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Mathematical models about changes of plankton populations can help study trendence in marine ecosystems. Random noise is common in marine ecosystems, arising from internal dynamics or external environmental factors. To study the dynamic characteristics of oceanic systems more accurately, the state estimation of the phytoplankton–zooplankton model (PZ model’s) Julia sets affected by additive noise and multiplicative noise is performed to mitigate its effects. The study focuses on two state estimation methods: filtering and prediction, drawing inspiration from particle filtering and moving average principles. The final image analysis demonstrates that both methods effectively reduce noise interference.

In the process of signal transmission, an inevitable phenomenon is that the signal may change abruptly at certain discrete moments, negatively contributing to the performance of the system. In this paper, we focus on the distributed state estimation problem for continuous-time linear time-invariant (LTI) systems with intermittent abrupt jumps in communication information. First, the phenomenon of intermittent sudden jumps during information transmission is characterized as impulsive communication disturbances. Under impulsive communication disturbances, a distributed reduced order observer (DROO) is designed with each local observer grouped with two modules: a reduced-order observer and a consensus-based observer. Then, sufficient conditions for the existence of the DROO are presented, by using the graph theory and impulsive analysis. The relationship between the feedback gain and the unstable system matrix, the network topology, the impulse intensity, and the average impulsive interval is obtained. Finally, the validity of the proposed DROO under impulsive communication disturbances is substantiated by numerical simulations.

Having a better motion model in the state estimator is one way to improve target tracking performance. Since the motion model of the target is not known a priori, either robust modeling techniques or adaptive modeling techniques are required. The neural extended Kalman filter is a technique that learns unmodeled dynamics while performing state estimation in the feedback loop of a control system. This coupled system performs the standard estimation of the states of the plant while estimating a function to approximate the difference between the given state-coupling function model and the behavior of the true plant dynamics. At each sample step, this new model is added to the existing model to improve the state estimate. The neural extended Kalman filter has also been investigated as a target tracking estimation routine. Implementation issues for this adaptive modeling technique, including neural network training parameters, were investigated and an analysis was made of the quality of performance that the technique can have for tracking maneuvering targets.

Multi-rate controllers are useful in providing fast control updates using slow measurements. The multi-rate control loop involves up-sampling, down-sampling, and systems considered at different timescales. The challenge is then, to present complete frequency domain model of the loop. This paper presents the frequency domain model of the loop which is suitable for analysis and design of controllers. The approach is illustrated through a numerical example.

In this paper, a state estimation problem is considered, where sensor data are transmitted with finite communication capacity constraint. To reduce the sensor data transmission, only one sensor data is transmitted at each period among multiple sensors. We propose a dynamic scheduling algorithm, which is based on the difference between the current sensor data and the last transmitted sensor value. The proposed algorithm chooses sensor data, which have the largest contribution to the estimation performance. With the proposed algorithm, when a sensor data is chosen and transmitted, some information can be derived from not transmitted sensor data. This information is also used for better estimation performance.

In this paper, the delay-dependent state estimation problem for switched Hopfield neural networks with time-delay is investigated. Based on the Lyapunov–Krasovskii stability theory, a new delay-dependent state estimator for switched Hopfield neural networks is established to estimate the neuron states through available output measurements such that the estimation error system is asymptotically stable. The gain matrix of the proposed estimator is characterized in terms of the solution to a linear matrix inequality (LMI), which can be checked readily by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed state estimator.

In this article, we use a variant of a recently introduced algebraic state estimation method obtained from a fast output signal time derivatives computation process. The fast time derivatives calculations are entirely based on the consequences of using the "algebraic approach" in linear systems description (basically, module theory and non-commutative algebra). Here, we demonstrate, through computer simulations, the effectiveness of the proposed algebraic approach in the accurate and fast (i.e. nonasymptotic) estimation of the chaotic states in some of the most popular chaotic systems. The proposed state estimation method can then be used in a coding–decoding process of a secret message transmission using the message-modulated chaotic system states and the reliable transmission of the chaotic system observable output. Simulation examples, using Chen's chaotic system and the Rossler system, demonstrate the important features of the proposed fast state estimation method in the accurate extraction of a chaotically encrypted messages. In our simulation results, the proposed approach is shown to be quite robust with respect to (computer generated) transmission noise perturbations. We also propose a way to evade computational singularities associated with the local lack of observability of certain chaotic system outputs and still carry out the encrypting and decoding of secret messages in a reliable manner.

In this paper we consider the problem of estimating the parameters of a nonlinear dynamical system given a finite time series of observations that are contaminated by observational noise. The least squares method is a standard method for parameter estimation, but for nonlinear dynamical systems it is well known that the least squares method can result in biased estimates, especially when the noise is significant relative to the nonlinearity. In this paper, it is demonstrated that by combining nonlinear noise reduction and least squares parameter fitting it is possible to obtain more accurate parameter estimates.

In this paper, we present the application of the gradient descent of indeterminism (GDI) shadowing filter to a chaotic system, that is the ski-slope model. The paper focuses on the quality of the estimated states and their usability for forecasting. One main problem is that the existing GDI shadowing filter fails to provide stability to the convergence of the root mean square error and the last point error of the ski-slope model. Furthermore, there are unexpected cases in which the better state estimates give worse forecasts than the worse state estimates. We investigate these unexpected cases in particular and show how the presence of the humps contributes to them. However, the results show that the GDI shadowing filter can successfully be applied to the ski-slope model with only slight modification, that is, by introducing the adaptive step-size to ensure the convergence of indeterminism. We investigate its advantages over fixed step-size and how it can improve the performance of our shadowing filter.

This paper investigates the state estimation problem of power systems. A novel, fast and accurate state estimation algorithm is presented to solve this problem based on the one-dimensional denoising autoencoder and deep support vector machine (1D DA–DSVM). Besides, for further reducing the computation burden, a partitioning method is presented to divide the power system into several sub-networks and the proposed algorithm can be applied to each sub-network. A hybrid computing architecture of Central Processing Unit (CPU) and Graphics Processing Unit (GPU) is employed in the overall state estimation, in which the GPU is used to estimate each sub-network and the CPU is used to integrate all the calculation results and output the state estimate. Simulation results show that the proposed method can effectively improve the accuracy and computational efficiency of the state estimation of power systems.

We show that if H = ℂ^d then there exists a system of d + 1 measurements which allows to recover an unknown state ρ on H from the probabilities of results of these measurements. Moreover, we show that a randomly chosen system of d + 1 measurements has the above property with probability 1. We also present some novel properties of known mutually unbiased bases.

Quantum tomography requires repeated measurements of many copies of the physical system, all prepared by a source in the unknown state. In the limit of very many copies measured, the often-used maximum-likelihood (ML) method for converting the gathered data into an estimate of the state works very well. For smaller data sets, however, it often suffers from problems of rank deficiency in the estimated state. For many systems of relevance for quantum information processing, the preparation of a very large number of copies of the same quantum state is still a technological challenge, which motivates us to look for estimation strategies that perform well even when there is not much data. After reviewing the concept of minimax state estimation, we use minimax ideas to construct a simple estimator for quantum states. We demonstrate that, for the case of tomography of a single qubit, our estimator significantly outperforms the ML estimator for small number of copies of the state measured. Our estimator is always full-rank, and furthermore, has a natural dependence on the number of copies measured, which is missing in the ML estimator.

In this work, we apply the nonlinear filtering theory to the estimation of the partially observed dynamics of anthracnose which is a phytopathology. The signal here is the inhibition rate and the observations are the fruit volume and the rotted volume. We propose stochastic models based on deterministic models studied previously in the literature, in order to represent the noise introduced by uncontrolled variations on parameters and errors on the measurements. Under the assumption of Brownian noises, we prove the well-posedness of the models in either they take into account the space variable or not. The filtering problem is solved for the nonspatial model giving Zakai and Kushner–Stratonovich equations satisfied respectively by the unnormalized and the normalized conditional distribution of the signal with respect to the observations. A prevision problem and a discrete filtering problem are also studied for the realistic cases of discrete and possibly incomplete observations. We illustrate the filter behavior through figures displaying the average estimation relative error and a 95% confidence region obtained after a hundred of numerical simulations with initial conditions taken randomly with respect to uniform law.

Functional near infrared spectroscopy (fNIRS) is a technique that is used for noninvasive measurement of the oxyhemoglobin (HbO2) and deoxyhemoglobin (HHb) concentrations in the brain tissue. Since the ratio of the concentration of these two agents is correlated with the neuronal activity, fNIRS can be used for the monitoring and quantifying the cortical activity. The portability of fNIRS makes it a good candidate for studies involving subject's movement. The fNIRS measurements, however, are sensitive to artifacts generated by subject's head motion. This makes fNIRS signals less effective in such applications. In this paper, the autoregressive moving average (ARMA) modeling of the fNIRS signal is proposed for state-space representation of the signal which is then fed to the Kalman filter for estimating the motionless signal from motion corrupted signal. Results are compared to the autoregressive model (AR) based approach, which has been done previously, and show that the ARMA models outperform AR models. We attribute it to the richer structure, containing more terms indeed, of ARMA than AR. We show that the signal to noise ratio (SNR) is about 2 dB higher for ARMA based method.

In this note, we consider a new unknown input observer design for nonlinear systems. The main idea consists in determining the estimation error and mean value theorem parameters ($\beta$) to introduce them into proposed observer structure. This process is designed on the basis of mean value theorem and genetic algorithm. The stability study relies on the use of a classical quadratic Lyapunov function. The observer’s gains are determined systematically. For the validation of theoretical development proposed in this paper, we consider two practical realizations that deals with the secure communication problem.

The use of tethered Unmanned Aircraft Systems (UAS) in aerial robotic applications is a relatively unexplored research field. This work addresses the attitude and position estimation of a small-size unmanned helicopter tethered to a moving platform using a multi-sensor data fusion algorithm based on a numerically efficient sigma-point Kalman filter implementation. For that purpose, the state prediction is performed using a kinematic process model driven by measurements of the inertial sensors (accelerometer and gyroscope) onboard the helicopter and the subsequent correction is done using information from additional sensors like magnetometer, barometric altimeter, LIDAR altimeter and magnetic encoders measuring the tether orientation relative to the helicopter. Assuming the tether is kept taut by an actuated device on the platform during the system operation, the helicopter position is estimated relative to the anchor point. Although this configuration avoids the need of a GPS, a standard operation mode for estimation of the absolute position (the position relative to the inertial reference frame) incorporating corrections with the GPS position and velocity measurements, is also implemented in order to highlight the benefits of the proposed tethered setup. The filter performance is evaluated in simulations.

In this paper, modeling, control and state estimation of a manipulating unmanned aerial vehicle (UAV) consisting of a quadcopter equipped with a two degree-of-freedom robotic manipulator is discussed. In the first step, Euler–Lagrange approach is adopted to model the coupled dynamics of the quadcopter and its robotic manipulator. Having linearized the obtained model, a linear quadratic regulator is designed to achieve simultaneous control of the quadcopter and the manipulator. Finally, a UKF-based algorithm is employed to obtain state estimation of the system. For a case study, simulation results are presented to verify feasibility of the proposed approach.

The state estimator is a fundamental algorithm used in modern power industry to estimate the steady state of the system. The gross errors in input data of power system SE algorithm can considerably effect the accuracy of estimated measurements. Although, the commonly used state estimator algorithms utilize some statistical tests to detect the bad data, they are unable to properly deal with the gross errors with smaller magnitude and higher probabilities. This paper develops a new procedure based on the GLR test to effectively detect the bad measurements in the SE algorithm. The proposed strategy can detect, identify and to estimate the size of gross errors. This method is implemented on both single and multiple bad measurements cases to comparatively investigate the abilities of this algorithm. The obtained results confirm that the proposed algorithm has greater power of detecting and identifying the bad measurements compared to the estimator based on the conventional Chi-square and normalized residual test statistics. The IEEE-14 bus test system has been used to validate the theoretical results in this work and its practical implementation in state estimation problems.

State fusion estimation based on measurements missing stochastically with a certain probability is studied. An effective algorithm is presented based on Federated square root filter, Kalman filter and missing measurements checking. Theoretical analysis and simulation results show the effectiveness of the algorithm.

In target tracking system, sensor platforms may be mobile. When the motion states of the platforms are unknown, the measurement data of the sensors in different platforms cannot be effectively converged, thereby resulting difficulties in sensors' registration. Therefore, an algorithm for mobile multi-platform multi-sensor bias registration is proposed in this paper when the motion states of the sensors platforms are unknown. In this algorithm, the UKF (Unscented Kalman Filter) algorithm is used for state estimation and the Gaussian mean-shift (Mean-shift) algorithm is used to get the estimate of bias. Simulation results showed that the bias of sensors could precisely obtained when the initial motion state in a given is precise enough.