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The problem of state estimation for nonlinear systems with unknown state or measurement delays is still an open problem. In this paper, we consider the case of measurement delay and propose an approach that combines a delay identifier with a suitable high-gain observer in order to achieve simultaneous estimation of state and delay. We provide sufficient conditions that guarantee the exponential convergence to zero of the errors, globally with respect to the system variables and locally with respect to the delay estimation. We validate the method through an example concerning population models.

This paper concerns the state estimation problem for linear discrete-time non-Gaussian systems. It is known that filters based on quadratic functions of the measurements processes (Quadratic Filter) improve the estimation accuracy of the optimal linear filter. In order to enlarge the class of systems, which can be processed by a Quadratic Filter, we rewrite the system model by introducing an output injection term. The resulting filter, named the Feedback Quadratic Filter, can be applied also to non asymptotically stable systems. We prove that the performance of the Feedback Quadratic Filter depends on the gain parameter of the output term, which can be chosen so that the estimation error is always less than or equal to the Quadratic Filter.

We consider the tracking problem of a point moving in a three-dimensional space using only measurements of distance from a set of reference points. The approach followed in this paper is to derive a linear map with multiplicative noise through a quadratic transformation of the distance measurements. A suitable rewriting by means of an output injection term makes the multiplicative noise of the linear map amenable to be processed by recursive estimators. These estimators are guaranteed to be internally stable and the variance of the estimation error is estimated. We compare the performance of the resulting algorithm for the linear and quadratic case with standard alternatives.

This paper proposes an optimal control law for linear systems affected by input delays. Specifically we prove that when the delay functions are known it is possible to generate the optimal control for arbitrarily large delay values by using a DDE without distributed terms. The solution can be seen as a chain of predictors whose size depends on the maximum delay.

The class of strict-feedback systems enjoys special properties that make it similar to linear systems. This paper proves that such a class is equivalent, under a change of coordinates, to the wider class of feedback linearisable systems with multiplicative input, when the multiplicative terms are functions of the measured variables only. We apply this result to the control problem of feedback linearisable nonlinear MIMO systems with input and/or output delays. In this way, we provide sufficient conditions under which a separation result holds for output feedback control and moreover a predictor-based controller exists. When these conditions are satisfied, we obtain that the existence of stabilising controllers for arbitrarily large delays in the input and/or the output can be proved for a wider class of systems than previously known.

This paper investigates the control problem of linear systems affected by an unknown constant input delay by means of a finite-dimensional state feedback. The proposed solution extends an approach used in the case of known delays by means of a suitably developed delay identifier. A more general result about the convergence to zero of the controlled system when the delay estimation error only converges to some neighborhood of zero is provided. Numerical examples show the effectiveness of the proposed approach.

This paper proposes a new method to simultaneously estimate the state and the delay of a linear time delay system. The approach is based on the definition of an augmented linear time-varying model whose state is composed by both the original state vector and the delay. The estimation is then carried out by developing an appropriate observer for the augmented system. A numerical example shows the effectiveness of the proposed methodology.

This note studies the LQ and LQG problems for linear time invariant systems with a single time-varying input delay and instantaneous (memoryless) state feedback. We extend the memoryless state feedback solution proposed in [1] in two directions. We prove that in the deterministic case a memoryless state feedback can be in general optimal only up to a certain delay, for which we provide a sufficient, and sometimes strict, bound. Moreover, we show that this memoryless control is optimal also in the case of time-varying delays and that the quadratic cost functional has the same value as in the case without delay. For time varying delays the control law requires that the relationship between time points in which the input is generated and applied is known and invertible even if the delay function needs not to be differentiable or even continuous. Finally, we prove that the cost functional is bounded also in the stochastic case for the same delay interval as in the deterministic case, but with a larger cost than the delay-less LQG solution.

The problem of state estimation for nonlinear systems with unknown state delays is still an open problem. In this paper, we propose to add a delay identifier to suitable high-gain observers in order to achieve simultaneous estimation of state and delay. In the case of one constant delay in the state, we provide sufficient conditions to guarantee the exponential convergence to zero of the errors, globally with respect to the initial choice of the system state variables and locally with respect to the initial delay estimation. We validate the method through an example concerning chaotic oscillators.

We consider the filtering problem of LTI continuous-time systems with known and bounded measurement delays. The aim of the technical note is the design of a finite-dimensional sub-optimal filter whose performance in terms of the estimation error is comparable to optimal infinite-dimensional approaches. We show that the proposed approach allows for a precise characterization of the relationship between measurement delay and the covariance of the estimation error. In the time-varying case no restrictive hypotheses on the delay function are needed. The proposed filter can therefore be applied to delay functions for which traditional infinite-dimensional approaches cannot be straightforwardly applied.

This paper concerns the state estimation problem for linear discrete-time systems with non-Gaussian state and output noises. A sub-optimal quadratic filter algorithm is proposed. In order to enlarge the class of systems allowed to be processed, a novel approach based on the output injection stabilization is derived. Also a second benefit to the estimate performances, due to the possibility of assignment of the system eigenvalues, is investigated. Numerical results validate the effectiveness of the proposed method.

In this paper the classical problem of planar tracking is studied. The approach here proposed is based on the idea of considering, as system output, a vector of “virtual” measurements directly obtained from the actual ones. In this way, the measurement map is split into the sum of a linear time-varying transformation of the state and an uncorrelated white noise process, which is generally nongaussian. The resulting model is amenable for applying standard linear and polynomial Kalman like algorithms avoiding any linearization procedure of the measurement map, which is required by other standard suboptimal solutions (e.g. EKF). Finally, the proposed algorithms are checked through numerical simulations.

This paper introduces a novel multi-view deconvolution technique for 3-D images. An optimal Kalman-based minimum variance restoration algorithm is allowed to combine a series of image samples acquired from different viewing directions. The extended algorithm is based on the definition of a stochastic state-space representation of the image, which embeds the description of blurring effects and noise disturbances. The consistency of this model gives guarantee for high restoration performances. The extension to the data fusion is obtained by suitably including the multi-view acquisition procedure within the representation. The final algorithm results to be effective for improving the resolution and the isotropy of the estimated image, as shown by the reported numerical results.

This paper concerns with the state estimation problem of nonlinear systems with sampled noisy measurements. The main idea is to exploit a result of the analysis of nonlinear systems, which considers a class of state-space nonlinear models admitting the design of a deterministic observer with linear error dynamics. Such systems are supposed to provide sampled noisy measurements. A consistent filtering technique is then suitably developed, using the same approach of the mentioned classical result.

This paper proposes a new method for removing noise and blurring from 3D microscopy images. The main contribution is the definition of a space-variant generating model of a 3-D signal, which is capable to stochastically describe a wide class of 3-D images. Unlike other approaches, the space-variant structure allows the model to consider the information on edge locations, if available. A suitable description of the image acquisition process, including blurring and noise, is then associated to the model. A state-space realization is finally derived, which is amenable to the application of standard Kalman filter as an image restoration algorithm. The so obtained method is able to remove, at each spatial step, both blur and noise, via a linear minimum variance recursive one-shot procedure, which does not require the simultaneous processing of the whole image. Numerical results on synthetic and real microscopy images confirm the merit of the approach.

In this paper the problem of output feedback stabilizability for a class of MIMO discrete-time nonlinear systems is considered. The proposed solution is based on an ad-hoc separation assumption that could be satisfied for the class of nonlinear systems characterized to have the full vector relative degree and the drift-observability properties. Numerical results for the simple academic case of pendulum show the effectiveness of this approach.

A new approach to the deconvolution and filtering of 3-D microscopy images is introduced in this paper. A state-space representation of the image is derived according to the assumption that the whole image can be modelled by an ensemble of smooth 3-D Gaussian random fields. Blurring and noise are then easily included in the representation. Making use of this model the image restoration is carried out by means of a Kalman-based minimum variance estimation algorithm. The reported simulation results show high performances of the proposed approach.

This paper describes a new efficient approach to the conventional nonlinear tracking problem in a nongaussian setting that consists in the transformation of the nonlinear output measurement function in a linear form by the definition of a virtual measurement process. Such a procedure leads to the use of an efficient filter capable to take into account the nongaussanity of the transformed measurement noise process. This key feature is also exploited to consider and suitably manage a nongaussian and more realistic motion behaviour of the target object. Compared with the traditional approaches (e.g., extended Kalman filter (EKF) and unscented Kalman filter (UKF)) used in passive localization, the proposed method has potential advantages in robustness, convergence speed, and tracking accuracy.

In this paper it is studied the classical problem of target tracking by a new approach consisting in the treatment of the classical nonlinear measurement process in a form amenable for polynomial filtering without the need of the measure map linearization, as required by other standard sub-optimal algorithms. The main idea is to transfer the nonlinearity of the measure map into a modification of the noise sequence distribution in a nongaussian white sequence. This is indeed the property required for Kalman filtering which, although non more optimal, remains to be the optimal linear filtering algorithm. Conditions for polynomial filtering are also satisfied, allowing to face the nongaussian nature of the modified noise sequence. Simulations show high performances of the proposed algorithm.

In this paper it is proposed a new approach to the solution of the classical state estimation problem for a general time-varying perspective system. The solution is achieved by the definition of a virtual output which has the property to convert the original nonlinear output measurement function into a linear time-varying one. This allows the computation of an efficient observer gain matrix by the real-time solution of a suitable delay Riccati equation. Numerical results show high performances of the observer.

This paper introduces a new approach to SLAM which combines an Information Filter and a non linear optimizer. The basic idea of the suggested technique is to use the Information Filter when the system non linearities are negligible, and to switch to the use of the non linear optimizer when the non linearities are not negligible. Extensive simulations are provided in order to evaluate the performance of the proposed approach. In particular, a comparison with the Exactly Sparse Delayed-state Filers (ESDF) technique is carried out.