Search Results (14)

Carrier Smoothing Code (CSC), as a low-pass filter, has been widely used in GNSS positioning processing to reduce pseudorange noise via carrier phases. However, current CSC methods do not consider the systematic bias between the code and carrier phase observation, also known as Satellite-induced Code Bias (SICB). SICB has been identified in the BDS-2 and the bias will reduce the accuracy or reliability of the CSC. To confront bias, an improved CSC algorithm is proposed by considering SICB for GEO, IGSO, and MEO satellites in BDS constellations. The correction model of SICB for IGSO/MEO satellites is established by using a 0.1-degree interval piecewise weighted least squares Third-order Curve Fitting Method (TOCFM). The Variational Mode Decomposition combined with Wavelet Transform (VMD-WT) is proposed to establish the correction model of SICB for the GEO satellite. To verify the proposed method, the SICB model was established by collecting 30 Multi-GNSS Experiment (MGEX) BDS stations in different seasons of a year, in which the BDS data of ALIC, KRGG, KOUR, GCGO, GAMG, and SGOC stations were selected for 11 consecutive days to verify the effectiveness of the algorithm. The results show that there is obvious SICB in the BDS-2 Multipath (MP) combination, but the SICB in the BDS-3 MP is smaller and can be ignored. Compared with the modeling in the references, TOCFM is more suitable for IGSO/MEO SICB modeling, especially for the SICB correction at low elevation angles. After the VMD-WT correction, the Root Mean Square Error (RMSE) of SICB of B1I, B2I, and B3I in GEO satellites is reduced by 53.35%, 63.50%, and 64.71% respectively. Moreover, we carried out ionosphere-free Single Point Positioning (IF SPP), Ionosphere-free CSC SPP (IF CSC SPP), CSC single point positioning with the IGSO/MEO SICB Correction based on the TOCFA Method (IGSO/MEO SICB CSC), and CSC single point positioning with the IGSO/MEO/GEO SICB correction based on VMD-WT and TOCFA (IGSO/MEO/GEO SICB CSC), respectively. Compared to IF SPP, the average improvement of the IGSO/MEO/GEO SICB CSC algorithm in the north, east, and up directions was 24.42%, 27.94%, and 24.98%, respectively, and the average reduction in 3D RMSE is 24.54%. Compared with IF CSC SPP, the average improvement of IGSO/MEO/GEO SICB CSC is 7.03%, 6.50%, and 10.48% in the north, east, and up directions, respectively, while the average reduction in 3D RMSE was 9.86%. IGSO/MEO SICB mainly improves the U direction positioning accuracy, and GEO SICB mainly improves the E and U direction positioning accuracy. After the IGSO/MEO/GEO SICB correction, the overall improvement was about 10% and positioning improved to a certain extent. Full article

Nonlinear functions are widely used as activation functions in artificial neural networks, which have a great impact on the fitting ability of artificial neural networks. Due to the complexity of the activation function, the computation of the activation function and its derivative requires a lot of computing resources and time during training. In order to improve the computational efficiency of the derivatives of the activation function in the back-propagation of artificial neural networks, this paper proposes a method based on piecewise linear approximation method to calculate the derivative of the activation function. This method is hardware-friendly and universal, it can efficiently compute various nonlinear activation functions in the field of neural network hardware accelerators. In this paper, we use least squares to improve a piecewise linear approximation calculation method that can control the absolute error and get less number of segments or smaller average error, which means fewer hardware resources are required. We use this method to perform a segmented linear approximation to the original or derivative function of the activation function. Both types of activation functions are substituted into a multilayer perceptron for binary classification experiments to verify the effectiveness of the proposed method. Experimental results show that the same or even slightly higher classification accuracy can be achieved by using this method, and the computation time of the back-propagation is reduced by 4–6% compared to the direct calculation of the derivative directly from the function expression using the operator encapsulated in PyTorch. This shows that the proposed method provides an efficient solution of nonlinear activation functions for hardware acceleration of neural networks. Full article

Drugs seem to diffuse in different manners in a delivery device due to the increment of the device pore size during swelling. However, the diffusion parameter, D, is often assumed constant. In this work, a new developed controlled drug release model with a time-dependent diffusion parameter is compared to one- and two-phase models. The new model was obtained as an improvement of the previous constant and piece-wise constants models. The models are developed by solving an advection–diffusion equation using the Landau transformation method and the separation of variables method. To test these models, we fit experimental data by the developed models using the least squares fitting technique. The curve-fitting result shows that the least squares error of the two-phase and the time-dependent models are 10 times smaller than the single-phase model. The CPU time for the time-dependent model is the lowest, showing that a time-dependent model is the best option among all three tested models considering both factors of the determined least squares error and the time consumption. Full article

Analysis of instrumental variables is an effective approach to dealing with endogenous variables and unmeasured confounding issue in causal inference. We propose using the piecewise linear model to fit the relationship between the continuous instrumental variable and the continuous explanatory variable, as well as the relationship between the continuous explanatory variable and the outcome variable, which generalizes the traditional linear instrumental variable models. The two-stage least square and limited information maximum likelihood methods are used for the simultaneous estimation of the regression coefficients and the threshold parameters. Furthermore, we study the limiting distribution of the estimators in the correctly specified and misspecified models and provide a robust estimation of the variance-covariance matrix. We illustrate the finite sample properties of the estimation in terms of the Monte Carlo biases, standard errors, and coverage probabilities via the simulated data. Our proposed model is applied to an education-salary data, which investigates the causal effect of children’s years of schooling on estimated hourly wage with father’s years of schooling as the instrumental variable. Full article

Determination of bamboo age is an important task for bamboo forest management and bamboo utilization. However, the bamboo age is usually manually determined in the field, which is time-consuming and labor-intensive. Due to the ability to generate very high-density point clouds, terrestrial laser scanning (TLS) has been applied in forestry to acquire forest parameters. This study evaluated the potential of using the laser echo intensity data generated by TLS technology to determine the Moso bamboo age represented by “du.” The intensity data were first corrected for the distance and incidence angle effects using an intensity correction method that constructed an empirical correction model by fitting piecewise polynomials to the intensity data collected based on a reference target. Then the models expressing the relationship between intensity and bamboo culm section number were constructed for different bamboo du by fitting polynomials to the intensity data of individual bamboo culms through least-squares adjustment. For a bamboo plant whose age is determined, the bamboo du could be determined based on the constructed intensity-culm section models. The proposed bamboo age determination method was tested at a site in a managed Moso bamboo forest in Lin’an District, Hangzhou City, Zhejiang Province, China. From the test site, 56 and 120 bamboo plants with known bamboo ages were selected to construct the intensity-culm section models and to validate the bamboo age determination method, respectively. The bamboo age determination accuracies for each bamboo du were all above 90%. The result indicates a great potential for automatic determination of bamboo age in practice using TLS technology. Full article

The sigmoid activation function is popular in neural networks, but its complexity limits the hardware implementation and speed. In this paper, we use curvature values to divide the sigmoid function into different segments and employ the least squares method to solve the expressions of the piecewise linear fitting function in each segment. We then adopt an optimization method with maximum absolute errors and average absolute errors to select an appropriate function expression with a specified number of segments. Finally, we implement the sigmoid function on the field-programmable gate array (FPGA) development platform and apply parallel operations of arithmetic (multiplying and adding) and range selection at the same time. The FPGA implementation results show that the clock frequency of our design is up to 208.3 MHz, while the end-to-end latency is just 9.6 ns. Our piecewise linear fitting method based on curvature analysis (PWLC) achieves recognition accuracy on the MNIST dataset of 97.51% with a deep neural network (DNN) and 98.65% with a convolutional neural network (CNN). Experimental results demonstrate that our FPGA design of sigmoid function can obtain the lowest latency, reduce absolute errors, and achieve high recognition accuracies, while the hardware cost is acceptable in practical applications. Full article

The limit state function is important for the assessment of the longitudinal strength of damaged ships under combined bending moments in severe waves. As the limit state function cannot be obtained directly, the common approach is to calculate the results for the residual strength and approximate the limit state function by fitting, for which various methods have been proposed. In this study, four commonly used fitting methods are investigated: namely, the least-squares method, the moving least-squares method, the radial basis function neural network method, and the weighted piecewise fitting method. These fitting methods are adopted to fit the limit state functions of four typically sample distribution models as well as a damaged tanker and damaged bulk carrier. The residual strength of a damaged ship is obtained by an improved Smith method that accounts for the rotation of the neutral axis. Analysis of the results shows the accuracy of the linear least-squares method and nonlinear least-squares method, which are most commonly used by researchers, is relatively poor, while the weighted piecewise fitting method is the better choice for all investigated combined-bending conditions. Full article

In the CO₂ differential absorption lidar (DIAL) system, signals are simultaneously collected through analog detection (AD) and photon counting (PC). These two kinds of signals have their own characteristics. Therefore, a combination of AD and PC signals is of great importance to improve the detection capability (detection range and accuracy) of CO₂-DIAL. The traditional signal splicing algorithm cannot meet the accuracy requirements of CO₂ inversion due to unreasonable data fitting. In this paper, a piecewise least square splicing algorithm is developed to make signal splicing more flexible and efficient. First, the lidar signal is segmented, and according to the characteristics of each signal, the best fitting parameters are obtained by using the least square fitting with different steps. Then, all the segmented and fitted signals are integrated to realize the effective splicing of the near-field AD signal and the far-field PC signal. A weight gradient strategy is also adopted in signal splicing, and the weights of the AD and PC signals in the spliced signal change with the height. The splicing effect of the improved algorithm is evaluated by the measured signal, which are obtained in Wuhan, China, and the splice of the AD and PC signals in the range of 800–1500 m are completed. Compared with the traditional method, the evaluation parameter R² and the residual sum of squares of the spliced signal are greatly improved. The linear relationship between the AD and PC signals is improved, and the fitting R² of differential absorption optical depth reaches 0.909, indicating that the improved signal splicing algorithm can well splice the near-field AD signal and the far-field PC signal. Full article

Air pollution is a prominent problem all over the world, seriously endangering human life. To protect the environment and human health, timely and accurate air quality evaluations are imperative. Recently, with the increasing focus on air pollution, an evaluation tool that can offer intuitive air quality information is especially needed. Though the Air Quality Index (AQI) has played this role over the years, its intrinsic limitations discussed in this study (sharp boundary, biased evaluation, conservative strategy and incomplete criterion) are gradually apparent, limiting its air quality evaluation capability. Therefore, a novel paradigm, the Air Quality Fuzzy Comprehensive Evaluation (AQFCE), is proposed. In the preprocessing module, missing and reversal data are handled by a least square piecewise polynomial fitting and linear regression. An improved fuzzy comprehensive evaluation model is adopted to solve the AQI’s above limitations in the evaluation module. The early warning module provides a timely alert and recommendation. To validate the performance of the AQFCE, Beijing, Shanghai and Xi’an in China are selected for case studies, and daily and hourly concentration data of six conventional air pollutants from September 2018 to August 2019 are employed. For daily reports, the AQFCE and AQI have a high consistent rate and correlation coefficient regarding chief pollutants and levels, respectively, while examples show the level of the AQFCE is more reasonable. For hourly reports, AQI has antinomies and cannot reflect actual pollution, but the AQFCE is still effective. Current major pollutants, “weekend and holiday effect” and “peak type” of pollution are also revealed by the AQFCE. Experiment results prove that the AQFCE is accurate under different pollution conditions and an important supplement to the AQI. Furthermore, the AQFCE can provide health guideline for the public and assist the government in making environmental decisions and development policies. Full article

Since widespread applications of wireless sensors networks, low-speed traffic positioning based on the received signal strength indicator (RSSI) from personal devices with WiFi broadcasts has attracted considerable attention. This study presents a new range-based localization method for outdoor pedestrian positioning by using the combination of offline RSSI distance estimation and real-time continuous position fitting, which can achieve high-position accuracy in the urban road environment. At the offline stage, the piecewise polynomial regression model (PPRM) is proposed to formulate the Euclidean distance between the targets and WiFi scanners by replacing the common propagation model (PM). The online stage includes three procedures. Firstly, a constant velocity Kalman filter (CVKF) is developed to smooth the real-time RSSI time series and estimate the target-detector distance. Then, a least squares Taylor series expansion (LS-TSE) is developed to calculate the actual 2-dimensional coordinate with the replacement of existing trilateral localization. Thirdly, a trajectory-based technique of the unscented Kalman filter (UKF) is introduced to smooth estimated positioning points. In tests that used field scenarios from Guangzhou, China, the experiments demonstrate that the combined CVKF and PPRM can achieve the highly accurate distance estimator of <1.98 m error with the probability of 90% or larger, which outperforms the existing propagation model. In addition, the online method can achieve average positioning error of 1.67 m with the much better than classical methods. Full article

The ultimate limit state function is one of the premises for the assessment of structure strength and the safety of ships under severe conditions. In order to study the residual strength of damaged ships under the combined load of vertical and horizontal bending moments acting on the hull girder, the ultimate limit state function of a damaged ship under combined load, and its fitting methods are investigated in this paper. An improved Smith Method is adopted to calculate the residual load carrying capacity of damage ships, where the rotation and translation of the neutral axis of the damaged cross-section are obtained using a particle swarm optimisation method. Because the distribution curve of the residual load carrying capacity of a damaged ship under combined load is asymmetric, the application of traditional explicit polynomial fitting methods results in poor accuracy. In this study, a piecewise weighted least square fitting method is adopted so as to guarantee the continuity in the transitions, and a method is proposed for fitting the ultimate limit state function of a damaged ship under combined load. Calculations of the residual strength show that the improved Smith Method is more accurate than the original Smith Method for the accurate position of the neutral axis. The error analysis of the fitting methods shows that the ultimate limit state function that is fitted using a piecewise weight least square method is more accurate. Full article

In a high accuracy strapdown inertial navigation system (SINS), the ring laser gyroscope’s (RLG) bias changes and the performance decreases due to factors in the RLG’s self-heating and changes in ambient temperature. Therefore, it is important to study the bias temperature drift characteristics of RLGs in high, low, and variable temperature environments. In this paper, a composite temperature calibration scheme is proposed. The composite temperature model introduces the derivative term and the temperature derivative cross-multiplier on the basis of the static model and sets the overlap regions for the piecewise least squares fitting. The results show that the composite temperature model can compensate the bias trend term well at ambient temperature, improve the fitting accuracy, and smooth the output curve. The compensation method has a small amount of calculations and flexible parameter design. The precision of the laser gyros in one SINS is improved by about 64.9%, 15.7%, and 3.6%, respectively, which has certain engineering application value. Full article

For the laser tracking and positioning system of a moving target using a four-quadrant detector, the accuracy of laser spot position detection has a serious impact on the tracking performance of the system. For moving target tracking, the traditional spot position detection method of a four-quadrant detector cannot give better consideration to both detection accuracy and operation speed. In view of this, an improved method based on piecewise low-order polynomial least squares fitting and a Kalman filter is proposed. Firstly, the tracking and positioning mathematical model of the system is created, and the experimental device is established. Then, the shortcomings of traditional methods are analyzed, and the improved method and the real-time tracking and positioning algorithm of the system are studied. Finally, through the experiment, the system operation effects are compared and analyzed before and after the improvement. The experimental results of system dynamic tracking show that, the least squares fitting of the experimental data using a 5-segment and quadratic polynomial can achieve better results. By using the improved method, the maximum tracking distance of a moving object is increased from 12 m to more than 30 m. At a distance of 7.5 m, the maximum tracking speed can reach 2.11 m/s, and the root mean square error (RMSE) of the position is less than 4.59 mm. At 15.5 m, the maximum tracking speed is 2.04 m/s and the RMSE is less than 5.42 mm. Additionally, at 23.5 m, it is 1.13 m/s and 5.71 mm. Full article

The Orbita hyperspectral satellite (OHS) is the first hyperspectral satellite with surface coating technology for sensors in the world. It includes 32 bands from visible to near-infrared wavelengths. However, technology such as the fabricating process of complementary metal–oxide–semiconductor (CMOS) sensors makes the image contain a lot of random and unsystematic stripe noise, which is so bad that it seriously affects visual interpretation, object recognition and the application of the OHS data. Although a large number of stripe removal algorithms have been proposed, very few of them take into account the characteristics of OHS sensors and analyze the causes of OHS data noise. In this paper, we propose a destriping algorithm for OHS data. Firstly, we use both the adaptive moment matching method and multi-level unidirectional total variation method to remove stripes. Then a model based on piecewise linear least squares fitting is proposed to restore the vertical details lost in the first step. Moreover, we further utilize the spectral information of the OHS image, and extend our 2-D destriping method to the 3-D case. Results demonstrate that the proposed method provides the optimal destriping result on both qualitative and quantitative assessments. Moreover, the experimental results show that our method is superior to the existing single-band and multispectral destriping methods. Also, we further use the algorithm to the stripe noise removal of other real remote sensing images, and excellent image quality is obtained, which proves the universality of the algorithm. Full article