Sequential Estimation Method Research Articles

A modified sequential gradient-based method for the inverse estimation of transient heat transfer coefficients in non-linear one-dimensional heat conduction problems

In this communication, we introduce an online sequential implementation of a gradient-based method for reconstructing transient heat transfer coefficients in the context of non-linear one-dimensional heat conduction problems. Such a method employs a quasi-Newton updating strategy for computing the descent direction, in contrast with the traditional approach based on the conjugate gradient method. We denote the resulting procedure as the sequential quasi-Newton method (SQNM). The performance of the proposed algorithm was tested in the reconstruction of triangle-, sine-, and square-wave functions that models different transient heat transfer coefficients and compared with the results obtained using a standard sequential function specification method. The SQNM was capable of properly reconstruct the aforementioned exact functions independently of the location of the temperature sensors within the body. The proposed strategy is fast, robust, and reliable, which demonstrates the suitability of employing the sequential gradient-based implementation, together with the quasi-Newton updating strategy, for reconstructing transient heat transfer coefficients in the context of one- and two-dimensional non-linear heat conduction problems. Thus, the proposed method is a novel alternative strategy to other online inverse estimation procedures.

Probabilistic focalization for shallow water localization.

Localizing and tracking an underwater acoustic source is a key task for maritime situational awareness. This paper presents a sequential Bayesian estimation method for passive acoustic source localization in shallow water. The proposed probabilistic focalization approach associates detected directions of arrival (DOAs) to modeled DOAs and jointly estimates the time-varying source location. Embedded ray tracing makes it possible to incorporate environmental parameters that characterize the acoustic waveguide. Due to its statistical model, the proposed method can provide robustness in scenarios with severe environmental uncertainty. We demonstrate performance advantages compared to matched field processing using data collected during the SWellEx-96 experiment.

Sequential Parameter Estimation of Modal Dispersion Curves with an Adaptive Particle Filter in Shallow Water: Experimental Results

An adaptive particle filter method is presented for performing sequential geoacoustic estimation of a shallow water acoustic environment using the explosive sound sources. This approach treats environmental parameters and source–receiver distance as unknown random variables that evolve as the source moves. As a sequential estimation method, this approach reduces the expense of computation than genetic algorithm and yields results with the same accuracy. Comparing with standard Particle filter, proposed method can adjust control parameters to adapt to a rapidly changing environment. This approach is demonstrated on the shallow water sound propagation data which was collected during the ASIAEX 2001 experiment. The results indicate that the geoacoustic parameters are well estimated and source–receiver distance are also well determined.

A Two-layer Sequential State Estimation Method for electricity and heat Networks

As one of the main application forms of energy coupling utilization, the electric gas integrated energy system has been widely concerned. State estimation plays an important role in the operation monitoring and optimal scheduling of the electric gas integrated energy system. The state estimation is the basis of energy management of the electro-pneumatic coupling network, which can provide a high-precision global consistent solution for the subsequent optimal scheduling and safety evaluation of the electro-pneumatic coupling network. The steady state estimation model of gas network is established for grid connected operation or island mode, and the state estimation of complex gas network is realized. On this basis, the coupled state estimation model of electricity and gas is further established, and its performance in state estimation accuracy and bad data identification is tested.

Determining the number of breaks in large dimensional factor models with structural changes

This paper considers a large dimensional factor model with multiple structural changes in factor loadings. A novel two-step procedure is proposed to estimate the number of breaks. First, a sequential estimation method is applied to estimate break points one by one for a given number of breaks. Then the number of breaks can be consistently determined by some information criteria. Simulation results confirm the desired performance of the estimation procedure in finite samples.

A unified system for tree- and stand-level predictions

The unified system developed in this study comprises two components, one to predict survival and the other to predict diameter, both at tree and stand levels. The tree survival model defaults to the stand survival model when tree diameter reaches a certain value. Similarly, the tree diameter growth model defaults to the quadratic mean diameter model when tree diameter is equal to quadratic mean diameter. The annual growth approach was used to accommodate growth intervals of different lengths. Parameters of the unified system can be estimated together (Simultaneous Estimation) or separately in two phases (Sequential Estimation). Also investigated was the Disaggregation method in which tree attributes (survival probabilities and diameters) were adjusted to match outputs from the stand-level models (number of trees and basal area per unit area).Results indicated that, overall, the Disaggregation approach gave a better performance than did the Unadjusted approach. On the other hand, the Sequential Estimation narrowly surpassed the Simultaneous Estimation method (overall rank of 1.00 versus 1.10). Parameters of the unified system should be estimated by use of the Sequential Estimation method because it is a simpler method which involves only a subset of the parameters at each estimation phase.

Sequential estimation of borehole resistance and ground thermal properties through thermal response test

Borehole thermal resistance and ground thermal properties (thermal conductivity and heat capacity) are the key parameters to implement the ground source heat pump (GSHP), usually obtained by thermal response test. In this study, a novel sequential parameters estimation method for the above three parameters is proposed, and the sensitivity analysis by using a special correlation method is performed to decide the best estimation sequences. At first, the Spearman partial rank correlation coefficient was used to represent the correlation between the estimated thermal properties and fluid temperature for the line source model (ILS), then the estimation sequence for the three parameters could be determined by the correlation results. Lastly, with the estimation step, Monte Carlo method was adopted to determine the parameters replacing conventional iterative algorithms. In addition, the effect of value bounds and initial inputs as well as random samples was investigated. The results showed that compared to the other estimation steps, the estimation sequence following borehole resistance firstly, then thermal conductivity, heat capacity lastly could get the best precision with 4.5%, 0.4%, 1% respectively. Specially, the estimation precision for ground heat capacity could be promoted by the sequential estimation. Also, the effect of value bounds on estimation precision was nearly eliminated by the proposed method.

Second-order extended particle filter with exponential family observation model

Particle filter is the most widely used Bayesian sequential state estimation method for nonlinear dynamic systems. When importance sampling is adopted, it is still a challenge to select an appropriate importance function for sampling to avoid particle degeneracy. This paper suggests a novel particle filter, called second-order extended particle filter, which uses conditional normal distribution to approximate the theoretical optimal importance function in sequential state estimation. The approximation is fulfilled through taking logarithm to the optimal importance function and implementing second-order Taylor expansion. This method is suitable for exponential family observation models, which have numerous applications in state estimation research field.

A Sequential Subspace Method for Millimeter Wave MIMO Channel Estimation

Data transmission over the mmWave in fifth-generation wireless networks aims to support very high speed wireless communications. A substantial increase in spectrum efficiency for mmWave transmission can be achieved by using advanced hybrid precoding, for which accurate channel state information is the key. Rather than estimating the entire channel matrix, directly estimating subspace information, which contains fewer parameters, does have enough information to design transceivers. However, the large channel use overhead and associated computational complexity in the existing channel subspace estimation techniques are major obstacles to deploy the subspace approach for channel estimation. In this paper, we propose a sequential two-stage subspace estimation method that can resolve the overhead issues and provide accurate subspace information. Utilizing a sequential method enables us to avoid manipulating the entire high-dimensional training signal, which greatly reduces the complexity. Specifically, in the first stage, the proposed method samples the columns of channel matrix to estimate its column subspace. Then, based on the obtained column subspace, it optimizes the training signals to estimate the row subspace. For a channel with $N_r$ receive antennas and $N_t$ transmit antennas, our analysis shows that the proposed technique only requires $O(N_t)$ channel uses, while providing a guarantee of subspace estimation accuracy. By theoretical analysis, it is shown that the similarity between the estimated subspace and the true subspace is linearly related to the signal-to-noise ratio (SNR), i.e., $O(\text{SNR})$, at high SNR, while quadratically related to the SNR, i.e., $O(\text{SNR}^2)$, at low SNR. Simulation results show that the proposed sequential subspace method can provide improved subspace accuracy, normalized mean squared error, and spectrum efficiency over existing methods.

Hybrid Robust Sequential Fusion Estimation for WSN-Assisted Moving-Target Localization With Sensor-Node-Position Uncertainty

This article presents a hybrid robust sequential fusion estimation (HRSFE) method for moving-target localization in mobile asynchronous wireless sensor networks (WSNs). The estimation error or inconsistency, caused by the uncertainties of sampling, communication, and sensor-node position, is considered fully and compensated by incorporating the sensor-node position with uncertainty into the state vector as well as introducing an adaptive fading factor into the cubature Kalman filter (CKF) to maintain the estimation consistency. In addition, a QR-decomposition-based square-root form of the cubature strong localization filter (SR-CSLF) is proposed to improve the accuracy and stability of the CSLF. Moreover, an HRSFE method is designed to estimate the augment state of the WSN-assisted moving-target-localization system, and the proposed estimation method combines the merits of both the SR-CSLF and SR-CKF effectively and is able to deal with the uncertainties of sampling, communication, and sensor-node position in a unified framework. Simulations and experiments of a WSN-assisted moving-target-localization system under various uncertainty settings are employed to demonstrate the effectiveness and superiorities of the proposed method.

Detection and Parameter Estimation of Solitary Internal Waves Using Distributed Acoustic Sensors

A method to detect solitary internal waves passing through the sensors area in shallow water and estimate their parameters is proposed in this paper using distributed acoustic sensors. The proposed detection method is based on cross correlation of the (envelop of) channel impulse responses estimated from broadband signals transmitted between the sensor nodes with the reference impulse responses in the absence of solitary internal waves. An iterative sequential parameter estimation method is proposed based on time domain matching of the measured channel impulse responses with modeled impulse responses. Simultaneous parameter estimation can be obtained using a global search method such as the matched field inversion. Simulation studies are carried out using environmental acoustic data collected in the northern South China Sea. The results show that the proposed method can effectively detect the existence of passing SIWs, and their parameters can be estimated with reasonable accuracy even under low signal-to-noise ratio conditions.

Sequential InSAR Time Series Deformation Monitoring of Land Subsidence and Rebound in Xi’an, China

Interferometric synthetic aperture radar (InSAR) time series deformation monitoring plays an important role in revealing historical displacement of the Earth’s surface. Xi’an, China, has suffered from severe land subsidence along with ground fissure development since the 1960s, which has threatened and will continue to threaten the stability of urban artificial constructions. In addition, some local areas in Xi’an suffered from uplifting for some specific period. Time series deformation derived from multi-temporal InSAR techniques makes it possible to obtain the temporal evolution of land subsidence and rebound in Xi’an. In this paper, we used the sequential InSAR time series estimation method to map the ground subsidence and rebound in Xi’an with Sentinel-1A data during 2015 to 2019, allowing estimation of surface deformation dynamically and quickly. From 20 June 2015 to 17 July 2019, two areas subsided continuously (Sanyaocun-Fengqiyuan and Qujiang New District), while Xi’an City Wall area uplifted with a maximum deformation rate of 12 mm/year. Furthermore, Yuhuazhai subsided from 20 June 2015 to 14 October 2018, and rebound occurred from 14 October 2018 to 17 July 2019, which can be explained as the response to artificial water injection. In the process of artificial water injection, the rebound pattern can be further divided into immediate elastic recovery deformation and time-dependent visco-elastic recovery deformation.

One-dimensional heat flux estimation by sequential method using feedback control system: AFSMC approach

In this article, a novel sequential method for estimation of heat flux in inverse heat conduction problems is proposed. This technique is based on the feedback control system theory in which adaptive fuzzy sliding mode controller (AFSMC) is utilized. The objective is to estimate the input heat flux associated with a flat plate according to the time history of measured output temperature. In this closed-loop control system, at each time instant, the AFSMC calculates the proper heat flux value to track the measured temperature with the desired input temperature. Some experiments are designed to investigate the ability and accuracy of proposed method in estimating the heat flux of a one-dimensional flat plate. The effects of noise in data and sensor location on the exactness of proposed method are also assessed. Moreover, the distribution of heat flux is considered to be in three forms: constant, step and triangular. The influential parameters of suggested method are tuned once and then used in all subsequent numerical tests. This method does not rely on scanning the entire time history of measured temperatures, and successfully operates in an online manner for a wide range of heat flux distribution functions and their associated abrupt changes.

3D-transient identification of surface heat sources through infrared thermography measurements on the rear face

A study of estimation of space and time distribution of heat flux at the front face of a thin plate is presented in this paper. This identification is carried out from the temperature data collected on the rear face by an infrared camera. The inversion procedure is based on a sequential estimation method: the state representation of the 3D parabolic model of heat conduction in solids. Of course, the parameterized heat flux distribution is discrete in both space (2D) and time. The high number of unknowns to be estimated simultaneously, as well as the measurement noise, makes the ill-posed character of this multi-dimensional inverse problem quite high. Regularization is implemented by using two techniques: the stabilization by the function specification method and the Tikhonov penalization.

A sequential method for estimating the optical properties of two-layer agro-products from spatially-resolved diffuse reflectance: Simulation

A sequential method for estimating the optical properties of two-layer biological tissues with spatially-resolved diffuse reflectance was proposed and validated using Monte Carlo simulations. The relationship between the penetration depth of detected photons and source-detector separation was first studied. Photons detected at larger source-detector separations generally penetrated deeper into the medium than those detected at small source-detector separations. The effect of each parameter involved in the two-layer diffusion model (i.e., the absorption and reduced scattering coefficients (μa and μs′) of each layer, and the thickness of top layer) on reflectance was investigated. It was found that the relationship between the optical properties and thickness of top layer was a critical factor in determining whether photons would have sufficient interactions with the top layer and also penetrate into the bottom layer. The constraints for the proposed sequential estimation method were quantitatively determined by the curve fitting procedure coupled with error contour map analyses. Results showed that the optical properties of top layer could be determined within 10% error using the semi-infinite diffusion model for reflectance profiles with properly selected start and end points, when the thickness of top layer was larger than two times its mean free path (mfp′). And the optical properties of the bottom layer could be estimated within 10% error by the two-layer diffusion model, when the thickness of top layer was <16 times its mfp′. The proposed sequential estimation method is promising for improving the estimation of the optical properties of two-layer tissues from the same spatially-resolved reflectance.

Sequential Quadratic Programming Method for Nonlinear Least Squares Estimation and Its Application

In this study, we propose a direction-controlled nonlinear least squares estimation model that combines the penalty function and sequential quadratic programming. The least squares model is transformed into a sequential quadratic programming model, allowing for the iteration direction to be controlled. An ill-conditioned matrix is processed by our model; the least squares estimate, the ridge estimate, and the results are compared based on a combination of qualitative and quantitative analyses. For comparison, we use two equality indicators: estimated residual fluctuation of different methods and the deviation between estimated and true values. The root-mean-squared error and standard deviation are used for quantitative analysis. The results demonstrate that our proposed model has a smaller error than other methods. Our proposed model is thereby found to be effective and has high precision. It can obtain more precise results compared with other classical unwrapping algorithms, as shown by unwrapping using both simulated and real data from the Jining area in China.

Optimal Estimation of Neural Recruitment Curves Using Fisher Information: Application to Transcranial Magnetic Stimulation.

This paper presents a novel method for fast and optimal determination of recruitment (input-output, IO) curve parameters in neural stimulation. A sequential parameter estimation (SPE) method was developed based on the Fisher information matrix (FIM), with a stopping rule based on successively satisfying a specified estimation tolerance. Simulated motor responses evoked by transcranial magnetic stimulation (TMS) were used as a test bed. Performance of FIM-SPE was characterized in 10 177 simulation runs for various IO parameter values corresponding to different virtual subjects, compared with uniform sampling. Unlike uniform sampling, FIM-SPE identifies and samples the areas of the IO curve that contain maximum information about the curve parameters. For the most relaxed stopping rule, the median number of samples required for convergence was only 17 for FIM-SPE versus 294 for uniform sampling. For the highest reliability stopping rule, more than 92% of the FIM-SPE runs converged, with a median of 88 samples, whereas all uniform sampling runs reached 1000 samples without converging. Compared to uniform sampling, FIM-SPE reduced estimation errors up to two-fold and required ten times fewer stimuli. FIM-SPE could improve the speed and accuracy of determination of IO curves for neural stimulation. A software implementation of the algorithm is provided online.

Sequential Gaussian Approximation Filter for Target Tracking With Nonsynchronous Measurements

This paper presents an adaptive sequential fusion estimation method for the target tracking with nonsynchronous measurements in wireless sensor networks (WSNs). Based on Gaussian assumption and Bayesian inference, a sequential cubature Kalman filtering (SCKF) method, as well as its square root form (SR-SCKF), is presented by applying the cubature rule to approximate the $function \times Gaussian$ integrals. By taking into consideration the time-varying properties of the measurement noise and the linearization errors, some adaptive factors are introduced into the SCKF to compensate for the measurement uncertainties based on Chi-square tests. The convergence analysis of the SCKF is presented. It is proved that the adaptive SCKF (ASCKF) has a better convergence property than the SCKF. Both simulations and experiments of a target tracking example are presented to show the effectiveness and superiority of the proposed ASCKF method.

Tire-Road Friction Coefficient Estimation under Constant Vehicle Speed Control

Abstract Tire-road friction coefficient (TRFC) is of critical importance for advanced vehicle control systems and autonomous vehicle applications. This paper presents a sequential tire longitudinal stiffness and TRFC estimation method for road vehicles by separate control of the front and rear wheels, for which only standard Kalman filter (KF) and recursive least squares (RLS) techniques are required. While braking torque is actively applied to rear wheels, the proportional-integral-derivative (PID) speed controller dictates the corresponding driving torque to front wheels to compensate the decrease of the vehicle longitudinal speed. Tire force of rear tires are estimated based on the KF, both longitudinal stiffness and TRFC of rear tires are identified using RLS technique. The proposed method has simple structure and the potential of estimating the parameters without severely affecting the vehicle’s desired longitudinal speed. Simulation results from vehicle dynamics software CarSim and Matlab/Simulink validate the effectiveness of the proposed method.

Does Rural–Urban Migration Improve Employment Quality and Household Welfare? Evidence from Pakistan

Urban migration unlocks new employment opportunities for rural dwellers in a productive manner. This study assessed the quality of employment of migrant workers, and its effect on rural households’ welfare. To this end, we used primary data collected from the four major districts of Lahore, Gujranwala, Faisalabad, and Sialkot in Punjab, Pakistan. These data include 504 immigrant and non-immigrant families in rural areas, and 252 migrant workers in urban destinations. We use IV probit and two-step sequential estimation methods for the empirical analysis. The study provides new insights for migration in Pakistan. First, migrant workers are better off in their new urban settings in terms of improved incomes and living conditions, but their social protection status is still poor. Second, the results of the employment quality models show that migration is a successful strategy for rural households to improve the quality of their employment. In addition, the characteristics of migrants and native households affect the relative improvement in the quality of employment and migrants’ conditions. Third, the results of the propensity score matching technique suggest that migration has a positive impact on rural households’ income, and these impacts are more pronounced in large cities. Based on the findings, the study recommends that the government should invest in quality education in rural areas, and ensure that social security schemes are provided for migrant workers in urban areas.