Filtering Problem Research Articles

Best multiband filter problem

This mini-review examines the problems of geometric function theory that arise in the synthesis of electric filters, and in particular the work of A. A. Gonchar on the generalisation of Zolotarev’s third problem. The modern development of this topic is described, in particular the method of algebro-geometric Ansatz.

Geometric optimal filtering for an articulated n‐trailer vehicle with unknown parameters

AbstractIn this article, we consider the equations of motion for an articulated ‐trailer vehicle with different masses and inertias in the presence of force and torque commands. We design a second‐order optimal filter to estimate the pose of the first vehicle and of the trailers exploiting the Lie group structure and the nonholonomic and hooking constraints. We consider the filtering problem from three different perspectives: in the first masses and inertias are time‐varying and perfectively known, in the second they are known only in the first part of the maneuver, but they are not updated over time. In the last case masses and inertias are considered within the state vector and therefore estimated by the filter. Depending on the needs in real‐life applications (e.g., whether the masses and inertias remain fixed or change during the maneuver and are unknown), the best‐performing filter can be used. The sensing system consists of a GPS‐like configuration (global positioning system) obtained by using an antenna attached to the leading car.

Implementation of unknown parameter estimation procedure for hybrid and discrete non‐linear systems

AbstractThe application of the hybrid extended Kalman filter (HEKF), hybrid unscented Kalman filter (HUKF), hybrid particle filter (HPF), and hybrid extended Kalman particle filter (HEKPF) is discussed for hybrid non‐linear filter problems, when prediction equations are continuous‐time and the update equations are discrete‐time, and also the discrete extended Kalman filter (DEKF), discrete unscented Kalman filter (DUKF), discrete particle filter (DPF), and discrete extended Kalman particle filter (DEKPF) for discrete‐time non‐linear filter problems, when prediction equations and update equations are discrete‐time. In order to assess the performance of the filters, the authors consider the non‐linear dynamics for a re‐entry vehicle. The filters are used in two hybrid and discrete states to estimate the position, velocity, and drag parameter associated with the re‐entry vehicle. Theoretical topics concerning estimating the drag parameter of a vehicle in re‐entry phase have been dealt with. Drag parameter estimation is carried out using a combination of hybrid filters and discrete filters as an effective estimator and fixed value, forgetting factor, and Robbins‐Monro stochastic approximation methods as the noise covariance matrix adjuster of the parameter.

Kalman filtering used for passive synthetic aperture

In practice, beamforming-based bearing estimators typically fail to account for the impact of environmental factors on the estimating results, resulting in the so-called mismatch problem. To deal with this issue, this paper reconstructs the bearing estimation as a Kalman filter problem, which emphasizes the role of physical models in underwater acoustic signal processing. Since passive synthetic aperture (PSA) is a spatial process including the temporal evolution of a moving array, it fits a Kalman filtering structure. Kalman filter is applied directly to a lake-test dataset collected by an autonomous underwater vehicle (AUV) shell-mounted array, and the experimental findings demonstrate that the bearing estimation results’ variation is significantly decreased than the conventional beamforming (CBF).

Filtering problem for sequences with periodically stationary multi-seasonal increments with spectral densities allowing canonical factorizations

We consider a stochastic sequence $\xi(m)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. The filtering problem is solved for this type of sequences based on observations with a periodically stationary noise. When spectral densities are known and allow the canonical factorizations, we derive the mean square error and the spectral characteristics of the optimal estimate of the functional $A{\xi}=\sum_{k=0}^{\infty}{a}(k) {\xi}(-k)$. Formulas that determine the least favourable spectral densities and the minimax (robust) spectralcharacteristics of the optimal linear estimate of the functional are proposed in the case where the spectral densities are not known, but some sets of admissible spectral densities are given.

Tracking Object’s Pose via Dynamic Tactile Interaction

It is a challenging task to localize and track an in-hand object in robotic domain. Researchers were mainly using the vision as major modality for extracting object’s pose. The vision approaches are fragile when the object is occluded by the robotic arm and hand. To this end, we propose a tactile-based DTI-Tracker (tracking object’s pose via Dynamic Tactile Interaction) approach and formalize the object’s tracking as a filter problem. An Extended Kalman Filter (EKF) is used to estimate the in-hand object pose exploiting the high spatial resolution tactile feedback. Given the initial estimation error, the proposed approach rapidly converges the estimation result to the real pose and the statistic evaluation shows the robustness of the proposed approach. We evaluate this method in physics simulation and real multi-fingered grasping setup while the object is static and movable. The proposed method is a potential tool to foster future research on dexterous manipulation using multifingered robotic hand.

Fluid dynamics analysis for a production line

Magnetic filters are used on companies for mass flux and volume flux values that helps to cover day-to-day production. This work begins describing the problem of magnetic filters fractures as industrial interest. A brief description of how magnetic filters must work on application, according to requirements on process line. On next sections is possible to find the explaining of structural fracture and mistakes on the design or data sheet usually not considered on guaranteed policy. Are mentioned more than one math modeling, taking the simplest to show the effective value of maximum pressure tolerated on magnetic filters differs from estimated for controlled conditions. Solutions shown on the article are a first approach of a future general model theory that could explain how applied science works on a factory where there is no time to stop production. This work relates math model and some values on application, meaning both the project hypothesis modeling on factories requirements for their equipment. Results depict volume, velocity, density, and pipeline relation to the pressure increase over the values on data sheet from quality department tests. Conclusions describe the connection of the math model analysis and with real situations on the application or possible structural damage. And its relationship with the proper function of magnetic filters for the purpose of lifespan analysis on future works. This work is a proof that on few weeks, companies can have a solution for their problems letting them to buy some time to avoid any future issue.

Asynchronous Fault Detection for Memristive Neural Networks With Dwell-Time-Based Communication Protocol.

This article studies the asynchronous fault detection filter problem for discrete-time memristive neural networks with a stochastic communication protocol (SCP) and denial-of-service attacks. Aiming at alleviating the occurrence of network-induced phenomena, a dwell-time-based SCP is scheduled to coordinate the packet transmission between sensors and filter, whose deterministic switching signal arranges the proper feedback switching information among the homogeneous Markov processes (HMPs) for different scenarios. A variable obeying the Bernoulli distribution is proposed to characterize the randomly occurring denial-of-service attacks, in which the attack rate is uncertain. More specifically, both dwell-time-based SCP and denial-of-service attacks are modeled by means of compensation strategy. In light of the mode mismatches between data transmission and filter, a hidden Markov model (HMM) is adopted to describe the asynchronous fault detection filter. Consequently, sufficient conditions of stochastic stability of memristive neural networks are devised with the assistance of Lyapunov theory. In the end, a numerical example is applied to show the effectiveness of the theoretical method.

Research on Radar Clutter Suppression Method Based on Stagger MTI

A large number of clutter interference signals were involved in radar echoes. Radar detection and tracking performance degrade when the signal-to-noise ratio of the echo signal is too low. Therefore, how to suppress clutter interference is a problem that is worth studying in designing. In this paper, the statistical characteristics of radar clutter were analyzed, and a clutter suppression method based on staggered MTI was proposed for the blind speed problem of traditional MTI filters. Simulation experiments verified the model and processing method of staggered filtering. The results indicated that the method improved the blind speed while effectively suppressing the clutter.

Study of the Protection and Energy Transmission Modes of One Phase Short Circuit to Ground in Inverters.

Research indicates that phase-to-ground short-circuits in a frequency converter can subject the rectifier diode and IGBT to excessive voltage and current, potentially causing damage if the component selection margin during hardware design is insufficient. In order to solve the above problems, this paper studies the design of the LCL filter and ground short circuit problem of the hundred-kilowatt inverter. Firstly, an analytical method for calculating the DC bus capacitance and reactor of the inverter is proposed. The interaction between the DC bus capacitance and the reactor parameters and performance is considered in the implementation process. The parameters of the DC bus capacitor and reactor are given. Secondly, the one-to-ground short circuit of the inverter is studied, and the energy flow mode and mathematical expression of the double boost circuit, considering the influence of the leakage inductance of the power transformer, are given. Based on the above analysis, a method for determining the rectifier diode and IGBT, considering the one-to-ground short circuit of the inverter, is proposed. Finally, a one-hundred-kilowatt inverter is developed, and the corresponding experiments are carried out. The feasibility of the proposed scheme is verified by simulation and experiment.

Space–time-range clutter suppression via tensor-based STAP for airborne FDA-MIMO radar

Frequency diverse array (FDA) multiple-input multiple-out (MIMO) radar has an inherent higher-dimensional data structure that can be exploited in temporal, spatial, and range-dependent dimensions for space–time-range adaptive processing (STRAP). This paper addresses the problem of tensor filters in application to space–time-range clutter suppression for FDA-MIMO radar. The characteristics of space–time-range clutter are discussed to establish the multidimensional signal models. FDA-MIMO radar can divide the secondary range cell within the range resolution cell of MIMO radar when they have the same matching filter bandwidth in the receive channel. Specifically, the target-free covariance information can be estimated from more secondary training cells for FDA-MIMO radar. According to the discussed properties of space–time-range clutter, namely secondary clutter rings, clutter degrees of freedom (DOFs), and the range-dimensional non-stationary characteristic, a tensor-based STRAP approach with range compensation is proposed to suppress clutter for FDA-MIMO radar. Numerical results verify the mentioned clutter characteristics and illustrate the importance of the samples number and range compensation operation for the proposed tensor filter. Finally, the STRAP performance benefits of FDA-MIMO radar over MIMO radar are discussed by simulations.

Potential artifacts in conservation laws and invariants inferred from sequential state estimation

Abstract. In sequential estimation methods often used in oceanic and general climate calculations of the state and of forecasts, observations act mathematically and statistically as source or sink terms in conservation equations for heat, salt, mass, and momentum. These artificial terms obscure the inference of the system's variability or secular changes. Furthermore, for the purposes of calculating changes in important functions of state variables such as total mass and energy or volumetric current transports, results of both filter and smoother-based estimates are sensitive to misrepresentation of a large variety of parameters, including initial conditions, prior uncertainty covariances, and systematic and random errors in observations. Here, toy models of a coupled mass–spring oscillator system and of a barotropic Rossby wave system are used to demonstrate many of the issues that arise from such misrepresentations. Results from Kalman filter estimates and those from finite interval smoothing are analyzed. In the filter (and prediction) problem, entry of data leads to violation of conservation and other invariant rules. A finite interval smoothing method restores the conservation rules, but uncertainties in all such estimation results remain. Convincing trend and other time-dependent determinations in “reanalysis-like” estimates require a full understanding of models, observations, and underlying error structures. Application of smoother-type methods that are designed for optimal reconstruction purposes alleviate some of the issues.

Partially known transition rates-based resilient [formula omitted] impulsive filtering for implicit hybrid systems subject to multidimensional impulsive operator

This work focuses on partially known transition rates-based resilient H∞ impulsive filtering for implicit hybrid systems subject to multidimensional impulsive operator. A novel timer-dependent Lyapunov–Krasovskii (L–K) functional is constructed, which can holistically capture the hybrid features with impulse instant, time delay and Markov jump modes information of implicit impulsive hybrid systems. The stochastic admissibility and H∞ performance criteria of residual systems are achieved by developing the underlying novel L–K functional. The robust fault detection issue is transformed into an H∞ filtering problem under two cases of fully- and partially-known transition rates, sufficient conditions for resilient H∞ impulsive fault detection filter are presented via linear matrix inequalities. The feasibility of the proposed resilient H∞ impulsive fault detection filter design method is proven by the simulation of DC motor device.

Tracking Magnetic Target Based on Internative Multi-Model Square Root Unscented Kalman Filter

Scalar magnetic sensors are widely used in magnetic detection and tracking because of their high sensitivity, wide detection range, and small attitude influence. Magnetic anomaly tracking usually uses scalar magnetometers arrays to retrieve the magnetic target position because the incomplete measurement of the geomagnetic field can’t be converted into a filtering problem. However, the workload of calculation is time-consuming, the target is easy to lose. Focusing on filtering divergent and targets easy to lose, tracking magnetic target based on Internative Multi-model Square Root Unscented Kalman Filter is proposed. Firstly, the magnetic anomaly signal is modeled based on moving magnetic target. Subsequently, the initial positioning of the magnetic target is based on dual-magnetometer trajectory planning. Finally, the IMM-SRUKF filter method is used to track magnetic targets adaptively. Both positioning and tracking of magnetic target based on IMM-SRUKF have been verified by simulation and experiments, the result shows that the magnetic target based on IMM-SRUKF can track target stably for a long time and adaptive to the target’s changed state, which indicates that the target is hard to lose.

Event-Triggered Extended Dissipativity Fuzzy Filter Design for Nonlinear Markovian Switching Systems against Deception Attacks

This article is concerned with the adaptive-event-triggered filtering problem as it relates to a class of nonlinear discrete-time systems characterized by interval Type-2 fuzzy models. The system under investigation is susceptible to Markovian switching and deception attacks. It is proposed to implement an improved event-triggering mechanism to reduce the unnecessary signal transmissions on the communication channel and formulate the extended dissipativity specification to quantify the transient dynamics of filtering errors. By resorting to the linear matrix inequality approach and using the information on upper and lower membership functions, stochastic analysis establishes sufficient conditions for the existence of the desired filter, ensuring the mean-squared stability and extended dissipativity of the augmented filtering system. Further, an optimization-based algorithm (PSO) is proposed for computing filter gains at an optimal level of performance. The developed scheme was finally tested through experimental numerical illustrations based on a single-link robot arm and a lower limbs system.

Identification of oestrus cows based on vocalisation characteristics and machine learning technique using a dual-channel-equipped acoustic tag

Timely and accurate detection of oestrus in cows is an essential element of the good management of dairy farms. At present, the detection of cows in oestrus by acoustic means is impeded by the problems of filtering, incomplete feature selection, and poor recognition accuracy. To overcome these difficulties, this study proposes a sound detection method for cows in oestrus based on machine learning technology using an optimal feature combination and an optimal time window. Firstly, a dual-channel sound detection tag consisting of a unidirectional microphone and an omnidirectional microphone (OM) was developed. The Least Mean Squares adaptive algorithm based on wavelet thresholds was used to filter the signals from the OM, and the dual-channel endpoint detection algorithm was used to identify the lowing of individual cows. The Friedman analysis was then used to select the sound features with significant differences before and after oestrus in terms of time, frequency, and cepstrum, and these were used to determine the most acceptable feature combination. We then analysed the effects of Back Propagation Neural Network (BPNN), Cartesian Regression Tree, Support Vector Machine, and Random Forest classification on the accuracy, precision, sensitivity, specificity, and F1 score of oestrus discrimination. Different time windows were used, and the discrimination performance of these algorithms was evaluated using the Area under Receiver Operating Characteristic Curve to find the most satisfactory match between the time window and the recognition algorithm. The dual-channel acoustic tag’s accuracy, precision, sensitivity, and specificity results were 91.25, 98.83, 91.75, and 83.68%, respectively. BPNN with the 70 ms time window and the feature combination (spectral roll-off + spectral flatness + Mel-Frequency Cepstrum Coefficients) was confirmed as the most suitable oestrus recognition method. The average accuracy, precision, sensitivity, specificity, and F1 score of this method were 97.62, 98.07, 97.17, 97.19, and 97.63%, respectively. Based on these results, the approach was shown to be a feasible means of oestrus detection in dairy cows. Based on its ability to differentiate cows and its consistency, it was demonstrated that sound has the potential to replace accelerometers as an early indicator of oestrus in dairy cows.

Integrated Navigation Method of Aerospace Vehicle Based on Rank Statistics

The large dynamic and high-speed flight of aerospace vehicle will bring unpredictable conditions to its navigation system, resulting in that its system random noise probability distribution will no longer meet the preconditions of Gaussian distribution preset by the existing filter algorithm, thus reducing the accuracy of the navigation system. So, it is very important to propose an effective method to solve the filter problem of the navigation system in non-Gaussian distribution to improve the accuracy of the navigation system. Therefore, an integrated navigation method of aerospace vehicle based on rank statistics (LRF) has been proposed in this paper. Firstly, based on the flight characteristics of aerospace vehicles, an accurate gravity calculation model has been established to improve the accuracy of system modelling. Then, the state equation and measurement equation of integrated navigation system have been established. In combination with the rank filter algorithm as well as the determined weights, sampling points are calculated and nonlinearly propagated through the transition matrix to achieve an accurate estimation about the predicted values of the state quantities and measurement quantities and the covariance matrix. In turn, it simulates the probability distribution of the system state effectively. Therefore, when the system random noise probability distribution of the aerospace vehicle does not meet the Gaussian distribution due to various interference factors in the actual flight process, the algorithm can simulate the probability distribution of the actual system to the greatest extent, to improve the accuracy of the integrated navigation system and enhance the reliability of the navigation system ultimately.

The autoregressive filter problem for multivariable degree one symmetric polynomials

The multivariable autoregressive filter problem asks for a polynomial $$p(z)=p(z_1, \ldots , z_d)$$ without roots in the closed d-disk based on prescribed Fourier coefficients of its spectral density function $$1/|p(z)|^2$$ . The conditions derived in this paper for the construction of a degree one symmetric polynomial reveal a major divide between the case of at most two variables vs. the the case of three or more variables. The latter involves multivariable elliptic functions, while the former (due to [Geronimo and Woerdeman (Ann Math 160(3):839-906, 2004)]) only involve polynomials. The three variable case is treated with more detail, and entails hypergeometric functions. Along the way, we identify a seemingly new relation between $${}_2 F_{1}\left( {\frac{1}{3},\frac{2}{3}\atop 1}; \ z\right) $$ and $${}_2 F_{1}\left( {\frac{1}{2},\frac{1}{2}\atop 1}; \ \widetilde{z}\right) $$ .

An augmented filtering method for shipborne HF hybrid sky-surface wave radar

Motivated by target tracking of HF Hybrid Sky-Surface (HF-HSSW) Radar which is a new radar system presented in recent years, this paper formulates a system modelling and filtering problem. Based on the dynamic geometry relationship between target and radar carrier, we derive the planar measurement model of HF-HSSW Radar and apply the augment method to the UKF . The joint estimation of target state and radar carrier state improves the accuracy of the postion. The performance comparison between AUKF and UKF is presented and discussed for a single target tracking scenario, the simulation and experimental results show that AUKF has better performance in HF-HSSW Radar's target tracking.

On the Lagrange Duality of Stochastic and Deterministic Minimax Control and Filtering Problems

On the Lagrange Duality of Stochastic and Deterministic Minimax Control and Filtering Problems