Gérard Salut

Optimal nonlinear filtering in GPS/INS integration

The application of optimal nonlinear/non-Gaussian filtering to the problem of INS/GPS integration in critical situations is described. This approach is made possible by a new technique called particle filtering, and exhibits superior performance when compared with classical suboptimal techniques such as extended Kalman filtering. Particle filtering theory is introduced and GPS/INS integration simulation results are discussed.

I.I.R. Volterra Filtering with Application to Bilinear Systems

A new nonlinear filtering technique by means of infinite impulse response (IIR) Volterra functionals is developed. It yields the projection onto the closed class of finite Volterra series with separable kernels of arbitrary degree k. Such an optimal estimator is finitely realizable as a bilinear system with parameters that are computable off line. Moreover, if the original system model is itself bilinear, this computation is finitely recursive through higher moments of degree 2 k. Two simple illustrating examples are developed: (i) estimation of the covariance of the internal white noise driving a linear system and (ii) filtering of a non-Gaussian linear system (driven by a Poisson process). The robustness with respect to the observation noise distribution is finally examined.

Minimum variance estimation of parameters constrained by bounds

This correspondence deals with an extension of minimum variance estimation when the parameter to be estimated is constrained by bounds. It is shown that a particular initial distribution allows finite-dimensional calculation and leads to a nonlinear filter. More precisely, it is shown that a truncated Gaussian distribution is preserved a long time, leading to a finite number of parameters to be computed. Proof of the main theorem is straightforward with significant application such as positive real amplitude estimation. Performance gains are shown on the LORAN-C signal reception example.

Lie algebraic canonical representations in nonlinear control systems

This paper is the applied counterpart to previous results [5] for linear-analytic control systems. It is mainly concerned with two canonical representations of the exponential type. They exhibit the Lie algebraic structure of the system in such a form that results on weak controllability are easily derived in an algebraic manner. The first representation is a single exponential of a canonical Lie series in Halls basis of the Lie algebra of vector fields. The second one is a factorization in terms of simpler exponentials of Halls basic vectors. Both of them exhibit, as canonical coefficients, an infinite set of characteristic parameters which are a minimal representation of the input paths, when no drift occurs in the system (or, equivalently, in the weak control case). The weak controllability theorem is easily derived from these results, in a purely algebraic way.

Lie algebraic representation results for nonstationary evolution operators

It is shown that a nonstationary evolution equation solution admits two universal representations. The first is a canonical factorization into an infinite product of exponentials. This representation involves a nonstandard “integral type” Lie algebra from which an extended Hall set can be extracted. This result can be thought of as the formal continuous analogue of a Lazard factorization of the free monoid.It is also shown that a second canonical representation into a single exponential is possible, thus making an earlier work of Magnus [6], continued by Michel [14], more precise. In the sequel, reverse time together with duality problems are discussed. Finally, the evolution operator for a general Lie derivative is shown to lead to tractable combinatorial problems.

Exact ARMA lattice predictors from autocorrelation functions

The paper derives an optimal linear L/sup 2/-predictor of ARMA-type in the lattice form of arbitrarily fixed dimensions for a process whose autocorrelation function is known. The algorithm preserves exact optimality at each step, as opposed to asymptotic convergence of more usual algorithms, at the expense of hereditary computation. Only the discrete-time case is examined. It is shown how the unnormalized (respectively normalized) lattice form may be reduced to only 4n-2 parameters (respectively 2n+1) for a nth-order projection on the past. The normalization algorithm for the forward and backward residuals uses only scalar square root computations. Some examples that show the accuracy of this technique compared with those using the classical ARMA form for the predictor, are given. >

Multisource discrimination using IIR Volterra filtering

This paper exhibits an algorithm based on Volterra-type processing in order to detect several independent sources on the same carrier frequency and to determine the number of them. The use of infinite impulse response (IIR) Volterra filtering to build a suitable discrimination test is dictated by the need of higher-order moments in this type of nonlinear problem, as well as the need of IIR for convergence.

IDMA Based Anti-collision in RFID Networks

Even though object identification is its main objective, it is generally accepted that there are some technological challenges that should be addressed in order to exploit the full potential of RFID (Radio frequency identification). The anti-collision problem is one of them. Despite the different proposed methods, it still needs further study on how to improve identification ability. This paper presents a novel algorithm with IDMA (Interleave division multiple access) scheme to resolve the anti-collision problem for RFID. IDMA, which is one of the most promising technologies for high data rate wireless systems, can be regarded as a special case of CDMA (Code division multiple access). In contrast to CDMA, which separates tags by signatures or spreading codes, distinct interleavers are the only means to separate tags for IDMA. In this paper, a RFID based IDMA receiver is proposed and compared to classical systems. Simulation results demonstrate that this system provides an improvement in performance in terms of bit error rate in dense scenarios (large number of tags) and it offers an efficient alternative to systems with classical spreading sequence.

An Efficient Noisy-ICA Based Approach to Multiuser Detection in IDMA Systems

Interleaved Division Multiple Access (IDMA) is a new access scheme that has been proposed in the literature to increase the capacity of wireless channels. The performance of such systems depends on the accuracy of the channel state information at the receiver. In this paper, a Noisy-Independent Component Analysis (N-ICA) based IDMA receiver for multiple access communication channels is proposed. The N-ICA component is applied as a post processor. Unlike other IDMA receivers, the proposed scheme detects and separates the transmitted symbols without channel state information tracking. The performance of the proposed technique is presented in terms of raw bit error rate (BER) without channel coding for different signal to noise ratios (SNR). Simulation results demonstrate that N-ICA post processor provides an improvement in performance in terms of bit error rate (BER) in loaded systems. When the system is not loaded, the proposed post processor presents the same performance as conventional IDMA receiver with less iterations leading to a complexity reduction.