Recursive Filtering Technique Research Articles

The use of adaptive multiple models for predefined exponential stability of control systems of uncertain discrete‐time nonlinear objects

SummaryIn this work, an adaptive multiple model pre‐assigned exponential convergence control scheme based on the time varying exponential function is demonstrated for a class of discrete‐time nonlinear systems. For coping with the noncausality problem from previous adaptive backstepping design method of nonlinear discrete‐time systems, a first‐order recursive filter is used in controller design procedures and the n‐step prediction model is not needed, thereby reducing the computational burden effectively. The time varying function is employed to force all states variables to convergence to zero with a pre‐defined rate which does not rely on the initial conditions of systems. In addition, the multiple model set is constructed to address unknown parameters problem and further the second level adaptive algorithm of unknown parameters is developed. A characteristic feature of the second‐level multi‐model adaptation algorithm is that it dynamically adapts to time changes in the identified model (it uses identification information better than the switching multiple model control). In a unified framework of second level adaption, a first‐order recursive filter and backstepping technique, a pre‐assigned exponential convergence controller is presented. Finally, the results about discrete‐time pre‐assigned exponential convergence method are compared with other methods using two case studies.

High-speed multi-dimensional relative navigation for uncooperative space objects

This work proposes a high-speed Light Detection and Ranging (LIDAR) based navigation architecture that is appropriate for uncooperative relative space navigation applications. In contrast to current solutions that exploit 3D LIDAR data, our architecture transforms the odometry problem from the 3D space into multiple 2.5D ones and completes the odometry problem by utilizing a recursive filtering scheme. Trials evaluate several current state-of-the-art 2D keypoint detection and local feature description methods as well as recursive filtering techniques on a number of simulated but credible scenarios that involve a satellite model developed by Thales Alenia Space (France). Most appealing performance is attained by the 2D keypoint detector Good Features to Track (GFFT) combined with the feature descriptor KAZE, that are further combined with either the H∞ or the Kalman recursive filter. Experimental results demonstrate that compared to current algorithms, the GFTT/KAZE combination is highly appealing affording one order of magnitude more accurate odometry and a very low processing burden, which depending on the competitor method, may exceed one order of magnitude faster computation.

A Low Complexity Linear Moving Average Filtering Technique for PAR Reduction in OFDM Systems

In this paper, a linear moving average recursive filtering technique is proposed to reduce the peak-to-average power ratio (PAR) of orthogonal frequency division multiplexing (OFDM) signals. The proposed low complexity technique is analyzed in an oversampled OFDM system and a simple distribution approximation of the oversampled and linearly filtered OFDM signals is also proposed. Corresponding time domain linear equalizers are developed to recover originally transmitted data symbols. Through extensive computer simulations, effects of the new filtering technique on the oversampled OFDM peak-to-average power ratio (PAR), power spectral density (PSD) and corresponding linear equalizers on the frequency selective Rayleigh fading channel transmission symbol-error-rate (SER) performance are investigated. The newly proposed recursive filtering scheme results in attractive PAR reduction, requires no extra fast Fourier transform/inverse fast Fourier transform (FFT/IFFT) operations, refrains from transmitting any side information, and reduces out-of-band radiation. Also, corresponding linear receivers are shown to perform very close to their frequency domain counterparts.

Quantitative identification of riverine nitrogen from point, direct runoff and base flow sources.

We present a methodological example for quantifying the contributions of riverine total nitrogen (TN) from point, direct runoff and base flow sources by combining a recursive digital filter technique and statistical methods. First, we separated daily riverine flow into direct runoff and base flow using a recursive digital filter technique; then, a statistical model was established using daily simultaneous data for TN load, direct runoff rate, base flow rate, and temperature; and finally, the TN loading from direct runoff and base flow sources could be inversely estimated. As a case study, this approach was adopted to identify the TN source contributions in Changle River, eastern China. Results showed that, during 2005-2009, the total annual TN input to the river was 1,700.4±250.2 ton, and the contributions of point, direct runoff and base flow sources were 17.8±2.8%, 45.0±3.6%, and 37.2±3.9%, respectively. The innovation of the approach is that the nitrogen from direct runoff and base flow sources could be separately quantified. The approach is simple but detailed enough to take the major factors into account, providing an effective and reliable method for riverine nitrogen loading estimation and source apportionment.

Real-time estimation of the poloidal wavenumber of ISTTOK tokamak magnetic fluctuations

The successful control of a fusion plasma discharge relies on the continuous improvement of existing diagnostics and on the development of new ones based on innovative concepts. It is equally important to provide efficient numerical tools capable of extracting, in real time, the most important physical quantities emerging from the collected data. This encompasses, for instance, the determination of the wavenumber and amplitude tracking of plasma instabilities, a necessary ingredient for establishing in real time the type of feedback control stabilization scheme to be used. In this paper, the characterization of the wavenumber spectra of unstable modes observed in ISTTOK plasma discharges is addressed using a set of two poloidal arrays of magnetic coils (Mirnov coils). In particular, the prospect for the estimation of the poloidal wavenumber in real time using recursive filtering techniques is investigated. It is shown that, in contrast with typical cross-spectrum analysis, where a large dataset is required to estimate the wavenumbers, with this innovative technique, the wavenumber spectra may be obtained in faster time scales.

Constraining water table depth simulations in a land surface model using estimated baseflow

Several recent studies have shown the significance of representing groundwater in land surface hydrologic simulations. However, optimal methods for model parameter calibration in order to realistically simulate baseflow and groundwater depth have received little attention. Most studies still use globally constant groundwater parameters due to the lack of available datasets for calibration. Moreover, when models are calibrated, various parameter combinations are found to exhibit equifinality in simulated total runoff due to model parameter interactions. In this study, a simple lumped groundwater model is incorporated into the Community Land Model (CLM), in which the water table is interactively coupled to soil moisture through the groundwater recharge fluxes. The coupled model (CLMGW) is successfully validated in Illinois using a 22-year (1984–2005) monthly observational dataset. Baseflow estimates from the digital recursive filter technique are used to calibrate the CLMGW parameters. The advantage obtained from incorporating baseflow calibration in addition to traditional calibration based on measured streamflow alone is demonstrated by a Monte Carlo-type simulation analysis. Using the optimal parameter sets identified from baseflow calibration, flow partitioning and water table depth simulations using CLMGW are improved, and the equifinality problem is alleviated. For other regions that lack observations of water table depth, the baseflow calibration approach can be used to enhance parameter estimation and constrain water table depth simulations.

Application of the Sequential Three-Dimensional Variational Method to Assimilating SST in a Global Ocean Model

Abstract A recursive filter or parameterized curve fitting technique is usually used in a three-dimensional variational data assimilation (3DVAR) scheme to approximate the background error covariance, which can only represent the errors of an ocean field over a predetermined scale. Without an accurate flow-dependent error covariance that is also local and time dependent, a 3DVAR system may not provide good analyses because it is optimal only under the assumption of an accurate covariance. In this study, a sequential 3DVAR (S3DVAR) is formulated in model grid space to examine if there is useful information that can be extracted from the observation. This formulation is composed of a series of 3DVARs, each of which uses recursive filters with different length scales. It can provide an inhomogeneous and anisotropic analysis for the wavelengths that can be resolved by the observation network, just as with the conventional Barnes analysis or successive corrections. Being a variational formulation, S3DVAR can deal with data globally with an explicit specification of the observation errors; explicit physical balances or constraints; and advanced datasets, such as satellite and radar. Even though the S3DVAR analysis can be viewed as a set of isotropic functions superpositioned together, this superposition is not prespecified as in a single 3DVAR approach but is determined by the information that can be resolved by observation. The S3DVAR is adopted in a global sea surface temperature (SST) data assimilation system, into which the shipboard SSTs and the 4-km Advanced Very High Resolution Radiometer (AVHRR) Pathfinder daily SSTs are assimilated, respectively. The results demonstrate that the proposed S3DVAR works better in practice than a single 3DVAR.

Hydrological characterisation of pesticide loads using hydrograph separation at different scales in a German catchment

Pesticide pollution of surface waters was studied in a 49.7 km 2 catchment in Germany. The loads were differentiated into point source (PSP) and non-point source pollution (NPSP). The contribution of runoff, interflow, groundwater, drainage and spray drift to river contamination was defined as NPSP. Pesticides discharged into the river via wastewater treatment plants and sewer overflows were considered as PSP. Hydrology and pesticide loads were studied on the scale of the entire catchment and in two sub-catchments not influenced by PSP. River discharges and concentrations of 19 pesticides were measured at four locations over 447 days. The total load detected in the entire catchment amounted to 3249 g active ingredient (a.i.). The stream flow data were separated into base and direct flow applying a non-linear reservoir separation algorithm. Single rainfall events leading to runoff and interflow dominated NPSP in the sub-catchments. For the sub-catchment Rossberg 87% and for Leidenhofen 71% of the pesticide load could be attributed to direct flow. This corresponded to 14 and 34% time of peak flow events for Rossberg and Leidenhofen, respectively. For the entire catchment only 15% of the NPSP was transported with direct flow with 49% attributed to base flow. The difference between the entire and the sub-catchment contribution was attributed to dilution, hysteresis and merging effects. Applying a digital recursive filter technique for hydrograph separation confirmed the results of the non-linear reservoir separation algorithm. The impact of the hydrograph separation technique on the hydrological characterisation of pesticide loads was insignificant. The results emphasise the dynamic nature of pesticide transport and its complex interaction between size and position of source areas along a stream flow network. The measured loads in the sub-catchments were scaled up to the entire catchment as an estimate for the total NPSP. The fraction of the area treated with a pesticide was found not to be an appropriate scaling factor. Research is required to develop adequate methods to scale detailed measurements of pesticide loads from small scales up to catchments with complex drainage systems.

Monitoring varying speed machinery vibrations—I. The use of non-stationary recursive filters

Varying speed machinery monitoring is fraught with difficulties due to non-stationary machine dynamics and vibrations. Most conventional signal processing methods based on digital sampling carried out in equal time intervals become inappropriate when monitoring the vibrations of varying speed machinery. Parts I and II of this paper present a new data acquisition technique which pre-processes varying speed signals so that conventional signal processing methods can be applied. It is based on the application of recursive filtering and angle domain analysis to non-stationary vibration analysis. The present paper, Part I, is primarily concerned with the recursive filtering technique. It is shown that the recursive filtering can be used as an effective and reliable method of pre-conditioning the original vibration signals. The theoretical background and some basic properties of the non-stationary recursive filtering approach are described. The approach is implemented and validated using computer simulation and experiments.

Faster Determination of the Intraseasonal Variability of Storm Tracks Using Murakami's Recursive Filter

Abstract Murakami's recursive filter technique is suitable for computing storm tracks with reduced needs in data length, and it decreases computing time by the factor 3.5. It is shown that the storm tracks differ only slightly from the ones obtained using the conventional Blackmon filtering approach. A problem identified with respect to the exact frequency of the 1.0 response of Murakami's filter appears to be of minor importance.

Recursive filtering technique for electronic speckle fringe patterns

The recursive filtering algorithm, a simple method of filtering electronic speckle pattern interferometric (ESPI) images, is presented and studied. Application software is specially developed for the new method. Experimental demonstration shows that the technique is the most effective and speedy method for the filtering of ESPI fringe patterns so far.

Optimal infinite impulse response zero crossing based edge detectors

We present formal optimality criteria and a complete design methodology for a family of zero crossing based, infinite impulse response (recursive) edge detection filters. In particular, we adapt the optimality criteria proposed by Canny ( IEEE Trans. Pattern Anal. Mach. Intelligence PAMI-8, 1986 , 679–714) to filters designed to respond with a zero crossing in the output at an edge location and additionally to impulse responses which are (allowed to be) infinite in extent. The spurious response criterion is captured directly by an appropriate measure of filter spatial extent for infinite responses. Infinite duration impulse responses may be implemented efficiently with recursive filtering techniques and so require constant computation time with respect to scale. As we will show, we can achieve both superior performance and increased speed by designing directly for an infinite impulse response than by any of the proposed finite duration approaches. We also show that the optimal filter which responds with a zero crossing in its output may not be implemented by designing the optimal peak responding filter (similar to Canny) and taking an additional derivative. It is necessary to formulate the criteria and design for a zero crossing response from the outset, else optimality is sacrificed. Filter parameters and performance criteria are presented for several designs, and experimental results are presented on a variety of images which demonstrate the behavior in the presence of very adverse noise, with respect to scale, and as compared to other “optimal” IIR filters which have been reported.

Digital subtraction angiography systems: assessing performance with phantoms.

A solid, acrylic phantom was developed to assess the iodine perceptibility of three digital subtraction angiography (DSA) systems, including one using a recursive filter technique. Three phantoms, designed to mimic flow of iodinated boluses through blood vessels, were used. Each contained four triangular boluses of different widths and of a specific iodine concentration. Motion, required to test recursively filtered DSA systems, was simulated by placing the phantoms on a motorized cart. The phantoms were also used to test flow curve generation in applicable systems. Intersystem differences in perceptibility were attributed to differences in system noise, system resolution, and dynamic range. Flow curves produced with the phantoms were similar to those obtained in patient studies.

A new digital technique for the measurement of mechanical vibration

The two‐channel FFT analyzers have revolutionized the measurement technique used for mechanical measurements. Recursive digital filter technique is in general use within acoustics. However, the true real time capability, eliminating the use of window functions like f.ex. Hanning along with born logarithmic frequency scale, offers great advantages for the measurement of mechanical vibrations. The measurement of vibrational net power flow, vibration modes and stress intensity by mechanical transducers will be discussed.

Two-dimensional recursive filtering using the rotated filter design technique

Two of the main problems encountered during the digital filtering of large two-dimensional arrays of data are those of core storage and excessive computational time. Recursive filters appear to offer a means of overcoming these difficulties. However, the recursive filtering technique has not been very popular for applications involving the typically large arrays common to earth science because of the filter stability design problem. Recently it was shown that if the rotated filter concept is used, stable circularly symmetrical two-dimensional recursive filters can be generated quickly and easily. The operators produced in this way can be applied as component cascades of complex bilinear filters in a two-dimensional difference equation. To test the effectiveness of this type of filter, a data set consisting of point determinations of ore grade in a major Canadian open pit copper mine was obtained and filtered by both the nonrecursive and the rotated filter method. The results showed that the rotated recursive filter compared very favorably in performance to, and required less storage than, the nonrecursive filter.