A Kalman filter method for estimation and prediction of space–time data with an autoregressive structure

Multivariate Kalman filtering for spatio-temporal processes

An increasing interest in models for multivariate spatio-temporal processes has been noted in the last years. Some of these models are very flexible and can capture both marginal and cross spatial associations amongst the components of the multivariate process. In order to contribute to the statistical analysis of these models, this paper deals with the estimation and prediction of multivariate spatio-temporal processes by using multivariate state-space models. In this context, a multivariate spatio-temporal process is represented through the well-known Wold decomposition. Such an approach allows for an easy implementation of the Kalman filter to estimate linear temporal processes exhibiting both short and long range dependencies, together with a spatial correlation structure. We illustrate, through simulation experiments, that our method offers a good balance between statistical efficiency and computational complexity. Finally, we apply the method for the analysis of a bivariate dataset on average daily temperatures and maximum daily solar radiations from 21 meteorological stations located in a portion of south-central Chile.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00477-022-02266-3.

MEMS Inertial Sensor Fault Diagnosis Using a CNN-Based Data-Driven Method

In this paper, we propose a novel fault diagnosis (FD) approach for micro-electromechanical systems (MEMS) inertial sensors that recognize the fault patterns of MEMS inertial sensors in an end-to-end manner. We use a convolutional neural network (CNN)-based data-driven method to classify the temperature-related sensor faults in unmanned aerial vehicles (UAVs). First, we formulate the FD problem for MEMS inertial sensors into a deep learning framework. Second, we design a multi-scale CNN which uses the raw data of MEMS inertial sensors as input and which outputs classification results indicating faults. Then we extract fault features in the temperature domain to solve the non-uniform sampling problem. Finally, we propose an improved adaptive learning rate optimization method which accelerates the loss convergence by using the Kalman filter (KF) to train the network efficiently with a small dataset. Our experimental results show that our method achieved high fault recognition accuracy and that our proposed adaptive learning rate method improved performance in terms of loss convergence and robustness on a small training batch.

Combining Spatio-Temporal Context and Kalman Filtering for Visual Tracking

As one of the core contents of intelligent monitoring, target tracking is the basis for video content analysis and processing. In visual tracking, due to occlusion, illumination changes, and pose and scale variation, handling such large appearance changes of the target object and the background over time remains the main challenge for robust target tracking. In this paper, we present a new robust algorithm (STC-KF) based on the spatio-temporal context and Kalman filtering. Our approach introduces a novel formulation to address the context information, which adopts the entire local information around the target, thereby preventing the remaining important context information related to the target from being lost by only using the rare key point information. The state of the object in the tracking process can be determined by the Euclidean distance of the image intensity in two consecutive frames. Then, the prediction value of the Kalman filter can be updated as the Kalman observation to the object position and marked on the next frame. The performance of the proposed STC-KF algorithm is evaluated and compared with the original STC algorithm. The experimental results using benchmark sequences imply that the proposed method outperforms the original STC algorithm under the conditions of heavy occlusion and large appearance changes.