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Adaptive filtering algorithms can be used on the time-domain processing of navigation receivers to suppress interference and maintain the navigation and positioning function. The filter length can affect the interference suppression performance and hardware utilization simultaneously. In practical engineering, the filter length is usually set to a large number to guarantee anti-jamming performance, which means a high-performance receiver requires a high-complexity anti-jamming filter. The study aims at solving the problem by presenting a design method for the optimal filter order in the time-domain anti-jamming receiver, with no need for detailed interference information. According to interference bandwidth and jam-to-signal ratio (JSR), the approach designed a band-stop filter by Kaiser window for calculating the optimal filter order to meet interference suppression requirements. The experimental results show that the time-domain filtering processing has achieved good interference suppression performance for engineering requirements with optimal filter order in satellite navigation receivers.

This paper develops a tool kit for designing low-pass filters to exhibit the smallest possible phase drop. Based solely on the stopband requirements, it is thus possible to find the best order for a filter to be employed in a feedback loop. That is shown for two much-used filter families, Butterworth and Bessel, in cases where the filter is specified to have a minimum attenuation above a certain frequency. It is argued that the phase drop can be represented by an equivalent filter delay. Design tools are then developed, which do not depend on the precise dynamics of the application process. The tools comprise not only the means for determining the optimal filter order and bandwidth, but also formulae and tables useful for obtaining the resulting filter delay. A simple approximation is subsequently developed, which links the minimum obtainable delay directly to said requirements. The filter order need not be known to apply this expression, and the filter family is represented in it by no more than a single constant. This rule of thumb is finally adapted to the area of anti-aliasing filters and there briefly compared to approximative formulae found in existing literature.

Non-contiguous orthogonal frequency division multiplexing (NC-OFDM) technique has been proposed in cognitive radio literature in which the Fourier transform is used to provide orthogonality between subcarriers and a cyclic prefix (CP) with temporal length greater than channel delay spread is added to each NC-OFDM symbol to mitigate intersymbol interference. Using CP, however, degrades spectrum efficiency since it does not carry useful information. Besides, in traditional NC-OFDM-based cognitive radio systems, CP is an effective source of interference with adjacent primary users. To cope with these issues, a cognitive radio system based on wavelet transform and NC-OFDM is proposed. Wavelets have appropriate localisation, limited length and orthogonality both in time and frequency domains. Analysis of signal-to-noise ratio (SNR) show that the SNR gain increases when the number of nullified subcarriers assigned to the secondary users is increased. Also, simulation results of the proposed scheme indicate that the nullifying process improves the system performance in terms of bit error rate. To select the optimum wavelet filter order, the effect of filter order in orthogonal wavelet families is also investigated. Simulation results show that a wavelet transform with a lower filter order should be used.

In commercial non-adaptive active noise control (ANC) applications, an IIR filter structure is often used to reduce real-time computations. On the contrary, an FIR filter structure is usually preferred in the filter design phase because the FIR filter design formulation can be convex and is simple to solve. To combine the benefits of both FIR and IIR filter structures, one common approach in ANC applications is to use an IIR filter structure to fit a pre-designed FIR filter. However, to ensure stability, most of the common IIR filter fitting approaches involve the computation and relocation of poles which can be difficult for high-order cases. In this current work, a stable IIR filter design approach that does not need the computation and relocation of poles is improved to be applicable in ANC applications. The results demonstrate that the proposed method can achieve better fitting accuracy and steady-state noise control performance in high-order non-adaptive applications when the pre-designed noise control FIR filter is fitted. Besides fitting the noise control filter, the proposed method can also be used to fit the secondary path and acoustic feedback path to reduce the required real-time computations if adaptive controllers are applied.

This paper presents reduced-order nonlinear filtering schemes based on a theoretical framework that combines stochastic dimensional reduction and nonlinear filtering. Here, dimensional reduction is achieved for estimating the slow-scale process in a multiscale environment by constructing a filter using stochastic averaging results. The nonlinear filter is approximated numerically using the ensemble Kalman filter and particle filter. The particle filter is further adapted to the complexities of inherently chaotic signals. In particle filters, an ensemble of particles is used to represent the distribution of the state of the hidden signal. The ensemble is updated using observation data to obtain the best representation of the conditional density of the true state variables given observations. Particle methods suffer from the “curse of dimensionality,” an issue of particle degeneracy within a sample, which increases exponentially with system dimension. Hence, particle filtering in high dimensions can benefit from some form of dimensional reduction. A control is superimposed on particle dynamics to drive particles to locations most representative of observations, in other words, to construct a better prior density. The control is determined by solving a classical stochastic optimization problem and implemented in the particle filter using importance sampling techniques.

In this paper an active controller for ground vehicles stability is presented. The objective of this controller is to force the vehicle to track a desired reference, ensuring safe driving conditions in the case of adhesion loss during hazardous maneuvers. To this aim, a nonlinear discrete-time inverse optimal control based on a neural network identification is designed, using a recurrent high order neural network (RHONN) trained by an Extended Kalman Filter. The RHONN ensures stability of the identification error, while the controller ensures the stability of the tracking errors. Moreover, a discrete-time reduced order state observer is utilized to reconstruct the lateral vehicle dynamic not usually available. For the control problem, the references of the lateral velocity and yaw rate are given by a dynamic system mimicking an ideal vehicle having not-decreasing tire lateral characteristics. The proposed approach avoids the identification of the Pacejka’s lateral parameters of the tires, so simplifying the input control determination. Moreover, an optimal control is proposed to optimize the actuator effort and power, usually bounded. Control gains are determined using optimal “nature-inspired\" algorithms such as particle swarm optimization. Test maneuvers, performed through the full vehicle simulator CarSim ® , have been used to test correctness, quality and performances of the observer, the neural identifier and the inverse optimal controller. Robustness of the reduced order discrete-time state observer is also discussed for different sample times. Finally, a fair comparison between optimal and non-optimal control schemes is presented, highlighting the numerical results obtained in simulation.

In this paper the optimal control and parameters design of fractional-order vehicle suspension system are researched, where the system is described by fractional-order differential equation. The linear quadratic optimal state regulator is designed based on optimal control theory, which is applied to get the optimal control force of the active fractional-order suspension system. A stiffness-damping system is added to the passive fractional-order suspension system. Based on the criteria, i.e. the force arising from the accessional stiffness-damping system should be as close as possible to the optimal control force of the active fractional-order suspension system, the parameters of the optimized passive fractional-order suspension system are obtained by least square algorithm. An Oustaloup filter algorithm is adopted to simulate the fractional-order derivatives. Then, the simulation models of the three kinds of fractional-order suspension systems are developed respectively. The simulation results indicate that the active and optimized passive fractional-order suspension systems both reduce the value of vehicle body vertical acceleration and improve the ride comfort compared with the passive fractional-order suspension system, whenever the vehicle is running on a sinusoidal surface or random surface.

Dynamic state estimation of floating offshore wind turbines (FOWTs) in complex marine environments is a core challenge for digital twin systems. This study proposes a joint estimation framework that integrates windowed dynamic mode decomposition (W-DMD) and an adaptive strong tracking Kalman filter (ASTKF). W-DMD extracts dominant modes under stochastic excitations through a sliding-window strategy and constructs an interpretable reduced-order state-space model. ASTKF is then employed to enhance estimation robustness against environmental uncertainties and noise. The framework is validated through numerical simulations under turbulent wind and wave conditions, demonstrating high estimation accuracy and strong robustness against sudden environmental disturbances. The results indicate that the proposed method provides a computationally efficient and interpretable tool for FOWT digital twins, laying the foundation for predictive maintenance and optimal control.

There is a growing interest in developing data‐driven reduced‐order models for atmospheric and oceanic flows that are trained on data obtained either from high‐resolution simulations or satellite observations. The data‐driven models are non‐intrusive in nature and offer significant computational savings compared to large‐scale numerical models. These low‐dimensional models can be utilized to reduce the computational burden of generating forecasts and estimating model uncertainty without losing the key information needed for data assimilation (DA) to produce accurate state estimates. This paper aims at exploring an equation‐free surrogate modeling approach at the intersection of machine learning and DA in Earth system modeling. With this objective, we introduce an end‐to‐end non‐intrusive reduced‐order modeling (NIROM) framework equipped with contributions in modal decomposition, time series prediction, optimal sensor placement, and sequential DA. Specifically, we use proper orthogonal decomposition (POD) to identify the dominant structures of the flow, and a long short‐term memory network to model the dynamics of the POD modes. The NIROM is integrated within the deterministic ensemble Kalman filter (DEnKF) to incorporate sparse and noisy observations at optimal sensor locations obtained through QR pivoting. The feasibility and the benefit of the proposed framework are demonstrated for the NOAA Optimum Interpolation Sea Surface Temperature (SST) V2 data set. Our results indicate that the NIROM is stable for long‐term forecasting and can model dynamics of SST with a reasonable level of accuracy. Furthermore, the prediction accuracy of the NIROM gets improved by almost one order of magnitude by the DEnKF algorithm. Plain Language Summary Data assimilation (DA) has been extensively used for integrating models and observations to improve weather forecasts and climate projections. The Earth system models are derived from fundamental governing equations and require the use of supercomputers to solve them numerically. One of the challenges in the DA cycle is the huge computational costs associated with these models. Therefore, new methods are warranted that can alleviate the cost of model integration within the DA cycle. Recent progress in machine learning (ML) offers an opportunity to build computationally efficient surrogate models solely from the observations and these cheap‐to‐evaluate surrogate models can accelerate the limiting bottlenecks of the DA cycle. Here, we develop a non‐intrusive low‐dimensional surrogate model that learns solely from past historical data to forecast the weekly average Sea Surface Temperature. The surrogate model is further integrated within the DA cycle for blending sparse and noisy discrete observations to improve the predictions. Overall, our results indicate that the merger of ML and DA could address the grand challenge of making use of observations to achieve robust prediction of the Earth system. Key Points A new model is developed using deep learning to forecast the temperature in NOAA Optimum Interpolation Sea Surface Temperature V2 data set This low‐dimensional surrogate model is integrated within data assimilation (DA) to incorporates real‐time sparse and noisy observations The proposed framework accelerates the DA cycle with a robust surrogate model to produce accurate state estimates

The methods currently available for designing a linear quadratic regulator for fractional-order systems are either based on sufficient-type conditions for the optimality of functionals or generate very complicated analytical solutions even for simple systems. It follows that the use of such methods is limited to very simple problems. The present paper proposes a practical method for designing a linear quadratic regulator (assuming linear state feedback), Kalman filter, and linear quadratic Gaussian regulator/controller for commensurate fractional-order systems (in Caputo sense). For this purpose, considering the fact that in dealing with fractional-order systems the cost function of linear quadratic regulator has only one extremum, the optimal state feedback gains of linear quadratic regulator and the gains of the Kalman filter are calculated using a gradient-based numerical optimization algorithm. Various fractional-order linear quadratic regulator and Kalman filter design problems are solved using the proposed approach. Specifically, a linear quadratic Gaussian controller capable of tracking step command is designed for a commensurate fractional-order system which is non-minimum phase and unstable and has seven (pseudo) states.