State estimation with biased observations

State estimation is difficult when the system has multiple modes of operation. Modal transitions create discontinuities in the reference point for the local state variables. The uncertain reference point increases the ambiguity in the state measurement. The paper presents an estimation algorithm that can be used in multimodal applications. The algorithm is shown to be superior to the Kalman filter when the state measurement is contaminated with a mode dependent offset. Despite the uncertain reference point in the observation, good estimates of the underlying entire state processes can be generated     

Fault estimation and prediction for nonlinear stochastic system with intermittent observations

This paper is concerned with the fault estimation and prediction problems for a class of nonlinear stochastic systems with intermittent observations. Based on the extended Kalman filter and Kalman filter, the fault and state are simultaneously estimated, and then, it is extended to the case of intermittent observations. Meanwhile, the boundedness of the estimation error is also discussed. Once the fault is detected, the parameters of each fault are identified by the linear regression method. Then, the future fault signal can be predicted by the parameters of the fault. The effectiveness of the proposed algorithm is verified by the simulation of the 3‐tank system.     

Bayesian hybrid state estimation for unequal-length batch processes with incomplete observations

This paper investigates state estimation problem for batch processes with unequal-length batches as well as incomplete observations. A Bayesian hybrid state estimation method is proposed based on two dimensional (2D) correlations of states. The states of equal-length segment of time are estimated according to both within-a-batch and batch-to-batch correlations, and the states of unequal-length segment are obtained according to the correlations within the batch. In this way, the batch process states can be achieved in both equal-length and unequal-length situations, of which the latter one is a more general case. In order to approximate state distribution of nonlinear system and to deal with the problem of incomplete observations, particle filter (PF) is employed. The proposed method shows its superiority with a nonlinear system and a gas-phase reaction process. Compared to a typical existing method, the proposed method provides better estimation accuracy in the situation of equal-length batches, also it shows less sensitivity to incomplete observations.     

Bussgang decomposition-based sparse channel estimation in wideband hybrid millimeter wave MIMO systems with finite-bit ADCs

Both the hybrid architecture and low precision analog-to-digital converters (ADCs) are considered to alleviate the burden of high power cost and hardware implementation of millimeter wave (mmWave) communication system. Accordingly, the channel estimation issue in wideband mmWave system with finite-bit ADCs becomes even challenging. To address this issue, the non-linear mmWave channel estimation problem is reformulated into a linear sparse signal recovery problem by utilizing the Bussgang decomposition. Then, based on the equivalent linear sparse model, a Bussgang decomposition-based OMP (BD-OMP) algorithm is proposed to both exploit the inherent sparsity of wideband mmWave channel and alleviate the quantization error. Furthermore, we analyze that the actual noise of linear sparse model consists of combined noise and distortion noise, which is related to the number of quantization bits, antennas, and received signal power in a large scale regime. In addition, the terminal condition of BD-OMP algorithm is derived based on the residual difference of two consecutive iterations, where the expectation of residual difference is the variance of the actual noise. Simulation results demonstrate that the proposed approach can significantly reduce the training overhead for estimating wideband mmWave channel with finite-bit ADCs at the receiver.     

State estimation for linear systems with observations partially corrupted by noise

This paper exploits the fact that any row vector of the observability matrix applied for transforming the state converts the latter to the new state component in the form of some derivative of the output component. Using the same but appropriately chosen vectors for transforming the system with the observation not fully corrupted by white noise we can accurately determine some state components. These vectors create the basis for the l-dimensional subspace of transformation vectors to the new accurately determinable state components. Using this basis the state transformation is constructed which in one step converts the singular linear filtering problem to a nonsingular one with state dimension decreased by l.     

State estimation and filtering in stochastic systems using adequate simplification

The method of order reduction in solving stochastic problems of state estimation and filtering is considered. The method presented concerns the case where mathematical models of objects being studied are defined by systems of nonstationary differential equations. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 98–102, September–October, 1999.     

State estimation for Markovian Jump Linear Systems with bounded disturbances

In this paper, we investigate the state estimation problem for a class of Markovian Jump Linear Systems (MJLSs) in the presence of bounded polyhedral disturbances. A set-membership estimation algorithm is first proposed to find the smallest consistent set of all possible states, which is shown to be expressed by a union of multiple polytopes. The posterior probabilities of the system jumping modes are then estimated by introducing the Lebesgue measure, based on which the optimal point estimate is further provided. Moreover, a similarity relationship for polytopes is defined and an approximate method is presented to calculate the Minkowski sum of polytopes, which can help reduce the computational complexity of the overall estimation algorithm.     

Stability analysis of hybrid stochastic delay differential equations with asynchronous switching and discrete observations

This paper studies the hybrid stochastic delay differential equations (SDDEs) with asynchronous switching and discrete observations. For SDDEs based on discrete observations, there are two methods: The discrete-time approach and the input time delay method. For linear solvable equations, the discrete-time approach is feasible but for unsolvable nonlinear hybrid SDSs, the results of the discrete-time approach have not been discussed. So, it is natural to ask: Is the discrete-time approach still workable for nonlinear hybrid SDSs? This paper focuses on this problem. By using tools of stochastic analysis, constructing Lyapunov functional and using the discrete-time approach, the stability of hybrid SDSs by discrete-time feedback control is obtained. Finally, a numerical example is presented to verify the theoretical result.     

State estimation for linear hybrid systems with periodic jumps and unknown inputs

In order to solve the state estimation problem for linear hybrid systems with periodic jumps and unknown inputs, some hybrid observers are proposed. The proposed observers admit a Luenberger‐like structure and the synthesis is given in terms of linear matrix inequalities (LMIs). Therefore, the proposed observer designs are completely constructive and provide some input‐to‐state stability properties with respect to unknown inputs. It is worth mentioning that the structure of the hybrid observers, as well as the structure of the LMIs, depends on some observability properties of the flow and jump dynamics, respectively. Then, in order to compensate the effect of the unknown inputs, a hybrid sliding‐mode observer is added to the Luenberger‐like observer structure, providing exponential convergence to zero of the state estimation error despite certain class of unknown inputs. The existence of the hybrid observers and the unknown input hybrid observer is guaranteed if and only if the hybrid system is observable and strongly observable, respectively. Some numerical examples illustrate the feasibility of the proposed estimation approach.     

State estimation for multi‐channel stochastic singular systems with multiplicative noise

The state estimation problem for multi‐channel singular systems with multiplicative noise is considered based on singular value decomposition. First, two equivalent reduced order subsystems are obtained via the decomposition. Then, in order to solve the estimation problem, the subsystems are rewritten into a new form. It is noted that the measurement noise here becomes colored noise, which contains the dynamic noise, measurement noise, and multiplicative noise of the original system. In this situation, existing filtering methods cannot be directly applied, so a modified filtering method is given. The recursive algorithm for the state estimation is obtained by the filtering method. In addition, the estimation of dynamic noise is derived via the algorithm. A simulation example is given to show the effectiveness of the proposed algorithm. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

State estimation by the ellipsoid method from continuous-time linear observations

Conclusion We have solved the state observation problem for the continuous system (5), (6) using the ellipsoid method. We have essentially proposed a family of algorithms that depend on the choice of the function . The main distinctive property of the observers considered in this article is that at any instant we know the ellipsoidal set which contains the state being estimated. This provides additional opportunities for controlling the estimation accuracy in execution time. The study was carried out under research project 12.3/69 of the State Committee of Science and Technology of Ukraine. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 108–119, July–August, 1995.     

State estimation of stochastic singular linear systems: convergence and stability

In this paper we present necessary and sufficient conditions of convergence of the generalized Riccati equation and stability for the state estimator developed by Darouach et al. (1993).     

Non-linear estimation with uncertain-delayed observations

This paper considers the state estimation of linear discrete-time systems with uncertain-delayed observations. Using a Gaussian approximation, a sub-optimal, recursive, nonlinear estimator is derived, and by means of a simulation study its performance is compared with that of the best linear filter based on the same observation model.     

A hybrid estimation of distribution algorithm for simulation-based scheduling in a stochastic permutation flowshop

The permutation flowshop scheduling problem (PFSP) is NP-complete and tends to be more complicated when considering stochastic uncertainties in the real-world manufacturing environments. In this paper, a two-stage simulation-based hybrid estimation of distribution algorithm (TSSB-HEDA) is presented to schedule the permutation flowshop under stochastic processing times. To deal with processing time uncertainty, TSSB-HEDA evaluates candidate solutions using a novel two-stage simulation model (TSSM). This model first adopts the regression-based meta-modelling technique to determine a number of promising candidate solutions with less computation cost, and then uses a more accurate but time-consuming simulator to evaluate the performance of these selected ones. In addition, to avoid getting trapped into premature convergence, TSSB-HEDA employs both the probabilistic model of EDA and genetic operators of genetic algorithm (GA) to generate the offspring individuals. Enlightened by the weight training process of neural networks, a self-adaptive learning mechanism (SALM) is employed to dynamically adjust the ratio of offspring individuals generated by the probabilistic model. Computational experiments on Taillard’s benchmarks show that TSSB-HEDA is competitive in terms of both solution quality and computational performance.     

State estimation scheme for nonlinear dynamical systems based on the stochastic approximation

An algorithm for the state estimation of multivariable nonlinear dynamic systems with noisy nonlinear observation systems is investigated on the basis of stochastic approximation procedure.Using an extended version of Dvoretzky's theorem, we derive a sufficient condition that estimation error converges to zero, both in the mean square and with probability one for noise-free multivariable dynamical systems. We then show that our estimation procedure makes the estimation error bounded in the mean square norm for noisy dynamical systems. Some numerical examples are presented for the illustration of the approach mentioned above.     

Adaptive sparse and dense hybrid representation with nonconvex optimization

Sparse representation has been widely used in signal processing, pattern recognition and computer vision etc. Excellent achievements have been made in both theoretical researches and practical applications. However, there are two limitations on the application of classification. One is that sufficient training samples are required for each class, and the other is that samples should be uncorrupted. In order to alleviate above problems, a sparse and dense hybrid representation (SDR) framework has been proposed, where the training dictionary is decomposed into a class-specific dictionary and a non-class-specific dictionary. SDR puts {\ell }_{\mathrm{1}} constraint on the coefficients of class-specific dictionary. Nevertheless, it over-emphasizes the sparsity and overlooks the correlation information in class-specific dictionary, which may lead to poor classification results. To overcome this disadvantage, an adaptive sparse and dense hybrid representation with nonconvex optimization (ASDR-NO) is proposed in this paper. The trace norm is adopted in class-specific dictionary, which is different from general approaches. By doing so, the dictionary structure becomes adaptive and the representationability of the dictionary will be improved. Meanwhile, a nonconvex surrogate is used to approximate the rank function in dictionary decomposition in order to avoid a suboptimal solution of the original rank minimization, which can be solved by iteratively reweighted nuclear norm (IRNN) algorithm. Extensive experiments conducted on benchmark data sets have verified the effectiveness and advancement of the proposed algorithm compared with the state-of-the-art sparse representation methods.     

Robust quantised control of hybrid stochastic systems based on discrete-time state and mode observations

This paper considers robust quantised feedback control for hybrid stochastic systems based on discrete-time state and mode observations. All of the existing results in this area design the quantised feedback control based on continuous observations of the state and mode for all time t ≥ 0. This is the first paper where we propose to use the quantised feedback control based on discrete-time observations of the state and mode. The key reason for this is to reduce the burden of communication by using not only the quantisation (i.e. in the direction of state axis), but also discrete-time observations of state and mode (i.e. in the direction of time axis). Thus, the designed quantised feedback controllers have to be based on discrete-time state and mode observations. Clearly, the new quantised feedback controllers are more practical and lower of cost in practice.     

State estimation for coupled output discrete-time complex network with stochastic measurements and different inner coupling matrices

A state estimation problem is studied for a class of coupled outputs discrete-time networks with stochastic measurements, i.e., the measurements are missing and disturbed with stochastic noise. The considered networks are coupled with outputs rather than states, are coupled with different inner coupling matrices rather than identical inner ones. By using Lyapunov stability theory combined with stochastic analysis, a novel state estimation scheme is proposed to estimate the states of discrete-time complex networks through the available output measurements, where the measurements are stochastic missing and are disturbed with Brownian motions which are caused by data transmission among nodes due to communication unreliability. State estimation conditions are derived in terms of linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the validity of the proposed scheme.