Dynamic Dictionary Algorithms for Model Order and Parameter Estimation

Parameter estimation is a vital part in constructing the best model of a dynamic system. This paper analyzed the performance of toothbrush rig parameter estimation using different model orders. Parameter estimation process of the system is performed through system identification. The approximate mathematical model that resemble the real system is obtained when the output is measured after loading the input signal. The application of real-coded genetic algorithm (RCGA) is proposed as optimization method in estimating the parameters of dynamic system. The best model is obtained by optimizing the objective function of mean squared errors. The performance is analyzed to get the approximate model of the real system using three different model orders with 10 times analysis for each model. A few criteria have been considered which are the optimization result of objective function, time execution and validation process. Real- coded genetic algorithm indicates that parameter estimation with model order 3 is chosen as the best model or the dynamic system as it has the highest performance compared to others.

The Bayes principle is applied to the joint model selection and parameter estimation of GTD model to explore the prior information. An algorithm using RJ-MCMC is designed. It not only has better model selection and parameter estimation performance than the non-Bayes algorithms, but also solves the mixed parameter estimation problem in GTD model effectively. The advantage of this algorithm is especially evident at low SNR, for short data and with closely-spaced components. Simulations verify the effectiveness of this algorithm.

Sample covariances, estimated as mean-lagged products of random data, are poor and inaccurate fundaments for the non-parametric spectral estimation with tapered and windowed periodograms. However, the autocovariance can be estimated efficiently with a parametric method as transformation of an estimated time series model, if the model type and model order are known a-priori. A recent development in time-series analysis gives the possibility to automatically select the model type and the model order for data with unknown characteristics. After the computation of hundreds of candidate models of different orders and types, a statistical criterion can select a single time series model. The accuracy of this identification from many candidates is sufficient to approach the performance that can be obtained with parametric estimation if the type and the order of the time series model would be known a priori. Hence, the accuracy (mean square error) of parametric covariance estimates is typically the same or better than what can be achieved by non-parametric mean-lagged-product estimates.

Most algorithms for blind source separation (BSS) or independent component analysis (ICA) assume an equal number of sources as sensors. For multichannel electrophysiological recordings, such as the electroencephalogram (EEG), however, there are often far fewer sources of neurophysiologically relevant activity than the number of sensors. This adds a model order estimation problem to the source separation problem. Conventional estimates of the number of sources are based on the dominant eigenvalues of the data covariance matrix, obtained from principal component analysis (PCA), whose corresponding eigenvectors are also used for prewhitening. It is well known that PCA is susceptible to noise, leading to incorrect model order estimates and data distortion, which in turn limit the accuracy of the source estimates. It is therefore highly desirable to determine the correct number of sources and their spatial topographies directly, without PCA-based data truncation or prewhitening. In this work, we present a stepwise BSS method for extracting only the sources necessary for a sufficiently good least-square fit to the data. This simultaneously yields model order and source estimates, which we examine at different noise levels. We also show how only a few neurophysiologically meaningful components can be extracted from 25-channel ictal EEG.

A fuzzy supervised learning method with dynamical parameter estimation for nonlinear discriminant analysis

Joint communication and positioning based on a unified signal structure yields synergy and can complement and assist system designs enabling higher coverage and quality of service for both communication and positioning. For the time of arrival (TOA) based joint communication and positioning the TOA estimation accuracy is crucial. It is known to translate directly into position estimation accuracy. In the presence of multipath propagation, the estimation accuracy of signal arrival times in return strongly depends on the actual as well as the estimated number of the physical path parameters, the model order. In this work, we assess the performance and the mutual impact of simultaneous model order and parameter estimation for channel-estimation-based joint communication and positioning. Besides introducing a terrestrial channel-estimation-based unified joint communication and positioning system framework, we discuss and numerically compare different methods to sequentially or jointly estimate the parameters and the model order. We show that a TOA error-minimizing model order estimation is preferable over estimating the correct model order. Furthermore, we compare the performance with a proposed focused order-related lower bound. This bound determines the optimal model order for a chosen estimator. It depends on the actual and hypothetical model order and it replaces the here unsuitable Cramer-Rao lower bound. Secondly, the comparison shows that employing the parameter and model order-dependent inverse Fisher information matrix yields a close-to-optimal approach. We numerically show for a realistic channel scenario with many multipath parameters that the method is still accurate.

In high-mobility scenarios envisioned for 6G communications, orthogonal time frequency space (OTFS) has emerged as a promising alternative to conventional orthogonal frequency division multiplexing (OFDM) schemes. To address the parameter estimation problem in OTFS-integrated radar and communication systems, we propose a two-stage parameter estimation framework based on sparse reconstruction and the Alternating Direction Method of Multipliers-Newton (ADMM-Newton), which exploits the sparsity of OTFS signals in the delay-Doppler (DD) domain to enable precise parameter estimation in high-mobility scenarios. In the first step, we construct an echo signal model for an OTFS-integrated radar-communication system and estimate the delay and Doppler integer grid values of the detected targets using a sparse reconstruction-based ADMM algorithm. In the second step, the estimates of the integer grid parameters are used as constraints for a more specific search. Fractional-precision estimations of the range and velocity parameters are obtained by iteratively solving for the Newton direction via the Newton algorithm. Finally, numerical simulations are executed to verify the proposed algorithm’s performance in parameter estimation in ISAC systems. The results demonstrate that the proposed algorithm achieves millimeter-level accuracy in velocity estimation under single-target simulation scenarios. Particularly in situations involving multiple sensing targets, the proposed method can estimate target range and velocity with centimeter-level accuracy. The proposed algorithm effectively eliminates notable differences between estimated and real values due to three targets interfering with one another, demonstrating strong estimation accuracy. Furthermore, in target conditions that are closely spaced, the proposed algorithm maintains robust estimation accuracy.

In the field of integrated sensing and communication (ISAC), achieving high-precision location information based on channel state information (CSI) has emerged as a research hotspot. Traditional subspace-based parameter estimation methods suffer from performance degradation when some sampling points missing due to heterogeneous interference source. Besides, the majority of methods ignore the influence of outliers on the precision of estimation results when identifying paths. This paper proposes a CSI purification algorithm based on the alternating direction method of multipliers (ADMM), which exploits the sparsity of the CSI matrix in conjunction with low-rank matrix recovery (LRMR) techniques to effectively mitigate interference and enhance path resolution. A parameter estimation method for dynamic outlier removal is adopted, which combines matrix pencil (MP) and density-based spatial clustering of applications with noise (DBSCAN) algorithm to dynamically adjust the input parameters to achieve the removal of outliers. We performed indoor measurements and showed that the CSI purification algorithm was able to reduce the median angle of arrival (AoA) error from 8.39° to 6.24° when half of the sampling points were missing. Besides, the addition of the dynamic outlier removal algorithm improves AoA estimation performance by 4.1%. In terms of localization measurement, the median localization error of the proposed system in the activity room and the meeting room is 0.39 m and 0.41 m, respectively. In the case of missing half of the data, the positioning accuracy of the proposed algorithm is 0.47 m, which is better than that of the mainstream algorithms.

Long-time coherent integration can remarkably improve the detection and motion parameter estimation ability of radar for maneuvering targets. Unfortunately, the linear range migration, quadratic range migration (QRM), and Doppler frequency migration (DFM) within the coherent processing interval seriously degrade the target detection and parameter estimation performance. In this regard, a novel coherent integration approach based on frequency autocorrelation function (FAF) and Lv’s distribution (LVD), i.e., FAF–LVD, is proposed in this paper. The QRM is firstly removed by the second-order keystone transform. Then, the FAF with a variable delay is introduced to remove the DFM, followed by the scaled Fourier transform to achieve coherent integration. Finally, the acceleration and velocity are estimated simultaneously by LVD. Analysis demonstrates that FAF–LVD could be efficiently implemented via complex multiplications, the fast Fourier transform (FFT) and inverse FFT. Detailed comparisons with several representative methods indicate that FAF–LVD achieves a better balance among computational complexity, detection ability, and parameter estimation performance. Extensive simulations are presented to validate the effectiveness of FAF–LVD method.

The purpose of this simulation study is to explore the limitation of the population PK/PD analysis using data from a clinical study and to help to construct an appropriate PK/PD design that enable precise and unbiased estimation of both fixed and random PD parameters in PK/PD analysis under different doses and Hill coefficients. Seven escalating doses of virtual drugs with equal potency and efficacy but with five different Hill coefficients were used in simulations of single and multiple dose scenarios with dense sampling design. A total of 70 scenarios with 100 subjects were simulated and estimated 100 times applying 1-compartment PK model and sigmoid Emax model. The bias and precision of the parameter estimates in each scenario were assessed using relative bias and relative root mean square error. For the single dose scenarios, most PD parameters of sigmoid Emax model were accurately and precisely estimated when the Cmax was more than 85% of EC50, except for typical value and inter-individual variability of EC50 which were poorly estimated at low Hill coefficients. For the multiple dose studies, the parameter estimation performance was not good. This simulation study demonstrated the effect of the relative range of sampled concentrations to EC50 and sigmoidicity on the parameter estimation performance using dense sampling design.

HighlightsWhat are the main findings?This paper presents a high-order phase compensation and parameter estimation algorithm designed for maneuvering targets, which effectively balances detection performance and computational efficiency.The proposed method achieves precise compensation of high-order range migrations without the need for exhaustive parameter search, thereby circumventing the blind speed sidelobe effect. Futhermore, the incorporation of a time-delay variable significantly improves the anti-noise capability of the approach.What is the implication of the main finding?This algorithm introduces a novel motion compensation technique to address the challenges of range migration, Doppler frequency migration, and Doppler ambiguity in detecting weak maneuvering targets. It achieves precise range migration compensation with enhanced accuracy and robustness, forming a vital preprocessing step for high-quality SAR imaging.The algorithm supports simultaneous multi-target processing and holds promising application potential in fields such as airborne radar detection, maritime moving target indication, cooperative observation by UAV formations, and other fields.This study focuses on the key challenges in detecting and estimating motion parameters of ground maneuvering targets for airborne radar sensors. The complex unknown motion states of the ground maneuvering target, including velocity, acceleration, and jerk, result in range migrations (RMs) and Doppler frequency migrations (DFMs). These effects severely degrade the long-time coherent accumulation performance of the airborne radar, thereby limiting the reliable detection and precise parameter estimation of maneuvering targets. To address this issue, a new detection and motion parameter estimation method based on the range frequency reversal transform (RFRT) and searching Lv’s distribution (SLVD), i.e., RFRT-SLVD, is proposed. Specifically, the third-order RM (TRM) and quadratic DFM (QDFM) are considered. The proposed method operates as follows: First, RMs are eliminated simultaneously via the RFRT operation, which multiplies the echo by its reversed data in the range frequency and slow-time domains, leveraging the symmetric equal-interval sampling property of the range frequency. Subsequently, a phase compensation function (PCF) related to the jerk is constructed to compensate the QDFM. Finally, the LVD is performed to remove residual DFMs and achieve effective signal energy accumulation. Additionally, the case of a fast-moving target with Doppler ambiguity is analyzed, and a method for estimating three motion parameters is provided. A key advantage of the proposed technique is its ability to directly compensate the RMs without requiring prior knowledge of the maneuvering target, while also avoiding the blind speed sidelobe (BSSL) effect. In comparison with existing algorithms, RFRT-SLVD achieves a balanced trade-off between parameter estimation performance and computational efficiency. Numerical analyses and experiments are conducted to validate the method, assessing its detection capability for ground maneuvering targets, Doppler ambiguity resolution in parameter estimation, computational complexity, and method applicability in multi-target scenarios.

Aiming at the problem that single‐network hopping signals have not fully utilised its frequency domain sparse characteristic in the parameter estimation, this study proposes a parameter estimation of frequency hopping (FH) signal based on multi‐measurement vector sparse Bayesian learning (MSBL) in modulation wideband converter (MWC). Since the FH signal is sparse in the frequency domain, the authors apply the MSBL method to estimate its parameters. After the signal is sampled by the MWC, the MSBL algorithm is used to reconstruct its support set. Then the time–frequency ridge method is used to estimate the signal's hop duration, time‐hopping, and carrier frequency based on the time–frequency map. Simulation experiments show that under the condition of low signal‐to‐noise ratio, the parameter estimation performance in the case can be improved by up to 65% and anti‐noise performance can be improved up to 6 db compared with the existing method. The result is very close to the Nyquist full sampling and can greatly improve the accuracy of the FH signal parameter estimation in the MWC system and relieve the pressure of the hardware.

This paper proposes a method to estimate the model order based on the singular values of a synthetic real matrix. The synthetic data matrix includes the complex observation data and its conjugate data, which fully exploits the existing data information, is more suitable for model order estimation of multiband signal fusion spectrum than the complex observation matrix. Simulation experiments show that this method has better results than the traditional model order estimation methods based on complex observation data matrix, the model order can be estimated at a lower signal to noise ratio (SNR).

Model order estimation is the most important but challenging step for system identification using an autoregressive moving average (ARMA) model. In this paper, we propose an artificial neural network (ANN) structure to estimate the best model order for ARMA modeling of linear, time-invariant systems using the system’s input and output data. The proposed algorithm creates an equivalent ANN structure corresponding to an ARMA model and chooses the best model order using the neural network’s mean squared error (MSE) loss function. The proposed method is validated on simulated ARMA model data and the performance is compared with the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). We considered three hypothetical linear systems and performed 100 Monte Carlo simulations for each model, with different data lengths, and with additive noise. For each of the three simulation models, the proposed method significantly outperformed the AIC and BIC in terms of the correct model order selection. Finally, the proposed ANN-based model order estimator was successfully applied to determine the dynamic relationship between heart rate (HR) and instantaneous lung volume (ILV) using an ARMA model. The results indicate that physiological and biological systems can be modeled with appropriate ARMA models obtained by the proposed algorithm to better understand the system dynamics.

This paper proposes a method to estimate parameters of untransposed transmission lines under different internal fault conditions. By employing a nonlinear least square approach combined with a multi-initialization strategy, the method achieves accurate estimation of line impedance parameters, particularly the inductive component, under low-resistance fault conditions. The core contribution of this work lies in revealing the distinct parameter identifiability, which is strongly dependent on the internal fault type and evaluating the sensitivity of different line parameters by using the proposed sensitivity formula. Specifically, the study demonstrates that only fault types involving the spatially special phase of the untransposed line exhibit enhanced parameter identifiability and estimation performance. Additionally, the inherent spatial symmetry of phases in the tower structure is reflected in the parameter estimation results for internal faults involving these phases.