Hammerstein model identification algorithm using Bezier-Bernstein approximation

A new identification algorithm is introduced for the Hammerstein model consisting of a nonlinear static function followed by a linear dynamical model. The nonlinear static function is characterised by using the Bezier-Bernstein approximation. The identification method is based on a hybrid scheme including the applications of the inverse of de Casteljau's algorithm, the least squares algorithm and the Gauss-Newton algorithm subject to constraints. The related work and the extension of the proposed algorithm to multi-input multi-output systems are discussed. Numerical examples including systems with some hard nonlinearities are used to illustrate the efficacy of the proposed approach through comparisons with other approaches.

The impact of traffic emissions on atmospheric ozone and OH: results from QUANTIFY

To estimate the impact of emissions by road, aircraft and ship traffic on ozone and OH in the present-day atmosphere six different atmospheric chemistry models have been used. Based on newly developed global emission inventories for road, ship and aircraft emission data sets each model performed sensitivity simulations reducing the emissions of each transport sector by 5%. The model results indicate that on global annual average lower tropospheric ozone responds most sensitive to ship emissions (50.6%±10.9% of the total traffic induced perturbation), followed by road (36.7%±9.3%) and aircraft exhausts (12.7%±2.9%), respectively. In the northern upper troposphere between 200–300 hPa at 30–60° N the maximum impact from road and ship are 93% and 73% of the maximum effect of aircraft, respectively. The latter is 0.185 ppbv for ozone (for the 5% case) or 3.69 ppbv when scaling to 100%. On the global average the impact of road even dominates in the UTLS-region. The sensitivity of ozone formation per NOx molecule emitted is highest for aircraft exhausts. The local maximum effect of the summed traffic emissions on the ozone column predicted by the models is 0.2 DU and occurs over the northern subtropical Atlantic extending to central Europe. Below 800 hPa both ozone and OH respond most sensitively to ship emissions in the marine lower troposphere over the Atlantic. Based on the 5% perturbation the effect on ozone can exceed 0.6% close to the marine surface (global zonal mean) which is 80% of the total traffic induced ozone perturbation. In the southern hemisphere ship emissions contribute relatively strongly to the total ozone perturbation by 60%–80% throughout the year. Methane lifetime changes against OH are affected strongest by ship emissions up to 0.21 (± 0.05)%, followed by road (0.08 (±0.01)%) and air traffic (0.05 (± 0.02)%). Based on the full scale ozone and methane perturbations positive radiative forcings were calculated for road emissions (7.3±6.2 mWm−2) and for aviation (2.9±2.3 mWm−2). Ship induced methane lifetime changes dominate over the ozone forcing and therefore lead to a net negative forcing (−25.5±13.2 mWm−2).

Modeling of complex-valued Wiener systems using B-spline neural network

In this brief, a new complex-valued B-spline neural network is introduced in order to model the complex-valued Wiener system using observational input/output data. The complex-valued nonlinear static function in the Wiener system is represented using the tensor product from two univariate B-spline neural networks, using the real and imaginary parts of the system input. Following the use of a simple least squares parameter initialization scheme, the Gauss-Newton algorithm is applied for the parameter estimation, which incorporates the De Boor algorithm, including both the B-spline curve and the first-order derivatives recursion. Numerical examples, including a nonlinear high-power amplifier model in communication systems, are used to demonstrate the efficacy of the proposed approaches.

B-spline neural network based digital baseband predistorter solution using the inverse of De Boor algorithm

In this paper a new nonlinear digital baseband predistorter design is introduced based on direct learning, together with a new Wiener system modeling approach for the high power amplifiers (HPA) based on the B-spline neural network. The contribution is twofold. Firstly, by assuming that the nonlinearity in the HPA is mainly dependent on the input signal amplitude the complex valued nonlinear static function is represented by two real valued B-spline neural networks, one for the amplitude distortion and another for the phase shift. The Gauss-Newton algorithm is applied for the parameter estimation, in which the De Boor recursion is employed to calculate both the B-spline curve and the first order derivatives. Secondly, we derive the predistorter algorithm calculating the inverse of the complex valued nonlinear static function according to B-spline neural network based Wiener models. The inverse of the amplitude and phase shift distortion are then computed and compensated using the identified phase shift model. Numerical examples have been employed to demonstrate the efficacy of the proposed approaches.

A Wiener model for memory high power amplifiers using B-spline function approximation

In this paper we introduce a new Wiener system modeling approach for memory high power amplifiers in communication systems using observational input/output data. By assuming that the nonlinearity in the Wiener model is mainly dependent on the input signal amplitude, the complex valued nonlinear static function is represented by two real valued B-spline curves, one for the amplitude distortion and another for the phase shift, respectively. The Gauss-Newton algorithm is applied for the parameter estimation, which incorporates the De Boor algorithm, including both the B-spline curve and the first order derivatives recursion. An illustrative example is utilized to demonstrate the efficacy of the proposed approach.

Wiener System identification using B-spline functions with De Boor recursion

A simple and effective algorithm is introduced for the system identification of Wiener system based on the observational input/output data. The B-spline neural network is used to approximate the nonlinear static function in the Wiener system. We incorporate the Gauss-Newton algorithm with De Boor algorithm (both curve and the first order derivatives) for the parameter estimation of the Wiener model, together with the use of a parameter initialization scheme. The efficacy of the proposed approach is demonstrated using an illustrative example.

Generalized beta generated distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets.

Modelling and inverting complex-valued Wiener systems

We develop a complex-valued (CV) B-spline neural network approach for efficient identification and inversion of CV Wiener systems. The CV nonlinear static function in the Wiener system is represented using the tensor product of two univariate B-spline neural networks. With the aid of a least squares parameter initialisation, the Gauss-Newton algorithm effectively estimates the model parameters that include the CV linear dynamic model coefficients and B-spline neural network weights. The identification algorithm naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. An accurate inverse of the CV Wiener system is then obtained, in which the inverse of the CV nonlinear static function of the Wiener system is calculated efficiently using the Gaussian-Newton algorithm based on the estimated B-spline neural network model, with the aid of the De Boor recursions. The effectiveness of our approach for identification and inversion of CV Wiener systems is demonstrated using the application of digital predistorter design for high power amplifiers with memory

A variational method to retrieve the extinction profile in liquid clouds using multiple field-of-view lidar

Liquid clouds play a profound role in the global radiation budget but it is difficult to remotely retrieve their vertical profile. Ordinary narrow field-of-view (FOV) lidars receive a strong return from such clouds but the information is limited to the first few optical depths. Wideangle multiple-FOV lidars can isolate radiation scattered multiple times before returning to the instrument, often penetrating much deeper into the cloud than the singly-scattered signal. These returns potentially contain information on the vertical profile of extinction coefficient, but are challenging to interpret due to the lack of a fast radiative transfer model for simulating them. This paper describes a variational algorithm that incorporates a fast forward model based on the time-dependent two-stream approximation, and its adjoint. Application of the algorithm to simulated data from a hypothetical airborne three-FOV lidar with a maximum footprint width of 600m suggests that this approach should be able to retrieve the extinction structure down to an optical depth of around 6, and total opticaldepth up to at least 35, depending on the maximum lidar FOV. The convergence behavior of Gauss-Newton and quasi-Newton optimization schemes are compared. We then present results from an application of the algorithm to observations of stratocumulus by the 8-FOV airborne “THOR” lidar. It is demonstrated how the averaging kernel can be used to diagnose the effective vertical resolution of the retrieved profile, and therefore the depth to which information on the vertical structure can be recovered. This work enables exploitation of returns from spaceborne lidar and radar subject to multiple scattering more rigorously than previously possible.

Multimodel estimates of intercontinental source-receptor relationships for ozone pollution

Understanding the surface O3 response over a “receptor” region to emission changes over a foreign “source” region is key to evaluating the potential gains from an international approach to abate ozone (O3) pollution. We apply an ensemble of 21 global and hemispheric chemical transport models to estimate the spatial average surface O3 response over east Asia (EA), Europe (EU), North America (NA), and south Asia (SA) to 20% decreases in anthropogenic emissions of the O3 precursors, NOx, NMVOC, and CO (individually and combined), from each of these regions. We find that the ensemble mean surface O3 concentrations in the base case (year 2001) simulation matches available observations throughout the year over EU but overestimates them by >10 ppb during summer and early fall over the eastern United States and Japan. The sum of the O3 responses to NOx, CO, and NMVOC decreases separately is approximately equal to that from a simultaneous reduction of all precursors. We define a continental-scale “import sensitivity” as the ratio of the O3 response to the 20% reductions in foreign versus “domestic” (i.e., over the source region itself) emissions. For example, the combined reduction of emissions from the three foreign regions produces an ensemble spatial mean decrease of 0.6 ppb over EU (0.4 ppb from NA), less than the 0.8 ppb from the reduction of EU emissions, leading to an import sensitivity ratio of 0.7. The ensemble mean surface O3 response to foreign emissions is largest in spring and late fall (0.7–0.9 ppb decrease in all regions from the combined precursor reductions in the three foreign regions), with import sensitivities ranging from 0.5 to 1.1 (responses to domestic emission reductions are 0.8–1.6 ppb). High O3 values are much more sensitive to domestic emissions than to foreign emissions, as indicated by lower import sensitivities of 0.2 to 0.3 during July in EA, EU, and NA when O3 levels are typically highest and by the weaker relative response of annual incidences of daily maximum 8-h average O3 above 60 ppb to emission reductions in a foreign region (<10–20% of that to domestic) as compared to the annual mean response (up to 50% of that to domestic). Applying the ensemble annual mean results to changes in anthropogenic emissions from 1996 to 2002, we estimate a Northern Hemispheric increase in background surface O3 of about 0.1 ppb a−1, at the low end of the 0.1–0.5 ppb a−1 derived from observations. From an additional simulation in which global atmospheric methane was reduced, we infer that 20% reductions in anthropogenic methane emissions from a foreign source region would yield an O3 response in a receptor region that roughly equals that produced by combined 20% reductions of anthropogenic NOx, NMVOC, and CO emissions from the foreign source region.

Digital predistorter design using B-Spline neural network and inverse of De Boor algorithm

This contribution introduces a new digital predistorter to compensate serious distortions caused by memory high power amplifiers (HPAs) which exhibit output saturation characteristics. The proposed design is based on direct learning using a data-driven B-spline Wiener system modeling approach. The nonlinear HPA with memory is first identified based on the B-spline neural network model using the Gauss-Newton algorithm, which incorporates the efficient De Boor algorithm with both B-spline curve and first derivative recursions. The estimated Wiener HPA model is then used to design the Hammerstein predistorter. In particular, the inverse of the amplitude distortion of the HPA's static nonlinearity can be calculated effectively using the Newton-Raphson formula based on the inverse of De Boor algorithm. A major advantage of this approach is that both the Wiener HPA identification and the Hammerstein predistorter inverse can be achieved very efficiently and accurately. Simulation results obtained are presented to demonstrate the effectiveness of this novel digital predistorter design.

Interferometric technique for measuring terahertz antenna phase patterns

A quasi-optical interferometric technique capable of measuring antenna phase patterns without the need for a heterodyne receiver is presented. It is particularly suited to the characterization of terahertz antennas feeding power detectors or mixers employing quasi-optical local oscillator injection. Examples of recorded antenna phase patterns at frequencies of 1.4 and 2.5 THz using homodyne detectors are presented. To our knowledge, these are the highest frequency antenna phase patterns ever recovered. Knowledge of both the amplitude and phase patterns in the far field enable a Gauss-Hermite or Gauss-Laguerre beam-mode analysis to be carried out for the antenna, of importance in performance optimization calculations, such as antenna gain and beam efficiency parameters at the design and prototype stage of antenna development. A full description of the beam would also be required if the antenna is to be used to feed a quasi-optical system in the near-field to far-field transition region. This situation could often arise when the device is fitted directly at the back of telescopes in flying observatories. A further benefit of the proposed technique is simplicity for characterizing systems in situ, an advantage of considerable importance as in many situations, the components may not be removable for further characterization once assembled. The proposed methodology is generic and should be useful across the wider sensing community, e.g., in single detector acoustic imaging or in adaptive imaging array applications. Furthermore, it is applicable across other frequencies of the EM spectrum, provided adequate spatial and temporal phase stability of the source can be maintained throughout the measurement process. Phase information retrieval is also of importance to emergent research areas, such as band-gap structure characterization, meta-materials research, electromagnetic cloaking, slow light, super-lens design as well as near-field and virtual imaging applications.

Towards understanding the climate of Venus

ESA’s Venus Express Mission has monitored Venus since April 2006, and scientists worldwide have used mathematical models to investigate its atmosphere and model its circulation. This book summarizes recent work to explore and understand the climate of the planet through a research program under the auspices of the International Space Science Institute (ISSI) in Bern, Switzerland. Some of the unique elements that are discussed are the anomalies with Venus’ surface temperature (the huge greenhouse effect causes the surface to rise to 460°C, without which would plummet as low as -40°C), its unusual lack of solar radiation (despite being closer to the Sun, Venus receives less solar radiation than Earth due to its dense cloud cover reflecting 76% back) and the juxtaposition of its atmosphere and planetary rotation (wind speeds can climb up to 200 m/s, much faster than Venus’ sidereal day of 243 Earth-days).