework for bearings-only multisensor-multitarget tracking. Numerical experimental results verify its effectiveness.

The cultivation of English listening and speaking abilities has been paid more attention nowadays, while diversified phonetic teaching strategies provide students with approaches to learn phonetics native speakers. This paper aims to study the phonetic teaching strategies, particularly the impact of online phonetic teaching videos on English learners in primary-secondary schools. The research provides the valid data of students’ level of phonetics and indicators’ teaching strategies in the actual teaching process. Through analysis, the author puts forward reasonable suggestions for improving students’ English listening and speaking abilities from the perspective of phonetic teaching strategies. In addition, through the analysis of the inadequacy of students’ learning abilities, promoting the mastery of phonetics will help improve students’ comprehensive qualities.

The problem of multi-sensor bearings-only target tracking is addressed in this work. A practical challenge in this problem stems from the data association in dense clutter. In order to avoid the increase of computational complexity with the increase of the number of sensors and clutter density, a two-stage multiple hypothesis tracking (MHT) algorithm is proposed. First, the first stage MHT is performed at each local sensor, and the measurements with effective data association are sent to the fusion center. Second, the measurements from different sensors are combined and augmented to form new measurement vectors, which are then converted to Cartesian coordinates by iterated least squares (ILS) estimator. Therefore, in the second stage MHT, the Kalman filter can be used to update the target track. The performance of the two-stage MHT algorithm is illustrated with an example.