Recursive least squares filter

About: Recursive least squares filter is a research topic. Over the lifetime, 8907 publications have been published within this topic receiving 191933 citations.

A fast converging algorithm for network echo cancellation

Abstract: The letter presents a novel method for network echo cancellation, based on a combination of normalized least mean square (NLMS) and proportionate NLMS (PNLMS) adaptive filtering algorithms. First, based on a rough analysis of PNLMS adaptation, it is indicated why, after PNLMS initial fast convergence, it slows down. Then, the method used to overcome this deficiency is presented. Last, by showing some of the simulations, its improvement over the PNLMS algorithm is shown.

Floating-point error analysis of recursive least-squares and least-mean-squares adaptive filters

Abstract: A floating-point error analysis of the Recursive LeastSquares (RLS) and Least-Mean-Squares (LMS) algorithms is presented. Both the prewindowed growing memory RLS algorithm (\lambda = 1) for stationary systems and the exponentially windowed RLS algorithm (\lambda for time-varying systems are studied. For both algorithms, the expression for the mean-square prediction error and the expected value of the weight error vector norm are derived in terms of the variance of the floating-point noise sources. The results point to a tradeoff in the choice of the forgetting factor \lambda . In order to reduce the effects of additive noise and the floatingpoint noise due to the inner product calculation of the desired signal, \lambda must be chosen close to one. On the other hand, the floating-point noise due to floating-point addition in the weight vector update recursion increases as \lambda \rightarrow 1 . Floating point errors in the calculation of the weight vector correction term, however, do not affect the steady-state error and have a transient effect. For the prewindowed growing memory RLS algorithm, exponential divergence may occur due to errors in the floatingpoint addition in the weight vector update recursion. Conditions for weight vector updating termination are also presented for stationary systems. The results for the LMS algorithm show that the excess mean-square error due to floating-point arithmetic increases inversely to loop gain for errors introduced by the summation in the weight vector recursion. The calculation of the desired signal prediction and prediction error lead to an additive noise term as in the RLS algorithm. Simulations are presented which confirm the theoretical findings of the paper.

Recursive Least Squares

Abstract: There appears to be a substantial amount of criticism levelled these days at the deleterious effect that computers are having on the algebraic (especially manipulative) skills of students. Clearly computers do have an important part to play in a subject such as statistics but the article by Searle (1983) reminds us that sensible algebraic pre-planning can often improve the accuracy of estimation procedures many of which will be carried out by computer. There are a wide variety of problems in the real world (steering supertankers, short-term prediction of power loads and economic planning are typical examples) which students are happy to discuss and where there is a rapid awareness that model structures are updated regularly as new data becomes available. When the model structure is well understood and data becomes available a t regular intervals of time, and particularly where the requirement is for rapid updating, then recursive or online procedures are most useful. Many recursive algorithms require substantial algebraic manipulation to make them easy to implement on a computer. Once this manipulation is completed however, the updating can be carried out rapidly and data storage is minimal.

A Recursive Maximum Likelihood Estimator for the Online Estimation of Electromechanical Modes With Error Bounds

Abstract: Accurate and near real-time estimates of electromechanical modes are of great importance since the modal damping is a key indicator of the stability of the power system. If the estimates of the electromechanical modes are to be useful, knowing the variability in the estimates is critically important. This paper presents a method of directly estimating the variance of each mode estimate in addition to estimating the frequency and damping of each mode in an online setting using a recursive maximum likelihood (RML) estimator. The variance estimates are achieved using two closed-form multidimensional Taylor series approximations, the details of which are fully derived here. The proposed method is validated using a Monte Carlo simulation with a low order model of the Western Electricity Coordinating Council (WECC) power system under both ambient and probing conditions, with multiple modes closely spaced in frequency, and is compared to the regularized robust recursive least squares (R3LS) method. It is also successfully applied to phasor measurement unit (PMU) data collected from the actual WECC system, also under both ambient and probing conditions.

Least squares methods

Abstract: In this chapter, we discuss the least squares/equation error techniques for parameter estimation, which are used for aiding the parameter estimation of dynamic systems (including algebraic systems), in general, and the aerodynamic derivatives of aerospace vehicles from the flight data, in particular. In the first few sections, some basic concepts and techniques of the least squares approach are discussed with a view to elucidating the more involved methods and procedures in the later chapters. Since our approach is model-based, we need to define a mathematical model of the dynamic (or static) system.