Showing papers on "Recursive least squares filter published in 1970"

A general recursive procedure for analysis of variance

Abstract: SUMMARY A general recursive least squares procedure for the analysis of experimental designs is described. Any experimental design can be analyzed with a finite sequence of sweeps, in each of which a set of effects for a factor of the model is calculated and subtracted from the vector of observations. The effects are usually either simple means or effective means, which are ordinary means divided by an efficiency factor. The analysis for a particular design and model is characterized by a set of K efficiency factors for each factor of the model, where K is the order of balance of that factor, and by a triangular control matrix of indicators (0 or 1), in which subdiagonal zeros indicate orthogonality between pairs of factors in the model, and diagonal zeros indicate factors that are completely aliased with previous factors. The control matrix determines the minimal sweep sequence for analysis. The procedure may be implemented in an adaptive or 'learning' form, in which the information that characterizes the analysis is determined progressively from preliminary analyses of special dummy variates, each generated from an arbitrarily assigned set of effects for a factor of the model. A simple extension of the procedure produces the multistratum analysis required for stratified designs such as split plots and confounded factorials. Observations commonly arise from designed experiments, the symmetries and pattern of which implicitly affect the analysis and inference from the data, but are not usually explicitly characterized and utilized in general linear model formulations. This paper describes a simple procedure for least squares analysis of experimental designs with respect to a linear factorial model, in which the sequence of operations required is fully determined and controlled by the symmetries and pattern in the design. The analysis process consists of a sequence of sweeps of the data vector, determined by the factors of the model, the sweep being the only form of arithmetic operation required. In a sweep for a factor of the model, a set of effects for that factor is calculated and subtracted

Discrete least squares and quadrature formulas

Abstract: The purpose of this paper is two-fold. Firstly, we explore some of the intimate connections between discrete least squares processes and quadratures. Secondly, we present an algorithm to construct Gauss-type integration formulas, and consider briefly the method proposed by Gautschi [2].

Fast predictive control for air-fuel ratio of SI engines using a nonlinear internal model

Abstract: With development of fast modern computers, it has become possible to extend model predictive control (MPC) method to automotive engine control systems, which is traditionally applied to plants with dynamics slow enough to allow computations between samples. In this paper MPC based on an adaptive neural network model is attempted for air fuel ratio (AFR), in which the model is adapted on-line to cope with nonlinear dynamics and parameter uncertainties. A radial basis function (RBF) network is employed and the recursive least squares (RLS) algorithm is used for weight updating. Based on the adaptive model, a MPC strategy for controlling air-fuel ratio is realized to a nonlinear simulation of the engines. Finally, both single-variable and multi- variable optimizations algorithms are used to find the optimal solution of MPC problems and are compared in term of their control performance and time consumption.

Reexamination of the prefiltering problem in a state-variable formulation (Corresp.)

Abstract: Optimal (least-mean-square linear) filtering of random signals prior to sampling may be represented as a Wiener-Kalman state-variable filter followed by a coder that synthesizes the signal to be sampled as a linear combination of the estimated states. Although the prefilter doubles the number of states of the overall presampling signal process, the postsampling reconstruction filter need only model the original signal generator and the coder. Overall optimization involves selecting the parameters of the coder to minimize a weighted time-averaged error criterion.

On finite-memory recursive filters (Corresp.)

Abstract: It has not been noted in the literature that finite-memory least-squares, recursive filters are unstable, and hence unsuited for a large number of recursions. This correspondence modifies the finite-memory least-squares recursive filters to allow for stable solutions.

Adaptive Forgetting-factor RLS-based Initialisation Per-tone Equalisation in Discrete Multitone Systems

Abstract: An adaptive forgetting-factor inverse square-root recursive least squares (AF-iQRRLS) with inverse of correlation matrix updating is presented for per-tone equalisation in discrete multitone-based systems. The proposed inverse covariance update of the square-root covariance Kalman filter is introduced to prepare for the signal flow graph (SFG). This reduced derivation of adaptive inverse square-root recursive least squares algorithm can modify via SFG. In order to reduce the computational complexity, the forgetting-factor parameter for each group called per-group forgettingfactor (PGFF) approach based on AF-iQRRLS algorithm is introduced. The forgetting-factor from the middle of each group is selected as a representative in order to find an optimal forgetting-factor parameter by using AF-iQRRLS algorithm. After convergence, it is fixed for remaining tones of whole group. Simulation results reveal that the trajectories of modified PGFF of the proposed algorithm for each individual tone can converge to their own equilibria. Moreover, the performance of the proposed algorithms are improved as compared with the existing algorithm.

Frequency-Domain Maximum-Likelihood Adaptive Filtering

Abstract: : Recent intensive study of adaptive (gradient-search) filtering in the time domain has not solved the problems with rate-of-convergence problem, which is a major difficulty with this technique. A recent study based on a set of time-stationary synthetic data shows that the time-domain maximum-likelihood adaptive filter converges very slowly to the optimum filter. After 3300 iterations of adaption with an adaptive rate of 10 percent of maximum value, the adaptive filter is still about 4 db away from the optimum filter in the sense of mean-square outputs. Time-domain adaptive filtering necessitates using only one convergence parameter for all filter coefficients, which may cause slow convergence for some data. Frequency-domain adaptive filtering may solve this problem, since different convergence parameters can be used for different frequency components. This report describes a frequency-domain maximum- likelihood adaptive-filtering algorithm analogous to the time-domain adaptive algorithm. This algorithm was used with a set of synthetic stationary data previously used for a time-domain adaptive-filtering study. Different filter lengths and convergence parameters were used. Results are compared with beamsteer and time-domain adaptive filter.

Least square estimation and optimal control of linear distributed-parameter systems

Abstract: This paper presents computational algorithms for weighting function estimation and optimal control synthesis in one-dimensional, linear distributed-parameter systems. Using the least square approach, functional gradient procedures are developed for estimating system weighting functions associated with either boundary or distributed control. Same functional gradient procedures are also used to generate the optimal control function when a final state quadratic error criterion is chosen. These algorithms should be suitable for on-line adaptive control since optimal control function itself can be used as input for estimation. Finally, results from computer simulation study of a heat diffusion system are presented. They clearly demonstrate the convergence of these algorithms.