Recursive weighted least squares estimation algorithm based on minimum model error principle

Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.

Recursive estimation algorithms for power controls of wireless communication networks

Power control problems for wireless communication networks are investigated in direct-sequence codedivision multiple-access （DS/CDMA） channels. It is shown that the underlying problem can be formulated as a constrained optimization problem in a stochastic framework. For effective solutions to this optimization problem in real time, recursive algorithms of stochastic approximation type are developed that can solve the problem with unknown system components. Under broad conditions, convergence of the algorithms is established by using weak convergence methods.

Neuro-fuzzy system modeling based on automatic fuzzy clustering

A neuro-fuzzy system model based on automatic fuzzy dustering is proposed. A hybrid model identification algorithm is also developed to decide the model structure and model parameters. The algorithm mainly includes three parts：1） Automatic fuzzy C-means （AFCM）, which is applied to generate fuzzy rttles automatically, and then fix on the size of the neuro-fuzzy network, by which the complexity of system design is reducesd greatly at the price of the fitting capability; 2） R.ecursive least square estimation （RLSE）. It is used to update the parameters of Takagi-Sugeno model, which is employed to describe the behavior of the system;3） Gradient descent algorithm is also proposed for the fuzzy values according to the back propagation algorithm of neural network. Finally,modeling the dynamical equation of the two-link manipulator with the proposed approach is illustrated to validate the feasibility of the method.

Cone Bearing Estimation Utilizing a Hybrid HMM and IFM Smoother Filter Formulation

Cone penetration testing (CPT) is a widely used geotechnical engineering in-situ test for mapping soil profiles and assessing soil properties. In CPT, a cone on the end of a series of rods is pushed into the ground at a constant rate and resistance to the cone tip is measured (qm). The qm values are utilized to characterize the soil profile. Unfortunately, the measured cone tip resistance is blurred and/or averaged which can result in the distortion of the soil profile characterization and the inability to identify thin layers. This paper outlines a novel and highly effective algorithm for obtaining cone bearing estimates qt from averaged or smoothed qm measurements. This qt optimal filter estimation technique is referred to as the qtHMM-IFM algorithm and it implements a hybrid hidden Markov model and iterative forward modelling technique. The mathematical details of the qtHMM-IFM algorithm are outlined in this paper along with the results from challenging test bed. The test bed simulations have demonstrated that the qtHMM-IFM algorithm can derive accurate qt values from challenging averaged qm profiles. This allows for greater soil resolution and the identification and quantification of thin layers in a soil profile.

A PILOT-ASSISTED NON-CYCLIC PREFIXED MIMO-SCFDE SYSTEM

A non-Cyclic Prefixed Multiple-Input Multiple-Output Single-Carrier Frequency-Domain Equalization (non-CP MIMO-SCFDE) system based on a recursive algorithm of Joint Channel Es- timation and Data Detection (recursive-JCEDD) is proposed in this paper. Unlike the traditional CP MIMO-SCFDE system, the transmitted block of the proposed system is designed in the way that block-type pilot sequences and Single-Carrier (SC) information sequences have been arranged alter- nately without any cyclic prefix before each SC information sequence. Moreover, a recursive-JCEDD algorithm based on interference cancellation is proposed for the corresponding receivers. Simulation results show that the Bit Error Rate (BER) of the proposed system based on the recursive-JCEDD algorithm is lower than traditional CP MIMO-SCFDE or MIMO-OFDM with channel estimation for more than 0.5 dB.

A note on constrained M-estimation and its recursive analog in multivariate linear regression models

In this paper, the constrained M-estimation of the regression coefficients and scatter parameters in a general multivariate linear regression model is considered. Since the constrained M-estimation is not easy to compute, an up-dating recursion procedure is proposed to simplify the computation of the estimators when a new observation is obtained. We show that, under mild conditions, the recursion estimates are strongly consistent. In addition, the asymptotic normality of the recursive constrained M-estimators of regression coefficients is established. A Monte Carlo simulation study of the recursion estimates is also provided. Besides, robustness and asymptotic behavior of constrained M-estimators are briefly discussed.

Recursive identification for multidimensional ARMA processes with increasing variances

In time series analysis, almost all existing results are derived for the case where the driven noise {wn} in the MA part is with bounded variance （or conditional variance）. In contrast to this, the paper discusses how to identify coefficients in a multidimensional ARMA process with fixed orders, but in its MA part the conditional moment E（｜｜wn｜｜^β｜Fn-1）, β 〉 2 is possible to grow up at a rate of a power of logn. The wellknown stochastic gradient （SG） algorithm is applied to estimating the matrix coefficients of the ARMA process, and the reasonable conditions are given to guarantee the estimate to be strongly consistent.

RECURSIVE METH0D FOR ARMA MODEL ESTIMATION (Ⅱ)

In this paper a new recursive method for ARMA model estimation is given. Same as in [1], theorder's estimator is strongly consistent, and the parameter's estimators defer to CLT and LILunder a natural condition. Compared with the previous metheds suggested by Hannan & Kavalieris(1984), Wang Shouren & Chen Zhaoguo (1985) and Franke (1985), this methed has some advantages:the amount of calculat on work is smaller, the minimum-phase property of coeffcient estimators canbe guaranteed,the BAN estimators for MA or AR model can be obtained directly,and the simulationshows that this method is more accurate in estimating the order and parameters.

Real-time fault detection method based on belief rule base for aircraft navigation system

Real-time and accurate fault detection is essential to enhance the aircraft navigation system’s reliability and safety. The existent detection methods based on analytical model draws back at simultaneously detecting gradual and sudden faults. On account of this reason, we propose an online detection solution based on non-analytical model. In this article, the navigation system fault detection model is established based on belief rule base （BRB）, where the system measuring residual and its changing rate are used as the inputs of BRB model and the fault detection function as the output. To overcome the drawbacks of current parameter optimization algorithms for BRB and achieve online update, a parameter recursive estimation algorithm is presented for online BRB detection model based on expectation maximization （EM） algorithm. Furthermore, the proposed method is verified by navigation experiment. Experimental results show that the proposed method is able to effectively realize online parameter evaluation in navigation system fault detection model. The output of the detection model can track the fault state very well, and the faults can be diagnosed in real time and accurately. In addition, the detection ability, especially in the probability of false detection, is superior to offline optimization method, and thus the system reliability has great improvement.

A Two-Dimensional Approach to Iterative Learning Control with Randomly Varying Trial Lengths

In this paper,iterative learning control(ILC)is considered to solve the tracking problem of time-varying linear stochastic systems with randomly varying trial lengths.Using the two-dimensional Kalman filtering technique,the authors can establish a recursive framework for designing the learning gain matrix along both time and iteration axes by optimizing the trace of input error covariance matrix.It is strictly proved that the input error converges to zero asymptotically in mean square sense and thus the tracking error covariance converges.The extensions to that prior distribution of nonuniform trial lengths is unknown are also investigated with an asymptotical estimation method.Numerical simulations are provided to verify the effectiveness of the proposed framework.

Indoor localization for pedestrians with real-time capability using multi-sensor smartphones

The localization of persons or objects usually refers to a position determined in a spatial reference system.Outdoors,this is usually accomplished with Global Navigation Satellite Systems(GNSS).However,the automatic positioning of people in GNSS-free environments,especially inside of buildings(indoors)poses a huge challenge.Indoors,satellite signals are attenuated,shielded or reflected by building components(e.g.walls or ceilings).For selected applications,the automatic indoor positioning is possible based on different technologies(e.g.WiFi,RFID,or UWB).However,a standard solution is still not available.Many indoor positioning systems are only suitable for specific applications or are deployed under certain conditions,e.g.additional infrastructures or sensor technologies.Smartphones,as popular cost-effective multi-sensor systems,is a promising indoor localization platform for the mass-market and is increasingly coming into focus.Today’s devices are equipped with a variety of sensors that can be used for indoor positioning.In this contribution,an approach to smartphone-based pedestrian indoor localization is presented.The novelty of this approach refers to a holistic,real-time pedestrian localization inside of buildings based on multisensor smartphones and easy-to-install local positioning systems.For this purpose,the barometric altitude is estimated in order to derive the floor on which the user is located.The 2D position is determined subsequently using the principle of pedestrian dead reckoning based on user's movements extracted from the smartphone sensors.In order to minimize the strong error accumulation in the localization caused by various sensor errors,additional information is integrated into the position estimation.The building model is used to identify permissible(e.g.rooms,passageways)and impermissible(e.g.walls)building areas for the pedestrian.Several technologies contributing to higher precision and robustness are also included.For the fusion of different linear and non-linear data,an advanced algorithm based on the Sequential Monte Carlo method is presented.

A New Approach to State Estimation for Uncertain Linear Systems in a Moving Horizon Estimation Setting

This paper addresses the state estimation problem for linear systems with additive uncertainties in both the state and output equations using a moving horizon approach. Based on the full information estimation setting and the game-theoretic approach to the H∞filtering, a new optimization-based estimation scheme for uncertain linear systems is proposed, namely the H∞-full information estimator, H∞-FIE in short. In this formulation, the set of processed data grows with time as more measurements are received preventing recursive formulations as in Kalman filtering. To overcome the latter problem, a moving horizon approximation to the H∞-FIE is also presented, the H∞-MHE in short. This moving horizon approximation is achieved since the arrival cost is suitably defined for the proposed scheme. Sufficient conditions for the stability of the H∞-MHE are derived. Simulation results show the benefits of the proposed scheme when compared with two H∞filters and the well-known Kalman filter.

NONPARAMETRIC APPROACH TO IDENTIFYING NARX SYSTEMS

This paper considers identification of the nonlinear autoregression with exogenous inputs(NARX system).The growth rate of the nonlinear function is required be not faster than linear withslope less than one.The value of f(·) at any fixed point is recursively estimated by the stochasticapproximation (SA) algorithm with the help of kernel functions.Strong consistency of the estimatesis established under reasonable conditions,which,in particular,imply stability of the system.Thenumerical simulation is consistent with the theoretical analysis.