on the statistical efficiency of the lms algorithm with nonstationary inputs a fundamental relationship exists between the quality of an adaptive solution and the amount of data used in obtaining it quality is defined here in terms of misadjustment the ratio of the excess mean square error mse in an adaptive solution to the minimum possible mse the higher the misadjustment the lower the quality is the quality of the exact least squares solution is compared with the quality of the solutions obtained by the orthogonalized and the conventional least mean square lms algorithms with stationary and nonstationary input data when adapting with noisy observations a filter trained with a finite data sample using an exact least squares algorithms will have a misadjustment given by m frac n n frac number of weights number of training samples if the same adaptive filter were trained with a steady flow of data using an ideal orthogonalized lms algorithm the misadjustment would be m frac n 4 tau mse frac number of weights number of training samples thus for a given time constant tau mse of the learning process the ideal orthogonalized lms algorithm will have about as low a misadjustment as can be achieved since this algorithm performs essentially as an exact least squares algorithm with exponential data weighting it is well known that when rapid convergence with stationary data is required exact least squares algorithms can in certain cases outperform the conventional widrow hoff lms algorithm it is shown here however that for an important class of nonstationary problems the misadjustment of conventional lms is the same as that of orthogonalized lms which in the stationary case is shown to perform essentially as an exact least squares algorithm

a unified derivation for fast estimation algorithms by the conjugate direction method abstract fast estimation algorithms inspired by the classical method of levinson have been developed in the areas of time series analysis system identification and signal processing this paper provides a unified derivation for the levinson durbin whittle wiggins robinson fast recursive least squares rls ladder or lattice and fast cholesky algorithms as special cases of the conjugate direction method cdm this gives a novel derivation and interpretation for all these methods

performance advantage of complex lms for controlling narrow band adaptive arrays in narrow band adaptive array applications the mean square convergence of the discrete time real least mean square lms algorithm is slowed by image frequency noises generated in the lms loops the complex lms algorithm proposed by widrow et al is shown to eliminate these noises yielding convergence of the mean squared error mse at slightly over twice the rate this paper includes a comprehensive analysis of the mse of adaptation for lms the analysis is based upon the method developed in the 1968 dissertation by k d senne and it represents the most complete treatment of the subject published to date

tight upper bounds on the minimum precision required of the divisor and the partial remainder in high radix division digit recurrence binary dividers are sped up via two complementary methods keeping the partial remainder in redundant form and selecting the quotient digits in a radix higher than 2 use of a redundant partial remainder replaces the standard addition in each cycle by a carry free addition thus making the cycles shorter deriving the quotient in high radix reduces the number of cycles by a factor of about h for radix 2 sup h to make the redundant partial remainder scheme work quotient digits must be chosen from a redundant set such as 2 2 in radix 4 the redundancy provides some tolerance to imprecision so that the quotient digits can be selected based on examining truncated versions of the partial remainder and divisor no closed form formula for the required precision in the partial remainder and divisor as a function of the quotient digit set and the range of the partial remainder is known we establish tight upper bounds on the required precision for the partial remainder and divisor the bounds are tight in the sense that each is only one bit over a well known simple lower bound we also discuss the implications of these bounds for the quotient digit selection process

design of a radix 4 division unit with simple selection table a radix 4 division architecture is presented which partially overlaps the updating of the remainder with the digit selection procedure it is obtained by separating the radix 4 digit selection process into two concurrent substeps the proposed unit requires a simple selection table and involves a small extra expense for the additional hardware compared to the usual radix 4 division units four possible implementations are derived from the general model with different types of substeps the high level evaluation shows that the proposed architectures offer an efficient alternative

least squares adaptive lattice and transversal filters a unified geometric theory a unified theory is presented to characterize least squares adaptive filters in either lattice or transversal filter form for nonstationary processes the derivations are based upon a geometric formulation of least squares estimation and on the concept of displacement rank a few basic geometric relations are shown to underlie the various algorithms insights into the fundamental concepts that unify lattice and transversal filter approaches to least squares adaptive filters are also given the general results are illustrated by applications to the so called pre windowed and growing memory covariance formulations of the deterministic least squares problem

vers un algorithme pour la reduction stable des revetements p cycliques de la droite projective sur un corps p adique in his ph d thesis c lehr offers an algorithm which gives the stable model for p cyclic covers of the projective line over a p adic field under the conditions that the branch locus whose cardinal is m 1 has the so called equidistant geometry and m p in this note we give an algorithm also in the equidistant geometry case but without condition on m in particular we are able to study the reduction at 2 of hyperelliptic curves with equidistant branch locus

higher radix square rooting a general discussion on nonrestoring square root algorithms is presented showing bounds and constraints delimiting the space of feasible algorithms for all the choices of radix digit set and representation of the partial remainder two classes of algorithms are then derived from the general discussion and it is shown how it is possible to determine two parameters with a relevant impact on the implementation the number of radicand bits to be inspected in order to obtain a starting value and the number of partial remainder bits to be examined for digit selection the algorithms for the specific case of radix 4 digit set 2 1 0 1 2 and partial remainder represented in carry save form are derived in order to show that the algorithms introduced can lead to better results than those obtained with algorithms previously presented

radix 4 square rot without initial pla a systematic derivation of a radix 4 square root algorithm using redundant residual and result is presented unlike other similar schemes it does not use a table lookup or pla for the initial step resulting in a simpler implementation without any time penalty the scheme can be integrated with division and incorporates an on the fly conversion and rounding of the result thus eliminating a carry propagate step to obtain the final result the result digit selection uses 3 bits of the result and 7 bits of the estimate of the residual

over redundant digit sets and the design of digit by digit division units over redundant digit sets are defined as those ranging from spl minus s to s with s spl ges b b being the radix this paper presents new techniques for the direct computation of division that use an over redundant digit set for representing the quotient instead of simply redundant ones used previously in particular general criteria for synthesizing the digit selection rules and remainder updating are given for any radix and index of redundancy a methodology combining the use of over redundant digit sets with the prescaling of the divisor is also studied in order to achieve radix b division units with trivial digit selection functions it is also shown for the specific case of radix 4 that using a prescaling slightly wider than in a radix 4 unit by m d ercegovac and t lang 1990 possible to avoid the digit selection table the paper also presents a modified algorithm for on the fly conversion of the result into the irredundant form the proposed methodology can be considered as an alternative to existing division techniques

efficient least squares fir system identification if finite impulse response fir system identification is performed by minimizing the squared error between the measured system output and an estimate from an fir system output a set of least squares normal equations to be solved for the fir system coefficients is obtained if the assumed fir system is of duration m samples the usual solution for the m least squares simultaneous equations requires a number of computational operations proportional to m3and storage of normal equation coefficients proportional to m2 the set of normal equations has an underlying structure however that can be exploited to yield a solution with computational operations proportional to m2and storage proportional to m such an efficient algorithmic solution is presented here

approximate projected consensus for convex intersection computation convergence analysis and critical error angle in this paper we study an approximate projected consensus algorithm for a network to cooperatively compute the intersection of convex sets where each set corresponds to one network node instead of assuming exact convex projection that each node can compute we allow each node to compute an approximate projection with respect to its own set after receiving the approximate projection information nodes update their states by weighted averaging with the neighbors over a directed and time varying communication graph the approximate projections are related to projection angle errors which introduces state dependent disturbance in the iterative algorithm projection accuracy conditions are presented for the considered algorithm to converge the results indicate how much projection accuracy is required to ensure global consensus to a point in the intersection set when the communication graph is uniformly jointly strongly connected in addition we show that pi 4 is a critical angle for the error of the projection approximation to ensure the boundedness finally the results are illustrated by simulations

square rooting algorithms for integer and floating point numbers an algorithm for evaluating the square root of integers and real numbers is developed the procedure consists of two parts one to obtain a close estimate of the square root and the other to modify the initial value iteratively until a precise root is evaluated the major effort in this development has been concentrated on two objectives high speed and no division operation other than division by 2 the first objective is achieved through a simple two step procedure for getting the first estimate and then modifying it by employing a fast converging iteration technique the second objective is also fulfilled through applying bit shift operation rather than division operation the algorithm is simulated for both integer and real numbers and the results are compared to two methods being widely used the results tabulated show considerable improvement in speed compared to these other two methods

a fast radix 4 division algorithm and its architecture in this paper we present a fast radix 4 division algorithm for floating point numbers this method is based on svoboda s division algorithm and the radix 4 redundant number system the algorithm involves a simple recurrence with carry free addition and employs prescaling of the operands in the proposed divider implementation each radix 4 digit belonging to set 3 3 of the quotient and partial remainder is encoded using two radix 2 digits belonging to the set 1 0 1 and this leads to hardware simplicity the quotient digits are determined by observing three most significant radix 2 digits of the partial remainder and independent of the divisor the architecture presented for the proposed algorithm is faster than previously proposed radix 4 dividers which require at least four digits of the partial remainder to be observed to determine quotient digits

incremental computation of squares and sums of squares an incremental algorithm for computation of sums of squares is presented that is suitable for both most significant bit msb first and least significant bit lsb first bit sequential operation by exploiting symmetry properties of numerical values and evaluation times in the bit product matrix it is shown how incremental multipliers can be converted to perform squaring at reduced hardware cost and sum of squaring at a hardware cost to that of scalar multiplication by the elimination of redundant computation existing hardware modules are either reduced in size or assigned to the evaluation of a second squaring computation the corresponding hardware architectures are derived from a simple conversion of existing incremental scalar multipliers this conversion process is less practical on standard serial parallel or serial pipeline multipliers a digit on line algorithm is outlined for magnitude extraction operations on plane vectors

periodic symmetric functions serial addition and multiplication with neural networks this paper investigates threshold based neural networks for periodic symmetric boolean functions and some related operations it is shown that any n input variable periodic symmetric boolean function can be implemented with a feedforward linear threshold based neural network with size of o log n and depth also of o log n both measured in terms of neurons the maximum weight and fan in values are in the order of o n under the same assumptions on weight and fan in values an asymptotic bound of o log n for both size and depth of the network is also derived for symmetric boolean functions that can be decomposed into a constant number of periodic symmetric boolean subfunctions based on this results neural networks for serial binary addition and multiplication of n bit operands are also proposed it is shown that the serial addition can be computed with polynomially bounded weights and a maximum fan in in the order of o log n in o n log n serial cycles finally it is shown that the serial multiplication can be computed in o n serial cycles with o log n size neural gate network and with o n log n latches

an on line square root algorithm in this correspondence a systematic derivation of an on line square root algorithm is presented the algorithm operates on variables represented in the normalized radix r floating point system in a digit by digit fashion with an on line delay of 1 the approach used in deriving the square root algorithm is described in detail the basic characteristics of hardware level implementation are also discussed

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

a variable step vs adaptive filter algorithm in recent work a new version of an lms algorithm has been developed which implements a variable feedback constant for each weight of an adaptive transversal filter this technique has been called the vs variable step algorithm and is an extension of earlier ideas in stochastic approximation for varying the step size in the method of steepest descents the method may be implemented in hardware with only modest increases in complexity approx 15 percent over the lms widrow hoff algorithm it is shown that an upper bound for the convergence time is the classical mean square error time constant and examples are given to demonstrate that for broad signal classes both narrow band and broad band the convergence time is reduced by a factor of up to 50 in noise canceller applications for the proper selection of variable step parameters finally the vs algorithm is applied to an iir filter and simulations are presented for applications of the vs fir and iir adaptive filters

higher radix square root with prescaling a scheme for performing higher radix square root based on prescaling of the radicand is presented to reduce the complexity of the result digit selection the scheme requires several steps namely multiplication for prescaling the radicand square root multiplication for prescaling for the division and division online algorithms are used to reduce the overall time and pipelining to reuse the different modules an estimate of the execution time for a radix 256 unit for double precision square root and a comparison with other implementations indicate that the proposed approach is an alternative to consider when designing a square root unit

distributed optimal control for multi agent trajectory optimization this paper presents a novel optimal control problem referred to as distributed optimal control that is applicable to multiscale dynamical systems comprised of numerous interacting agents the system performance is represented by an integral cost function of the macroscopic state that is optimized subject to a hyperbolic partial differential equation known as the advection equation the microscopic control laws are derived from the optimal macroscopic description using a potential function approach the optimality conditions of the distributed optimal control problem are first derived analytically and then demonstrated numerically through a multi agent trajectory optimization problem

a unified treatment of fast algorithms for identification we propose a unified description of several so called fast algorithms the projection operator technique is used to derive least squares ladder or lattice algorithms in the filter and the predictor forms this technique usually associated with orthogonal projection operations is extended to oblique projections the first application is an easy derivation of the exact instrumental variable ladder algorithm which to our knowledge has not previously been described in the literature a second application is a new derivation based on the operator technique of an algorithm for the fast calculation of gain matrices for recursive estimation schemes

distributed convex optimization via continuous time coordination algorithms with discrete time communication this paper proposes a novel class of distributed continuous time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents we establish the exponential convergence of the proposed algorithm under i strongly connected and weight balanced digraph topologies when the local costs are strongly convex with globally lipschitz gradients and ii connected graph topologies when the local costs are strongly convex with locally lipschitz gradients when the local cost functions are convex and the global cost function is strictly convex we establish asymptotic convergence under connected graph topologies we also characterize the algorithm s correctness under time varying interaction topologies and study its privacy preservation properties motivated by practical considerations we analyze the algorithm implementation with discrete time communication we provide an upper bound on the stepsize that guarantees exponential convergence over connected graphs for implementations with periodic communication building on this result we design a provably correct centralized event triggered communication scheme that is free of zeno behavior finally we develop a distributed asynchronous event triggered communication scheme that is also free of zeno with asymptotic convergence guarantees several simulations illustrate our results

convergence properties of an adaptive digital lattice filter convergence properties of a continuously adaptive digital lattice filter used as a linear predictor are investigated for both an unnormalized and a normalized gradient adaptation algorithm the parcor coefficient mean values and the output mean square error mse are approximated and a simple model is described which approximates these quantities as functions of time calculated curves using this model are compared with simulation results results obtained for a two stage lattice are then compared with the two stage least mean square lms transversal filter algorithm demonstrating that it is possible but unlikely for the transversal filter to converge faster than the analogous lattice filter

lattice filter parameterization and modeling of nonstationary processes a general theory of constant parameter modular lattice models for discrete time nonstationary second order processes is presented a complete parametrization of such processes in terms of schur and congruence coefficients is derived by developing a natural connection between the displacement structure of a covariance matrix and schur s test for positive definiteness of matrices schur coeffieients provide a simple solution to problems of covariance extension and rational spectral approximation for nonstationary covariances and they coincide with the well known reflection or parcor coefficients when the covariance is stationary the congruence coefficients provide the time varying gains of a tapped delay line realization of the whitening filter for the process a constant parameter realization of the same filter is derived by combining a lattice filter structure with a tapped delay line both with time invariant gains this configuration also provides a recursive relation for the congruence coefficients namely a generalized levinson szego recursion the tapped delay line part of the realization can be eliminated by introducing the concept of admissibility admissibility also reduces the parametrization of a nonstationary process to schur coefficients alone in analogy to stationary processes which are completely characterized by their parcor coefficients

recursive least squares ladder estimation algorithms recursive least squares ladder estimation algorithms have attracted much attention recently because of their excellent convergence behavior and fast parameter tracking capability compared to gradient based algorithms we present some recently developed square root normalized exact least squares ladder form algorithms that have fewer storage requirements and lower computational requirements than the unnormalized ones a hilbert space approach to the derivations of magnitude normalized signal and gain recursions is presented the normalized forms are expected to have even better numerical properties than the unnormalized versions other normalized forms such as joint process estimators e g adaptive line enhancer and arma pole zero models will also be presented applications of these algorithms to fast or zero startup equalizers adaptive noise and echo cancellers non gaussian event detectors and inverse models for control problems are also mentioned

square root covariance ladder algorithms square root normalized ladder algorithms provide an efficient recursive solution to the problem of multichannel autoregressive model fitting a simplified derivation of the general update formulas for such ladder forms is presented and is used to develop the growing memory and sliding memory covariance ladder algorithms new ladder form realizations for the identified models are presented leading to convenient methods for computing the model parameters from estimated reflection coefficients a complete solution to the problem of possible singularity in the ladder update equations is also presented

decentralized estimation of laplacian eigenvalues in multi agent systems in this paper we present a decentralized algorithm to estimate the eigenvalues of the laplacian matrix that encodes the network topology of a multi agent system we consider network topologies modeled by undirected graphs the basic idea is to provide a local interaction rule among agents so that their state trajectory is a linear combination of sinusoids oscillating only at frequencies function of the eigenvalues of the laplacian matrix in this way the problem of decentralized estimation of the eigenvalues is mapped into a standard signal processing problem in which the unknowns are the finite number of frequencies at which the signal oscillates

second order convergence analysis of stochastic adaptive linear filtering the convergence of an adaptive filtering vector is studied when it is governed by the mean square error gradient algorithm with constant step size we consider the mean square deviation between the optimal filter and the actual one during the steady state this quantity is known to be essentially proportional to the step size of the algorithm however previous analyses were either heuristic or based upon the assumption that successive observations were independent which is far from being realistic actually in most applications two successive observation vectors share a large number of components and thus they are strongly correlated in this work we deal with the case of correlated observations and prove that the mean square deviation is actually of the same order or less than the step size of the algorithm this result is proved without any boundedness or barrier assumption for the algorithm as it has been done previously in the literature to ensure the nondivergence our assumptions are reduced to the finite strong memory assumption and the finite moments assumption for the observation they are satisfied in a very wide class of practical applications

high radix multiplier dividers theory design and hardware this paper describes the theory and design of digital high radix multiplier dividers patent pending the theory of high radix division is extended to high radix multiplier dividers that can perform fused multiplication and division operations using a single recurrence relation with the fused implementation of multiplication and division the two operations can be executed using a single instruction implying only a single rounding operation the recurrence relation is described the quotient digit selection function derived and important design parameters together with their optimal values and relations are defined efficient design procedure and implementation hardware are described and important system parameter values for various radix systems computed compared to pure dividers the multiplier divider requires a slightly more complex data path and quotient digit selection function

convergence of an adaptive linear estimation algorithm in this work we prove the almost sure convergence of an adaptive linear estimator governed by a stochastic gradient algorithm with decreasing step size in the presence of correlated observations two complementary contributions are added to the famous 1977 ljung theorem first we drop the condition of nondivergence of the algorithm assumed by ljung while that condition can be ensured by adding a barrier the convergence of the suitably bounded algorithm itself is not established even on the basis of ljung theorem here the barrier problem is overcome by proving that it is not necessary for the convergence our second contribution is to generalize the model describing the correlated observations no state space model is used and no linear relationship between the observations and the signal to be estimated needs to be assumed instead we use a decreasing covariance model that agrees with a very wide class of practical applications

fast recursive least squares transversal filters for adaptive filtering fast transversal filter ftf implementations of recursive least squares rls adaptive filtering algorithms are presented in this paper substantial improvements in transient behavior in comparison to stochastic gradient or lms adaptive algorithms are efficiently achieved by the presented algorithms the true not approximate solution of the rls problem is always obtained by the ftf algorithms even during the critical initialization period first n iterations of the adaptive filter this true solution is recursively calculated at a relatively modest increase in computational requirements in comparison to stochastic gradient algorithms factor of 1 6 to 3 5 depending upon application additionally the fast transversal filter algorithms are shown to offer substantial reductions in computational requirements relative to existing fast rls algorithms such as the fast kalman algorithms of morf ljung and falconer 1976 and the fast ladder lattice algorithms of morf and lee 1977 1981 they are further shown to attain steady state unnormalized or improve upon first n initialization steps the very low computational requirements of the efficient rls solutions of carayannis manolakis and kalouptsidis 1983 finally several efficient procedures are presented by which to ensure the numerical stability of the transversal filter algorithms including the incorporation of soft constraints into the performance criteria internal bounding and rescuing procedures and dynamic range increasing square root normalized variations of the transversal filters

very high radix square root with prescaling and rounding and a combined division square root unit an algorithm for square root with prescaling and selection by rounding is developed and combined with a similar scheme for division since division is usually more frequent than square root the main concern of the combined implementation is to maintain the low execution time of division while accepting a somewhat larger execution time for square root the algorithm is presented in detail including the mathematical development of bounds for the first square root digit and for the scaling factor the proposed implementation is described evaluated and compared with other combined div sqrt units the comparisons show that the proposed scheme potentially produces a significant speed up for division whereas for square root the speed up is small

design of a hih speed square root multiply and divide unit in this paper radix 4 algorithms for square root and division are developed the division algorithm evaluates the more useful function xz y these algorithms are shown to be suitable for implementing as a unified hardware unit which evaluates square root division and multiplication cost reductions in the hardware are obtained by use of gate arrays a design based on the motorola mca2500 series of macrocell gate array mca is presented at a cost of 9 mca s and 16 commercial ecl 100 k parts a 64 bit square root can be evaluated in 750 us using worst case delays division takes 710 ns and multiplication 325 ns redundancy in the digit set together with carry save adders are used to achieve this high performance

effective methods for vanishing cycles of p cyclic covers of the p adic line abstract this paper studies the stable reduction of p cyclic covers x p k 1 of the projective line over p adic fields so far an algorithm to effectively determine the stable reduction of such covers is only known under additional hypothesis on the branch locus of the cover here rather than restricting the type of cover we consider the general case and obtain results on the structure of the special fiber xk of the stable reduction of x special attention is payed to making all constructions effective the central result is a formula computing the number of vanishing cycles on xk in particular we give criteria for the special fiber of the stable reduction to be tree like and for when x is a mumford curve refining the analysis of vanishing cycles we describe an algorithm that computes all the components of positive p rank in the stable model

distributed optimal coordination for multiple heterogeneous euler lagrangian systems abstract in this paper we consider the distributed optimal coordination doc problem for multi agent systems with the agents in the form of euler lagrangian el dynamics we propose two different distributed protocols for the heterogeneous continuous time el agents to achieve the optimization task by constructing suitable lyapunov functions we prove the global convergence to the optimal coordination of the el systems in the case with parametric uncertainties and the global exponential convergence in the case without parametric uncertainties furthermore we estimate the regret bound for an uncertain doc problem with time varying cost functions and inexact gradients finally we provide a numerical example to validate the theoretical results

design of high speed digital divider units the division operation has proved to be a much more difficult function to generate efficiently than the other elementary arithmetic operations this is due primarily to the need to test the result of one iteration before proceeding to the next the technique described in this contribution reduces the iteration time by the use of a redundant quotient representation which avoids the need to complete the arithmetic operation a borrow save subtractor analogous to a carry save adder can then be used for the arithmetic further improvement is obtained by use of a lookahead decoding technique cost reductions are obtained either by use of uncommitted logic arrays or by a novel borrow save system using commercially available adder circuitry a comparison of a number of divider units with a wide range of cost and speed is included

square rooting algorithms for high speed digital circuits two binary algorithms for the square rooting of a number or of a sum of two numbers are presented they are based on the classical nonrestoring method the main difference lies in the replacement of subtractions and additions by a parallel reduction f three summands which may be positive and negative to two summands to eliminate the carry propagation two of three summands form the successive partial remainder their most significant bit triples sometimes together with a sign bit of the earlier partial remainder are used to determine digits 1 0 1 of a redundant square root notation these digits are transformed during the square rooting process into the conventional notation square root bits which are next used in further square rooting steps to form the third reduced summands

normalized lattice algorithms for least squares fir system identification recently developed algorithms for least squares identification of autoregressive models are extended in this paper so as to facilitate least squares identification of finite impulse response models the algorithms belong to the class of square root normalized lattice algorithms hence they share the computational efficiency and good numerical behavior of the latter two versions are presented one for identifying time invariant models and the other for tracking time varying parameters new lattice form realizations of the identified fir models are given the general framework is then specialized to the important cases of prediction and smoothing

exponential convergence of distributed primal dual convex optimization algorithm without strong convexity abstract this paper establishes exponential convergence rates for a class of primal dual gradient algorithms in distributed optimization without strong convexity the convergence analysis is based on a carefully constructed lyapunov function by evaluating metric subregularity of the primal dual gradient map we present a general criterion under which the algorithm achieves exponential convergence to facilitate practical applications of this criterion several simplified sufficient conditions are derived we also prove that although these results are developed for the continuous time algorithms they carry over in a parallel manner to the discrete time algorithms constructed by using euler s approximation method

computational improvement of the fast rm h _ infty filter based on information of input predictor a computationally reduced version of the fast hinfin filter fhf is derived under the assumption that the input signal to the unknown system can be represented by an autoregressive ar model whose order m is much lower than the filter length n the resulting filter referred to as the predictor based fast hinfin filter p fhf has a computational requirement of 3n o m multiplications per iteration which is considerably lower than the requirement for the fhf if is sufficiently smaller than n the validity of the p fhf are confirmed by computer simulations

convergence models for lattice joint process estimators and least squares algorithms a simple model characterizing the convergence properties of an adaptive digital lattice filter using gradient algorithms has been reported 1 this model is extended to the least mean square lms lattice joint process estimator 5 and to the least squares ls lattice and fast kalman algorithms 9 16 the models in each case are compared with computer simulation the single stage lms lattice analysis presented in 1 is also applied to the ls lattice results indicate that for stationary inputs the lms lattice and ls algorithms exhibit similar behavior