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The estimate process of a moving target trajectory is a well-known problem, where the main objective is to improve the estimation of object position. During the tracking are presented errors or variations between the true position and the estimated. In this paper, we treat such variations as a Gauss-Markov colored measurement noise (CMN). The estimation process is performed in predict and update, where the prediction indicates the next position of the bounding box, and the update is a correction step, which includes the new measurement of the tracking model and helps to improve the estimation. Looking for this improvement we use Kalman and Unbiased Finite Impulse Response filters in the standard version and modified for CMN to demonstrate the filter with the best performance. To test the most robust filter we use a high coloredness factor. The tests were carried out with simulated data (ideal and no ideal conditions) and with benchmark data (no ideal conditions). The UFIR modified for the CMN algorithm showed favorable results with high precision and low RMSE in the object tracking process with benchmark data and under no ideal conditions. While KF CMN showed better results under ideal conditions.

Object tracking is an area of study of great interest to various researchers, where the main objective is to improve estimation of the trajectory of a moving object. This is due to the fact that in the object tracking process there are usually variations between the true position of the moving object and the estimated position, that is, the object is not exactly followed throughout its trajectory. These variations can be thought of as Colored Measurement Noise (CMN) caused by the object and the movement of the camera frame. In this paper, we treat such differences as Gauss-Markov colored measurement noise.We use Finite Impulse Response and Kalman Filters with a recursive strategy on the tracking: predict and update. To demonstrate the filter with the best performance, tests were carried out with simulated trajectories and with benchmarks from a database available online. The UFIR modified for CMN algorithm showed favorable results with high precision and accuracy in the object tracking process with benchamark data and under no ideal conditions.While KF CMN showed better results in tests with simulated data under ideal conditions.

This work presents the development of a tracking system for a three-wheeled omnidirectional mobile robot. This kind of robot can perform rotation and translation in any pose. The arc-length segment described by the omni-wheels controls the trajectory of the robot. We present a simplified kinematic model in state-space. The observation system is based on an UltraWide Band ranging sensor. Finally made the state estimation using some classic positioning algorithms and compare the results against Finite Impulse Response Filter state estimators.

In this article, a comparison of the UFIR and Kalman filter to estimate a tracking vehicle system variables is developed considering two possible observation output models. The time stamp approach and the predictive compensation are used to analyze the problem from multiple perturbations, which produces random delayed data and losses during transmissions. For the estimation, a transformation model and a decorrelation covariance matrices are developed with the aim of assure optimal conditions and minimizing the estimation error. Finally, several real situations, miss modeling, uncertain noise covariances, and uncertain probabilities are proposed to demonstrate the effectiveness and robustness of the filter proposed.

The H₂ finite impulse response (FIR) filtering approach allows for optimal object tracking under harsh industrial conditions. In this brief, we propose a bias-constrained H₂ optimal unbiased FIR (H₂-OUFIR) filter for linear discrete time-invariant systems under bounded disturbances, data errors, and initial errors. The H₂-OUFIR filter is derived using the backward Euler method by minimizing the squared Frobenius norm of the weighted transfer function. A bias-constrained suboptimal H₂ FIR filtering algorithm using a linear matrix inequality (LMI) is also designed. Based on experimental examples of global positioning system (GPS)-based vehicle tracking and video human tracking, it is shown that the batch H₂-OUFIR filter operating on short horizons with full error matrices is able to outperform the Kalman, optimal finite impulse response (OFIR), and unbiased finite impulse response (UFIR) filters.

Blood sugar monitoring in diabetic patients is commonly provided with timing jitter caused by human factors. In this paper we address the problem by developing the robust H2 optimal finite impulse response (OFIR) filter under under possible disturbances, initial errors, and measurement errors. The filter is applied to data collected daily before breakfast from diabetic patients. It is shown that the robust H2-OFIR filter improves the accuracy of the OFIR filter by the factor of less than the fractional time jitter. That is, for large fractional timing jitter of 10% the improvement would be less than 10% that is small. Otherwise, it is worth using robust estimators.

In visual object tracking, the estimation of the trajectory of a moving object is a widely studied problem. In the object tracking process, there are usually variations between the real position of the objet in the scene and the estimated position, that is, the object is not exactly followed throughout its trajectory. These variations can be considered as color measurement noise (CMN) caused by the object and the camera frame movement. In this paper, we treat such differences as Gauss-Markov coloring measurement noise. We use Finite Impulse Response filters and Kalman filter with a recursive strategy in tracking: predict and update. To demonstrate the best performance, tests were carried out with simulated trajectories and with benchmarks from a database available online. The OUFIR and UFIR algorithms showed favorable results with high precision and accuracy in the object tracking task.

A novel approach is proposed to $H_2$ finite impulse response (FIR) prediction in discrete-time state-space. The biased-constrained $H_2$ optimal unbiased FIR ( $H_2$ -OUFIR) predictor derived under disturbances and measurement errors is shown to have the maximum likelihood form and be equivalent to the OUFIR predictor under Gaussian noise. The derivation is provided using the backward Euler method by minimizing the squared weighted Frobenius norm. A bias-constrained suboptimal $H_2$ FIR filtering algorithm using the linear matrix inequality is also designed. The $H_2$ -OUFIR predictor performance is investigated by simulations and experimentally in a comparison with the Kalman and unbiased FIR predictors.

This work presents an object tracking process using Kalman and UFIR filters, standard and modified for Colored Measurement Noise (CMN). UFIR CMN showed favorable results with no ideal conditions, and KF CMN for ideal conditions.

Visual object tracking is commonly accompanied with large variations in the image frame size and position, as caused by the object dynamics and low frame rate. In this paper, we treat such variations as a Gauss-Markov colored measurement noise (CMN), modify the Kalman filter and unbiased finite impulse response filter using the backward Euler method and employing measurement differencing, and apply to some simulated and benchmark data. It is shown that the modified filters can suppress efficiently both the slow frame variations associated with CMN and fast variations associated with white noise. Extensive experimental investigations conducted for the "Car4" benchmark database has demonstrated a high efficiency of the modified algorithms.

Air pollution continues to be a significant risk to public health. It is an important issue that affects everyone and should be studied to take actions that help mitigate the risk. This research’s main objective is to explore air quality from 2010 to 2018 in metropolitan zones of Guadalajara, Monterrey, and the Valley of Mexico. Air quality is analyzed based on the concentrations of criteria pollutants: carbon monoxide (CO), nitrogen dioxide (NO 2 ), ozone (O 3 ), particulate matter less than or equal to 2.5 micrometers (PM 2.5 ), particulate matter less than or equal to 10 micrometers (PM 10 ), and sulfur dioxide (SO 2 ). In this paper, six stages are proposed:1) data collection; 2) data cleansing; 3) descriptive analysis. 4) design of cluster analysis models and main components; 5) application of machine learning models; 6) interpretation and analysis of results. This study has concluded that higher mean hourly concentrations for pollutants, CO, NO 2 , O 3 , PM 2.5 , and SO 2 were found in Guadalajara Metropolitan Zone. In contrast, the highest mean hourly concentration of PM 10 was found in the Monterrey Metropolitan Zone. Furthermore, the pollutant with the highest effect in the three critical zones was PM 2.5 , presenting high concentrations with hazardous air quality levels. Finally, the area with the worst air quality was Guadalajara Metropolitan Zone.