Inverse QR Decomposition Research Articles

Mechanical System Inspired Microscopic Traffic Model: Modeling, Analysis, and Validation

In this paper, we develop a mechanical system inspired microscopic traffic model to characterize the longitudinal interaction among a chain of vehicles. In particular, we propose a mass-spring-damper-clutch based car-following (CF) model that can naturally capture the car-following behavior of a rational driver. Specifically, the spring and damper can well characterize the driver’s tendency to maintain the same speed as the vehicle ahead while keeping a (speed-dependent) desired spacing. It is also capable of characterizing the impact of the following vehicle on the preceding vehicle, which is generally neglected in existing models. A new string stability criterion is defined for the considered multi-vehicle dynamics, and stability analysis is performed on the system parameters and time delays. An efficient online parameter identification algorithm, sequential recursive least squares with inverse QR decomposition (SRLS-IQR), is developed to estimate the driving-related model parameters. These real-time estimated parameters can be employed in advanced longitudinal control systems to enable accurate prediction of vehicle trajectories for improved safety and fuel efficiency. The proposed model and the parameter identification algorithm are validated on NGSIM, a naturalistic driving dataset, as well as our own connected vehicle driving data. Promising performance is demonstrated.

A digital hardware implementation of spiking neural networks with binary FORCE training

The brain, a network of spiking neurons, can learn complex dynamics by adapting its spontaneous chaotic activity. One of the dominant approaches used to train such a network, the FORCE method, has recently been applied to spiking neural networks. This method employs a pool of randomly connected spiking neurons, called a reservoir, to create chaos and uses the recursive least square (RLS) method to change its dynamic to what is required to follow a teacher signal. Here, we propose a digital hardware architecture for spiking FORCE with some modifications to the original method. First, to reduce the memory usage in hardware implementation, we show that careful binarization of the reservoir weights could preserve its initial chaotic activity. Second, we generate the connection matrix on-the-fly instead of storing the whole matrix. Third, a single processor systolic array implementation of the RLS using the inverse QR decomposition is exploited to update the readout layer weights. This implementation is not only more hardware-friendly but also more numerically stable in reduced precision than the standard RLS implementation. Fourth, we implement the design in both single and custom-precision floating-point number systems. Finally, we implement a network of 510 Izhikevic neurons on a Xilinx Artix-7 FPGA with 32, 24, and 18 bits floating-point numbers. To confirm the correctness of our architecture, we successfully train our hardware using three different teacher signals.

Double-Talk Robust Multichannel Acoustic Echo Cancellation Using Least-Squares MIMO Adaptive Filtering: Transversal, Array, and Lattice Forms

In this paper, we address the problem of noise-robust multiple-input multiple-output (MIMO) adaptive filtering that is optimal in least-squares sense with application to multichannel acoustic echo cancellation. We formulate the problem as minimization of a multichannel least-squares cost function that incorporates near-end speech and noise statistics resulting in a novel noise-robust framework for MIMO adaptive filtering. Although the issue of numerical stability has been widely explored in the context of recursive least-squares (RLS) filtering, a rigorous mathematical treatment of the MIMO case in the context of numerically stable noise-robust multichannel echo cancellation remains absent. Guided by quantization-error modeling, we resolve the issue of numerical instability in our noise-robust scheme by utilizing transversal RLS filtering of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Type 2</i> . Thereafter, an explicit derivation of its inverse QR-decomposition (IQRD) counterpart based on Givens rotations is presented. We also derive computationally efficient lattice forms for our noise-robust RLS Type-2 and IQRD algorithms. It is highlighted that propagation of angle-normalized errors occurs <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">naturally</i> within the numerically stable least-squares lattice (LSL). Thus, our approach combines the four sought after attributes in a multichannel echo cancellation scheme, i.e., computational efficiency, numerical stability, fast convergence and tracking, and robustness against noise. We analyze our formulations using simulations in terms of convergence, re-convergence, robustness in the presence of double-talk, and numerical stability.

A New Microscopic Traffic Model Using a Spring-Mass-Damper-Clutch System

Microscopic traffic models describe how cars interact with their neighbors in an uninterrupted traffic flow and are frequently used for reference in advanced vehicle control design. In this paper, we propose a novel mechanical system-inspired microscopic traffic model using a mass-spring-damper-clutch system. This model naturally captures the ego vehicle’s resistance to large relative speed and deviation from a (driver- and speed-dependent) desired relative distance when following the lead vehicle. Compared with the existing car-following (CF) models, this model offers physically interpretable insights into the underlying CF dynamics and is able to characterize the impact of the ego vehicle on the lead vehicle, which is neglected in the existing CF models. Thanks to the nonlinear wave propagation analysis techniques for mechanical systems, the proposed model, therefore, has great scalability so that multiple mass-spring-damper-clutch systems can be chained to study the macroscopic traffic flow. We investigate the stability of the proposed model on the system parameters and the time delay using the spectral element method. We also develop a parallel recursive least square with inverse QR decomposition (PRLS-IQR) algorithm to identify the model parameters online. These real-time estimated parameters can be used to predict the driving trajectory that can be incorporated into advanced vehicle longitudinal control systems for improved safety and fuel efficiency. The PRLS-IQR is computationally efficient and numerically stable, and therefore, it is suitable for online implementation. The traffic model and the parameter identification algorithm are validated on both the simulations and naturalistic driving data from multiple drivers. Promising performance is demonstrated.

Holographic Blind Watermarking Algorithm of Three- Dimensional Mesh Model Based on QR Decomposition

This paper proposes a holographic blind watermarking algorithm of the three-dimensional mesh model based on QR decomposition. Firstly the three-dimensional model is pre-processed by moving the model center to the coordinate origin and doing PCA analysis. Secondly the model's geometric feature matrix is constructed by using the distance from the three-dimensional mesh model vortex to the model center in the column coordinate system. Then the watermarking in- formation generated by the holographic encrypted technology is embedded into the normalized and blocked model's geo- metric feature matrix based on QR decomposition. Finally the watermark is embedded into three-dimensional mesh model via inverse QR decomposition and inverse normalization operation. The experimental results indicate that this algorithm can resist translation, rotation, scaling, vertex reordering, noise and cropping attack, which has good robustness. This method can effectively protect the three-dimensional mesh model intellectual property.

Enhanced Blind Equalization for Optical DP-QAM in Finite Precision Hardware

In this letter, we apply the inverse QR decomposition-constant modulus algorithm (IQRD-CMA), blind equalization technique, for impaired 14 GBd DP-16 quadratic-amplitude modulation optical modulated signal. The IQRD-CMA is considered here to mitigate the effect of residual chromatic dispersion (CD) and polarization mode dispersion (PMD). We evaluate the performance of the proposed inverse QR decomposition in terms of convergence rate, steady-state/residual mean square error (MSE), and bit error rate (BER), in comparison with standard blind constant modulus algorithm (CMA) and recursive least squares (RLS-CMA). Assuming infinite precision, the IQRD-CMA and RLS-CMA achieve similar performance and induce the same computational complexity; however, both largely outperform standard CMA for wide ranges of CD and PMD. However, for finite precision hardware, compared with RLS-CMA, the proposed blind IQRD-CMA clearly achieves one order of BER magnitude at 8- and 10-b resolutions, and further reduces the steady-state MSE by 3 dB. Moreover, results show that IQRD-CMA maintains the system stability at acceptable number of bits resolutions. In addition, this letter addresses the tradeoff between the complexity and the performance of all these equalizers for several precision settings.

An inverse QRD-RLS algorithm for linearly constrained minimum variance adaptive filtering

In this paper an inverse QR decomposition based recursive least-squares algorithm for linearly constrained minimum variance filtering is proposed. The proposed algorithm is numerically stable in finite precision environments and is suitable for implementation in systolic arrays or DSP vector architectures. Its performance is illustrated by simulations of a blind receiver for a multicarrier CDMA communication system and compared with previously proposed inverse QR decomposition recursive least-squares algorithms.

A Regularized Inverse QR Decomposition Based Recursive Least Squares Algorithm for the CMAC Neural Network

The Cerebellar Model Articulation Controller (CMAC) neural network is an associative memory that is biologically inspired by the cerebellum, which is found in the brains of animals. The standard CMAC uses the least mean squares algorithm (LMS) to train the weights. Recently, the recursive least squares (RLS) algorithm was proposed as a superior algorithm for training the CMAC online as it can converge in one epoch, and does not require tuning of a learning rate. However, the RLS algorithm was found to be very computationally demanding. In this work, the RLS computation time is reduced by using an inverse QR decomposition based RLS (IQR-RLS) algorithm which is also parallelized for multi-core CPUs. Furthermore, this work shows how the IQR-RLS algorithm may be regularized which greatly improves the generalization capabilities of the CMAC.

Efficient Recursive Least Squares Methods forthe CMAC Neural Network

The Cerebellar Model Articulation Controller (CMAC) neural network is an associative memory that is biologically inspired by the cerebellum, which is found in the brains of animals. The standard CMAC uses the least mean squares algorithm to train the weights. Recently, the recursive least squares (RLS) algorithm was proposed as a superior algorithm for training the CMAC online as it can converge in just one epoch, and does not require tuning of a learning rate. However, the RLS algorithm was found to be very computationally demanding as its computational complexity is dependent on the square of the number of weights required which can be huge for the CMAC. Here, we show a more efficient RLS algorithm that uses inverse QR decomposition and additionally provides a regularized solution, improving generalization. However, while the inverse QR decomposition based RLS algorithm reduces computation time significantly; it is still not fast enough for use in CMACs greater than two dimensions. To further improve efficiency we show that by using kernel methods the CMAC computational complexity can be transformed to become dependent on the number of unique training data. Additionally, it is shown how modeling error can be improved through use of higher order basis functions.

Inverse QR iterative method for subspace tracking

The Bi-LS method based on QR decomposition provides a convenient framework for developing efficient subspace tracking algorithms. To overcome the shortcoming of the backsubstitution step and improve the parallel architecture of the Bi-LS algorithms, a Bi-LS subspace tracking algorithm based on Inverse QR (IQR) decomposition is developed. The proposed IQR iterative algorithm for subspace tracking is well suited for the parallel implementation in the systolic array. Simulation results are presented to illustrate the effectiveness of the proposed IQR subspace tracking algorithm.

Adaptive linearly constrained inverse QRD-RLS beamforming algorithm for moving jammers suppression

A general, linearly constrained (LC) recursive least squares (RLS) array-beamforming algorithm, based on an inverse QR decomposition, is developed for suppressing moving jammers efficiently. In fact, by using the inverse QR decomposition-recursive least squares (QRD-RLS) algorithm approach, the least-squares (LS) weight vector can be computed without back substitution and is suitable for implementation using a systolic array to achieve fast convergence and good numerical properties. The merits of this new constrained algorithm are verified by evaluating the performance, in terms of the learning curve, to investigate the convergence property and numerical efficiency, and the output signal-to-interference-and-noise ratio. We show that our proposed algorithm outperforms the conventional linearly constrained LMS (LCLMS) algorithm, and the one using the fast linear constrained RLS algorithm and its modified version.

An order downdating algorithm for tracking system order and parameters in recursive least squares identification

A new time and recursive method for on-line tracking of system and parameters using recursive least squares (RLS) is presented. The method consists of two parts: a time updating portion that uses existing RLS inverse QR decomposition algorithms and a new computationally efficient order downdating portion that calculates the model parameters and residual error energies for an entire set of models with varying from one to some prespecified maximum model order.

Recursive least-squares algorithms of modified Gram-Schmidt type for parallel weight extraction

This paper presents some new algorithms for parallel weight extraction in the recursive least-squares (RLS) estimation based on the modified Gram-Schmidt (MGS) method. These are the counterparts of the algorithms using an inverse QR decomposition based on the Givens rotations and do not contain the square root operation. Systolic-array implementations of the algorithms are considered on a 2-D rhombic array. Simulation results are also presented to compare the finite word-length effect of these new algorithms and existing algorithms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A Method for Recursive Least Squares Filtering Based Upon an Inverse QR Decomposition

A new computationally efficient algorithm for re- cursive least squares filtering is derived, which is based upon an inverse QR decomposition. The method solves directly for the time-recursive least squares filter vector, while avoiding the highly serial backsubstitution step required in previously de- rived direct QR approaches. Furthermore, the method employs orthogonal rotation operations to recursively update the filter, and thus preserves the inherent stability properties of QR ap- proaches to recursive least squares filtering. The results of sim- ulations over extremely long data sets are also presented, which suggest stability of the new time-recursive algorithm. Finally, parallel implementation of the resulting method is briefly dis- cussed, and computational wavefronts are displayed.