Adaptive Robust Filtering Algorithm for BDS Medium and Long Baseline Three Carrier Ambiguity Resolution

For classical TCAR(three carrier ambiguity resolution)algorithm is affected by ionospheric delay and measurement noise,it is difficult to reliably fix ambiguity at medium and long baselines.An improved TCAR algorithm which takes the influence of ionospheric delay into account and has good adaptive robustness is proposed.On the basis of the non-geometric TCAR model,ionospheric delay is obtained by linearly combining extra-wide-lane with fixed ambiguity,and then wide-lane ambiguity is solved.Solving narrow-lane ambiguity by adaptive robust filtering by constructing optimal combination observation,which can effectively improve the fixed success rate of narrow-lane ambiguity and reduce the adverse effects of gross error.Experimental results show that the improved TCAR algorithm can guarantee a high fixed correct rate of wide-lane ambiguity,effectively improve fixed success rate of narrow-lane ambiguity,and has a good ability to resist gross error.

Study on Robust H_∞ Filtering in Networked Environments

This paper is concerned with the robust H ∞ filter problem for networked environments, which are subject to both transmission delay and packet dropouts randomly. By employing random series which have Bernoulli distributions taking value of 0 or 1, the data transmission model is obtained. Based on state augmentation and stochastic theory, the sufficient condition for robust stability with H ∞ constraints is derived for the filtering error system. The robust filter is designed in terms of feasibility of one certain linear matrix inequality （LMI）, which is formed by adopting matrix congruence transformations. A numerical example is given to show the effectiveness of the proposed filtering method.

Robust L_1 filtering with pole constraint in a disk via parameter-dependent Lyapunov functions

The problem of robust L 1 filtering with pole constraint in a disk for linear continuous polytopic uncertain systems is discussed. The attention is focused on design a linear asymptotically stable filter such that the filtering error system remains robustly stable, and has a L 1 performance constraint and pole constraint in a disk. The new robust L 1 performance criteria and regional pole placement condition are obtained via parameter-dependent Lyapunov functions method. Upon the proposed multiobjective performance criteria and by means of LMI technique, both full-order and reduced-order robust L 1 filter with suitable dynamic behavior can be obtained from the solution of convex optimization problems. Compared with earlier result in the quadratic framework, this approach turns out to be less conservative. The efficiency of the proposed technique is demonstrated by a numerical example.

Robust H-infinity filtering on uncertain systems under sampled measurements

This paper is concerned with the problem of robust H-infinity filtering on uncertain systems under sampled measurements, both continuous disturbance and discrete disturbance are considered in the systems. The parameter uncertainty is assumed to be time-varying norm-bounded. The aim is to design an asymptotically stable filter, using the locally sampled measurements, which ensures both the robust asymptotic stability and a prescribed level of H-infinity performance for the filtering error dynamics for all admissible uncertainties. The derivation process is simplified by introducing auxiliary systems and the sufficient condition for the existence of such a filter is proposed. During the study, the main results were expressed as LMIs by employing various matrix techniques. Using LMI toolbox of Matlab software, it is very convenient to obtain the appropriate filter. Finally, a numerical example shows that the method is effective and feasible.

Robust H_∞ filtering for discrete-time systems with Markovian switching and time-delays

The robust H∞ filtering problem for uncertain discrete-time Markovian jump linear systems with mode- dependent time-delays is investigated. Attention is focused on designing a Markovian jump linear filter that ensures robust stochastic stability while achieving a prescribed H∞ performance level of the resulting filtering error system, for all admissible uncertainties. The key features of the approach include the introduction of a new type of stochastic Lyapunov functional and some free weighting matrix variables. Sufficient conditions for the solvability of this problem are obtained in terms of a set of linear matrix inequalities. Numerical examples are provided to demonstrate the reduced conservatism of the proposed approach.

Robust H-infinity filtering for time-delaysystems with missing measurements:a parameter-dependent approach

Robust H-infinity filtering for a class of uncertain discrete-time linear systems with time delays and missing measurements is studied in this paper. The uncertain parameters are supposed to reside in a convex polytope and the missing measurements are described by a binary switching sequence satisfying a Bernoulli distribution. Our attention is focused on the analysis and design of robust H-infinity filters such that, for all admissible parameter uncertainties and all possible missing measurements, the filtering error system is exponentially mean-square stable with a prescribed H-infinity disturbance attenuation level. A parameter-dependent approach is proposed to derive a less conservative result. Sufficient conditions are established for the existence of the desired filter in terms of certain linear matrix inequalities （LMIs）. When these LMIs are feasible, an explicit expression of the desired filter is also provided. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method.

Robust H_∞ filtering for discrete-time impulsive systems with uncertainty

This paper investigates robust filter design for linear discrete-time impulsive systems with uncertainty under H∞ performance. First, an impulsive linear filter and a robust H∞ filtering problem are introduced for a discrete-time impulsive systems. Then, a sufficient condition of asymptotical stability and H∞ performance for the filtering error systems are provided by the discrete-time Lyapunov function method. The filter gains can be obtained by solving a set of linear matrix inequalities （LMIs）. Finally, a numerical example is presented to show effectiveness of the obtained result.

Krein space approach to robust H_∞ filtering for linear uncertain systems

A novel Krein space approach to robust H∞ filtering for linear uncertain systems is developed. The parameter uncertainty, entering into both states and measurement equations, satisfies an energy-type constraint. Then a Krein space approach is used to tackle the robust H∞ filtering problem. To this end, a new Krein space formal system is designed according to the original sum quadratic constraint （SQC） without introducing any nonzero factors into it and, consequently, the estimate recursion is obtained through the filter gain in Krein space. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.

Robust adaptive UKF based on SVR for inertial based integrated navigation

Aiming at the problem that the traditional Unscented Kalman Filtering(UKF) algorithm can't solve the problem that the measurement covariance matrix is unknown and the measured value contains outliers,this paper proposes a robust adaptive UKF algorithm based on Support Vector Regression(SVR).The algorithm combines the advantages of support vector regression with small samples,nonlinear learning ability and online estimation capability of adaptive algorithm based on innovation.Firstly,the SVR model is trained by using the innovation in the sliding window,and the new innovation is monitored.If the deviation between the estimated innovation and the measured innovation exceeds a given threshold,then measured innovation will be replaced by the predicted innovation,and then the processed innovation is used to calculate the measurement noise covariance matrix using the adaptive estimation algorithm.Simulation experiments and measured data experiments show that SVRUKF is significantly better than the traditional UKF,robust UKF and adaptive UKF algorithms for the case where the covariance matrix is unknown and the measured values have outliers.

Robust H-infinity filter design for uncertaintime-delay singular stochastic systems withMarkovian jump

This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It6 stochastic differential formula, sufficient conditions for the solvability of these problems are obtained. Furthermore, It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.

Modified robust finite-horizon filter for discrete-time systems with parameter uncertainties and missing measurements

A robust finite-horizon Kalman filter is designed for linear discrete-time systems subject to norm-bounded uncertainties in the modeling parameters and missing measurements.The missing measurements were described by a binary switching sequence satisfying a conditional probability distribution,the commonest cases in engineering,such that the expectation of the measurements could be utilized during the iteration process.To consider the uncertainties in the system model,an upperbound for the estimation error covariance was obtained since its real value was unaccessible.Our filter scheme is on the basis of minimizing the obtained upper bound where we refer to the deduction of a classic Kalman filter thus calculation of the derivatives are avoided.Simulations are presented to illustrate the effectiveness of the proposed approach.

Adaptive robust cubature Kalman filtering for satellite attitude estimation

This paper is concerned with the adaptive robust cubature Kalman filtering problem for the case that the dynamics model error and the measurement model error exist simultaneously in the satellite attitude estimation system. By using Hubel-based robust filtering methodology to correct the measurement covariance formulation of cubature Kalman filter, the proposed filtering algorithm could effectively suppress the measurement model error. To further enhance this effect and reduce the impact of the dynamics model error, two different adaptively robust filtering algorithms,one with the optimal adaptive factor based on the estimated covariance matrix of the predicted residuals and the other with multiple fading factors based on strong tracking algorithm, are developed and applied for the satellite attitude estimation. The quaternion is employed to represent the global attitude parameter, and three-dimensional generalized Rodrigues parameters are introduced to define the local attitude error. A multiplicative quaternion error is derived from the local attitude error to maintain quaternion normalization constraint in the filter. Simulation results indicate that the proposed novel algorithm could exhibit higher accuracy and faster convergence compared with the multiplicative extended Kalman filter, the unscented quaternion estimator, and the adaptive robust unscented Kalman filter.

New approaches to robust l2-l∞ and H∞ filtering for uncertain discrete-time systems

The problems of robust I2-I∞ and H∞ filtering for discrete-time systems with parameter uncertainty residing in a polytope are investigated in this paper. The filtering strategies are based on new robust performance criteria derived from a new result of parameter-dependent Lyapunov stability condition, which exhibit less conservativeness than previous results in the quadratic framework. The designed filters guaranteeing a prescribed I2-I∞ or H∞ noise attenuation level can be obtained from the solution of convex optimization problems, which can be solved via efficient interior point methods. Numerical examples have shown that the filter design procedures proposed in this paper are much less conservative than earlier results.

A two-step robust adaptive filtering algorithm for GNSS kinematic precise point positioning

In kinematic navigation and positioning,abnormal observations and kinematic model disturbances are one of the key factors affecting the stability and reliability of positioning performance.Generally,robust adaptive filtering algorithm is used to reduce the influence of them on positioning results.However,it is difficult to accurately identify and separate the influence of abnormal observations and kinematic model disturbances on positioning results,especially in the application of kinematic Precise Point Positioning(PPP).This has always been a key factor limiting the performance of conventional robust adaptive filtering algorithms.To address this problem,this paper proposes a two-step robust adaptive filtering algorithm,which includes two filtering steps:without considering the kinematic model information,the first step of filtering only detects the abnormal observations.Based on the filtering results of the first step,the second step makes further detection on the kinematic model disturbances and conducts adaptive processing.Theoretical analysis and experiment results indicate that the two-step robust adaptive filtering algorithm can further enhance the robustness of the filtering against the influence of abnormal observations and kinematic model disturbances on the positioning results.Ultimately,improvement of the stability and reliability of kinematic PPP is significant.

Low-cost adaptive square-root cubature Kalman filter forsystems with process model uncertainty

A novel low-cost adaptive square-root cubature Kalmanfilter （LCASCKF） is proposed to enhance the robustness of processmodels while only increasing the computational load slightly.It is well-known that the Kalman filter cannot handle uncertainties ina process model, such as initial state estimation errors, parametermismatch and abrupt state changes. These uncertainties severelyaffect filter performance and may even provoke divergence. Astrong tracking filter （STF）, which utilizes a suboptimal fading factor,is an adaptive approach that is commonly adopted to solvethis problem. However, if the strong tracking SCKF （STSCKF）uses the same method as the extended Kalman filter （EKF） tointroduce the suboptimal fading factor, it greatly increases thecomputational load. To avoid this problem, a low-cost introductorymethod is proposed and a hypothesis testing theory is applied todetect uncertainties. The computational load analysis is performedby counting the total number of floating-point operations and it isfound that the computational load of LCASCKF is close to that ofSCKF. Experimental results prove that the LCASCKF performs aswell as STSCKF, while the increase in computational load is muchlower than STSCKF.

H_-/H_∞ fault detection filter design for interval time-varying delays switched systems

The problem of the robust fault detection filter design for time-varying delays switched systems is considered in the framework of mixed H-/H∞. Firstly, the weighted H∞ performance index is utilized as the robustness performance, and the H- index is used as the sensitivity performance for obtaining the robust fault detection filter. Then a novel multiple Lyapunov-Krasovskii function is proposed for deriving sufficient existence conditions of the robust fault detection filter based on the average dwell time technique. By introducing slack matrix variable, the coupling between the Lyapunov matrix and system matrix is removed, and the conservatism of results is reduced. Based on the robust fault detection filter, residual is generated and evaluated for detecting faults. In addition, the results of this paper are dependent on time delays,and represented in the form of linear matrix inequalities. Finally,the simulation example verifies the effectiveness of the proposed method.

Performance Analysis of GNSS/MIMU Tight Fusion Positioning Model with Complex Scene Feature Constraints

In order to meet the requirements of high-precision vehicle positioning in complex scenes,an observation noise adaptive robust GNSS/MIMU tight fusion model based on the gain matrix is proposed considering static zero speed,non-integrity,attitude,and odometer constraint models.In this model,the robust equivalent gain matrix is constructed by the IGG-Ⅲmethod to weaken the influence of gross error,and the on-line adaptive update of observation noise matrix is carried out according to the change of actual observation environment,so as to improve the solution performance of filtering system and realize high-precision position,attitude and velocity measurement when GNSS signal is unlocked.A real test on a road over 600 km demonstrates that,in about 100 km shaded environment,the fixed rate of GNSS ambiguity resolution in the shaded road is 10%higher than that of GNSS only ambiguity resolution.For all the test,the positioning accuracy can reach the centimeter level in an open environment,better than 0.6 m in the tree shaded environment,better than 1.5 m in the three-dimensional traffic environment,and can still maintain a positioning accuracy of 0.1 m within 10 s when the satellite is unlocked in the tunnel scene.The proposal and verification of the algorithm model show that low-cost MIMU equipment can still achieve high-precision positioning when there are scene feature constraints,which can meet the problem of high-precision vehicle navigation and location in the urban complex environment.

Quantized robust H-two filtering for Markovian jump linear systems over networks with nonaccessible mode information

This paper is concerned with the problems of H-two filtering for discrete-time Markovian jump linear systems subject to logarithmic quantization. We assume that only the output of the system is available, and therefore the mode information is nonaccessible. In this paper, a mode-independent quantized H-two filter is designed such that filter error system is stochastically stable. To this end, sufficient conditions for the existence of an upper bound of H-two norm are presented in terms of linear matrix inequalities. Considering uncertainty of system matrices, a robust H-two filter is designed. The proposed method is also applicable to cover the case where the transition probability matrix is not exactly known but belongs to a given polytope. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed approach.

Anonymous crowdsourcing-based WLAN indoor localization

In order to solve the problem of location privacy under big data and improve the user positioning experience,a new concept of anonymous crowdsourcing-based WLAN indoor localization is proposed by employing the Micro-Electro-Mechanical System(MEMS)motion sensors as well as WLAN module in off-the-shelf smartphones.First of all,the crowdsourced motion traces with similar Received Signal Strength(RSS)sequences are assembled into a motion graph.Second,the mobility map is constructed according to traces segmentation and clustering.Third,the pixel template matching is adopted to physically label the pre-constructed mobility map.Finally,the robust Extended Kalman Filter(EKF)is designed to perform localization by matching the newly-collected RSS measurements against the mobility map.The extensive experimental results show that the proposed approach is capable of constructing a physically-labeled mobility map from the sporadically-collected crowdsourced motion traces as well as achieving satisfactory localization accuracy in a cost-efficient manner.

Regularized Robust Filter for Spacecraft Attitude Determination

A modified regularized robust filter is proposed for spacecraft attitude determination in the presence of relative misalignment of attitude sensors. The filter is designed to minimize the worst-possible residual norm on condition that there is parametric uncertainty in the measurement model. The weighting matrix of the residual norm is designed to minimize the upper bound of the estimation error variance. The performance of the proposed attitude determination robust filter is illustrated with the use of real test data from a real three-floated gyroscope. Simulation results demonstrate that the attitude estimation accuracy is improved by using the proposed algorithm.