In almost all industrial processes, there is a need to carry out control, diagnostics, fault detection, identification, and monitoring^{[1, 2]}. In modern industries, many variables need to be measured to achieve optimal automation and computing. However, in some cases, this is an arduous and expensive task due to the unavailability of reliable devices, time delays, errors in the measurement system, high cost of devices, and a hostile environment for primary measuring^{[3]}. In order to overcome many of the above issues, state estimators are used to make estimates through measurements of other variables related to the hardtomeasure variables. In industrial applications, state estimators are implemented as software routines in dedicated hardware, usually known as soft or virtual sensors.
In this respect, continuous research of state estimation techniques allows applications in areas such as electrical and electromechanical systems, aeronautical and navigation systems, robotics, and recently in chemical and biotechnological processes. A recent paper proposed a classification of observers applied in chemical processes^{[4]}. This classification is composed of six classes based on the review of current applications in specific chemical process systems. The classes are: Luenbergerbased observers, finitedimensional system observers, Bayesian estimators, disturbance and fault detection observers, artificial intelligence (AI)based observers and hybrid observers. Another recent research paper presents a tutorial on the main Gaussian filters and estimation^{[5]}. In that paper, the main Gaussian filters are explained in detail, considering linear optimal filtering, nonlinear filtering, adaptive filtering, and robust filtering. In addition, the authors describe a 200year history of the main classical contributions to estimation theory. Finally, the authors highlight some trends such as the adaptive Kalman filter, the adaptive filter with parameter tuning, the adaptive filter with joint estimation of states and parameters, multiple models adaptive filtering and variable structure filtering and its variants. However, both classifications do not consider problems such as delay and multirate associated with available information from sensors or offline analysis equipment. This kind of information is available in several processes but it is not commonly used despite allowing for an improvement in the quality of the estimation. Additionally, a recent review of multisensor distributed fusion estimation (DFE) taking into account data quantization, random transmission delays, packet dropouts and fading measurements is described in [6]. The proposed classification was based on some DFE algorithms in the literature and in the analysis of the phenomena of sensor networks. However, in this classification, the algorithms are only limited to the Kalman filter and its modifications. In addition, the phenomena of sensors network are not taken into account within the different applications of the estimation techniques. Therefore, a taxonomic classification that considers the phenomenon of acquisition, storage and use of nonuniform and delayed information of real applications is necessary. In addition, a classification that relates stochastic and deterministic estimation techniques is important.
Nonuniform and delayed information produces collateral problems in state estimation techniques: multisampling, asynchronism, data loss, and variability in the degree of reliability of the information (precision or accuracy). For the handling of such information, specialized methods are required. In this regard, some authors have developed different methods based on stochastic estimation techniques^{[7–12]}. These methods are arranged into two types: measurement fusion and augmented state space methods. Methods based on measurement fusion are only suitable for discretetime systems. Those methods are designed for the Kalman filter and its variants. In contrast, the methods based on augmented state retain the original statespace representation of the process, making it more promising to facilitate their extension to different types of estimators. Furthermore, the conservation of the state space representation allows for the subsequent analysis of convergence, observability, and robustness of the estimator.
Some authors present deterministic estimation techniques with asynchronous and delayed measurements for hybrid systems, with a continuoustime model for the process and a discretetime model for the effects of sensor and sampling. Such observers are arranged into four types: piecewise observers^{[13]}, cascade observers^{[14, 15]}, distributed observers^{[16]}, and partial state observers^{[17–20]}. These deterministic estimation techniques allow the solution of problems presented in the state estimation independently or in stages, i.e., the adaptation of a hybrid estimator according to the needs of the system. Some partial stages may be signal processing, data prediction or estimation of unknown parameters.
Although state estimation with asynchronous and delayed information is a subject of current research, to the best of our knowledge, there is no review paper summarizing and collecting the whole spectrum of different estimation techniques, its limitations, tools, and applications. Some papers work on applied specific problems and a few show state estimation in bioprocess with delay measurement^{[21–23]}. Moreover, there is no unified conceptual framework and taxonomy tools that enable researchers in this field to use and identify appropriate tools for their particular problems.
Therefore, in this paper, a review of the main methods and concepts for processes with nonuniform and delayed information is described. Additionally, a taxonomic organization of the reported methods is proposed. This taxonomic organization allows for faster selection of a state estimator incorporating nonuniform and delayed information. Finally, a comprehensive list of applications of state estimators in different processes is shown.
The paper is organized as follows. In Section 2, a framework to address the use of nonuniform and delayed information on estimation and control tasks is proposed. Section 3 presents the main methods for using nonuniform and delayed information on state estimation techniques and explains the proposed taxonomy for these methods. In Section 4, some applications reported in the literature are presented and analyzed. Finally, conclusions are summarized.
2 Nonuniform and delayed information in industrial processes 2.1 Basic definitionsIn industrial processes, a large amount of information is stored in a supervisory control and data acquisition (SCADA) system. To handle the gathered information for state estimation and process control tasks, it is necessary to characterize and identify their sources and associated problems. For the taxonomy presented in current work, Definitions 1–4 are required:
Definition 1. Information is all symbolic representation of an event. This representation has meaning to whoever receives those symbols and helps him to interpret the world and to reduce the uncertainty.
Definition 2. A source of information is any origin of information as previously defined.
Definition 3. Delay is the time lapse that a signal takes from its source in a process until its reception at a storage or processing place.
Definition 4. Multisampling or asynchronism is the effect that occurs when the sampling time between two signals is not the same. In industrial processes, this effect occurs by the difference in the time response and delay of sensor technology.
2.2 Sources of informationSources of information can be classified according to the characteristics of acquisition and storage in two types. In the first type, called online, there are online sensors connected to the SCADA system for measuring simple and common variables like level, temperature, flow, pressure, etc. In the second type, called offline, more complex variables are obtained from samples taken from the process which are processed in the laboratory or by specialized equipment to obtain the variable value. A common example of offline variables are the analysis variables like concentration. Values of offline variables are stored in the SCADA system with a prestated time interval. Although online measurement is the best option, some offline variables must be used due to cost or unavailability of online sensors for some variables required for process analysis and control.
A representation of the sources of information is shown in Fig. 1. From Fig. 1, it can be seen that the variables of a process may be inputs, outputs and states. Each variable may be known (measured) or unknown (unmeasured). In the diagram, the measured inputs are marked as
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Fig. 1. Sources of information in an industrial process 
2.3 Acquisition and storage of information
In a SCADA system, all information is stored at discrete times, according to Assumptions 1–4^{[8, 14]}:
Assumption 1. Sampling delays associated with online measurements are considered negligible compared to the sampling delays associated with offline measurements.
Assumption 2. All the measurements available at the timeinstant
Assumption 3. The information obtained from the uniform measurements is more susceptible to problems of noise and precision than that obtained from laboratory or specialized equipment analysis. The first one is subject to the characteristics of the signal conditioning system of the sensors. In the second, strict adherence to highquality standards is assumed, even if measurements are nonuniform.
Assumption 4. Offline information is subject to human error while storing it into the SCADA system. Errors can be represented as spurious or missing data.
A characterization of phenomena occurring in the acquisition and storage of data from each source of information is presented in Fig. 2. In Fig. 2, the lower horizontal line represents the time instant at which the sampling is performed. Moreover, the upper horizontal line represents the time instant at which measurements are acquired and stored in the SCADA system. The straightdashed vertical lines represent the online measurements obtained by the sensors. Note that these measurements are sampled with a fixed sampling period
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Fig. 2. Characterization of phenomena occurring in the acquisition and storage of information sources. Source: modified from [8]. 
Offline measurements, obtained from the analysis of samples in laboratory or specialized equipment, are represented with a continuous and curved line. It is worth mentioning that offline measurements may have different measurement delays
Definition 5. A uniform (synchronous and undelayed) measurement is a measurement that is available at every constant period of time. See straight and dashed line in Fig. 2.
Definition 6. A nonuniform measurement is a measurement that is not necessarily available at every constant period of time. In addition, once the measurement is available, the obtained information is related with old system trajectories. See curved and continuous lines in Fig. 2.
Definition 7. An integral measure is an offline measurement characteristic in which a measurement value can be effective or valid over a given time period
It must be clarified that the term nonuniform information does not refer to the type of distribution or a statistical characteristic of the data. In this regard, and according to the above definitions, the process information is considered nonuniform when the sampling time or the delay time is different between physical measurements.
On the other hand, the information storage process can have two instances: major and minor, defined as:
Definition 8. A minor instance case concerns the case where only uniform measurements are available at a given timeinstant
Definition 9. A major instance case concerns the case where all measurements (uniform and nonuniform) are available at a given timeinstant
An industrial process in presence of nonuniform and delayed information can be represented as a discretetime nonlinear system of the form:
$x(k + 1)= f(x(k), u(k), \varepsilon (k))$  (1) 
where
In practical applications, two cases concerning the system outputs can be available at every timeinstant
Minor instance
$\begin{split}& {y(k) = {h_1}(x(k), {v^1}(k))}\\& {{y_\theta }(k) = [\;]}\end{split}$  (2) 
Major instance
$\begin{split}& y(k) = {h_1}(x(k), {v^1}(k))\\& {y_\theta }(k) = {h_2}(x(k), {v^2}(k))\end{split}$  (3) 
where the subscript
The estimation problem concerns the use of model (1) and the available measurements (2) and (3) to find an estimation of the system state
Problem 1. Given a system model (1): How to incorporate nonuniform measurements into the state estimation process under Assumptions 1 to 4, and considering both minor and major instances in a common framework?
In this section, the basic concepts were defined and the phenomenon of the acquisition and storage of industrial information sources was characterized. According to the characteristics of the information sources mentioned, their use in state estimation techniques is not a trivial matter. Collateral problems can occur such as: multisampling or asynchrony, missing and spurious data and redundant information, among others^{[8, 9]}. Therefore, in the next section, a review of methods to use nonuniform and delayed information in state estimation techniques is presented.
3 Methods to use nonuniform and delayed information in state estimation techniquesFrom the literature, it is possible to identify different tools developed from the information and control theory to manage and incorporate nonuniform and delayed information in state estimation techniques. In this paper, two types of systems will be discussed: stochastic and deterministic systems.
3.1 State estimation in stochastic systems with delayed measurementsSeveral methods have been proposed for state estimation when the plant is modeled by a discretetime stochastic model. In this case, the models consist of a deterministic part and a stochastic component characterized by the mean and the variance in the measurement noise and model noise. Fig. 3 shows the main methods reported for state estimation techniques incorporating nonuniform and delayed information^{[7–12]}. Below, a discussion of each method is presented.
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Fig. 3. Methods to incorporate nonuniform and delayed information in stochastic state estimation techniques 
3.1.1 Methods based on measurement fusion
These methods are developed for the use of multisensors or redundant measurements. For example, in [24], the position of a wheelchair is estimated using the fusion of two sources of information to improve the performance of the estimator. A source of measurement is obtained from a compass and an odometer, and the other from the same compass and an accelerometer.
In the literature, three variants of methods based on measurement fusion are presented: filter recalculation, Alexander′s method and parallel filter. These methods are based on the readjustment of the estimate in the major instance. In filter recalculation, the readjustment of the current state is performed by recalculating the entire trajectory of the Kalman filter. The recalculation is performed from the sampling
The methods based on measurement fusion only apply to discretetime systems. These are developed to work with the Kalman filter and its variants^{[25, 26]}.
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Fig. 4. Algorithm flowchart for measurement fusion methods 
3.1.2 Methods based on state augmentation
The methods based on state augmentation are based on enlargement of the state space with information from offline measurements and subsequently an extended model is incorporated into the state estimation technique, following the algorithm illustrated in Fig. 5. In Fig. 5,
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Fig. 5. Algorithm flowchart for state augmentation methods 
3.1.3 Mathematical description of a linear system with augmented state
Due to the importance of augmented state methods, a brief mathematical description of augmented state representation for a linear system is presented based on [7]. System (1) can be represented as a discretetime linear system as
$x(k+1)=A x(k)+B u(k)+\varepsilon(k).$  (4) 
And according to the minors (2) and (3) instances for the discretetime linear system (4), we have
Minor instance
$\begin{split}&y(k) = Cx(k) + {v^1}(k)\\[3pt]&{y_\theta }(k) = [\;].\end{split}$  (5) 
Major instance
$\begin{split}&y(k) = Cx(k) + {v^1}(k)\\[3pt]&{y_\theta }(k) = {C_\theta }x(kN) + {v^2}(kN)\end{split}$  (6) 
where
Now, by the concept of state augmentation, the order of the system can be increased such that the system contains the information of nonuniform and delayed measurements, as shown in (7).
$\begin{split}& Z(k + 1) = \Phi Z(k) + \Gamma U(k) + \Psi \varepsilon (k)\\[3pt]& Y(k) = \Xi Z(k) + {v^1}(k)\end{split}$  (7) 
where the matrices of the augmented state space
Note the high order of the augmented system produced by the augmentation methods of fixedlag smoothing and measurement. This can lead to high computational cost when the estimation uses higher order and complex models^{[7]}.
Now, the above representation can be extended to the nonlinear system (1). For this, the augmented state vector
$\begin{split}& F = {\left. {\displaystyle\frac{{\partial f}}{{\partial x}}} \right_{(x(k), u(k))}},{F_u} = {\left. {\displaystyle\frac{{\partial f}}{{\partial u}}} \right_{(x(k), u(k))}}\\[8pt]& {H_1} = {\left. {\displaystyle\frac{{\partial {h_1}}}{{\partial x}}} \right_{(x(k), u(k))}},{H_2} = {\left. {\displaystyle\frac{{\partial {h_2}}}{{\partial x}}} \right_{(x(kN), u(kN))}}\end{split}$  (8) 
where
$Z(k) = [x{(k)^{{T}}}{{ }}{x^{{T}}}(k1){{ }} \cdots {x^{{T}}}(kN)] \qquad \qquad $  (9) 
$\begin{split}& {\Phi ^*} = \left[{\begin{array}{*{20}{c}}F&0& \cdots &0&0\\[5pt]I&0& \cdots &0&0\\[5pt]0&I& \cdots &0&0\\[5pt] \vdots & \ddots & \ddots & \ddots & \vdots \\[5pt]0&0& \cdots &I&0\end{array}} \right],\Gamma = \left[{\begin{array}{*{20}{c}}{{F_u}}\\[5pt]0\\[5pt]0\\[5pt] \vdots \\[5pt]0\end{array}} \right]\\[5pt]& {\Xi ^*} = \left[{\begin{array}{*{20}{c}}{{H_1}}&0& \cdots &0&0\\[5pt]0&0& \cdots &0&{{H_2}}\end{array}} \right].\end{split}$  (10) 
This method smooths the past
In this section, different techniques to incorporate nonuniform and delayed measurements in deterministic estimation strategies are presented. In these strategies, the system is considered as a hybrid system, i.e., the process is modeled as a continuoustime system and the effects of sensor and sampling are represented as a discretetime system (see Fig. 6).
According to Fig. 6, the process can be represented by
$\begin{split}& \dot x\left( t \right) = f\left( {x\left( t \right), u\left( t \right)} \right)\\[3pt]& x\left( 0 \right) = {x_o}\\[3pt]& {y_i}\left( t \right) = h\left( {x\left( t \right)} \right)\end{split}$  (11) 
where
$z_i\left(t\right)=y_i\left(t\theta\right).$  (12) 
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Fig. 6. Hybrid system scheme for deterministic estimates with delayed measurements. Source: modified from [13, 14] 
In the present review, such techniques have been grouped into four types of methods according to their structure: piecewise observer^{[13]}, cascade or chain observer^{[14, 15]}, distributed observer^{[16]}, and partial state observer^{[19, 20]}. These deterministic techniques solve the problems of state estimation independently or in stages. A brief description of the main characteristics of each method of this family follows.
3.2.1 Piecewise observersThis type of observers is based on the theory of piecewise continuoustime hybrid systems (PCHS), a particular class of hybrid systems characterized by autonomous switchings and controlled impulses^{[13]}. In [13], a scheme composed of four linear piecewise continuoustime hybrid systems (LPCHS), one reduced order discretetime luenberger (RODL) observer, and one block of reconstruction calculation were proposed as shown in Fig. 7.
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Fig. 7. Piecewise continuoustime observer scheme. Source: modified from [13] 
The inputs of the piecewise continuoustime observer (PCO) are the delayed measurement and the current process input and output are the estimates of the current state
1) First stage. Delayed measurement
2) Second stage. LPCHS III and input
3) Third stage. RODL observer is used to obtain the delayed estimated state
4) Fourth stage. The reconstruction calculation block is used to get the discretetime undelayed state
5) Fifth stage. Finally, using the LPCHS IV with the inputs of
This method has two stages, one for state estimation and the other one to account for delay effects. Depending on the nature of the information, multisampling or with unknown delay, the stage of information processing may be previously or subsequently implemented at the estimation stage, as shown in Figs. 8 and 9. In this respect, since the estimation and data processing are performed by separated stages, it is possible to use either stochastic or deterministic state estimation techniques. However, in the literature, only deterministic estimation techniques are reported^{[14, 15, 22, 29]}.
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Fig. 8. Observerpredictor scheme for delay feedback 
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Fig. 9. Predictorobserver scheme for feedforward delay 
Regarding the stage of information processing, different elements to reduce the effects of delay are used. In [29], a switching element is proposed to incorporate delayed measurements. Other authors propose to use a Smith predictor^{[30]}. In the latter applications, the cascade observerpredictor is extended to use variable delay and multisampling, which are useful for applications with unknown delay. Due to the importance of cascade observerpredictor, in the present work, some features of this method are presented below.
The Cascade observerpredictor scheme (Fig. 8) has two stages. The first stage is called observation and normally is executed employing any observer structure. However, the problem considered in this review is to estimate the current state
${\dot x^p}\left( t \right) = {\dot {\hat x}^\theta }\left( t \right) + f\left( {{x^p}\left( t \right)} \right)  f\left( {{x^p}\left( {t  \theta } \right)} \right)$  (13) 
where the prediction of the current state is denoted by
The stability of the previously mentioned observerpredictor structure is such that the estimated state asymptotically/exponentially converges to the system trajectories (11) and (12), if the estimates provided by the observer converge in an asymptotic/exponential way to the delayed system state^{[15]}.
3.2.3 Distributed observersA recent development in the field of state estimation for largescale process systems is distributed observers^{[31]}. This observer uses a network of interconnected estimators for each subsystem. This network consists of several estimator nodes. At each node, embedded computation, communication and power modules are included^{[16, 32]}. A node acts as a local observer by computing estimates through its own model and available measurements. The communication module allows a sensor node to share information with other nodes in the network within a specified communication topology. This scheme is presented in Fig. 10.
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Fig. 10. Distributed observer scheme. Source: modified from [16] 
In [16, 32], a distributed observer was proposed. There, for each node of the estimator, a predictor and a moving horizon state estimator (MHE) are embedded. In that proposed approach, the predictor subsystem handles communication delays and data losses directly while the local MHEs take advantage of the predictions given by the predictors. Applications of this distributed estimation scheme for systems with nonuniform and delayed information are focused on largescale systems, where the system can be modeled as several subsystems, such as electrical power systems^{[16, 32, 33]}.
3.2.4 Partial state observersFinally, in this method, the estimation structures that use a reducedorder Luenberger observer with estimation or extrapolation approximations of delayed or asynchronous measurements are grouped. For example, in [17], a polynomial extrapolation is used. That is, slow measurements can be predicted for sample times where only fast measurements are available. Other applications are presented in [18–20] and will be discussed in Section 4.
3.3 Proposed taxonomyThis section shows a taxonomic proposal for available tools reported in the literature for incorporating nonuniform and delayed information in state estimation techniques. The proposed taxonomy has hierarchical levels as shown in Fig. 11.
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Fig. 11. Tools taxonomy for incorporating nonuniform and delayed measurements in state estimation techniques 
In Fig. 11, the first hierarchical level is classified according to the type of estimator used. The second level classifies different methods to incorporate nonuniform and delayed information. Each method has different uses according to characteristics of information such as known delay, variable delay, multiple system outputs and multirate sampling, among others, as presented in Section 3. Finally, in the third level, some of the tools reported in the literature and their respective seminal references are presented to give the works supporting the proposal.
Table 2 presents a comparison of two of the most important structures reported in the literature for state estimation of systems in the presence of nonuniform and delayed measurements: the extended Kalman filter (EKF) with the state augmentation method and the chain observerpredictor algorithm. Table 2 shows some characteristics of the two families of state estimation approaches (stochastic and deterministic) for systems with nonuniform and delayed measurements. The analysis presented in Table 2 is supported by references^{[21, 22]}. In these papers, estimation techniques were applied to estimating biomass in the
4 Applications of state estimators employing nonuniform and delayed information
In this section, some applications of different state estimators employing nonuniform and delayed information are presented in Table 3 as reported in the literature. The tools used in each application are analyzed according to the previously proposed taxonomy (see Fig. 11). Some applications for each of the six methods presented in the taxonomy are listed. In addition, for each application, some characteristics like author/year, estimator type, uses, system model, tools, and others are reported. The first column shows the reference. The second column is the estimator type, indicating the estimator structure. The next column shows the particular applications in which the proposed estimator was simulated and validated. The fourth column shows the type of required model for the proposed estimator structure. The fifth column describes the tool used to incorporate the nonuniform and delayed information. Finally, in the other characteristics column, some particular characteristics of the application are described. The applications are organized according to the method and chronological order of their publication.
In general, the applications in Table 3 show the following trends:
1) The asynchronous and delayed measurements are presented in various fields, from electromechanical systems to bioprocesses and navigation systems. However, there are still many real applications that could use this information, for example, largescale systems. In addition, many of the published papers work with hypothetical models or laboratoryscale models, but there are not a lot of industrial applications.
2) There is a general trend to use stochastic estimators when considering real plants. In this case, models are assumed discrete and linear time invariant, probably because most of the tools have been developed for this type of models. However, linear models do not always represent the actual behavior of the processes, since they can be removed from the linearization conditions or undergo significant changes in their inputs. Therefore, developments that focus on nonlinear models are required.
3) Regarding the stochastic tools, there is a very marked use of Kalman filter and its modifications. That is, there is a lot of credibility in this algorithm due to its ability to handle noise and modeling uncertainty. But Kalman filtering assumes a model with linear dynamics and it supposes noise with a Gaussian probability distribution function. Additionally, the Kalman filter algorithm needs initial values for the estimate state and for the covariance matrix, but such values are not easy to find, and therefore they are assumed by the designer.
4) The methods based on “state augmentation” present more recent applications than the methods based on “fusion measurement”. In this regard, some authors defend the greater favorability for the use of methods based on “state augmentation”, due to its possible extension to deterministic estimation techniques^{[7]}. However, these methods present similar problems to those described in the previous item with the use of Kalman filter. Moreover, the extension of these methods to deterministic estimation techniques is not a trivial matter because the strong switching required at each measurement instance (major and minor) causes problems with the convergence of the estimator.
5) Regarding the deterministic estimators, there is a strong tendency to use them to validate the results in numerical cases. These estimators use nonlinear models. Most of the deterministic structures use the observerpredictor combination to produce a wellperforming estimate. However, there is a lack of application of these methods in real cases that consider not only the management of measurement and delayed input but also the multisampling. In addition, a greater diffusion of the results is necessary.
6) On the other hand, the deterministic tools for the incorporation of nonuniform and delayed information basically consist of distributed observers due to the great influence that this area has recently had in the control field. These tools, in many cases, designed in blocks or with hybrid structures, allow a greater flexibility of expansion of the system to be observed and its application in large scale systems. But in turn, this flexibility causes problems of standardization and generalization of the tools or methods, so they are developed for specific problems.
7) To achieve the technological transfer of state estimators using nonuniform and delayed information, it is necessary to validate the methods in different real applications. For example, in large industries such as oil, sugar or textile, it would be useful to promote the use of all information obtained by sensors and results of laboratory tests for estimation and control of these processes. It is even possible to extend the use of nonuniformed and delayed information in largescale systems such as hydrometeorological networks, interconnected electrical systems, water systems or the integrated mass transport system.
8) Some recent works, which were not included in Table 3 because they were applied to control systems and identification, propose novel techniques and tools for systems with nonuniform and delayed information. These novel techniques and tools could be extrapolated to the problem of state estimation. For example in [53], a recursive Bayesian identification algorithm with covariance resetting is proposed to identify systems with nonuniformly sampled input data. In [54], a robust finitetime
In this paper, a set of useful definitions acting as a framework for research in state estimation with nonuniform and delayed information were reviewed and information sources found from industrial processes were characterized. Also, different methods to incorporate nonuniform and delayed measurements in state estimation techniques were presented in general terms. After that, a taxonomy to collect and classify different methods and tools reported for estimation was proposed. This classification was performed according to the type of estimator and model used in each technique. In addition, the taxonomic classification considers the phenomenon of acquisition, storage and use of nonuniform and delayed information from real applications and also incorporates both stochastic and deterministic estimation techniques. Finally, through proposed taxonomy, different reported applications in the literature were summarized in a table and then analyzed and criticized. A critical analysis of the references showed that it is still necessary to investigate modeling uncertainty, to reformulate the state augmentation method for incorporating non uniform and delayed information in deterministic estimators, to expand deterministic methods to other phenomena of sensor networks such as multisampling, to improve the performance of these types of estimators in the case of variable parameters, and finally, to apply the techniques developed in real processes, particularly in largescale systems.
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