Traditional Parameter Estimation Research Articles

Robust continuous-variable quantum key distribution in the finite-size regime

Quantum key distribution (QKD) has been proven to be theoretically unconditionally secure. However, any theoretical security proof relies on certain assumptions. In QKD, the assumption in the theoretical proof is that the security of the protocol is considered under the asymptotic case where Alice and Bob exchange an infinite number of signals. In the continuous-variable QKD (CV-QKD), the finite-size effect imposes higher requirements on block size and excess noise control. However, the local local oscillator (LLO) CV-QKD system cannot be considered time-invariant under long blocks, especially in cases of environmental disturbances. Thus, we propose an LLO CV-QKD scheme with time-variant parameter estimation and compensation. We first establish an LLO CV-QKD theoretical model under the temporal modes of continuous-mode states. Then, a robust method is used to compensate for arbitrary frequency shift and arbitrary phase drift in CV-QKD systems with longer blocks, which cannot be achieved under traditional time-invariant parameter estimation. Besides, the digital signal processing method predicated on high-speed reference pilots can achieve a time complexity of O(1). In the experiment, the frequency shift is up to 89.05 MHz/s and phase drift is up to 3.036 Mrad/s using a piezoelectric transducer (PZT) to simulate the turbulences in the practical channel. With a signal-to-interference ratio (SIR) of −51.67 dB, we achieve a secret key rate (SKR) of 0.29 Mbits/s with an attenuation of 16 dB or a standard fiber of 80 km. This work paves the way for future long-distance field-test experiments in the finite-size regime.

Stochastic Model for Novel Mixture Distribution with Properties and Its Application

Medical research is the one of the most important applications of statistical analysis. A great deal of occasions, specific statistical considerations are needed for cancer research in order to determine the model that best fits the survival data. In this paper, the proposed a new two parameter continuous distribution. It is called a new mixture distribution (NMD). Some statistical properties of the distribution are derived such as, the moments, moments generating function, reliability analysis. Also, the distribution of order statistics is presented and entropies are derived. The application of the maximum likelihood estimate technique to the performance of traditional parameter estimation. Two authentic data sets describing cancer patients' survival are used to empirically demonstrate the potential importance and usability of the proposed distribution. Comparing the new mixture distribution to some other competing distribution, the analysis's results demonstrated that it performed quite well.

Power modeling of degraded PV systems: Case studies using a dynamically updated physical model (PV-Pro)

Power modeling, widely applied for health monitoring and power prediction, is crucial for the efficiency and reliability of Photovoltaic (PV) systems. The most common approach for power modeling uses a physical equivalent circuit model, with the core challenge being the estimation of model parameters. Traditional parameter estimation either relies on datasheet information, which does not reflect the system's current health status, especially for degraded PV systems, or requires additional I-V characterization, which is generally unavailable for large-scale PV systems. Thus, we build upon our previously developed tool, PV-Pro (originally proposed for degradation analysis), to enhance its application for power modeling of degraded PV systems. PV-Pro extracts model parameters from production data without requiring I-V characterization. This dynamic model, periodically updated, can closely capture the actual degradation status, enabling precise power modeling. PV-Pro is compared with popular power modeling techniques, including persistence, nominal physical, and various machine learning models. The results indicate that PV-Pro achieves outstanding power modeling performance, with an average nMAE of 1.4 % across four field-degraded PV systems, reducing error by 17.6 % compared to the best alternative technique. Furthermore, PV-Pro demonstrates robustness across different seasons and severities of degradation. The tool is available as a Python package at https://github.com/DuraMAT/pvpro.

Two improved generalized extended stochastic gradient algorithms for CARARMA systems

The paper innovatively proposes two improved generalized extended stochastic gradient (GESG) algorithms for the controlled autoregressive autoregressive moving average (CARARMA) system with autoregressive moving average (ARMA) model noise. Firstly, we propose a latest estimation based weighted generalized extended stochastic gradient (LE-WGESG) algorithm, which introduces multiple momentary corrections in the traditional parameter estimation process. By carefully adjusting the weighting coefficients of the correction quantities at different moments, the algorithm has a rapid and greater efficient convergence property. More importantly, utilizing the theory of moving data window, this paper also proposes a multi-innovation based latest estimated weighted generalized extended stochastic gradient (MI-LE-WGESG) algorithm, which can better capture the interactions among multiple correction terms and further improve the predictive ability of the model.

Kalman tracking and parameter estimation of continuous gravitational waves with a pulsar timing array

Abstract Continuous nanohertz gravitational waves from individual supermassive black hole binaries may be detectable with pulsar timing arrays. A novel search strategy is developed, wherein intrinsic achromatic spin wandering is tracked simultaneously with the modulation induced by a single gravitational wave source in the pulse times of arrival. A two-step inference procedure is applied within a state-space framework, such that the modulation is tracked with a Kalman filter, which then provides a likelihood for nested sampling. The procedure estimates the static parameters in the problem, such as the sky position of the source, without fitting for ensemble-averaged statistics such as the power spectral density of the timing noise, and therefore complements traditional parameter estimation methods. It also returns the Bayes factor relating a model with a single gravitational wave source to one without, complementing traditional detection methods. It is shown via astrophysically representative software injections in Gaussian measurement noise that the procedure distinguishes a gravitational wave from pure noise down to a characteristic wave strain of h0 ≈ 2 × 10−15. Full posterior distributions of model parameters are recovered and tested for accuracy. There is a bias of ≈0.3 rad in the marginalised one-dimensional posterior for the orbital inclination ι, introduced by dropping the so-called ‘pulsar terms’. Smaller biases $\lesssim 10~{{\%}}$ are also observed in other static parameters.

Reduced and All-at-Once Approaches for Model Calibration and Discovery in Computational Solid Mechanics

Abstract In the framework of solid mechanics, the task of deriving material parameters from experimental data has recently re-emerged with the progress in full-field measurement capabilities and the renewed advances of machine learning. In this context, new methods such as the virtual fields method and physics-informed neural networks have been developed as alternatives to the already established least-squares and finite element-based approaches. Moreover, model discovery problems are emerging and can also be addressed in a parameter estimation framework. These developments call for a new unified perspective, which is able to cover both traditional parameter estimation methods and novel approaches in which the state variables or the model structure itself are inferred as well. Adopting concepts discussed in the inverse problems community, we distinguish between all-at-once and reduced approaches. With this general framework, we are able to structure a large portion of the literature on parameter estimation in computational mechanics -- and we can identify combinations that have not yet been addressed, two of which are proposed in this paper. We also discuss statistical approaches to quantify the uncertainty related to the estimated parameters, and we propose a novel two-step procedure for identification of complex material models based on both frequentist and Bayesian principles. Finally, we illustrate and compare several of the aforementioned methods with mechanical benchmarks based on synthetic and experimental data.

Multicycle Parameter Estimations in Coupled Earth System Models Based on Multiscale Sensitivity Responses in the Context of Low-Order Models

Abstract Climate model simulations tend to drift away from the real world because of model errors induced by an incomplete understanding and implementation of dynamics and physics. Parameter estimation uses data assimilation methods to optimize model parameters, which minimizes model errors by incorporating observations into the model through state-parameter covariance. However, traditional parameter estimation schemes that simultaneously estimate multiple parameters using observations could fail to reduce model errors because of the low signal-to-noise ratio in the covariance. Here, based on the saturation time scales of model sensitivity that depend on different parameters and model components, we design a new multicycle parameter estimation scheme, where each cycle is determined by the saturation time scale of sensitivity of the model state associated with observations in each climate system component. The new scheme is evaluated using two low-order models. The results show that due to high signal-to-noise ratios sustained during the parameter estimation process, the new scheme consistently reduces model errors as the number of estimated parameters increases. The new scheme may improve comprehensive coupled climate models by optimizing multiple parameters with multisource observations, thereby addressing the multiscale nature of component motions in the Earth system. Significance Statement Parameter estimation is used to reduce model errors by optimizing the model parameter values with observational information, which is important for improving long-term predictions. In previous parameter estimation methods, multisource observations have not yet been sufficiently used because the quality and dimension size of the optimized parameters are limited. Here, based on the multiscale nature of component motion in the Earth system, we develop a new parameter estimation method that makes full use of multisource observations. The new method processes the parameters being estimated sequentially according to sensitivity magnitudes and saturation time scales so that the parameters can be continuously optimized. This new method has large application potential for weather and climate reanalyses and predictions.

Research on Damage Identification of Truss Structures based on Bayesian Updating and Rejection Sampling Method

The research on the early damage detection method of truss structure has important practical value for taking remedial measures in time and reducing the hidden danger of safety. In this study, a specific structural truss beam was designed and the seismic action was simulated. Subsequently, specific nodes are analyzed to assess the resulting structural damage. Bayesian updating method solves the uncertainty problem effectively by introducing the prior distribution and updating the posterior distribution with new observation data. This allows the model to infer global patterns from local information and represent the predicted outcomes in probabilistic form. Compared with the traditional parameter estimation methods, Bayesian updating can make full use of the existing observational data and obtain more reliable and accurate model prediction results in the case of limited data. The Bayesian method of updating the truss structure is flexible and adaptable, allowing updates and adjustments to be made at any given time based on new observational data. As a result, it has significant advantages in analyzing and predicting real-time data and is suitable for scenarios where models need to be dynamically adjusted.

Parameter estimation of ground moving targets in synthetic aperture radar systems based on vortex echo data

Ground Moving Target Indication is a critical field within synthetic aperture radar (SAR) research, as traditional SAR images are defocused and displaced due to the target’s trajectory-direction velocity and radial velocity, respectively. Therefore, an accurate estimation of the target’s motion parameters is required. This study introduces a two-dimensional method for estimating target motion parameters using vortex SAR. It utilises the Bessel magnitude and spatial phase term from vortex echo data to calculate the pitch and azimuth angle, from which the motion parameters of ground slow-motion targets are derived. The proposed algorithm operates faster and has a lower computational cost than the traditional parameter estimation algorithm. Its efficacy was confirmed through simulation experiments and mean square error analysis of the estimated parameters.

Non-cooperative underwater acoustic MFSK time-frequency representation optimization method based on sparse reconstruction

The performance of the traditional non-cooperative underwater acoustic (UWA) multiple frequency shift key (MFSK) recognition and parameter estimation method based on time-frequency representation (TFR) is affected by TFR energy divergence. Herein, a sparse TFR estimation model for UWA MFSK is presented. The model exploits the properties of MFSK TFR element sparsity and row sparsity, which can effectively reduce the impact of the channel and does not require any a priori information. To achieve better TFR performance, we propose an inversion fitting method that can effectively improve the frequency resolution, while keeping the time resolution unchanged. Simulation and experimental results show that the Peak Signal to Noise Ratio (PSNR) of the proposed method reaches 21dB with the increase of Signal to Noise Ratio (SNR), indicating that the proposed method has high carrier frequency reconstruction and noise suppression performance. The proposed method can continuously reduce the value of Average Carrier Frequency Offset (ACFO) under inversion fitting method, indicating that inversion fitting method can further reduce the energy divergence and improve frequency resolution.

Enhanced Particle Swarm Optimization Algorithm for Sea Clutter Parameter Estimation in Generalized Pareto Distribution

Accurate parameter estimation is essential for modeling the statistical characteristics of ocean clutter. Common parameter estimation methods in generalized Pareto distribution models have limitations, such as restricted parameter ranges, lack of closed-form expressions, and low estimation accuracy. In this study, the particle swarm optimization (PSO) algorithm is used to solve the non-closed-form parameter estimation equations of the generalized Pareto distribution. The goodness-of-fit experiments show that the PSO algorithm effectively solves the non-closed parameter estimation problem and enhances the robustness of fitting the generalized Pareto distribution to heavy-tailed oceanic clutter data. In addition, a new parameter estimation method for the generalized Pareto distribution is proposed in this study. By using the difference between the statistical histogram of the data and the probability density function/cumulative distribution function of the generalized Pareto distribution as the target, an adaptive function with weighted coefficients is constructed to estimate the distribution parameters. A hybrid PSO (HPSO) algorithm is used to search for the best position of the fitness function to achieve the best parameter estimation of the generalized Pareto distribution. Simulation analysis shows that the HPSO algorithm outperforms the PSO algorithm in solving the parameter optimization task of the generalized Pareto distribution. A comparison with other traditional parameter estimation methods for generalized Pareto distribution shows that the HPSOHPSO algorithm exhibits strong parameter estimation performance, is efficient and stable, and is not limited by the parameter range.

An effective QUATRE algorithm based on reorganized mechanism and its application for parameter estimation in improved photovoltaic module

The traditional parameter estimation methods for photovoltaic (PV) module are strictly limited by the reference standards. On the basis of the double diode model (DDM), this paper proposes a modified PV module that is independent of the reference conditions and can be used for the transformation and reconfiguration of PV module. With respect to the issue of the slow convergence precision and the tendency to trap in the local extremum of the QUATRE algorithm, this research incorporates the QUATRE algorithm with recombination mechanism (RQUATRE) to tackle the problem of parameter estimation for the improved PV modules described above. Simulation data show that the RQUATRE wins 29, 29, 21, 17 and 15 times with the FMO, PIO, QUATRE, PSO and GWO algorithms on the CEC2017 test suite. In addition, in a modified PV module for the parameter extraction problem, the final experimental results achieved a value of 2.99 × 10−3 at RMSE, all better than the accuracy values of the compared algorithms. In the fitting process of IAE, the final values are also all less than 10%, which can satisfy the fitting needs.

Reinforcement Learning Based Parameter Lookup Table Generating Method for Optimal Torque Control of Induction Motors

In the optimal control of induction motors, it is a challenging task to maintain the optimal torque over the varying operation conditions. This paper proposes a parameter look-up table generating method, that can achieve an optimal torque over a wide range of currents and speeds, even though the commands of current are not set correctly. Based on the motor’s testing data, this method uses a reinforcement-learning algorithm to generate parameter look-up tables iteratively. Experimental results show that the proposed method can learn appropriate parameters from the running data to output an optimal torque. The comparative studies show that the proposed method can generate 5%-25% more torque than traditional model-based parameter estimation methods, over a wide range of currents and speeds. Furthermore, the proposed method has a faster convergence feature and a higher identification resolution than many conventional search-based methods.

Power system wideband oscillation estimation, localization, and mitigation

AbstractWith the development of the energy structure of the power system, the characterization of the observed oscillation in the power system has steadily evolved. With the increasingly high penetration of distributed energy sources and power electronic devices, such as the photovoltaic, wind power and charging pile, the basic mechanism, frequency ranges and propagation of oscillation would become more dynamic and complex. Therefore, the traditional parameter estimation, as well as the suppression methods would also suffer from dynamic oscillations. To this end, this paper first investigates the oscillation propagation and typical events caused by the oscillations. Next, the oscillation model estimation method including the model‐based and data‐driven based methods is discussed. The benefits and difficulties of various parameter estimate techniques are highlighted. Under this context, the validity and limitations of the current power system stability are summarized. Furthermore, the different oscillation damping and mitigation measures are compared, and the major adaptability and limitations are listed for the specific application scenarios. Conclusions are drawn, and the wideband oscillation becomes the future research objective where the future work is presented at the end of the paper.

Target location and velocity estimation with the multistatic MU‐MIMO‐OFDM modulation signal

AbstractIn passive radar and joint communication and radar sensing (JCRS), target sensing with the multiuser multiple input multiple output orthogonal frequency division multiplexing (MU‐MIMO‐OFDM) modulation signal is gaining increasing interest. Multiple transmit nodes emitting the MU‐MIMO‐OFDM modulation signals at the same carrier frequency and one receiver collecting the target‐reflected signals for target location and velocity estimation are considered. This is a typical scenario when using the fifth‐generation (5G) communication network signal for target sensing. In this scenario, the echo signals corresponding to different transmit nodes are not resolved in the receiver, and the modulated data symbols cannot be removed from the received signals. Most traditional parameter estimation methods in passive radar and JCRS may not be suitable here. A location and velocity estimation method with the received echo signals is proposed. Specifically, the location parameters are extracted directly from the received echo signals. The location estimation is cast into a block sparse vector reconstruction problem. The variational Bayesian sparsity learning (VBSL) method is exploited for the reconstruction of the block sparse vector. Accelerated VBSL methods are developed for improving the computational efficiency. Simulations verify the effectiveness of the proposed methods.

Phase transition retrieval through in situ observations

The aim of the investigation is to retrieve phase transitions upon heating moisture-containing materials using available observations of the specimen moisture state. Experimental data processing is treated as an approximation by the class of model functions that satisfy a given differential equation. The problem formulation differs from traditional parameter estimation and function reconstruction problems in that it is based on a relaxing regularization of a complex mathematical object. A given sample approximation is constructed under the condition that the measured data weakly capture changes in the state of an object. Such a case requires a high-resolution method for data processing that ensures the best consistency with observations. Regularization is applied to account for the ill-conditioned discretization of the mathematical model of the phenomenon and to ensure the approximation of a reconstructed function using a high-dimensional mathematical basis. The data processing of three moisture-containing materials demonstrates for the first time that thin-layer drying can involve a series of phase transitions. The latter causes a drop in the drying rate, which prevents moisture removal. Traditional postprocessing of the experimentally determined drying curve and its direct differentiation do not reflect mass transfer blocking and lead to a restricted interpretation of the experimental data. A proposed high-resolution processing of in situ observations, based on the application of the conventional thermal model, yields significant information on latent phenomena.

A Joint Parameters Estimation Method for Azimuth Multichannel TOPS SAR

Multi-channel parameter estimation is a key technology for azimuth multi-channel terrain observation by progressive scans synthetic aperture radar (MC TOPS SAR) systems. Normally, for the traditional multichannel parameter estimation algorithms, the mismatch parameters are concluded as phase error, baseline error, and Doppler centroid. The beam rotation speed error is ignored. However, for MC TOPS SAR, beam rotation speed error will degrade the reconstruction performance of the Doppler spectrum. Moreover, only part of the mismatch parameters can be estimated for the traditional algorithms. To address those problems, a joint parameters estimation algorithm for TOPS SAR based on spatial time cross-correlation coefficient (STCCC) is proposed. Combined with phase wrapping and the least-squares method (LSM), the algorithm is capable of realizing a joint parameters estimation of channel consistency error, azimuth baseline error, Doppler centroid frequency, and beam rotation speed estimation without iteration. The real data processing result shows that the method can effectively realize MC TOPS SAR data error estimation.

Estimating number of group targets arranged in linear array via forward‐backward matrix pencil method

AbstractAn efficient number estimation method is proposed for target detection by using the forward‐backward matrix pencil method. Compared with the traditional parameter estimation methods, the proposed method can work well even for sparse signals. At first, the radar cross section of the group targets arranged in linear array is obtained at some certain angles or frequencies. Then, the Hankel‐Toeplitz matrix is constructed from the known radar echoes, and the singular value decomposition is performed on this matrix. Finally, the number of the group targets arranged in linear array can be accurately estimated by setting an appropriate threshold to select the singular value with a large proportion. In addition, the influence of different signal‐to‐noise ratios (SNR) on the estimation results is also discussed. In order to enhance the accuracy, several groups of different echoes are used to estimate the number of group targets jointly. The simulation results demonstrate that the proposed method is effective and accurate in estimating the number of group targets arranged in linear array. Moreover, the estimation result of the proposed method in this paper is not affected by the noise, which shows that this method has better robustness.

Low-Variance Parameter Estimation Approach for Real-Time Optimization of Noisy Process Systems

Uncertainty is inherent to the measurement and modeling of process systems, where it can have significant impacts on the efficacy of optimization techniques. This work proposes a scheme to address uncertainty as it pertains to real-time optimization (RTO), where noisy measurements are used to estimate model parameters and account for model uncertainty. The parameter estimation (PE) step that accompanies RTO requires plant measurements that are often noisy; this can cause the propagation of noise to the parameter estimates, which may result in poor RTO performance. An information content (IC) metric for choosing the most information-rich measurements and an algorithm to select a favorable subset of measurements, as well as filtering for erroneous parameters, are proposed in this work to improve the PE problem performance. The resulting low-variance PE (lv-PE) algorithm yields parameter estimates that are closer to the true parameter values over many RTO periods. The proposed scheme is tested against a regular RTO/PE on a forced circulation evaporator and the Williams–Otto CSTR. The former case displays the effect of the proposed scheme in avoiding constraint violations, while the latter case shows the economic improvements that the proposed scheme can yield. Both case studies show a reduction in estimate variability with respect to the traditional PE approach; thus, the proposed framework is attractive for the optimization of noisy process systems.

A physics-based neural network for flight dynamics modelling and simulation

The authors have developed a novel physics-based nonlinear autoregressive exogeneous neural network model architecture for flight modelling across the entire flight envelope, called FlyNet. When using traditional parameter estimation and output-error methods, aircraft models are captured about a single point in the flight envelope using a first-order Taylor series to approximate forces and moments. To enable analysis throughout the entire operational envelope, the traditional models can be extended by interpolating or stitching between a number of these single-condition models. This paper completes the evolutionary next step in aircraft modelling to consider all second-order Taylor series terms instead of a subset of those and by exploiting the ability of neural networks to capture more complex and nonlinear behaviour for the efficient development of a continuous flight simulation model valid across the entire envelope. This method is valid for fixed- and rotary-wing aircraft. The behaviour of a conventional model is compared to FlyNet using flight test data collected from the National Research Council of Canada’s Bell 412HP in forward flight.