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Recursive prediction error identification using the nonlinear Wiener model

The nonlinear Wiener model, consisting of a linear dynamic block in cascade with a static nonlinearity, is considered. A recursive prediction error identification algorithm, based on the Wiener model, is derived. The linear dynamic block is modelled as a SISO transfer function operator, and the static nonlinearity is approximated with a piecewise linear function. A theoretical analysis of the method is carried out, and conditions for local convergence to the true parameter vector are given. In particular, the analysis shows that the input signal should be such that there is signal energy in the whole range of the piecewise linear approximation. A numerical example illustrates the performance of the algorithm further. Practical guidelines on how to apply the algorithm are also included in the paper.

Adaptive Enhanced Cell-ID Fingerprinting Localization by Clustering of Precise Position Measurements

Cell identity (cell ID) is the backbone positioning method of most cellular-communication systems. The reasons for this include availability wherever there is cellular coverage and an instantaneous response. Due to these advantages, technology that enhances the accuracy of the method has received considerable interest. This paper presents a new adaptive enhanced cell-ID (AECID) localization method. The method first clusters high-precision position measurements, e.g., assisted-GPS measurements. The high-precision position measurements of each cluster are tagged with the same set of detectable neighbor cells, auxiliary connection information (e.g., the radio-access bearer), as well as quantized auxiliary measurements [e.g., roundtrip time]. The algorithm proceeds by computation and tagging of a polygon of minimal area that contains a prespecified fraction of the high-precision position measurements of each tagged cluster. A novel algorithm for calculation of a polygon is proposed for this purpose. Whenever AECID positioning is requested, the method first looks up the detected neighbor cells and the auxiliary connection information and performs required auxiliary measurements. The polygon corresponding to the so-obtained tag is then retrieved and sent in response to the positioning request. The automatic self-learning algorithm provides location results in terms of minimal areas with a guaranteed confidence, adapted against live measurements. The AECID method can, therefore, also be viewed as a robust fingerprinting algorithm. The application to fingerprinting is illustrated by an example where quantized path-loss measurements from six base stations are combined.

On identification of FIR systems having quantized output data

In this paper, we present a novel algorithm for estimating the parameters of a linear system when the observed output signal is quantized. This question has relevance to many areas including sensor networks and telecommunications. The algorithms described here have closed form solutions for the SISO case. However, for the MIMO case, a set of pre-computed scenarios is used to reduce the computational complexity of EM type algorithms that are typically deployed for this kind of problem. Comparisons are made with other algorithms that have been previously described in the literature as well as with the implementation of algorithms based on the Quasi-Newton method.

Adaptive filtering using quantized output measurements

A normalized stochastic gradient adaptive filtering algorithm based on a finite impulse response (FIR) model is discussed. The algorithm identifies the system exactly, given only coarsely quantized output measurements. A description of the quantizer is included in the overall input-output model, and the scheme exploits an approximation of the derivative of the quantizer. Using an associated differential equation, global convergence is established to a zero output error (except for possible colored measurement disturbances) parameter setting or to the boundary of the model set.

Recursive prediction error identification and scaling of non-linear state space models using a restricted black box parameterization

A recursive prediction error algorithm for identification of systems described by non-linear ordinary differential equation (ODE) models is presented. The model is an ODE model, parameterized with coefficients of a multi-variable polynomial that describes one component of the right-hand side function of the ODE. This avoids over-parameterization problems. The selected model can also handle systems with more complicated right-hand side structure, by identification of a local input-output equivalent system in the coordinate system of the selected state variables. A novel technique based on scaling of the sampling period is proposed. The technique can improve the conditioning of the identification problem, thereby enhancing the chances of convergence to the correct minimum of the criterion. The algorithm is applied to live data from a system consisting of two cascaded tanks, with promising results. A MATLAB software package, which implements the proposed algorithm and a set of support scripts, can be freely downloaded from http://www.it.uu.se/research/reports/.

Soft Uplink Load Estimation in WCDMA

Wideband code-division multiple-access (WCDMA) enhanced uplink (EUL) channel transmissions are typically scheduled to time intervals where the interference and load conditions of a cell are favorable-hence, load estimation is central for EUL performance. This paper first proves that the uplink load, which is expressed as the rise over thermal (RoT), is unobservable with any linear estimation technique using measurements in a single radio base station (RBS) of (1) received total wideband power (RTWP) and (2) cell channel powers. A soft nonlinear Bayesian load estimator is proposed to circumvent these problems. The three-stage algorithm first estimates the RTWP, as well as residual power consisting of the sum of the thermal noise floor power and the neighbor cell interference. A time-variable Kalman estimator is used for this first step. The thermal noise power is then approximated by the Bayesian conditional probability density function (pdf) of the minimum of the estimated residual power. The 1-D conditional pdf of the RoT then follows from the quotient of two pdfs-the estimated pdf of the RTWP and the estimated conditional pdf of the thermal noise power. After discretization, the optimal RoT is calculated as a conditional mean.

Estimation of Uplink WCDMA Load in a Single RBS

The measurement of uplink load is important for the scheduling of enhanced uplink channels in WCDMA systems. This measurement is particularly difficult since the thermal noise power floor is unobservable when using power measurements in a single base station. The problem is due to the neighbor cell interference. The paper proposes a work around, using a novel algorithm for soft Bayesian estimation of a conditional probability distribution of the minimum of filtered power samples, this minimum approximating the thermal noise power floor of the digital receiver. The load can then be estimated from the total wideband power of the cell and the estimated minimum. The discretized conditional pdf is one-dimensional - hence the algorithm has a low complexity. Details of the implementation are described in the paper, together with measured results.

Optimal recursive state estimation with quantized measurements

A set of exact nonlinear filters is derived and analyzed. The filters perform recursive state estimation when only coarsely quantized output signals are available. A system with the dynamics given by n integrators, together with a uniform prior on the state vector, form the model assumptions. In the case with one integrator, properties of the quantizer allows the construction of an exact recursive algorithm for the updating of the probability density function (p.d.f.), using only the corners of a convex polygon defining the region where the p.d.f. is nonzero. It is also shown how to generalize the algorithm to handle multiple measurements quantized with vector quantizers.

Online nonlinear identification of the effect of drugs in anaesthesia using a minimal parameterization and BIS measurements

This paper addresses the problem of modeling and identification of the Depth of Anaesthesia (DoA). It presents a new MISO Wiener model for the pharmacokinetics and pharmacodynamics of propofol and remifentanil, when jointly administered to patients undergoing surgery. The models most commonly used to describe the effect of drugs in the human body are overparameterized Wiener models. In particular, in an anaesthesia environment, the high number of patient-dependent parameters coupled with the insufficient excitatory pattern of the input signals (drug dose profiles) and the presence of noise make robust identification strategies difficult to find. In fact, in such clinical application the user cannot freely choose the input signals to enable accurate parameter identification. A new MISO Wiener model with only four parameters is hence proposed to model the effect of the joint administration of the hypnotic propofol and the analgesic remifentanil. An Extended Kalman Filter (EKF) algorithm was used to perform the nonlinear online identification of the system parameters. The results show that both the new model and the identification strategy outperform the currently used tools to infer individual patient response. The proposed DoA identification scheme was evaluated in a real patient database, where the DoA is quantified by the Bispectral Index Scale (BIS) measurements. The results obtained so far indicate that the developed approach will be a powerful tool for modeling and identification of anaesthetic drug dynamics during surgical procedures.

User choices and model validation in system identification using nonlinear Wiener models

Abstract The issue of user choices in system identification is of paramount importance. This paper therefore attempts to systematically discuss user choices for algorithms based on a specific class of nonlinear models, namely the Wiener model. In particular, the paper addresses model selection, user choices in algorithms, sampling, input signal selection as well as disturbance handling and modelling errors. Validation methods applicable to Wiener type systems are also discussed. A new method based on mean residual analysis is presented. Parts of the discussion of the paper applies also to general nonlinear system identification.