We consider the problem of stochastic identification of multiple sinusoids from intermittently missing measurements of superimposed signal. An alternate problem formulation is presented as estimation of amplitude and frequency of the sinusoids from missing measurements. The popularly known estimation methods, such as the extended Kalman filter (EKF) and cubature Kalman filter (CKF) may fail or suffer from poor accuracy if the measurements are missing. In this paper, we redesign the EKF to handle this irregularity in measurements and apply the modified EKF for the formulated estimation problem. In this regard, we introduce a modified measurement model incorporating the possibility of missing measurements. Subsequently, we rederive the relevant parameters of the EKF, such as measurement estimate, measurement error covariance, and state-measurement cross-covariance, for the modified measurement model. Furthermore, we rederive the posterior covariance with minimized trace and study the stability of the resulting extension of the EKF. The results reveal the superior performance of the modified EKF compared with the ordinary Gaussian filters and existing filters-based estimation of the sinusoids in the presence of intermittently missing measurements.

The practicality of administrative measures for covid-19 prevention is crucially based on quantitative information on impacts of various covid-19 transmission influencing elements, including social distancing, contact tracing, medical facilities, vaccine inoculation, etc. A scientific approach of obtaining such quantitative information is based on epidemic models of SIR family. The fundamental SIR model consists of S-susceptible, I-infected, and R-recovered from infected compartmental populations. To obtain the desired quantitative information, these compartmental populations are estimated for varying metaphoric parametric values of various transmission influencing elements, as mentioned above. This paper introduces a new model, named SEIRRPV model, which, in addition to the S and I populations, consists of the E-exposed, Re-recovered from exposed, R-recovered from infected, P-passed away, and V-vaccinated populations. Availing of this additional information, the proposed SEIRRPV model helps in further strengthening the practicality of the administrative measures. The proposed SEIRRPV model is nonlinear and stochastic, requiring a nonlinear estimator to obtain the compartmental populations. This paper uses cubature Kalman filter (CKF) for the nonlinear estimation, which is known for providing an appreciably good accuracy at a fairly small computational demand. The proposed SEIRRPV model, for the first time, stochastically considers the exposed, infected, and vaccinated populations in a single model. The paper also analyzes the non-negativity, epidemic equilibrium, uniqueness, boundary condition, reproduction rate, sensitivity, and local and global stability in disease-free and endemic conditions for the proposed SEIRRPV model. Finally, the performance of the proposed SEIRRPV model is validated for real-data of covid-19 outbreak.

State estimation in cyber-physical systems is a challenging task involving integrating physical models and measurements to estimate dynamic states accurately in practical machine-to-machine and IoT deployments. However, integrating advanced wireless communication and intelligent measurements has increased vulnerability of external intrusion through a centralized server. This study addresses the challenge of Gaussian filtering for a specific type of stochastic nonlinear system vulnerable to cyber attacks and delayed measurements. These attacks occur randomly when data is transmitted from sensor nodes to remote filter nodes. To address this issue, a new cyber attack model is proposed that combines false data injection attacks and delayed measurement into a unified framework. The study also analyzes the stochastic stability of the proposed filter and establishes sufficient conditions to ensure that the filtering error remains bounded even in the presence of randomly occurring cyber attacks and delayed measurements. The proposed methodology is demonstrated and compared with other widely used approaches using simulated data to highlight its effectiveness and usefulness.

This article designs an advanced Gaussian filtering algorithm for improving accuracy in the presence of time-delay in measurements. The proposed method uses a Bernoulli random variable and a geometric random variable to reformulate the delay modeling strategy. Subsequently, the traditional Gaussian filtering method for the modified measurement model is rederived. The proposed method precludes two major drawbacks of the existing delay filtering methods, including a priori knowledge of many delay probabilities and an ambiguous selection of an upper bound of delay. Thus, the proposed method outperforms the existing delay filtering methods and the same is validated from the simulation results. The proposed method is a general modification of the traditional Gaussian filtering and applies to all conventionally popular Gaussian filters.

Traditionally, Kalman filter (KF) is designed with the assumptions of non-delayed measurements and additive white Gaussian noises. However, practical problems often fail to satisfy these assumptions and the conventional Kalman filter suffers from poor estimation accuracy. This paper proposes a modified Kalman filter to address both the problems of delayed measurements and non-Gaussian noises. The proposed filter is updated using correntropy maximization criterion, which is suitable for non-Gaussian noise environments. It falls short of a closed-form solution due to analytically complex equations that appear during the filtering. We use fixed-point iterative method to find an approximate solution. The delayed measurement problem is addressed by implementing a likelihood-based approach to identify the delay. Based on the identified delay information, the measurement is used to update the desired state in the subsequent past instant. To perform real-time filtering, the estimated state is further updated up to the current time instant using the process dynamics. The performance analysis validates the improved accuracy of the proposed method compared to the ordinary Kalman filter and its existing extensions.

In this paper, the Cubature Kalman filter (CKF) is implemented for tracking maneuvering targets such as ballistic missiles, aircraft, etc. Its high accuracy at a relatively low computational cost makes it suitable for real-life applications. The coordinated model is adopted for modeling of the maneuvering targets. The simulation results for this filter are observed for maneuvering targets with varying turn rate. The performance is analyzed in terms of the root mean square error (RMSE) computed over a large number of Monte-Carlo runs. The simulation results reveal a successful tracking of the moving targets using the CKF. From simulations, we observe that RMSE increases with the turn rate.