Distributed Estimation in Networks of Linear Time-invariant Systems

Wed 31 Aug 2022 09:39:12 AEST

This paper is concerned with the problem of distributed Kalman filtering in a network of several interconnected subsystems. We consider networks, which can be either homogeneous or heterogeneous, of linear time-invariant subsystems, given in state-space form. We propose a distributed Kalman filtering scheme for this setup. The proposed scheme provides estimates based only on locally available measurements. We compare its outcomes with those of a centralized Kalman filter, which offers the best minimum error variance estimate, using all measurements available all over the network. We show that the estimate produced by the proposed method asymptotically approaches to that of the centralized Kalman filter, i.e., the optimal one with global knowledge of all network parameters, and we are able to bound the convergence rate. Moreover, if the initial states of all subsystems are mutually uncorrelated, the estimates of these two schemes are identical at each time step.

A new smoothing algorithm for jump Markov linear systems

Wed 16 Aug 2023 09:14:41 AEST

This paper presents a method for calculating the smoothed state distribution for Jump Markov Linear Systems. More specifically, the paper details a novel two-filter smoother that provides closed-form expressions for the smoothed hybrid state distribution. This distribution can be expressed as a Gaussian mixture with a known, but exponentially increasing, number of Gaussian components as the time index increases. This is accompanied by exponential growth in memory and computational requirements, which rapidly becomes intractable. To ameliorate this, we limit the number of allowed mixture terms by employing a Gaussian likelihood mixture reduction strategy, which results in a computationally tractable, but approximate smoothed distribution. The approximation error can be balanced against computational complexity in order to provide an accurate and practical smoothing algorithm that compares favourably to existing state-of-the-art approaches.

Estimation of general nonlinear state-space systems

Wed 11 Apr 2018 17:29:32 AEST

This paper presents a novel approach to the estimation of a general class of dynamic nonlinear system models. The main contribution is the use of a tool from mathematical statistics, known as Fishers’ identity, to establish how so-called “particle smoothing” methods may be employed to compute gradients of maximum-likelihood and associated prediction error cost criteria.

The effect of regularization on variance error

Wed 11 Apr 2018 17:20:40 AEST

This note addresses the problem of quantifying the effect of noise induced error(so called “variance error”) in system estimates found via a regularised cost criterion. It builds on recent work by the authors in which expressions for nonregularised criterions are derived which are exact for finite model order. Those new expressions were established to be very different to previous quantifications that are widely used but based on asymptotic in model order arguments. A key purpose of this note is to expose a rapprochement between these new finite model order, and the preexisting asymptotic model order quantifications. In so doing, a further new result is established. Namely, that variance error in the frequency domain is dependent on the choice of the point about which regularization is affected.

The fundamental role of general orthonormal bases in system identification

Wed 11 Apr 2018 16:45:03 AEST

The purpose of this paper is threefold. Firstly, it is to establish that contrary to what might be expected, the accuracy of well-known and frequently used asymptotic variance results can depend on choices of fixed poles or zeros in the model structure. Secondly, it is to derive new variance expressions that can provide greatly improved accuracy while also making explicit the influence of any fixed poles or zeros. This is achieved by employing certain new results on generalized Fourier series and the asymptotic properties of Toeplitz-like matrices in such a way that the new variance expressions presented here encompass pre-existing ones as special cases. Via this latter analysis a new perspective emerges on recent work pertaining to the use of orthonormal basis structures in system identification. Namely, that orthonormal bases are much more than an implementational option offering improved numerical properties. In fact, they are an intrinsic part of estimation since, as shown here, orthonormal bases quantify the asymptotic variability of the estimates whether or not they are actually employed in calculating them.

Maximum likelihood estimation of state space models from frequency domain data

Wed 11 Apr 2018 16:14:31 AEST

This paper addresses the problem of estimating linear time invariant models from observed frequency domain data. Here an emphasis is placed on deriving numerically robust and efficient methods that can reliably deal with high order models over wide bandwidths. This involves a novel application of the expectation-maximization algorithm in order to find maximum likelihood estimates of state space structures. An empirical study using both simulated and real measurement data is presented to illustrate the efficacy of the solutions derived here.

A VLSI 8x8 MIMO near-ML decoder engine

Wed 11 Apr 2018 16:12:39 AEST

Multiple-Input Multiple-Output (MIMO) systems are of significant interest due to their ability to increase the capacity of wireless communications systems, but for these to be useful they must also be practical for implementation in VLSI circuits. A particularly difficult part of these systems is the decoder, where the optimal maximum-likelihood (ML)solution is desirable, but cannot be directly implemented due to its exponential complexity. The paper presents the first published 8 x 8 MIMO detection engine with an integrated channel preprocessing unit, achieving near-ML BER results at 57.6Mbps, using QPSK in an extended HSDPA application. Other novelties include the high speed sorting mechanism and power saving features.

The waterbed effect in spectral estimation

Wed 11 Apr 2018 16:03:13 AEST

In this lecture note, we present a textbook-like derivation of the waterbed effect result in Ninness (2003). Compared with Ninness, our analysis is much simpler and yet slightly more general in that it is not limited to rational spectral densities as in Ninness (it is noted, however, that Ninness has also derived a closed-form expression for the finite-m CRB on the relative variance of /spl Phi/(/spl omega/, /spl theta//spl circ/), which we do not).

Variance error quantifications that are exact for finite-model order

Wed 11 Apr 2018 15:58:49 AEST

This paper is concerned with the frequency domain quantification of noise induced errors in dynamic system estimates. Preceding and seminal work on this problem has suggested general expressions that are approximations whose accuracy increases with observed data length and model order. In the interests of improved accuracy, this paper provides new expressions whose accuracy depends only on data length. They are therefore “exact” for arbitrarily small true model order. Other authors have recognized the importance of such expressions and have derived them for the case of finite-impulse response-like model structures in which denominators are fixed at true values and only numerator terms are estimated. This paper progresses beyond this situation to address the more general output-error and Box–Jenkins structures in which full dynamics models (both numerator and denominator terms) and noise models may be estimated. A key aspect of the work here is that it establishes that the variance quantification problem is equivalent to that of deriving the reproducing kernel for a subspace that depends on the model structure being employed.

Analysis of the variability of joint input-output estimation methods

Wed 11 Apr 2018 15:55:19 AEST

It has been recently established that, when estimating parametric models on the basis of closed loop data, the frequency domain variability of direct and various indirect methods may significantly differ from one another. This paper continues this work by analysing the performance of certain common joint input-output estimation methods.

The asymptotic CRLB for the spectrum of ARMA processes

Wed 11 Apr 2018 15:29:41 AEST

This paper addresses the issue of quantifying the frequency domain accuracy of ARMA spectral estimates as dictated by the Cramer--Rao Lower Bound (CRLB). Classical work in this area has led to expressions that are asymptotically exact as both data length and model order tend to infinity, although they are commonly used in finite model order and finite data length settings as approximations. More recent work has established quantifications which, for AR models, are exact for finite model order. By employing new analysis methods based on rational orthonormal parameterisations, together with the ideas of reproducing kernel Hilbert spaces, this paper develops quantifications that extend this previous work by being exact for finite model order in all of the AR, MA and ARMA system cases. These quantifications, via their explicit dependence on poles and zeros of the underlying spectral factor, reveal certain fundamental aspects of the accuracy achievable by spectral estimates of ARMA processes.

A stochastic approach to estimation in H∞

Wed 11 Apr 2018 15:24:18 AEST

This paper examines the problem of system identification from frequency response data. Recent approaches to this problem, known collectively as "Estimation in H∞", involve deterministic descriptions of noise corruptions to the data. In order to provide "worst-case" convergence with respect to these deterministic noise descriptions, non-linear in the data algorithms are required. In contrast, this paper examines "worst-case" estimation in H infinity when the disturbances are subject to mild stochastic assumptions and linear in the data algorithms are employed. Issues of convergence, error bounds, and model order selection are considered.

Aspects of linear estimation in H∞

Wed 11 Apr 2018 15:07:41 AEST

A recent but rapidly maturing field in the area of system identification has been that of estimation in H∞. Greatly influencing this work has been the phenomenon that no linear in the data algorithm exists which is robustly convergent. This paper conducts a study of the nature of this issue by combining specific new analysis together with existing results from the mathematics literature on the topic of polynomial approximation theory. Particular attention is paid in this paper to the role of model order, and this leads to the consideration of model order selection from a deterministic worst case perspective.

Sampling zeros and the Euler-Frobenius polynomials

Wed 11 Apr 2018 15:06:14 AEST

We show that the zeros of sampled-data systems resulting from rapid sampling of continuous-time systems preceded by a zero-order hold (ZOH) are the roots of the Euler-Frobenius polynomials. Using known properties of these polynomials, we prove two conjectures of Hagiwara et al. (1993), the first of which concerns the simplicity, negative realness, and interlacing properties of the sampling zeros of ZOH- and first-order hold (FOH-) sampled systems. To prove the second conjecture, we show that in the fast sampling limit, and as the continuous-time relative degree increases, the largest sampling zero for FOH-sampled systems approaches 1/e, where e is the base of the natural logarithm.

Soft output multiuser detection via a Markov chain Monte Carlo approach

Wed 11 Apr 2018 15:02:07 AEST

This paper investigates the use of computational Bayesian methods for multiuser detection (MUD) of synchronous direct-sequence code-division multiple access (DS-CDMA) systems. The Markov chain Monte Carlo (MCMC) multiuser detection methods proposed in this paper are iterative, and offer near-optimal performance with manageable complexity even at high system loads. Moreover, posterior symbol probabilities produced by the detector are suitable for use as prior probabilities for soft-input channel decoders.

A VLSI optimised parallel tree search for MIMO

Wed 11 Apr 2018 14:22:31 AEST

Multiple input-multiple output (MIMO) systems are of great interest due to their ability to significantly increase the capacity of wireless communications systems, but for these to be useful they must also be practical for implementation in very large scale integrated (VLSI) circuits. A particularly difficult part of these systems is the detector, where the maximum-likelihood (ML) solution cannot be directly implemented due to its exponential complexity. Lattice decoders, such as the sphere search, exhibit near-ML performance with reduced complexity, but their application is still limited by computational requirements. Here, a number of optimisations are presented, designed to reduce the computational cost of the sphere search in the context of VLSI implementation for MIMO applications. We also propose parallel implementation strategies for such a detector, suitable for implementation in VLSI. This is then combined with a single-pass tree search approach and it is demonstrated that it can be designed so that the error-rate performance is not significantly impaired.

Estimation of 1/f noise

Wed 11 Apr 2018 14:21:21 AEST

Several models have emerged for describing 1/fγ noise processes. Based on these, various techniques for estimating the properties of such processes have been developed. This paper provides theoretical analysis of a new wavelet-based approach which has the advantages of having low computational complexity and being able to handle the case where the 1/fγ noise might be embedded in a further white-noise process. However, the analysis conducted here shows that these advantages are balanced by the fact that the wavelet-based scheme is only consistent for spectral exponents γ in the range γ∈(0, 1). This is in contradiction to the results suggested in previous empirical studies. When γ∈(0, 1) this paper also establishes that wavelet-based maximum-likelihood methods are asymptotically Gaussian and efficient. Finally, the asymptotic rate of mean-square convergence of the parameter estimates is established and is shown to slow as γ approaches one. Combined with a survey of non-wavelet-based methods, these new results give a perspective on the various tradeoffs to be considered when modeling and estimating 1/fγ noise processes.

Quantifying the accuracy of Hammerstein model estimation

Wed 11 Apr 2018 14:07:00 AEST

This paper investigates the accuracy of the linear component that forms part of an overall Hammerstein model-structure estimate, and a key finding is that the process of estimating the non-linear element can have a strong effect on the associated estimate of the linear dynamics. Furthermore, this effect is not explained simply by way of considering how the input spectrum is changed by the non-linearity. Instead, it arises that the linear model-estimate variability may be dominated by a term that depends on the frequency response of the linear system itself. Amongst other things, the main results derived here have experiment design implications for Hammerstein system estimation.

Robust maximum-likelihood estimation of multivariable dynamic systems

Wed 11 Apr 2018 14:01:54 AEST

This paper examines the problem of estimating linear time-invariant state-space system models. In particular it addresses the parametrization and numerical robustness concerns that arise in the multivariable case. These difficulties are well recognised in the literature, resulting (for example) in extensive study of subspace based techniques, as well as recent interest in ``data driven'' local co-ordinate approaches to gradient search solutions. The paper here proposes a different strategy that employs the Expectation Maximisation (EM) technique. The consequence is an algorithm that is iterative, and locally convergent to stationary points of the (Gaussian) Likelihood function. Furthermore, theoretical and empirical evidence presented here establishes additional attractive properties such as numerical robustness, avoidance of difficult parametrization choices, the ability to estimate unstable systems, the ability to naturally and easily estimate non-zero initial conditions, and moderate computational cost. Moreover, since the methods here are Maximum-Likelihood based, they have associated known and asymptotically optimal statistical properties.

A 4 x 4 FPGA-based wireless testbed for LTE applications

Wed 11 Apr 2018 13:53:59 AEST

We present early results from a 4x4 2.4GHz ISM band multiple-input multiple-output (MIMO) testbed developed at the University of Newcastle for over-the-air evaluation of MIMO algorithms. To provide maximum flexibility for development of 3GPP Long Term Evolution (LTE) algorithms, the testbed is designed around a field-programmable gate array (FPGA). The testbed features a simple GUI interface for testbed control as well as a MATLAB interface allowing real channel measurements to be used in algorithm development and evaluation. These features are illustrated here with experimental results from the implementation of Alamouti Space-Time Coding with 64-QAM.

Convergence of Markov-Chain Monte–Carlo approaches to multiuser and MIMO detection

Wed 11 Apr 2018 13:52:00 AEST

Markov-chain Monte–Carlo methods have been demonstrated to offer an attractive alternative to the design of approximate (near optimal) maximum a-posteriori (MAP) detectors for synchronous direct-sequence code-division multiple access (DS-CDMA) and multi-input, multi-output (MIMO) multiple antenna applications. Central to evaluating these method is understanding their convergence properties. In other works, this has been established via simulation, and the underlying theoretical basis has been identified. The contribution of this paper is to extend the theoretical understanding by rigorously establishing both convergence and convergence rate results for a wide class of Metropolis–Hastings methods.

Rational basis functions for robust identification from frequency and time-domain measurements

Wed 11 Apr 2018 13:30:46 AEST

This paper investigates the use of general bases with fixed poles for the purposes of robust estimation. These bases, which generalise the common FIR, Laguerre and two--parameter Kautz ones, are shown to be fundamental in the disc algebra provided a very mild condition on the choice of poles is satisfied. It is also shown, that by using a min--max criterion, these bases lead to robust estimators for which error bounds in different norms can be explicitly quantified. The key idea facilitating this analysis is to re--parameterise the model structures into new ones with equivalent fixed poles, but for which the basis functions are orthonormal in H₂(D).

Model predictive control applied to constraint handling in active noise and vibration control

Wed 11 Apr 2018 12:51:08 AEST

The difficulties imposed by actuator limitations in a range of active vibration and noise control problems are well recognized. This paper proposes and examines a new approach of employing model predictive control (MPC). MPC permits limitations on allowable control action to be explicitly included in the computation of an optimal control action. Such techniques have been widely and successfully applied in many other areas. However, due to the relatively high computational requirements of MPC, existing applications have been limited to systems with slow dynamics. This paper illustrates that MPC can be implemented on inexpensive hardware at high sampling rates using traditional online quadratic programming methods for nontrivial models and with significant control performance dividends.

Estimating state-space models in innovations form using the expectation maximisation algorithm

Wed 11 Apr 2018 12:47:53 AEST

The expectation maximisation (EM) algorithm has proven to be effective for a range of identification problems. Unfortunately, the way in which the EM algorithm has previously been applied has proven unsuitable for the commonly employed innovations form model structure. This paper addresses this problem, and presents a previously unexamined method of EM algorithm employment. The results are profiled, which indicate that a hybrid EM/gradient-search technique may in some cases outperform either a pure EM or a pure gradient-based search approach.

Recovering the spectrum of a low level signal from two noisy measurements using the cross power spectral density

Wed 11 Apr 2018 12:36:41 AEST

The article describes a method for estimating the spectrum or RMS value of a low-level signal corrupted by noise. If two identical sensors can be employed simultaneously and the additive noise sources are uncorrelated, the cross power spectrum can recover the power spectrum of the underlying signal. When using the Welch method to estimate the cross power spectrum, the estimation process is shown to be biased but consistent, with a variance that is inversely proportional to the number of data sets. The proposed technique is demonstrated experimentally to recover the vibration spectrum of a piezoelectric cantilever. The dual sensor method reduces the effective noise floor by three orders of magnitude and recovers spectral features that were otherwise lost in noise.

Orthonormal basis functions for continuous-time systems and Lp convergence

Wed 11 Apr 2018 12:15:33 AEST

In this paper, model sets for linear-time-invariant continuous-time systems that are spanned by fixed pole orthonormal bases are investigated. These bases generalize the well-known Laguerre and two-parameter Kautz cases. It is shown that the obtained model sets are everywhere dense in the Hardy space H 1(Π) under the same condition as previously derived by the authors for the denseness in the (Π is the open right half plane) Hardy spaces H p(Π), 1

On the worst-case divergence of the least-squares algorithm

Wed 11 Apr 2018 12:12:29 AEST

In this paper, we provide a H ∞ norm lower bound on the worst-case identification error of least-squares estimation when using FIR model structures. This bound increases as a logarithmic function of model complexity and is valid for a wide class of inputs characterized as being quasi-stationary with covariance function falling off sufficiently quickly.

On the CRLB for combined model and model order estimation of stationary stochastic processes

Wed 11 Apr 2018 12:10:37 AEST

This letter is concerned with quantifying the Cramér-Rao lower bound for model-based spectral density estimation in the case of joint model and model-order estimation. In particular, the results here extend previous work by providing closed-form frequency domain expressions that, among other things, highlight the effect of order estimation bias on the total accuracy of model-based spectral density estimation.

Maximum-likelihood parameter estimation of bilinear systems

Wed 11 Apr 2018 11:45:36 AEST

This paper addresses the problem of estimating the parameters in a multivariable bilinear model on the basis of observed input-output data. The main contribution is to develop, analyze, and empirically study new techniques for computing a maximum-likelihood based solution. In particular, the emphasis here is on developing practical methods that are illustrated to be numerically reliable, robust to choice of initialization point, and numerically efficient in terms of how computation and memory requirements scale relative to problem size. This results in new methods that can be reliably deployed on systems of nontrivial state, input and output dimension. Underlying these developments is a new approach (in this context) of employing the expectation-maximization method as a means for robust and gradient free computation of the maximum-likelihood solution.

Performance aspects of linear multiuser receivers

Wed 11 Apr 2018 11:28:35 AEST

Previous analysis of linear multiuser receivers for DS-CDMA signals has considered the signal-to-interference (SIR) performance in large systems with each user employing random spreading sequences. Unfortunately, it is only in the special case of the received powers of all users being equal that a resulting integral equation for the SIR has an explicit solution with demonstrable approximation accuracy for finite-sized systems. This paper presents an alternative approach to calculating the SIR performance of MMSE receivers which relies primarily on the law of large numbers, and provides an estimate for the SIR that is valid for arbitrary distributions of the received interferer power.

On gradient-based search for multivariable system estimates

Wed 11 Apr 2018 10:55:14 AEST

This paper addresses the design of gradient-based search algorithms for multivariable system estimation. In particular, the paper here considers so-called ldquofull parametrizationrdquo approaches, and establishes that the recently developed ldquodata-driven local coordinaterdquo methods can be seen as a special case within a broader class of techniques that are designed to deal with rank-deficient Jacobians. This informs the design of a new algorithm that, via a strategy of dynamic Jacobian rank determination, is illustrated to offer enhanced performance.

An optimised parallel tree search for multiuser detection with VLSI implementation strategy

Wed 11 Apr 2018 10:55:13 AEST

Multiuser detection (MUD) strategies have the potential to significantly increase the capacity of wireless communications systems, but for these to be useful they must also be practical for implementation in VLSI circuits. In particular, while the maximum-likelihood (ML) solution is optimal in bit error rate, it cannot be directly implemented due to its exponential computational complexity. Lattice decoders, such as the sphere search, exhibit near-optimal ML performance with reduced complexity, but their application is still limited by computational requirements. Here, a number of optimisations are presented, designed to reduce the computational cost of the sphere search, in the context of VLSI implementation. We also propose parallel implementation strategies for such a detector. This is then combined with a single-pass tree search approach that can be designed to not significantly impair error-rate performance. While the design is targeted towards a MUD application, the concepts may also be applied to a multiple-input multiple-output (MIMO) system, or similar applications.

Nonlinear model predictive control of an inverted pendulum

Wed 11 Apr 2018 10:37:28 AEST

In this paper, nonlinear model predictive control is applied to an inverted pendulum apparatus. The sample interval for control calculations is 25 milli-seconds and the associated non-convex constrained optimisation problem involves 61-variables with 241-constraints. Despite this being a challenging problem, it was solved online using a standard sequential quadratic programming approach on a modest hardware platform. The efficacy of the control algorithm is validated via experimental results.

Time-scale modification of speech signals

Wed 11 Apr 2018 10:33:24 AEST

This paper presents methods for independently modifying the time and pitch scale of acoustic signals, with an emphasis on speech signals. The algorithms developed here use parametric (sinusoidal) modeling techniques introduced by other authors, but new perspectives on the role of vocal tract decomposition and maintaining phase relationships between sinusoidal tracks are derived that achieve improved output quality with decreased computational load. Simulation results are provided to illustrate performance, and the algorithms developed here have been demonstrated capable of implementation on simple DSP hardware.

ASIC and FPGA implementation strategies for model predictive control

Wed 11 Apr 2018 10:21:46 AEST

This paper considers the system architecture and design issues for implementation of on-line Model Predictive Control (MPC) in Field Programmable Gate Arrays (FPGAs) and Application Specific Integrated Circuits (ASICs). In particular, the computationally itensive tasks of fast matrix QR factorisation, and subsequent sequential quadratic programming, are addressed for control law computation. An important aspect of this work is the study of appropriate data word-lengths for various essential stages of the overall solution strategy.

On the frequency domain accuracy of closed-loop estimates

Wed 11 Apr 2018 09:33:55 AEST

It has been argued that the frequency domain accuracy of high model-order estimates obtained on the basis of closed-loop data is largely invariant to whether direct or indirect approaches are used. The analysis underlying this conclusion has employed variance expressions that are asymptotic both in the data length and the model order, and hence are approximations when either of these are finite. However, recent work has provided variance expressions that are exact for finite (possibly low) model order, and hence can potentially deliver more accurate quantification of estimation accuracy. This paper, and a companion one, revisits the study of identification from closed-loop data in light of these new quantifications and establishes that, under certain assumptions, there can be significant differences in the accuracy of frequency response estimates. These discrepencies are established here and in the companion paper to be dependent on what type of direct, indirect or joint input-output identification strategy is pursued.

Constructing Metropolis-Hastings proposals using damped BFGS updates

Wed 04 Sep 2019 12:17:02 AEST

The computation of Bayesian estimates of system parameters and functions of them on the basis of observed system performance data is a common problem within system identifcation. This is a previously studied issue where stochastic simulation approaches have been examined using the popular Metropolis-Hastings (MH) algorithm. This prior study has identified a recognised difficulty of tuning the proposal distribution so that the MH method provides realisations with sufficient mixing to deliver efficient convergence. This paper proposes and empirically examines a method of tuning the proposal using ideas borrowed from the numerical optimisation literature around efficient computation of Hessians so that gradient and curvature information of the target posterior can be incorporated in the proposal.

Sparse Bayesian ARX models with flexible noise distributions

Wed 04 Sep 2019 12:17:00 AEST

This paper considers the problem of estimating linear dynamic system models when the observations are corrupted by random disturbances with nonstandard distributions. The paper is particularly motivated by applications where sensor imperfections involve significant contribution of outliers or wrap-around issues resulting in multi-modal distributions such as commonly encountered in robotics applications. As will be illustrated, these nonstandard measurement errors can dramatically compromise the effectiveness of standard estimation methods, while a computational Bayesian approach developed here is demonstrated to be equally effective as standard methods in standard measurement noise scenarios, but dramatically more effective in nonstandard measurement noise distribution scenarios.

Design of fractional-order hammerstein control auto-regressive model for heat exchanger system identification: Treatise on fuzzy-evolutionary computing

Tue 23 Apr 2024 09:53:44 AEST

Parameter estimation of nonlinear dynamical Hammerstein processes is a renowned stiff optimization problem with extensive applications in the design, robustness and stability analysis. Introduction of the fractional calculus theories and concepts further escalates the competency of accurate modelling of Hammerstein system but at the cost of increase in the stiffness of parameter estimation and complexity. This study deals with a presentation of new design of fractional-order nonlinear Hammerstein control auto-regressive (FO-NHCAR) model for heat exchanger system by introducing fractional derivative of polynomial based transformation operator in linear dynamic block. The system identification problem of FO-NHCAR heat exchanger system is constructed by exploiting approximation theory in mean squared error sense taken between the actual and estimated responses. Exhaustive simulations are conducted via well-known global search efficacy of the fuzzy-evolutionary computing paradigm i.e., fuzzy-genetic algorithms (GAs), for FO-NHCAR heat exchanger model by variation in signal to noise ratios, model’s degrees of freedom, fractional orders, and Hammerstein kernels. The parameter vectors of FO-NHCAR models are identified consistently with the fuzzy-GAs for various noisy environments with negligible proximity error. Results comparison on rigorous statistical analysis further endorse the efficient, accurate, robust and stable performance of fuzzy- GAs for estimation of FO-NHCAR heat exchanger system parameters.

Variational State and Parameter Estimation

Thu 29 Feb 2024 14:53:53 AEDT

This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this work, a variational approach is used to provide an assumed density which approximates the desired, intractable, distribution. The approach is deterministic and results in an optimisation problem of a standard form. Due to the parametrisation of the assumed density selected first and second order derivatives are readily available which allows for efficient solutions. The proposed method is compared against state-of-the-art Hamiltonian Monte Carlo in two numerical examples.

Accurate Gaussian mixture model smoothing using a two-filter approach

Thu 18 Jul 2019 12:36:18 AEST

We present a general and computationally tractable method for the operation of a Backwards Information Filter on a linear Gaussian Mixture Model system, which can be used to generate the smoothed density. Unlike other methods, the algorithm proposed here does not make unimodal approximations, and is exact with the exception of the mode reduction strategy.

Smoothed state estimation via efficient solution of linear equations

Thu 17 Jan 2019 13:57:48 AEDT

This paper addresses the problem of computing fixed interval smoothed state estimates of a linear time varying Gaussian stochastic system. There already exist many algorithms that perform this computation, but all of them impose certain restrictions on system matrices in order for them to be applicable. This paper develops a new forwards-backwards pass algorithm that is applicable under the mildest restrictions possible - namely that the smoothed state distribtions exists in forms that can be characterised by means and covariances, for which this paper also develops a new necessary and sufficient condition.

Variational system identification for nonlinear state-space models

Thu 06 Jul 2023 15:58:19 AEST

This paper considers parameter estimation for nonlinear state-space models, which is an important but challenging problem. We address this challenge by employing a variational inference (VI) approach, which is a principled method that has deep connections to maximum likelihood estimation. This VI approach ultimately provides estimates of the model as solutions to an optimisation problem, which is deterministic, tractable and can be solved using standard optimisation tools. A specialisation of this approach for systems with additive Gaussian noise is also detailed. The proposed method is examined numerically on a range of simulated and real examples focusing on the robustness to parameter initialisation; additionally, favourable comparisons are performed against state-of-the-art alternatives.

Distributed Kalman filter in a network of linear systems

Thu 01 Sep 2022 12:08:19 AEST

This paper is concerned with the problem of distributed Kalman filtering in a network of interconnected subsystems with distributed control protocols. We consider networks, which can be either homogeneous or heterogeneous, of linear time-invariant subsystems, given in the state-space form. We propose a distributed Kalman filtering scheme for this setup. The proposed method provides, at each node, an estimation of the state parameter, only based on locally available measurements and those from the neighbor nodes. The special feature of this method is that it exploits the particular structure of the considered network to obtain an estimate using only one prediction/update step at each time step. We show that the estimate produced by the proposed method asymptotically approaches that of the centralized Kalman filter, i.e., the optimal one with global knowledge of all network parameters, and we are able to bound the convergence rate. Moreover, if the initial states of all subsystems are mutually uncorrelated, the estimates of these two schemes are identical at each time step.

A VLSI 8 x 8 MIMO Near-ML detector with preprocessing

Sat 24 Mar 2018 08:42:43 AEDT

Multiple-input multiple-output (MIMO) systems are of significant interest due to their ability to increase the capacity of wireless communications systems, but for these to be useful they must also be practical for implementation in VLSI circuits. A particularly difficult part of these systems is the detector, where the optimal maximum-likelihood solution is desirable, but cannot be directly implemented due to its exponential complexity. This paper addresses this challenge and presents a digital circuit design for an 8×8 MIMO detection problem. A key feature is the integrated channel preprocessing unit, which performs the channel decomposition functions that are either omitted or performed “off-line” in other designs. The proposed device achieves near maximum likelihood bit error rate results at 57.6 Mbps. Other novelties include a high speed sorting mechanism and power saving features.

A MATLAB software environment for system identification

Sat 24 Mar 2018 08:33:31 AEDT

This paper describes a Matlab based software environment for the estimation of dynamic systems. It has been developed primarily as a vehicle for profiling novel approaches relative to existing methods within a common software framework in order to streamline comparisons. Key features of the toolbox include simplicity of use (particularly via automated entry of unspecified values) and the support of a wide range of scalar and multivariable model structures. The development of this software is an ongoing project, with earlier progress being reported on previously. This paper details recent advancements, including the provision of a graphical user interface environment.

Estimation of generalised Hammerstein-Wiener systems

Sat 24 Mar 2018 08:33:31 AEDT

This paper examines the use of a so-called "generalised Hammerstein-Wiener" model structure that is formed as the concatenation of an arbitrary number of Hammerstein systems. The latter are taken here to be memoryless non-linearities followed by linear time invariant dynamics. Hammerstein, Wiener, Hammerstein-Wiener and Wiener-Hammerstein models are all special cases of this structure. The parameter estimation of this model is investigated by using a standard prediction error criterion coupled with a robust gradient based search algorithm. This approach is profiled using the Wiener-Hammerstein system benchmark data, which illustrates it to be effective and, via Monte-Carlo simulation, relatively robust against capture in local minima.

Some system identification challenges and approaches

Sat 24 Mar 2018 08:33:31 AEDT

The field of control-oriented system identification is mature. Nevertheless, it is still very active. This is because there are many important unsolved challenges. Of these, this paper considers a selection. This involves considering the estimation of general nonlinear model structures, together with accurate error bounds, using methods that scale well to models of high dimension. A particular strength of the system identification field is that it has always actively sought to understand, embrace and develop ideas from other fields, such as statistics, mathematics and econometrics. This paper proposes a continuation of this successful strategy by proposing and profiling the adoption of new ideas originating in statistics, signal processing and statistical mechanics.

Bayesian system identification via Markov chain Monte Carlo techniques

Sat 24 Mar 2018 08:10:44 AEDT

The work here explores new numerical methods for supporting a Bayesian approach to parameter estimation of dynamic systems. This is primarily motivated by the goal of providing accurate quantification of estimation error that is valid for arbitrary, and hence even very short length data records. The main innovation is the employment of the Metropolis–Hastings algorithm to construct an ergodic Markov chain with invariant density equal to the required posterior density. Monte Carlo analysis of samples from this chain then provides a means for efficiently and accurately computing posteriors for model parameters and arbitrary functions of them.

Bayesian dynamic system estimation

Sat 24 Mar 2018 08:03:32 AEDT

This paper is directed at developing methods for delivering Bayesian estimates of dynamic system parameters, and functions of them (such as frequency response), for general problems. There are several motivations for the work. One is that due to computational load problems, such methods for Bayesian estimation do not currently exist. A second is that there are theoretical and practical motivations for considering adding Bayesian methods to the toolbox of system identification methods. A final one is that current advances in multi-core desktop processing are now making possible (via the algorithms discussed in this paper) the potential to compute Bayesian estimates for problems that have previously only been able to be addressed by prediction error, maximum-likelihood, and related techniques.

A novel input design approach for systems with quantized output data

Sat 24 Mar 2018 08:01:58 AEDT

In this paper, we explore the problem of input design for systems with quantized measurements. For the input design problem, we calculate and optimize a function of the Fisher Information Matrix (FIM). The calculation of the FIM is greatly simplified by using known relationships of the derivative of the likelihood function, and the auxiliary function arising from the Expectation Maximization (EM) algorithm. To optimize the FIM, we design an experiment using a recently published method based on graph theory. A numerical example shows that the proposed experiment can be successfully used in quantized systems.

Estimation of linear systems using a Gibbs sampler

Sat 24 Mar 2018 08:00:39 AEDT

This paper considers a Bayesian approach to linear system identification. One motivation is the advantage of the minimum mean square error of the associated conditional mean estimate. A further motivation is the error quantifications afforded by the posterior density which are not reliant on asymptotic in data length derivations. To compute these posterior quantities, this paper derives and illustrates a Gibbs sampling approach, which is a randomized algorithm in the family of Markov Chain Monte Carlo methods. We provide details on a numerically robust implementation of the Gibbs sampler. In a numerical example, the proposed method is illustrated to give good convergence properties without requiring any user tuning.

Parallel implementation of particle MCMC methods on a GPU

Sat 24 Mar 2018 08:00:39 AEDT

This paper examines the problem of estimating the parameters describing system models of quite general nonlinear and multi-variable form. The approach is a computational one in which quantities that are intractable to evaluate exactly are approximated by sample averages from randomized algorithms. The main contribution is to illustrate the viability and utility of this approach by examining how high computational loads can be simply managed using commodity hardware. The proposed algorithms and solution architectures are profiles on concrete examples.

UNIT: a freely available system identification toolbox

Sat 24 Mar 2018 07:58:55 AEDT

This paper presents a Matlab-based software package for the estimation of dynamic systems. It has been developed primarily as a platform to support the objective evaluation of novel approaches relative to existing methods within a common software framework. This is designed to streamline comparisons. The work here provides an explanation of the toolbox's design and use together with an overview of the underlying supported models and algorithms. An application study involving a lightly damped resonant system and a simulation example involving two non-linear systems are also presented in order to illustrate the use and capabilities of the toolbox.

Identification of Hammerstein-Wiener models

Sat 24 Mar 2018 07:58:54 AEDT

This paper develops and illustrates a new maximum-likelihood based method for the identification of Hammerstein-Wiener model structures. A central aspect is that a very general situation is considered wherein multivariable data, non-invertible Hammerstein and Wiener nonlinearities, and colored stochastic disturbances both before and after the Wiener nonlinearity are all catered for. The method developed here addresses the blind Wiener estimation problem as a special case.

Fast linear model predictive control via custom integrated circuit architecture

Sat 24 Mar 2018 07:58:42 AEDT

This paper addresses the implementation of linear model predictive control (MPC) at millisecond range, or faster, sampling rates. This is achieved by designing a custom integrated circuit architecture that is specifically targeted to the MPC problem. As opposed to the more usual approach using a generic serial architecture processor, the design here is implemented using a field-programmable gate array and employs parallelism, pipelining, and specialized numerical formats. The performance of this approach is profiled via the control of a 14th-order resonant structure with 12 sample prediction horizon at 200-μs sampling rate. The results indicate that no more than 30 μs are required to compute the control action. A feasibility study indicates that the design can also be implemented in 130 nm CMOS technology, with a core area of 2.5 mm². These results illustrate the feasibility of MPC for reasonably complex systems, using relatively cheap, small, and low-power computing hardware.

Generalised Hammerstein-Wiener system estimation and a benchmark application

Sat 24 Mar 2018 07:58:06 AEDT

This paper examines the use of a so-called “generalised Hammerstein–Wiener” model structure that is formed as the concatenation of an arbitrary number of Hammerstein systems. The latter are taken here to be memoryless non-linearities followed by linear time invariant dynamics. Hammerstein, Wiener, Hammerstein–Wiener and Wiener–Hammerstein models are all special cases of this structure. The parameter estimation of this model is investigated using a standard prediction error criterion coupled with a robust gradient based search algorithm. This approach is profiled using a Wiener–Hammerstein Benchmark example, which illustrates it to be effective and, via Monte-Carlo simulation, relatively robust against capture in local minima.

System identification of nonlinear state-space models

Sat 24 Mar 2018 07:56:22 AEDT

This paper is concerned with the parameter estimation of a general class of nonlinear dynamic systems in state-space form. More specifically, a Maximum Likelihood (ML) framework is employed and an Expectation Maximisation (EM) algorithm is derived to compute these ML estimates. The Expectation (E) step involves solving a nonlinear state estimation problem, where the smoothed estimates of the states are required. This problem lends itself perfectly to the particle smoother, which provides arbitrarily good estimates. The maximisation (M) step is solved using standard techniques from numerical optimisation theory. Simulation examples demonstrate the efficacy of our proposed solution.

Asymptotic optimality of the maximum-likelihood Kalman filter for Bayesian tracking with multiple nonlinear sensors

Sat 24 Mar 2018 07:50:39 AEDT

Bayesian tracking is a general technique for state estimation of nonlinear dynamic systems, but it suffers from the drawback of computational complexity. This paper is concerned with a class of Wiener systems with multiple nonlinear sensors. Such a system consists of a linear dynamic system followed by a set of static nonlinear measurements. We study a maximum-likelihood Kalman filtering (MLKF) technique which involves maximum-likelihood estimation of the nonlinear measurements followed by classical Kalman filtering. This technique permits a distributed implementation of the Bayesian tracker and guarantees the boundedness of the estimation error. The focus of this paper is to study the extent to which the MLKF technique approximates the theoretically optimal Bayesian tracker. We provide conditions to guarantee that this approximation becomes asymptotically exact as the number of sensors becomes large. Two case studies are analyzed in detail.

Variance error, reproducing kernels, and orthonormal bases

Sat 24 Mar 2018 07:49:13 AEDT

This chapter continues on these themes of exposing the links between rational orthonormal bases and the system identification problem. The main feature of this chapter is that it will progress to consider more general model structures, especially those not specifically formulated with respect to an orthonormal basis. At the same time that we generalize this aspect. we will focus another by considering only the noise-induced error. We will not discuss bias error. as it will be analysed in detail in the following chapters, and was also addressed in the previous one. Many of the underlying ideas necessary for the developments here have already been introduced, but in the interests of the reader who is seeking to 'dip into' chapters individually, a brief introduction to essential background ideas and notation will be made at the expense of some slight repetition. In precis then, the sole focus of this chapter is to examine and quantify noise induced estimation errors in the frequency domain, and there are four essential points to be made here in relation to this. 1. The quantification of noise-induced error (variance error) is equivalent to the quantification of the reproducing kernel for a particular function space Xn; 2. This function space Xn, depends on the model structure, as well as on input and noise spectral densities. Hence. it is not independent of model structure; 3. The quantification of the reproducing kernel, and hence the quantification of variance error, depends crucially on the construction of a rational orthonormal basis for the afore-mentioned function space Xn; 4. The variance error quantifications that result are quite different to certain pre-existing ones, while at the same time are often much more accurate. This latter point will be established here empirically by simulation example.

Parameter estimation for discrete-time nonlinear systems using EM

Sat 24 Mar 2018 07:47:51 AEDT

In this paper we consider parameter estimation of general stochastic nonlinear statespace models using the Maximum Likelihood method. This is accomplished via the employment of an Expectation Maximisation algorithm, where the essential components involve a particle smoother for the expectation step, and a gradient-based search for the maximisation step. The utility of this method is illustrated with several nonlinear and non-Gaussian examples.

Robust maximum-likelihood estimation of multivariable dynamic systems

Sat 24 Mar 2018 07:43:02 AEDT

This paper examines the problem of estimating linear time-invariant state-space system models. In particular, it addresses the parametrization and numerical robustness concerns that arise in the multivariable case. These difficulties are well recognised in the literature, resulting (for example) in extensive study of subspace-based techniques, as well as recent interest in 'data driven' local co-ordinate approaches to gradient search solutions. The paper here proposes a different strategy that employs the expectation-maximisation (EM) technique. The consequence is an algorithm that is iterative, with associated likelihood values that are locally convergent to stationary points of the (Gaussian) likelihood function. Furthermore, theoretical and empirical evidence presented here establishes additional attractive properties such as numerical robustness, avoidance of difficult parametrization choices, the ability to naturally and easily estimate non-zero initial conditions, and moderate computational cost. Moreover, since the methods here are maximum-likelihood based, they have associated known and asymptotically optimal statistical properties. (c) 2005 Elsevier Ltd. All rights reserved.

On the reachability property for networks of linear time-invariant subsystems

Sat 24 Mar 2018 07:34:23 AEDT

In this paper, we study networks of discrete-time linear time-invariant subsystems. Our focus is on situations where subsystems are connected to each other through a time-invariant topology and where there exists a base-station whose aim is to control the subsystems into any desired destinations. However, the base-station can only communicate with some of the subsystems that we refer to as leaders. There are no direct links between the base-station and the rest of subsystems, known as followers, as they are only able to liaise among themselves and with some of the leaders. The current paper formulates this framework as the well-known reachability problem for linear systems. Then to address this problem, we introduce notions of leader-reachability and base-reachability. We present algebraic conditions under which these notions hold. It turns out that if subsystems are represented by minimal state space representations, then base-reachability always holds. Hence, we focus on leader-reachability and investigate the corresponding conditions in detail. We further demonstrate that when the networked system parameters i.e. subsystems' parameters and interconnection matrices, assume generic values then the whole network is both leader-reachable and base-reachable.

A nonlinear programming approach to exposure optimization in scanning laser lithography

Sat 24 Mar 2018 07:28:44 AEDT

Laser scanning lithography is a maskless method for exposing films of photoresist during semiconductor manufacturing. In this method a focused beam is scanned over a surface with varying intensity to create features in the photoresist. Given the shape of a desired feature, an exposure pattern must be found that approximates this shape in the developed photoresist. This can be cast as an optimization problem, which is complicated by the non-negative nature of the exposure function and the non-linear photochemistry of the film. In this article, a nonlinear programming approach is described that results in a tractable optimization problem which accounts for all of the practical constraints encountered in laser scanning lithography.

Distributed weighted least-squares estimation for power networks

Sat 24 Mar 2018 07:26:52 AEDT

The paper presents a fully distributed scheme to optimal parameter estimation, with application in multi-area interconnected power systems. In this scheme, each area performs its own local parameter estimation based on low-dimensional local and boundary measurements as well as the estimate of boundary parameters from its neighbors. We show, under certain assumptions, that the distributed estimation scheme provides the same accurate unbiased estimate as the centralized weighted least-squares estimate with finite time convergence. The distributed estimation scheme is robust to communication link failures, delays, and asynchronism of control centers in different areas. A simulation using the IEEE 118-bus system is included to demonstrate the performance.

On identification of networked systems with time-invariant topology

Sat 24 Mar 2018 07:26:52 AEDT

This paper studies the problem of identification for networked systems. We consider both heterogeneous and homogeneous networks. It is assumed that the interconnection topology is time-invariant and known. We demonstrate how the parameter matrices of each individual subsystem can be identified from the input-output information obtained from the whole network. To this end, the well-known technique of Maximum-likelihood (ML) is exploited for obtaining estimations of system matrices.

Parallel MCMC algorithm for Bayesian system identification

Sat 24 Mar 2018 07:17:53 AEDT

A generalised framework for Metropolis-Hastings admits many algorithms as specialisations and allows for synthesis of multiple methods to create a parallel algorithm, with no tuning required, to efficiently draw uncorrelated samples, from the posterior density in Bayesian systems identification, at lower computational cost in comparison with conventional samplers. Two automatic annealing schemes demonstrate complementary robustness in detecting multi-modal distribution.

Identification of nonlinear state-space models using joint state particle smoothing

Sat 24 Mar 2018 07:17:24 AEDT

On the basis of a previous expectation maximization (EM) algorithm, this paper applies the particle Markov chain Monte Carlo (MCMC) technique to estimate nonlinear state-space models (SSMs). The smoothed simultaneous particles for joint states are generated by importance resampling (IR) and are directly used to compute a log-likelihood function and its Jacobian vector and Hessian matrix. As a result, a relatively less computational load can thus be obtained, which is crucial to practical applications of the particle MCMC. In addition, the SSM parameters can be recursively iterated by the more efficient Newton method, in which an optimal step length for parameter update in each iteration is optimized by a 1-D search method. This presented identification method has a good global parameter convergence in case iteration parameters are initialized from quite large intervals of their respective true values. Finally, a numerical simulation for identification of a classical SSM is used to show the effectiveness of the studied identification method.

An improved square-root algorithm for RTS Kalman smoothing

Sat 24 Mar 2018 07:16:36 AEDT

This paper improves on a noted square-root RTS Kalman smoothing algorithm proposed by Park and Kailath for the application purpose. This improved square-root RTS algorithm is able to additionally accommodate arbitrary exogenous known input, as such case is quite common in the real-world applications. In addition, hyperbolic Householder transformations are employed to avoid the computation of the difference of two positive semi-definite matrices. The Givens rotations based unitary transformations are further used to make the resulting algorithm have higher computational efficiency. The relevant implementation steps of this algorithm is also addressed. Finally, a numerical simulation is given to verify this improved algorithm.

Reunderstanding slice sampling as parallel MCMC

Sat 24 Mar 2018 07:16:22 AEDT

A robust slice sampler, which guarantees no repeated samples, is found as a special case of Metropolis sampling that can interact with parallel chains to efficiently sample from multi-modal densities even with possibly isolated support sets. The algorithm is completely automated with no tuning required. Implications to particle filtering design for on-line state and parameter joint estimation is also discussed.

Compensation of attacks on consensus networks

Sat 24 Mar 2018 07:09:55 AEDT

In this paper, we propose a methodology for compensation of attacks on consensus networks. We assume that the network achieves its desired consensus value under a normal operational setting i.e. when the networked system is not under attack. We propose an adaptive based technique to ensure that the networked system maintains its desired behavior when the system inputs are under some false-date injection attacks. The proposed method adaptively estimates attack signals and compensates their effects. We demonstrate the good performance of our proposed compensation scheme through simulation studies that consider both constant and time-varying attack signals.

Data to Controller for Nonlinear Systems: An Approximate Solution

Mon 24 Oct 2022 09:17:38 AEDT

This letter considers the problem of determining an optimal control action based on observed data. We formulate the problem assuming that the system can be modeled by a nonlinear state-space model, but where the model parameters, state and future disturbances are not known and are treated as random variables. Central to our formulation is that the joint distribution of these unknown objects is conditioned on the observed data. Crucially, as new measurements become available, this joint distribution continues to evolve so that control decisions are made accounting for uncertainty as evidenced in the data. The resulting problem is intractable which we obviate by providing approximations that result in finite dimensional deterministic optimization problems. The proposed approach is demonstrated in simulation on a nonlinear system.

Expectation maximization based FitzHugh-Nagumo model identification under unknown Gaussian measurement noise

Mon 20 Nov 2023 14:40:09 AEDT

This paper applies a new expectation maximization (EM) based identification method to estimate a generic FitzHugh-Nagumo (FHN) model under unknown Gaussian measurement noise. It is well noted that such FHN model is an elementary neuronal dynamics description and plays a significant role in deep understanding and basic analysis for complicated mechanisms of some neural diseases. Different from the most existing relevant identification methods, the applied new method is additionally capable of supplying users with variance estimation for the unknown measurement noise corrupting on the membrane potential apart from model parameter estimates. All unknown parameters can be iteratively estimated by a particle smoothing based EM algorithm, which consists of an expectation (E) step and a maximization (M) step. Smoothed joint-state particles are produced by a new particle smoothing algorithm to evaluate an expectation of a log-likelihood function in the E step, and the model parameters and noise variance can then be efficiently optimized by the gradient based methods in the M step. The resulting estimations own global convergence for a relatively wide range of parameter initializations. Finally, good convergence behaviors of the estimated model parameters and noise variance are demonstrated by a numerical simulation for a classic FHN model by using 10 simulation realizations with random initializations varying within ±100% of their respective true values.

Large-Amplitude Dithering Mitigates Glitches in Digital-to-Analogue Converters

Mon 18 Jul 2022 12:30:21 AEST

Glitches introduce impulse-like disturbances which are not be readily attenuated by low-pass filtering. This article presents a model that describes the behaviour of glitches, and a method for mitigation based on a large-amplitude dither signal. Analytical and experimental results demonstrate that a dither signal with sufficient amplitude can mitigate the effect of glitches, when used in conjunction with a low-pass filter. The dither signal in conjunction with low-pass filtering essentially converts a glitch from a high-frequency to low-frequency disturbance.

A Numerically Robust Bayesian Filtering Algorithm for Gaussian Mixture Models

Fri 19 Jan 2024 12:39:16 AEDT

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this problem involves an exponential growth in the number of mixture terms and this is handled here by utilising a Gaussian mixture reduction step after both the time and measurement update steps. In addition, a numerically robust square-root implementation of the unified algorithm is presented and this algorithm is profiled on several simulated systems, including the state estimation for a challenging non-linear system.

Parameter estimation for Jump Markov Linear Systems

Fri 16 Feb 2024 11:21:01 AEDT

Jump Markov linear systems (JMLS) are a useful model class for capturing abrupt changes in system behaviour that are temporally random, such as when a fault occurs. In many situations, accurate knowledge of the model is not readily available and can be difficult to obtain based on first principles. This paper presents a method for learning parameter values of this model class based on available input–output data using the maximum-likelihood framework. In particular, the expectation–maximisation method is detailed for this model class with attention given to a deterministic and numerically stable implementation. The presented algorithm is compared to state-of-the-art methods on several simulation examples with favourable results.

Smoothed State Estimation via Efficient Solution of Linear Equations

Fri 15 Mar 2024 11:59:44 AEDT

This article addresses the problem of computing fixed-interval smoothed state estimates of a linear time-varying Gaussian stochastic system. There already exist many algorithms that perform this computation, but all of them impose certain restrictions on system matrices in order for them to be applicable, and the restrictions vary considerably between the various existing algorithms. This article establishes a new sufficient condition for the fixed-interval smoothing density to exist in a Gaussian form that can be completely characterized by associated means and covariances. It then develops an algorithm to compute these means and covariances with no further assumptions required. This results in an algorithm more generally applicable than any one of the multitude of existing algorithms available to date.

On maximum likelihood identification of errors-in-variables models

Fri 11 Jan 2019 14:33:32 AEDT

In this paper, we revisit maximum likelihood methods for identification of errors-in-variables systems. We assume that the system admits a parametric description, and that the input is a stochastic ARMA process. The cost function associated with the maximum likelihood criterion is minimized by introducing a new iterative solution scheme based on the expectation-maximization method, which proves fast and easily implementable. Numerical simulations show the effectiveness of the proposed method.