Recursive Inverse Research Articles

Adaptive Algorithm for Motion Artifacts Removal in Wearable Biomedical Sensors During Physical Exercise

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Objective:</i> Motion artifacts (MA) are significant sources of noise in the wearable devices that are used to collect biological information from the human body. Photoplethysmography (PPG) is an example of the sensors embedded in many of these devices. PPG signals are highly influenced by MA, especially when the motion involves the organ that the PPG sensor is attached to. The aim of this paper is to build an adaptive algorithm and multiresolution analysis technique to denoise the raw PPG signals, suppress the MAs and accurately estimate the HR as an example of MA suppression in the wearable devices. The challenge here is to find the right selection considering high accuracy and low-computational complexity. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Methods:</i> Discrete wavelet transform recursive inverse (DWT-RI) adaptive filter algorithm in addition to multiresolution analysis is implemented to suppress MAs and estimate the HR using the simultaneously recorded accelerations in the three dimensions as reference signals for the adaptive algorithm. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Results:</i> The proposed algorithm has a low computational cost and results in an absolute average error of 1.17 beats per minute (BPM) when tested on 12 subjects from a well-known database for this purpose. The performance of the proposed algorithm is compared to the other existing methods in literature used for noise removal and motion artifact suppression. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Conclusion:</i> DWT-RI adaptive algorithm can successfully suppress motion artifacts in PPG signals with a low computational complexity and outperforms several alternatives in terms of the average absolute error.

Recursive inverse dynamics sensitivity analysis of open-tree-type multibody systems

We present a first-order recursive approach to sensitivity analysis based on the application of the direct differentiation method to the inverse Lagrangian dynamics of rigid multibody systems. Our method is simple and efficient and is characterized by the following features. Firstly, it describes the kinematics of multibody systems using branch connectivity graphs and joint-branch connectivity matrices. For most mechanical systems with an open-tree kinematic structure, this method turns out to be more efficient compared to other kinematic descriptions employing joint or link connectivity graphs. Secondly, a recursive sensitivity analysis is presented for a dynamic system with an open-tree kinematic structure and inverse dynamic equations described in terms of the Lagrangian formalism. Thirdly, known approaches to recursive inverse dynamic and sensitivity analyses are modified to include dynamic systems with external forces and torques acting simultaneously at all joints. Finally, the proposed method for sensitivity analysis is easy to implement and computationally efficient. It can be utilized to evaluate the derivatives of the dynamic equations of multibody systems in gradient-based optimization algorithms. It also allows less experienced users to perform sensitivity analyses using the power of high-level programming languages such as MATLAB. To illustrate the method, simulation results for a human body model are discussed. The shortcomings of the method and possible directions for future work are outlined.

A recursive inverse dynamics algorithm for robotic manipulators with elastic joints and its application to control

High-order inverse dynamics is important for the trajectory tracking control of the elastic-joint manipulators. Usually it is undesirable to establish third-order or fourth-order inverse dynamics through the symbolic Lagrangian method, because of its complicated customization and higher computational complexity, which is not suitable for real-time control for multi-joint [Formula: see text] manipulators. Based on the Subsystem of Newton-Euler formulation and the recently proposed elastic joint Newton-Euler algorithm (EJNEA), a novel recursive algorithm (Sub-EJNEA) is proposed in this paper. The Sub-EJNEA obtains a linear complexity [Formula: see text], and has a more compact form and clear physical meaning. Based on the Sub-EJNEA, a recursive control method is proposed, which can be seen as an enhancement of the feedback linearization (FL-E) control method. When facing with friction and external disturbances, a combined controller FL-E-RISE is proposed. Finally, to verify the correctness of the recursive algorithm and the effectiveness of the proposed control schemes, simulation results with the Baxter manipulator are presented.

Discrete-wavelet-transform recursive inverse algorithm using second-order estimation of the autocorrelation matrix

The recursive-least-squares (RLS) algorithm was introduced as an alternative to LMS algorithm with enhanced performance. Computational complexity and instability in updating the autocolleltion matrix are some of the drawbacks of the RLS algorithm that were among the reasons for the intrduction of the second-order recursive inverse (RI) adaptive algorithm. The 2nd order RI adaptive algorithm suffered from low convergence rate in certain scenarios that required a relatively small initial step-size. In this paper, we propose a newsecond-order RI algorithm that projects the input signal to a new domain namely discrete-wavelet-transform (DWT) as pre step before performing the algorithm. This transformation overcomes the low convergence rate of the second-order RI algorithm by reducing the self-correlation of the input signal in the mentioned scenatios. Expeirments are conducted using the noise cancellation setting. The performance of the proposed algorithm is compared to those of the RI, original second-order RI and RLS algorithms in different Gaussian and impulsive noise environments. Simulations demonstrate the superiority of the proposed algorithm in terms of convergence rate comparedto those algorithms.

Non-invasive fetal ECG extraction using discrete wavelet transform recursive inverse adaptive algorithm.

Fetal heart activity adds significant information about the status of the fetus health. Early diagnosis of issues in the heart before delivery allows early intervention and significantly improves the treatment. This paper presents a new adaptive filtering algorithm for fetal electrocardiogram (FECG) extraction from the maternal abdominal signal, known in literature as abdominal electrocardiogram (AECG) signal. Fetal QRS complex waves will be identified and extracted accurately for fetal health care and monitoring purposes. We use discrete wavelet transform recursive inverse (DWT-RI) adaptive filtering algorithm for this objective. Thoracic maternal electrocardiogram (MECG) is used as a reference in the proposed algorithm and FECG components are extracted from AECG signal after suppressing the MECG projections. The proposed algorithm is compared to other typical adaptive filtering algorithms, least mean squares (LMS), recursive least squares (RLS), and recursive inverse (RI). Fetal QRS waveforms successful identification and extraction from AECG signal is evaluated objectively and visually and compared to other algorithms. We validated the proposed algorithm using both synthetic data and real clinical data. The proposed algorithm is capable of extracting fetal QRS waveforms successfully from AECG and outperforms other adaptive filtering algorithms in terms of accuracy and positive predictivity.

Discrete wavelet transform-based RI adaptive algorithm for system identification

In this paper, we propose a new adaptive filtering algorithm for system identification. The algorithm is based on the recursive inverse (RI) adaptive algorithm which suffers from low convergence rates in some applications; i.e., the eigenvalue spread of the autocorrelation matrix is relatively high. The proposed algorithm applies discrete-wavelet transform (DWT) to the input signal which, in turn, helps to overcome the low convergence rate of the RI algorithm with relatively small step-size(s). Different scenarios has been investigated in different noise environments in system identification setting. Experiments demonstrate the advantages of the proposed DWT recursive inverse (DWT-RI) filter in terms of convergence rate and mean-square-error (MSE) compared to the RI, discrete cosine transform LMS (DCTLMS), discrete-wavelet transform LMS (DWT-LMS) and recursive-least-squares (RLS) algorithms under same conditions.

A new perspective towards decomposition of the generalized inertia matrix of multibody systems

This paper presents a new perspective into the decomposition of the Generalized Inertia Matrix (GIM) of multibody systems with open kinematic architecture, serial or tree-type. Links and kinematic pairs are the two constituting elements of multibody systems. In this work, we propose to decompose a multi-branch multibody system into several kinematic modules. Each module is a set of serially connected links like a serial-chain system. Such a description allows one to obtain a block decomposition $\bar{\mathbf{U}}\bar{\mathbf{D}}\bar{\mathbf{U}}^{T}$ of the GIM where $\bar{\mathbf{U}}$ and $\bar{\mathbf{D}}$ are the block upper-triangular and diagonal matrices, respectively. The results provide a recursive inverse of the GIM on module-level. Many new perspectives leading to macroscopic purview of the complex multibody systems are provided. Empowered with the proposed decomposition, an inter- and intra-modular efficient and numerically stable recursive dynamics algorithm for forward dynamics and simulation was possible. While recursive expressions are derived for a four degree-of-freedom gripper, numerical results are shown for a spatial biped.

Recursive inverse algorithm: Mean-square-error analysis

The recently proposed recursive inverse (RI) adaptive algorithm has shown improved performance compared to some well-known adaptive algorithms [1]. However, there has been no detailed study of its performance. In this paper, we provide an analytical treatment of the ensemble-average learning curve of the RI algorithm. A novel analytical result which describes the learning behavior of the RI algorithm is obtained. It is shown that within limits of approximation, the excess mean-square-error (MSE) of the algorithm approaches zero and the RI algorithm converges to a lower steady-state MSE than the LMS algorithm. The results show that the theoretical and experimental MSE curves of the RI algorithm are in agreement. Also, the MSE analysis of the RI algorithm in a nonstationary environment, where the optimum weight is assumed to be randomly changing about a fixed vector, is derived.

A 2-D Second-Order Recursive Inverse Adaptive Filtering Algorithm

 Abstract—In this paper, a two-dimensional (2-D) version of the recently proposed second order Recursive Inverse (2nd order RI) algorithm is introduced. In the proposed algorithm, instead of estimating the inverse autocorrelation matrix, a second order estimate of the autocorrelation matrix and cross correlation vector, which provide an improved and a more stable performance, are used. Also, the filter coefficients are updated along both the horizontal and vertical directions on a 2-D plane. The performance of the proposed algorithm is compared to that of the 2-D RLS algorithm in Adaptive Line Enhancer (ALE) problem. Simulation results show that the proposed algorithm leads to an improved performance compared to that of the 2-D RLS algorithm.

Recursive inverse adaptive algorithm: a second-order version, a fast implementation technique, and further results

A variable step-size and first-order recursive estimate of the autocorrelation matrix have been used in the update equation of the recently proposed recursive inverse (RI) algorithm. These lead to an improved performance of the RI algorithm compared with some well-known adaptive algorithms. In this paper, the RI algorithm is first briefly reviewed. An improved version of the RI algorithm, which uses a second-order recursive estimation of the correlations, is introduced. A general fast implementation technique for the RI algorithms is presented. The performances of the fast RI and fast second-order RI algorithms are compared to that of the RLS algorithm in stationary white and correlated noise environments in a noise cancellation setting. The simulation results show that the fast RI algorithms outperform the others compared either in speed of convergence and/or the computational complexity when the MSE is held constant. The performance of the original RI algorithms is compared to that of the RLS algorithm in a system identification setting. Simulations show that the RI algorithms perform similar or better than the other algorithms.

Robust Recursive Inverse Adaptive Algorithm in Impulsive Noise

The recently proposed Recursive Inverse (RI) algorithm has shown a significant performance improvement compared to that of the Recursive Least Squares (RLS) algorithm, in various noise environments. However, both algorithms fail to converge in certain impulsive noise environments, especially if the Signal-to-Noise Ratio (SNR) is low. In this paper, a Robust RI algorithm is proposed. Analytical results show that robustness against impulsive noise is achieved by choosing the weights on the basis of the L1 norms of the autocorrelation matrix and the cross-correlation vector. Simulation results confirm that the proposed algorithm provides an improved performance, with a reduction in computational complexity, compared to those of the RLS and the Robust RLS in white and correlated impulsive noise.

Recursive Inverse Dynamics of Mobile Multibody Systems With Joints and Wheels

This paper is related to the inverse-dynamic modeling of mobile multibody systems articulated with joints and wheels. An easily-implementable algorithm, which is based on Newton-Euler (NE) recursive dynamics, is proposed. From imposed joint and/or actuated-wheel motions, the algorithm performs fast calculations of the control torques, as well as the overall rigid motions involved in locomotion tasks. The engineering applications include tree-like mobile manipulators, satellite-reorientation systems, and modular robots, such as snake-like robots, eel-like robots, and a snakeboard.

A 2-D recursive inverse adaptive algorithm

In this paper, a 2-D form of the recently proposed recursive inverse (RI) adaptive algorithm is introduced. The filter coefficients can be updated along both the horizontal and vertical directions on a 2-D plane. The proposed approach uses a variable step size and avoids the use of the inverse autocorrelation matrix in the coefficient update equation, which leads to an improved and more stable performance. Performance of the 2-D RI algorithm is compared to that of the 2-D RLS algorithm in an image deconvolution and an adaptive line enhancer problem settings. The simulation results show that the proposed 2-D RI algorithm leads to an improved performance compared to that of the 2-D RLS algorithm.

English

A method to determine the moving tank and missile impact forces on a bridge is developed. The presentmethod is an online adaptive recursive inverse algorithm, which is composed of the Kalman filter and therecursive least square estimator (RLSE), to estimate the force inputs on the bridge structure. The state equationsof the bridge structure were constructed by using the model superposition and orthogonal technique. Byadopting this inverse method, the moving tank and missile impact force inputs acting on the bridge structuresystem can be estimated from the measured dynamic responses. Besides, this work presents an efficientweighting factor applied in the RLSE, which is capable of providing a reasonable estimation results. The resultsobtained from the simulations show that the method is effective in determining the moving tank and missileimpact forces, so that the acceptable results can be obtained.Defence Science Journal, 2008, 58(6), pp.752-761, DOI:http://dx.doi.org/10.14429/dsj.58.1703

A METHOD FOR QUASI-STATIC ANALYSIS OF TOPOLOGICALLY VARIABLE LATTICE STRUCTURES

The proposed time-independent quasi-static approach for simulations of lattice structures with imperfections is based on integration of the Inverse Broyden's Method suitable for finding the equilibrium state for a large system of atoms interacting through strongly nonlinear potentials and the Recursive Inverse Matrix Algorithm (RIMA) capable of updating the inverse matrix when topological changes (broken or new bonds between the atoms) take place. In this approach, the crystal structure is treated as a truss system while the forces between the atoms situated at the nodes are defined by the inter-atomic potentials. Since both the Broyden's and the RIMA algorithms deal with the inverse matrices of the structure their coupling makes the procedure computationally efficient. In addition, the method allows analysis of lattices subjected to mixed boundary conditions. The developed code was verified by the comparison with an alternative numerical procedure based on energy minimization technique. The model and the code developed were applied to the case of a 2D hexagonal lattice with the mode I crack embedded into the structure. For the cases considered, it was observed that the crack nucleation and growth were accompanied by the dislocation emission.

Recursive travel-time inversion: A tool for real-time seismic tomography

Abstract A new recursive inverse scheme is applied to a currently popular problem named seismic travel-time tomography, in order to enhance the efficiency and reliability in obtaining a new velocity model if a small number of new data are added to a large data set in the past. In comparison with conventional inverse schemes in seismic tomography, either least-squares or iterative types, this scheme does not require large amounts of matrix-type computations but utilizes the amount of modification in model parameters responsible for each new data set. We also introduce the computation of a collocation travel time (i.e., from a given station to every grid point) for the reference velocity model inverted by the data for all the past events, using a ray tracing scheme called the Huygens’ method (Saito, 2001), suitable to computations prior to a new event. Combining the above information already stored with the recursive inverse scheme, we can obtain a new or updated velocity model immediately after a new event takes place, because a temporal interval between two events is usually very long in a given local area. Since the model is revised at each recursive step, we perform ray tracings with the updated reference model to get more accurate ray paths and travel times than the conventional inversion schemes that use all the ray tracings for the same reference model. We first showed the validity and stability of the proposed method with synthetic data. We then applied the new approach to the P-wave travel-time data recorded in the Hidaka, south-central Hokkaido, Japan, region, and compared our result with other previous results. Our result shares the overall feature with the previous ones. In addition, a new low-velocity zone is detected in the east of the Hidaka mountains at the depth of 10 km, corresponding to the collision zone of two arcs, due to the use of the updated reference velocity model at each recursive step. We also confirmed that the order of data does not affect the final result, so that the present approach is shown as an appropriate tool for so-called real-time seismic tomography: a updated velocity model is immediately obtained at each time that a new event takes place, in order to monitor temporal variations of model parameters such as velocity structure on the real-time basis.

Regularization of RIF blind image deconvolution

Blind image restoration is the process of estimating both the true image and the blur from the degraded image, using only partial information about degradation sources and the imaging system. Our main interest concerns optical image enhancement, where the degradation often involves a convolution process. We provide a method to incorporate truncated eigenvalue and total variation regularization into a nonlinear recursive inverse filter (RIF) blind deconvolution scheme first proposed by Kundar, and by Kundur and Hatzinakos. Tests are reported on simulated and optical imaging problems.

Micro instabilities in a system of particles in silos during filling process

The process of filling a silo with particles is simulated by placing them one-by-one at random locations. A planar problem is considered and the particles are represented by disks. After each disk is placed on the system of disks already in a silo, the distribution of normal and shear stresses is recalculated, and if any shear stress exceeds the predetermined limit, then a slide takes place. It is found that a few particles can be involved in a slide simultaneously representing a micro-avalanche. This physical instability in the system is reflected in the numerical instability associated with sudden topological changes. A Recursive Inverse Matrix Algorithm (RIMA) is implemented to handle such changes. It allows efficient addition/removal of contact interfaces between the particles by updating the inverse matrix of the system rather then generating and solving a system of equations after each topological change. The extent of instabilities is determined numerically using RIMA update algorithm iteratively. As a result of irreversible events taking place during the filling operation, the final stress distribution in a filled silo is loading history-dependent. A numerical example of filling a silo with 500 particles is given as an illustration.

Combination of TOPEX/POSEIDON data with a hydrographic inversion for determination of the oceanic general circulation and its relation to geoid accuracy

A global estimate of the absolute oceanic general circulation from a geostrophic inversion of in situ hydrographic data is tested against and then combined with an estimate obtained from TOPEX/POSEIDON altimetric data and a geoid model computed using the JGM-3 gravity-field solution. Within the quantitative uncertainties of both the hydrographic inversion and the geoid estimate, the two estimates derived by very different methods are consistent. When the in situ inversion is combined with the altimetry/geoid scheme using a recursive inverse procedure, a new solution, fully consistent with both hydrography and altimetry, is found. There is, however, little reduction in the uncertainties of the calculated ocean circulation and its mass and heat fluxes because the best available geoid estimate remains noisy relative to the purely oceanographic inferences. The conclusion drawn from this is that the comparatively large errors present in the existing geoid models now limit the ability of satellite altimeter data to improve directly the general ocean circulation models derived from in situ measurements. Because improvements in the geoid could be realized through a dedicated spaceborne gravity recovery mission, the impact of hypothetical much better, future geoid estimates on the circulation uncertainty is also quantified, showing significant hypothetical reductions in the uncertainties of oceanic transport calculations. Full ocean general circulation models could better exploit both existing oceanographic data and future gravity-mission data, but their present use is severely limited by the inability to quantify their error budgets.

On the synthesis of function inverses

We present a method for synthesising recursive inverses for first-order functions. Since inverse functions are not, in general, single-valued, we introduce a powerdomain to define their semantics, in terms of which we express their transformation into recursive form. First, inverses that require unification at run-time are synthesised and these are then optimised by term-rewriting based on a set of axioms that facilitates a form of compile-time unification. The optimisations reduce the dependency on run-time unification, in many instances removing it entirely to give a recursive inverse. The efficiency of the use of relations in two modes is thereby improved, so enhencing extended functional languages endowed with logical variables and narrowing semantics. Our function-level, axiomatised system is more generally applicable than previous approaches to this type of optimis tion, and in general induces more mechanisable transformation systems.