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

Abstract

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.

Additional carbon inputs to reach a 4 per 1000 objective in Europe: feasibility and projected impacts of climate change based on Century simulations of long-term arable experiments

“…Zhang et al (2017) estimated that the amount of N inputs from livestock manure applied to European croplands was 3.9 Tg N in 2014, for a cropland area of 127 Mha in 2015 (Goldewijk et al, 2017). Cattle manure, which represents the highest proportion of manure produced and applied to croplands, has an average C : N ratio ranging between 10 and 30 (multiple sources from Fuchs et al, 2014, andPellerin et al, 2019). With these data, we can roughly estimate the application of C manure from livestock in European agricultural soils as ranging between 0.30 and 0.92 MgC ha −1 each year.…”

A Method for Solving LiDAR Waveform Decomposition Parameters Based on a Variable Projection Algorithm

“…e objective function only containing nonlinear parameters is optimized using the LM algorithm. To ensure global optimization, once the nonlinear parameters are calculated for a given iteration, the linear parameters are calculated using equation (15) until the overall gradient is less than a threshold value. For the convenience of expression, in the following text, the traditional LM method without the separation of parameters is referred to as LM unSep .…”

“…In general, the Gaussian decomposition of waveforms consists of two steps: (1) determining the number of Gaussian components and their initial parameters and (2) optimizing and postprocessing the characteristic parameters. A majority of parameter estimation methods regard all Gaussian parameters as nonlinear variables [15] and then employ the nonlinear optimization method to solve the parameters. Liu et al [16] combined this method with sequential quadratic programming (SQP), developing a gradient-based optimization algorithm; it determined the optimal time delays and system parameters in a novel dynamic optimization problem for nonlinear multistage systems.…”

Accuracy verification and evaluation of Sentinel-1A repeat track differential interferometric synthetic aperture radar in monitoring mining subsidence

“…Its basic principle is to generate an interferogram by conjugate multiplication of two radar complex images before and after deformation, remove topographical factors using the difference from the external DEM to generate a differential interferogram, and then extract the deformation information of the ground targets from the differential interferogram. [16][17][18][19] Phase φ of the interferogram is closely related to the radar imaging parameters, antenna position, incident angle, and the elevation of the ground targets, which can be expressed as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 1 1 6 ; 9 7 φ ¼ φ flat þ φ topo þ φ def þ φ atm þ φ noise ;…”