Since the novel work of Berkes and Philipp((3)) much effort has been focused on establishing almost sure invariance principles of the form [GRAPHICS] where {x(i), i=1, 2, 3,...} is a sequence of random vectors and {X(...
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Since the novel work of Berkes and Philipp((3)) much effort has been focused on establishing almost sure invariance principles of the form [GRAPHICS] where {x(i), i=1, 2, 3,...} is a sequence of random vectors and {X(t), t greater than or equal to 0} is a Brownian motion. In this note, we show that if {A(k), k=1, 2, 3,...} and {b(k), k=1, 2, 3,...} are processes satisfying almost-sure bounds analogous to Eq. (1), (where {X(t), t greater than or equal to 0} could be a more general Gauss-Markov process) then {h(k), k= 1, 2, 3,...}, the solution of the stochastic approximation or adaptive filtering algorithm h(k+1)=h(k)+1/k(b(k)-A(k)h(k)) for k=1,23,... (2) also satisfies an almost sure invariance principle of the same type.
Many stochastic approximation procedures result in a stochastic algorithm of the form (1) h(k+1) = h(k) + 1/k (b(k) - A(k)h(k)), for all k = 1, 2, 3,.... Here, {b(k), k = 1, 2, 3,...} is a R(d)-valued process, {A(k), ...
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Many stochastic approximation procedures result in a stochastic algorithm of the form (1) h(k+1) = h(k) + 1/k (b(k) - A(k)h(k)), for all k = 1, 2, 3,.... Here, {b(k), k = 1, 2, 3,...} is a R(d)-valued process, {A(k), k = 1, 2, 3,...} is a symmetric, positive semidefinite Re-dxd-valued process, and {h(k), k = 1, 2, 3,...} is a sequence of stochastic estimates which hopefully converges to (2) h corresponds to [(N - infinity)lim 1/N (k = 1)Sigma(N) EA(k)](-1).{(N --> infinity)lim 1/N (k = 1)Sigma(N) Eb(k)} (assuming everything here Is well defined). In this correspondence, we give an elementary proof which relates the almost sure convergence of {h(k), k = 1, 2, 3,...} to strong laws of large numbers for {b(k), k = 1, 2, 3,...} and {A(k), k = 1, 2, 3,...}.
This paper presents two recursive algorithms for parametric identification in the presence of both, noise and model uncertainties. The estimates provided by these algorithms are not invalidated by the observed input-o...
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This paper presents two recursive algorithms for parametric identification in the presence of both, noise and model uncertainties. The estimates provided by these algorithms are not invalidated by the observed input-output data and the assumed system and uncertainty structures.
In this note, a robust identification method of non linear systems using the Hammerstein model is presented. The main property of the proposed approach is that parameters of the linear and nonlinear parts are estimate...
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In this note, a robust identification method of non linear systems using the Hammerstein model is presented. The main property of the proposed approach is that parameters of the linear and nonlinear parts are estimated in a recursive way while the global convergence is guaranted. The proposed method consists first to transform the non linear representation into an input-output model linear in parameters, after, a regular transformation based on the pseudo-inverse technique allows us to estimate in the least squares sense parameters vector of the original realization. For the case of correlated noise, to model measurement disturbances, we propose a simple technique based on the pseudo-linear regression method and we investigate all parameters dependencies to obtain a consistent solution. Sufficient conditions for global convergence are derived. Two numerical examples with different correlation structures and different Signal to Noise Ratio values are provided.
A lossless divide-and-conquer (D&C) principle, implemented via an orthogonality projection, is described and illustrated with a recursive solution of the Traveling Salesman Problem (TSP), which is executable on a ...
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A lossless divide-and-conquer (D&C) principle, implemented via an orthogonality projection, is described and illustrated with a recursive solution of the Traveling Salesman Problem (TSP), which is executable on a massively parallel and distributed computer. The lossless D&C principle guides us to look near the desirable boundary and to seek for a characteristic vector V (e.g. displacement vector in TSP) such that V approximate to A + B where two resultant vectors A and B (located one in each sub-domains to be divided) should be orthogonal to each other having no cross product terms, i.e. (A, B) = (B, A) = 0. In the case of parallel computing this goal amounts to minimum communication cost among processors. Then the global optimization of the whole domain: Min. \\V\\(2) = Min. \\A\\(2) + Min. \\B\\(2) can be losslessly divided into two sub-domains that each can seek its own optimized solution separately (by two separate sets of processors without inter-communication during processing). Such a theorem of orthogonal division error (ODE) for lossless D&C is proved, and the orthogonal projection is constructed for solving a large-scale TSP explicitly.
Many filter design problems in signal processing can be formulated as a quadratic programming problem with linear inequality constraints. The authors present new recursive procedures for solving this kind of problem. ...
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Many filter design problems in signal processing can be formulated as a quadratic programming problem with linear inequality constraints. The authors present new recursive procedures for solving this kind of problem. Using a constraint transcription technique, this inequality constrained quadratic programming problem can be approximated as an unconstrained minimisation problem. Two types of optimisation methods are developed to serve this unconstrained problem in a recursive adjusting manner. Analysis and simulation results on the proposed recursive procedures applied to the design of envelope-constrained filters are presented.
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 wh...
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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.
The aim of the given paper is the development of optimal and tuned models and ordinary well-known on-line procedures of unknown parameter estimation for inverse systems (IS) using current observations to be processed....
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A recursive equation which subsumes several common adaptive filtering algorithms is analyzed for general stochastic inputs and disturbances by relating the motion of the parameter estimate errors to the behavior of an...
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A recursive equation which subsumes several common adaptive filtering algorithms is analyzed for general stochastic inputs and disturbances by relating the motion of the parameter estimate errors to the behavior of an unforced deterministic ordinary differential equation (ODE). Local stability of the ODE implies long term stability of the algorithm while instability of the differential equation implies nonconvergence of the parameter estimates. The analysis does not require continuity of the update equation, and the asymptotic distribution of the parameter trajectories for all stable cases (under some mild conditions) is shown to be an Ornstein-Uhlenbeck process. The ODE's describing the motion of several common adaptive filters are examined in some simple settings, including the least mean square (LMS) algorithm and all three of its signed variants (the signed regressor, the signed error, and the sign-sign algorithms). Stability and instability results are presented in terms of the eigenvalues of a correlation-like matrix. This generalizes known results for LMS, signed regressor and signed error LMS, and gives new stability criteria for the sign-sign algorithm. The ability of the algorithms to track moving parameterizations can be analyzed in a similar manner, by relating the time varying system to a forced ODE. The asymptotic distribution about the forced ODE is again (under similar conditions) an Ornstein-Uhlenbeck process, whose properties can be described in a straightforward manner.
作者：
Henrik KureDina
Danish Informatics Network In the Agricultural Sciences Royal Veterinary and Agricultural University Bulowsvej 13 DK-1870 Frb. Copenhagen.
An alternative approach towards dynamic programming (DP) is presented: Recursions. A basic deterministic model and solution function are defined and the model is generalized to include stochastic processes, with the t...
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An alternative approach towards dynamic programming (DP) is presented: Recursions. A basic deterministic model and solution function are defined and the model is generalized to include stochastic processes, with the traditional stochastic DP model as a special case. Heuristic rules are included in the models simply as restrictions on decision spaces and a small slaughter pig marketing planning example illustrates the potential state space reductions induces by such rules.
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