new fast qr decomposition least squares adaptive algorithms this paper presents two new closely related adaptive algorithms for ls system identification the starting point for the derivation of the algorithms is the inverse cholesky factor of the data correlation matrix obtained via a qr decomposition qrd both algorithms are of o p computational complexity with p being the order of the system the first algorithm is a fixed order qrd scheme with enhanced parallelism the second is an order recursive lattice type algorithm based exclusively on orthogonal givens rotations with lower complexity compared to previously derived ones both algorithms are derived following a new approach which exploits efficient the and order updates of a specific state vector quantity

optimal inverse littlewood offord theorems abstract let i i 1 n be iid bernoulli random variables taking values 1 with probability 1 2 given a multiset v of n integers v 1 v n we define the concentration probability as v sup x p v 1 1 v n n x a classical result of littlewood offord and erd s from the 1940s asserts that if the v i are non zero then v is o n 1 2 since then many researchers have obtained improved bounds by assuming various extra restrictions on v about 5 years ago motivated by problems concerning random matrices tao and vu introduced the inverse littlewood offord problem in the inverse problem one would like to characterize the set v given that v is relatively large in this paper we introduce a new method to attack the inverse problem as an application we strengthen the previous result of tao and vu obtaining an optimal characterization for v this immediately implies several classical theorems such as those of sarkozy and szemeredi and halasz the method also applies to the continuous setting and leads to a simple proof for the net theorem of tao and vu which plays a key role in their recent studies of random matrices all results extend to the general case when v is a subset of an abelian torsion free group and i are independent variables satisfying some weak conditions

investigation of the forest fire model on a small world network it is shown that the forest fire model of bak et al run on a square lattice network with additional long range interactions in the spirit of a small world network results in a scale free system reminiscent of self organized criticality without recourse to fine tuning as the number of these long range interactions is increased the cluster size distribution exponent is found to decrease in magnitude as the small world regime is entered indicating a change in its universality class it is suggested that such a model could have applicability in the study of disease spreading in human populations

mean field theory of avalanches in self organized critical states abstract a new mean field approximation is proposed for the sandpile model of bak tang and wiesenfeld and the distribution of heights in the self organized critical state is calculated we treat several series of successive topples to approximate various avalanches in contrast to the previous mean field theory given by tang and bak which assumes the stationary condition among topples in an avalanche out theory takes into account long term behavior of the system the results are in good agreement with the values estimated by computer simulations even in low dimensions d 2 and 3 higher approximations obtained by including local correlations or by imposing a reducibility condition which is used in the cluster variation method are also shown

finite and infinite arithmetic progressions in sumsets we prove that if a is a subset of at least cn1 2 elements of 1 n where c is a sufficiently large constant then the collection of subset sums of a contains an arithmetic progression of length n as an application we confirm a long standing conjecture of erd os and folkman on complete sequences

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

random walk percolation based modeling of two phase flow in porous media breakthrough time and net to gross ratio estimation abstract fluid flow modeling in porous media has many applications in waste treatment hydrology and petroleum engineering in any geological model flow behavior is controlled by multiple properties these properties must be known in advance of common flow simulations when uncertainties are present deterministic modeling often produces poor results percolation and random walk rw methods have recently been used in flow modeling their stochastic basis is useful in dealing with uncertainty problems they are also useful in finding the relationship between porous media descriptions and flow behavior this paper employs a simple methodology based on random walk and percolation techniques the method is applied to a well defined model reservoir in which the breakthrough time distributions are estimated the results of this method and the conventional simulation are then compared the effect of the net to gross ratio on the breakthrough time distribution is studied in terms of shannon entropy use of the entropy plot allows one to assign the appropriate net to gross ratio to any porous medium

sliding window adaptive fast qr and qr lattice algorithms sliding window formulations of the fast qr and fast qr lattice algorithms are presented the derivations are based on the partial triangularization of raw data matrices three methods for window downdating are discussed the method of plane hyperbolic rotations the chambers method and the linpack algorithm a numerically ill conditioned stationary signal and a speech signal are used in finite wordlength simulations of the full qr nonfast fast qr and qr lattice algorithms all algorithms are observed to be numerically stable over billions of iterations for double precision mantissas 53 bits but as the number of bits is decreased in the mantissa the algorithms exhibit divergent behavior hence practically the algorithms can de regarded as numerically stable for long wordlengths

adaptive blind channel estimation by least squares smoothing a least squares smoothing lss approach is presented for the blind estimation of single input multiple output simo finite impulse response systems by exploiting the isomorphic relation between the input and output subspaces this geometrical approach identifies the channel from a specially formed least squares smoothing error of the channel output lss has the finite sample convergence property i e in the absence of noise the channel is estimated perfectly with only a finite number of data samples referred to as the adaptive least squares smoothing a lss algorithm the adaptive implementation has a high convergence rate and low computation cost with no matrix operations a lss is order recursive and is implemented in part using a lattice filter it has the advantage that when the channel order varies channel estimates can be obtained without structural change of the implementation for uncorrelated input sequence the proposed algorithm performs direct deconvolution as a by product

a generalized multichannel least squares lattice algorithm based on sequential processing stages a generalized multichannel least squares ls lattice algorithm which is appropriate for multichannel adaptive filtering and estimation is presented in this paper it is shown that a muitichannel ls estimation algorithm with a different number of parameters to be estimated in each channel can be implemented by cascading lattice stages of nondescending dimension to form a generalized lattice structure a new realization of a multichannel lattice stage is also presented this realization employs only scalar operations and has a computational complexity of 0 p2 for each p channel lattice stage

self organized critical forest fire model mean field theory and simulation results in 1 to 6 dimenisons we argue that the critical forest fire model ffm introduced by drossel and schwabl phys rev lett 69 1629 1992 is a critical branching process in the mean field approximation where the number s of trees burned in a forest fire is power law distributed with exponent s 5 2 the mean field model of the ffm in finite dimension is the percolation model and as in percolation the upper critical dimension is 6 simulations show that the ffm becomes increasingly percolationlike with increasing dimension d and is within error bars eully consistent with the percolation results when d 3

a class of square root and division free algorithms and architectures for qrd based adaptive signal processing the least squares ls minimization problem constitutes the core of many real time signal processing problems such as adaptive filtering system identification and adaptive beamforming recently efficient implementations of the recursive least squares rls algorithm and the constrained recursive least squares crls algorithm based on the numerically stable qr decomposition qrd have been of great interest several papers have proposed modifications to the rotation algorithm that circumvent the square root operations and minimize the number of divisions that are involved in the givens rotation it has also been shown that all the known square root free algorithms are instances of one parametric algorithm recently a square root free and division free algorithm has also been proposed in this paper we propose a family of square root and division free algorithms and examine its relationship with the square root free parametric family we choose a specific instance for each one of the two parametric algorithms and make a comparative study of the systolic structures based on these two instances as well as the standard givens rotation we consider the architectures for both the optimal residual computation and the optimal weight vector extraction the dynamic range of the newly proposed algorithm for qrd rls optimal residual computation and the wordlength lower bounds that guarantee no overflow are presented the numerical stability of the algorithm is also considered a number of obscure points relevant to the realization of the qrd rls and the qrd crls algorithms are clarified some systolic structures that are described in this paper are very promising since they require less computational complexity in various aspects than the structures known to date and they make the vlsi implementation easier

a unified square root free approach for qrd based recursive least squares estimation the generic formula for the givens rotation the most commonly used method for qr decomposition qrd updating requires explicit square root sqrt computations which constitute a computational bottleneck a unified systematic approach for sqrt free givens rotations is provided by properly choosing two parameters all previously known as well as new sqrt free methods are included in the unified approach this unified treatment is also extended to the qrd based recursive least squares rls problem for optimum residual acquisition without sqrt operations

recursive triangular array ladder algorithms two recursive least squares ladder algorithms for implementation on triangular systolic arrays are presented the first algorithm computes transversal forward backward predictor coefficients ladder reflection coefficients and forward backward residual energies this algorithm has a complexity of three multiplications and additions per rotational triangular array element a second algorithm is presented that facilitates the computation of only the ladder reflection coefficients and the forward backward residual energies at a cost of two multiplications and additions per rotational element this way both algorithms are computationally more efficient than the traditional recursive qr decomposition gentleman and kung array for any order the second algorithm is more efficient than cioffi s pipelineable linear array fast qr adaptive filter for an order of less than 22 in the prewindowed case and more efficient than the fast qr for an order of less than 43 in the more general covariance case a comparison of the presented algorithms and the prominent qr methods is given the algorithms remain unchanged and the number of arithmetic operations is not increased when finite duration windows are used the algorithms are based entirely on numerically stable and robust covariance recursions

near optimal bounds in freiman s theorem we prove that if for a finite set a of integers we have a a k a then a is contained in a generalized arithmetic progression of dimension at most k 1 2 and size at most exp k 1 2 a for some absolute constant c we also discuss a number of applications of this result

dependency of percolation critical exponents on the exponent of power law size distribution abstract the standard percolation theory uses objects of the same size moreover it has long been observed that the percolation properties of the systems with a finite distribution of sizes are controlled by an effective size and consequently the universality of the percolation theory is still valid in this study the effect of power law size distribution on the critical exponents of the percolation theory of the two dimensional models is investigated two different object shapes i e stick shaped and square are considered these two shapes are the representative of the fractures in fracture reservoirs and the sandbodies in clastic reservoirs the finite size scaling arguments are used for the connectivity to determine the dependency of the critical exponents on the power law exponent in particular the deviations of percolation exponents from their universal values as well as the connectivity behavior of such systems are investigated numerically as a result this extends the applicability of the conventional percolation approach to study the connectivity of systems with a very broad size distribution

identification of non linear effects in rotor systems using recursive qr factorization method there are several non linear and time variant effects in a rotor bearing dynamic system the non linear characteristics of the rolling element bearing internal damping unsymmetrical stiffness of the shaft cracks on the shaft and the radial clearance are the typical root causes of these effects 1 as rotating speeds increase and rotor weights decrease these non linear and time variant effects could significantly affect the dynamic characteristics of the rotor system 2 8 if these non linear and time variant effects are ignored the vibration response could lead to incorrect interpretation of the rotor system this will significantly affect the performance of the rotor vibration control schemes the accuracy of the diagnosis results and the performance of any schemes where an accurate rotor model is needed therefore the accurate identification of both the model structure and parameters of a rotor bearing system including the non linear effects is an important engineering problem a large body of literature concentrates on this area tiwari and vyas 9 developed a technique for estimating the non linear stiffness of rolling element bearings imam et al 10 completed an on line rotor crack detection and monitoring system krodkiewski and ding 11 found a method for on site estimation of the alignment of multi bearing rotor systems tasker and chopra 12 used the rotor stability data to estimate the non linear damping of the system compared to the parameter estimation the non linear model structure identification is quite difficult an optimal search scheme is usually needed to find an adequate model among all the possible ones desrochers and mohseni 13 used a model set that has a multi layered combinatorial tree structure they showed that searching the tree for the optimal n term model could be done in n stages kanjilal et al 14 developed a method for fast selection of significant variables in linear in the parameter models by using modified orthogonal triangular factorization also called qr factorization the distinctive characteristic of their method is that estimations of article in press

paper the block regularised parameter estimator and its parallelisation kulhavy s regularised parameter identification concept protects the adaptive recursive estimation of a linear regression model from numerical difficulties associated with standard exponential weighting in cases where the processed data is not sufficiently exciting unfortunately such robustness incurs a severe penalty in computational complexity which militates against practical applications this paper presents a new block regularised parameter estimator that is compatible with the requirements for implementation on a parallel architecture owing to the accumulated regularisation in blocks the achieved throughput of the estimator is an order of magnitude higher in comparison with the general framework of kulhavy and more comparable to recursive least squares on a systolic array the processing cells operate at almost 100 efficiency and are only connected to their nearest neighbours by one directional connections this new parameter estimator offers significant potential for identification adaptive filtering and adaptive control applications particularly in the real time domain

long arithmetic progressions in sumsets thresholds and bounds l a a1 al ai ai ai aj among the most well known results in all of mathematics are vinogradov s theorem which says that 3p p is the set of primes contains all sufficiently large odd numbers and waring s conjecture proved by hilbert hardy and littlewood hua and many others which asserts that for any given r there is a number l such that l nr n denotes the set of rth powers contains all sufficiently large positive integers see 29 for an excellent exposition concerning these results in recent years a considerable amount of attention has been paid to the study of finite sumsets given a finite set a and a positive integer l the natural analogue of vinogadov waring results is to show that under proper conditions the sumset la l a contains a long arithmetic progression let us assume that a is a subset of the interval n 1 n where n is a large positive integer the concrete problem we would like to address is to estimate the minimum length of the longest arithmetic progression in la l a as a function of l n and a we denote this function by f a l n f a l n following the notation in 13 many estimates for f a l n have been discovered by bourgain freiman halberstam green ruzsa and sarkozy see section 3 but most of these results focus on sets with very high density namely a is close to n estimating f a l n seems much harder and not much was known prior to our study

l sub 1 and l sub infinity minimization via a variant of karmarkar s algorithm simple iterative algorithms are presented for l sub 1 and l sub infinity minimization regression based on a variant of karmarkar s linear programming algorithm although these algorithms are based on entirely different theoretical principles to the popular irls iteratively reweighted least squares algorithm they have almost identical matrix operations also presented are the results of a monte carlo study comparing the numerical convergence properties of the karmarkar algorithm for l sub 1 minimization to those of an irls and a simplex algorithm the test problem involves l sub 1 estimation of ar autoregressive model parameters the karmarkar algorithm outperformed irls by achieving higher numerical accuracy in fewer iterations techniques for reducing the computational cost per iteration of the karmarkar l sub 1 algorithm are discussed

a fast quasi newton adaptive filtering algorithm the convergence rate of an adaptive system is closely related to its ability to track a time varying optimum basic adaptive filtering algorithms give poor convergence performance when the input to the adaptive system is colored more sophisticated algorithms which converge very rapidly regardless of the input spectrum algorithms typically require o n sup 2 computation where n is the order of the adaptive filter a significant disadvantage for real time applications also many of these algorithms behave poorly in finite precision implementation an adaptive filtering algorithm is introduced which employs a quasi newton approach to give rapid convergence even with colored inputs the algorithm achieves an overall computational requirement of o n and appears to be quite robust in finite precision implementations

on the duality between fast qr methods and lattice methods in least squares adaptive filtering the authors show that fast qr methods and lattice methods in least squares adaptive filtering are duals and follow from identical geometric principles whereas the lattice methods compute the residuals of a projection operation via the forward and backward prediction errors the qr methods compute instead the weights used in the projections within this framework the parameter identification problem is solved using fast qr methods by showing that the reflection coefficients and tap parameters of a least squares lattice filter operating in the joint process mode are immediately available as internal variables in the fast qr algorithms this parameter set can be readily exploited in system identification signal analysis and linear predictive coding for example the relations derived also lead to a fast least squares algorithm of minimal complexity that is a hybrid between a qr and a lattice algorithm the algorithm combines the order recursive properties of the lattice approach with the robust numerical behavior of the qr approach

length scales and power laws in the two dimensional forest fire model abstract we re examine a two dimensional forest fire model via monte carlo simulations and show the existence of two length scales with different critical exponents associated with clusters and with the usual two point correlation function of trees we check resp improve previously obtained values for other critical exponents and perform a first investigation of the critical behaviour of the slowest relaxational mode we also investigate the possibility of describing the critical point in terms of a distribution of the global density we find that some qualitative features such as a temporal oscillation and a power law of the cluster size distribution can nicely be obtained from such a model that discards the spatial structure

recursive least squares circular lattice and escalator estimation algorithms this note supplements the paper of sakai 1 about circular lattice filtering with the derivation of optimal recursive least squares circular lattice estimation algorithms the derivation is based on the geometric method of lee morf and friedlander 2 the same method is also applied to obtain an optimal recursive estimation algorithm for escalator structure of ahmed and youn 3

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

renormalization scheme for forest fire models we introduce a renormalization scheme for forest fire models in order to characterize the nature of the critical state and its scale invariant dynamics we study one and two dimensional models defining a characterization of the phase space that allows us to describe the evolution of the dynamics under a scale transformation we show the existence of a relevant critical parameter associated with a repulsive fixed point in the phase space from the renormalization group point of view these models are therefore critical in the usual sense because the fixed point value of the control parameter is crucial in order to get criticality this general scheme allows us to calculate analytically the critical exponent which describes the approach to the critical point along the repulsive direction and the exponent that characterizes the distribution of forest clusters at the critical point we obtain and respectively for the one and two dimensional cases in very good agreement with exact and numerical results

a pipelined structure for qr adaptive ls system identification a novel systolic array for ls system identification based on qr factorization via givens rotations is proposed the back substitution step is circumvented and the structure is fully pipelineable thus the method is appropriate for continuous sample by sample mode adaptive operation a modification of this structure is also suggested which is suitable for a wide range of linear algebraic operations and is solely based on givens rotations

long arithmetic progressions in sum sets and the number x sum free sets in this paper we obtain optimal bounds for the length of the longest arithmetic progression in various kinds of sum sets as an application we derive a sharp estimate for the number of sets a of residues modulo a prime n such that no subsum of a equals x modulo n where x is a fixed residue modulo n

spatio temporal self organization in a model of disease spreading abstract we investigate an extended version of the probabilistic forest fire model conceived as a model of disease spreading we show that the model self organizes spatially and temporally from random initial conditions into a well defined state with a characteristic length and time scale the time scale has a power law dependence on the correlation length i e z with a non trivial exponent of 0 83 in d 2 we show that stochastic input of susceptible individuals is essential for this behaviour a mean field approximation is presented predicting an exponent of z 1 2

three state model and chemical reactions a three state model is formulated in terms of raising and lowering operators as an application cyclic chemical reactions with three different species in the solid state are studied the evolution equations for the densities and for the correlation functions can be derived starting from a master equation in a generalized fock space representation on a lattice such a description guarantees the consideration of the excluded volume effect in contrast to the classical kinetic behaviour the system offers stable and unstable regimes depending on the averaged composition ratio

givens rotation based least squares lattice and related algorithms the author presents a general and systematic approach for deriving new ls least squares estimation algorithms that are based solely on givens rotations in particular this approach is used to derive efficient givens rotation based ls lattice algorithms the givens lattice algorithms by exploiting the relationship between the givens algorithms and the recursive modified gram schmidt algorithm it is shown that the time and order update of any order recursive ls estimation algorithm can be realized by employing only givens rotations applying this general conclusion to ls estimation of time series signals results in the givens lattice algorithms two givens lattice algorithms one with square roots and the other without are presented it is shown that the givens lattice algorithms are computationally more efficient than the fast qr algorithm of cioffi 1987 the derivation of other givens rotation based ls estimation algorithms and their systolic array implementations are discussed

schur type algorithms for spatial ls estimation with highly pipelined architectures a family of schur type spatial least squares algorithms is presented for solving the spatial ls estimation problem in which the correlation matrix is neither toeplitz nor near toeplitz by order recursion normalized spatial levinson and schur type algorithms are also derived highly pipelined architectures are designed to realize these recursions the reflection coefficients are first computed using the spatial schur type recursions then the forward and backward filter parameters are calculated by the spatial levinson type recursions a pyramid systolic array is demonstrated to calculate not only the filter parameters but also the ldu decomposition of the inverse cross correlation matrix at every clock phase this pyramid array can be mapped onto a two dimensional systolic array which has a simpler structure a square systolic array is developed to implement the levinson and schur type temporal recursive ls rls algorithms a highly concurrent architecture which exploits the parallelism of the spatial schur type recursions is illustrated to perform the ldu decomposition of the cross correlation matrix

a recursive modified gram schmidt algorithm for least squares estimation this paper presents a recursive form of the modified gram schmidt algorithm rmgs this new recursive least squares rls estimation algorithm has a computational complexity similar to the conventional rls algorithm but is more robust to roundoff errors and has a highly modular structure suitable for vlsi implementation its properties and features are discussed and compared to other ls estimation algorithms

modular and numerically stable fast transversal filters for multichannel and multiexperiment rls the authors present scalar implementations of multichannel and multiexperiment fast recursive least squares algorithms in transversal filter form known as fast transversal filter ftf algorithms by processing the different channels and or experiments one at a time the multichannel and or multiexperiment algorithm decomposes into a set of intertwined single channel single experiment algorithms for multichannel algorithms the general case of possibly different filter orders in different channels is handled geometrically this modular decomposition approach corresponds to a gram schmidt orthogonalization of multiple error vectors algebraically this technique corresponds to matrix triangularization of error covariance matrices and converts matrix operations into a regular set of scalar operations modular algorithm structures that are amenable to vlsi implementation on arrays of parallel processors naturally follow from the present approach numerically the resulting algorithm benefits from the advantages of triangularization techniques in block processing

on a question of erdős and moser for two finite sets of real numbers a and b one says that b is sum free with respect to a if the sum set b b b b b b b is disjoint from a forty years ago erd os and moser posed the following question let a be a set of n real numbers what is the size of the largest subset b of a which is sum free with respect to a in this paper we show that any set a of n real numbers contains a set b of cardinality at least g nln n which is sum free with respect to a where g n tends to infinity with n this improves earlier bounds of klarner choi and ruzsa and is the first superlogarithmic bound for this problem our proof combines tools from graph theory together with several fundamental results in additive number theory such as freiman s inverse theorem the balog szemeredi theorem and szemeredi s result on long arithmetic progressions in fact in order to obtain an explicit bound on g n we use the recent versions of these results obtained by chang and by gowers where significant quantitative improvements have been achieved

finite precision error analysis of qrd rls and star rls adaptive filters the qr decomposition based recursive least squares rls adaptive filtering qrd rls algorithm is suitable for vlsi implementation since it has good numerical properties and can be mapped onto a systolic array a new fine grain pipelinable star rls algorithm was developed the pipelined star rls algorithm pstar rls is useful for high speed applications the stability of qrd rls star rls and pstar rls has been proved but the performance of these algorithms in finite precision arithmetic has not yet been analyzed the authors determine expressions for the degradation in the performance of these algorithms due to finite precision by exploiting the steady state properties of these algorithms simple expressions are obtained that depend only on known parameters this analysis can be used to compare the algorithms and to decide the wordlength to be used in an implementation since floating or fixed point arithmetic representations may be used in practice both representations are considered the results show that the three algorithms have about the same finite precision performance with pstar rls performing better than star rls which does better than qrd rls these algorithms can be implemented with as few as 8 bits for the fractional part depending on the filter size and the forgetting factor used the theoretical expressions are found to be in good agreement with the simulation results

a class of least squares filtering and identification algorithms with systolic array architectures a unified approach is presented for deriving a large class of new and previously known time and order recursive least squares algorithms with systolic array architectures suitable for high throughput rate and vlsi implementations of space time filtering and system identification problems the geometrical derivation given is unique in that no assumption is made concerning the rank of the sample data correlation matrix this method utilizes and extends the concept of oblique projections as used previously in the derivations of the least squares lattice algorithms both the growing and sliding memory exponentially weighted least squares criteria are considered

adaptive volterra filtering with complete lattice orthogonalization the article presents a new recursive least squares rls adaptive nonlinear filter based on the volterra series expansion the main approach is to transform the nonlinear filtering problem into an equivalent multichannel but linear filtering problem then the multichannel input signal is completely orthogonalized using sequential processing multichannel lattice stages with the complete orthogonalization of the input signal only scalar operations are required instability problems due to matrix inversion are avoided and good numerical properties are achieved the avoidance of matrix inversion and vector operations reduce the complexity considerably making the filter simple highly modular and suitable for vlsi implementations several experiments demonstrating the fast convergence properties of the filter are also included

arma lattice identification a new hereditary algorithm this paper derives an identification solution of the arma type optimal linear predictor as a time varying lattice of arbitrarily fixed dimension for a process whose output signal only is known the projection technique introduced here leads to a hereditary algorithm that is the adaptive extension to raw data of the authors previous results on lattice realization from given autocorrelation functions it produces a minimum phase linear model of the signal whose nth order whiteness of the associated innovation has the following restricted meaning orthogonality to an n dimensional subspace memory of the past in a suitable hilbert sequence space the l sup 2 metric of that sequence space leads to a least squares identification algorithm that possesses a certainty equivalence principle with respect to the corresponding realization algorithm i e sample correlation products replace true correlation terms due to the detailed state space time varying computations this is possible here while avoiding the well known side errors from missing correlation products that usually occur in a blunt replacement of the output autocorrelation by averaged sample products application examples show the superiority of the hereditary algorithm over classical recursive and nonrecursive algorithms in terms of accuracy adaptivity and order reduction capabilities