Robust Kalman Filter Research Articles

Robust multiple model adaptive estimation for spacecraft autonomous navigation

This paper focuses on the development of a robust multiple model adaptive estimation (RMMAE) algorithm and its performance analysis. The main goal of this work is to enhance the robustness of the estimator against the model parameter identification error. A proof is provided that shows the convergence property of the proposed algorithm. Further analysis shows that the RMMAE algorithm guarantees a bounded energy gain from the model parameter identification error to the estimation error. The performance of the RMMAE is evaluated via simulations for spacecraft autonomous navigation. Simulation results demonstrate the effectiveness of the new algorithm compared with the extended Kalman filter (EKF), the unscented Kalman filter (UKF), the robust Kalman filter (RKF) and the multiple model adaptive estimation (MMAE).

Non-parametric location estimation in rough wireless environments for wireless sensor network

With the development of microelectronics, wireless communication and micro-electro-mechanical systems technologies, wireless sensor network (WSN) has received considerable attention. The location information is critical for application of WSN. The high accuracy localization result can be achieved when the propagation environment is line of sight. However, it is decreased extremely in non-line of sight (NLOS) environment. NLOS propagation which affects the accuracy of mobile localization is one of the most important challenges for WSN. In this paper, we propose a method to alleviate the influence of the NLOS error using the improved Kalman filter based on Gaussian mixture distributions (IKF-GMD). The NLOS detection is firstly introduced to identify the propagation condition of the beacon node. For the NLOS measurements, GMD algorithm is proposed to estimate the mean and variance of the measurements and multiple modes combination method is proposed to mitigate the NLOS error. The IKF-GMD approach can effectively mitigate the NLOS error and does not assume any statistical knowledge of the NLOS error. Simulation and experiment results demonstrate that the performance of the proposed IKF-GMD algorithm outperforms the Kalman filter and robust Kalman filter methods.

Robust cubature Kalman filter target tracking algorithm based on genernalized M-estiamtion

Target tracking has been introduced as a key point in the physical applications, such as passive sonar and chaotic communication etc. It is typically a nonlinear filtering problem to estimate the position and the velocity of a target from noise-corrupted measurements. Some approaches have been proposed for the problem, such as the extended Kalman filter, the unscented Kalman filter, and the cubature Kalman filter (CKF). However, they are effective only in the Gaussian and white assumption for the measurements. Actually, the measurements are easily polluted by the measurement outliers in practice. The measurement outliers may lead to inaccurate performance due to non-symmetrical or non-Gaussian property. In order to cope with the measurement outliers in nonlinear target tracking system, a robust filtering algorithm called the M-estimation based robust cubature Kalman filter (MR-CKF) is proposed for the target tracking problem. Firstly, the nonlinear measurement equation is transformed into an equivalently linear form according to the orthogonal vector, and then the Gaussian extremal function of the target tracking can be obtained by the constrained total least square (CTLS) criterion. By employing the Huber's robust score function, the Gaussian extremal function is further rendered into a robust extremal function, thus the generalized M-estimation can be introduced to the CKF without linearization approximation. The only difference between the Gaussian extremal function and the robust extremal function is the weight matrix, implying that the CKF solution framework does not change and the virtues of both the CKF and M-estimation can be fully utilized such as derivative-free, high accuracy and robust performance. Furthermore, an improved Huber equivalent weight function is designed for the MR-CKF based on the Mahalanobis distance. The outliers' judge threshold is determined according to the confidence level of Chi-square distribution and improper empirical value of the Huber's method can be avoided. In addition, the improved Huber weight function reduces weights of small outliers and removes large outliers, and this is more robust and reasonable than the Huber's method. Moreover, the statistical information of outliers is also not required. Theoretical analysis and numerical results show that the proposed filtering algorithm can improve the accuracy and robustness than the conventional robust algorithms.

Gravity Matching Aided Inertial Navigation Technique Based on Marginal Robust Unscented Kalman Filter

This paper is concerned with the topic of gravity matching aided inertial navigation technology using Kalman filter. The dynamic state space model for Kalman filter is constructed as follows: the error equation of the inertial navigation system is employed as the process equation while the local gravity model based on 9-point surface interpolation is employed as the observation equation. The unscented Kalman filter is employed to address the nonlinearity of the observation equation. The filter is refined in two ways as follows. The marginalization technique is employed to explore the conditionally linear substructure to reduce the computational load; specifically, the number of the needed sigma points is reduced from 15 to 5 after this technique is used. A robust technique based on Chi-square test is employed to make the filter insensitive to the uncertainties in the above constructed observation model. Numerical simulation is carried out, and the efficacy of the proposed method is validated by the simulation results.

A new noise covariance matrix estimation method of Kalman filter for satellite clock errors

The satellite clock plays a key role in the global navigation satellite system (GNSS). The accuracy of GNSS and its applications depend on the quality of the satellite clock. Therefore, precisely estimating and predicting the satellite clock is an important issue in the fields of GNSS and its application. As an optimal estimation algorithm, Kalman filter has been used to estimate and predict the satellite clock. However, in a conventional Kalman filter algorithm, the noise covariance matrices of satellite clock need to be predetermined, which restricts its further applications since the noise covariance matrices, especially the process noise covariance matrix, are usually unknown in the real cases. With inappropriate noise covariance matrices, the state estimation of conventional Kalman filter is suboptimal. To cope with this problem, a new noise covariance matrix estimation method of Kalman filter is proposed, and then we apply it to the problem of satellite clock estimation and prediction. Considering the fact that the process noise covariance matrix depends on the unknown noise parameters, the problem of estimating process noise covariance matrix can be solved by estimating the unknown noise parameters. First, the correlation between the Kalman innovations is used to establish a linear relationship with the unknown noise parameters. Then the unknown parameters can be estimated by least-squares estimation. Finally, the satellite clock can be estimated and predicted with the estimated noise parameters. In the new method, no prior information about the noise parameters is needed. Even with some extreme prior noise parameters, the new method can also work very well and has good convergence properties. For comparison, we conduct two experiments using the new method and the adaptively robust Kalman filter with classified adaptive factors based on opening windows separately, both results are consistent with each other very well, which verifies the correctness and effectiveness of this new method.

Robust Centralized Fusion Steady-State Kalman Filter with Uncertain Parameters and Measurement Noise Variances

For the linear discrete time multisensor system with uncertain model parameters and measurement noise variances, the centralized fusion robust steady-state Kalman filter is presented by a new approach of compensating the parameter uncertainties by a fictitious noise. Based on the Lyapunov equation, it is proved that for given fictitious noise variance, the variances of the actual filtering errors have a less-conservative upper bound when the uncertainty of parameters is limited in a sufficiently small region which is called as robust region of the parameter uncertainties. Further, a simulation example demonstrates how to search the robust region. It is also proved that the robust accuracy of the centralized fusion robust steady-state Kalman filter is higher than that of each local robust Kalman filter. A simulation example shows its effectiveness.

Robust Sequential Covariance Intersection Fusion Kalman Filtering over Multi-agent Sensor Networks with Measurement Delays and Uncertain Noise Variances

This paper deals with the problem of designing robust sequential covariance intersection (SCI) fusion Kalman filter for the clustering multi-agent sensor network system with measurement delays and uncertain noise variances. The sensor network is partitioned into clusters by the nearest neighbor rule. Using the minimax robust estimation principle, based on the worst-case conservative sensor network system with conservative upper bounds of noise variances, and applying the unbiased linear minimum variance (ULMV) optimal estimation rule, we present the two-layer SCI fusion robust steady-state Kalman filter which can reduce communication and computation burdens and save energy sources, and guarantee that the actual filtering error variances have a less-conservative upper-bound. A Lyapunov equation method for robustness analysis is proposed, by which the robustness of the local and fused Kalman filters is proved. The concept of the robust accuracy is presented and the robust accuracy relations of the local and fused robust Kalman filters are proved. It is proved that the robust accuracy of the global SCI fuser is higher than those of the local SCI fusers and the robust accuracies of all SCI fusers are higher than that of each local robust Kalman filter. A simulation example for a tracking system verifies the robustness and robust accuracy relations.

Two-level Robust Measurement Fusion Kalman Filter for Clustering Sensor Networks

This paper investigates the distributed fusion Kalman filtering over clustering sensor networks. The sensor network is partitioned as clusters by the nearest neighbor rule and each cluster consists of sensing nodes and cluster-head. Using the minimax robust estimation principle, based on the worst-case conservative system with the conservative upper bounds of noise variances, two-level robust measurement fusion Kalman filter is presented for the clustering sensor network systems with uncertain noise variances. It can significantly reduce the communication load and save energy when the number of sensors is very large. A Lyapunov equation approach for the robustness analysis is presented, by which the robustness of the local and fused Kalman filters is proved. The concept of the robust accuracy is presented, and the robust accuracy relations among the local and fused robust Kalman filters are proved. It is proved that the robust accuracy of the two-level weighted measurement fuser is equal to that of the global centralized robust fuser and is higher than those of each local robust filter and each local weighted measurement fuser. A simulation example shows the correctness and effectiveness of the proposed results.

Object Tracking with Robust Kalman Filter Based on Convex Optimization

Tracking moving objects with high accuracy is an important problem in fields of robot vision, video signal processing and pattern recognition. One of the widely used object tracking methods is Kalman filter. Conventional Kalman filter has a basic assumption that the noise obeys Gaussian distribution. However, in practice, the observed data also suffers from non-stationary sparse noise, which may cause performance deterioration for conventional Kalman filter. In this paper, we propose a robust Kalman filter based on convex optimization to remove not only the Gaussian noise but also such kind of sparse noise. Formulated as a convex optimization problem, the robust Kalman filter can be solved efficiently by Interior Point Method. Numerical results show that the proposed method is robust against sparse noise and achieves better performance while tracking objects under sparse noisy condition.

Improved robust finite-horizon Kalman filtering for uncertain networked time-varying systems

A novel robust finite-horizon Kalman filter is presented for networked linear time-varying systems with norm-bounded parameter uncertainty whether, or not, the data packets in the network are time-stamped. Measured data loss and latency in the communication link are both described by a Bernoulli distributed random sequence. Then, a two-stage recursive structure is employed for the robust Kalman filter. The filter parameters are determined such that the covariance of the estimation error does not exceed the prescribed upper bound. New augmented state-space model is employed to derive a procedure for computation of the filter parameters. The main novelty of the paper is to use the measurement reorganization technique for the robust Kalman filter design where the observation dropout and delay are both modeled by a stochastic process. Finally, the simulation results confirm the outperformance of the proposed robust Kalman filter compared to the rival methods in the literature.

Adaptive robust Kalman filtering for precise point positioning

The optimality of precise point postioning (PPP) solution using a Kalman filter is closely connected to the quality of the a priori information about the process noise and the updated mesurement noise, which are sometimes difficult to obtain. Also, the estimation enviroment in the case of dynamic or kinematic applications is not always fixed but is subject to change. To overcome these problems, an adaptive robust Kalman filtering algorithm, the main feature of which introduces an equivalent covariance matrix to resist the unexpected outliers and an adaptive factor to balance the contribution of observational information and predicted information from the system dynamic model, is applied for PPP processing. The basic models of PPP including the observation model, dynamic model and stochastic model are provided first. Then an adaptive robust Kalmam filter is developed for PPP. Compared with the conventional robust estimator, only the observation with largest standardized residual will be operated by the IGG III function in each iteration to avoid reducing the contribution of the normal observations or even filter divergence. Finally, tests carried out in both static and kinematic modes have confirmed that the adaptive robust Kalman filter outperforms the classic Kalman filter by turning either the equivalent variance matrix or the adaptive factor or both of them. This becomes evident when analyzing the positioning errors in flight tests at the turns due to the target maneuvering and unknown process/measurement noises.

Robust Kalman filter based on a fuzzy GARCH model to forecast volatility using particle swarm optimization

Stock market volatility comprises complex characteristics of time-varying irregular behavior and asymmetric clustering properties with respect to both positive and negative stock index returns. In this paper, we present a fuzzy-GARCH model to analyze asymmetric clustering properties and a robust Kalman filter to address the problem of the time-varying irregular behavior of volatility. In our approach, we first use a fuzzy system to analyze clustering regimes based on stock market index returns. Second, we use the clustering regimes of the first stage to set up generalized autoregressive conditional heteroskedasticity (GARCH) models and reformulated state space. Finally, we use a robust Kalman filter to reduce time-varying complexity when forecasting volatility. The proposed method is based on state space and joins the parameters of membership functions and GARCH models that are highly complex and nonlinear. We present an iterative algorithm based on particle swarm optimization to estimate parameters of the membership functions and GARCH models. The effectiveness of the approach is demonstrated on stock market data from the Taiwan Stock Exchange Weighted Index (Taiwan), Hang Seng Index (Hong Kong), and Japan Nikkei 225 Index (Japan). From the simulation results, we determine that forecasting of out-of-sample volatility performance is significantly improved when the GARCH model considers both asymmetric effect and robust adaptive forecasting.

Adaptive Huber-Based Filter for Hypersonic Cruise Vehicle Navigation

The navigation for hypersonic cruise vehicle (HCV) is a challenging task because of the complex vehicle dynamic and sensor measurement noise it suffered. This paper proposes a kind of adaptive robust Kalman filter using Mahalanobis distance for HCV navigation. The innovation-based adaptive estimation is discussed first. Based on Mahalanobis distance theory, a kind of robust covariance matrix estimation method is used to modify the innovation-based adaptive Kalman filter. Considering that the vehicle maneuver characteristics and noise statistics parameters varies during different periods, dual-frequency tuning for unknown noise statistics is designed based on this. The algorithm proposed by this paper is applied to hypersonic cruise vehicle navigation. Simulation has been made to verify the performance of the new algorithm according to HCV flight profile and characteristics; both Gaussian and non-Gaussian simulation are included.

Robust square-root cubature Kalman filter based on Huber’s M-estimation methodology

In practical engineering applications, the performance of the standard cubature Kalman filter (CKF) and its square-root version can be severely degraded due to outliers in measurement or contaminated distribution. In order to address the problem, a robust version of CKF is presented using Huber’s M-estimation methodology and square-root filtering framework. By making use of the Huber technique to reformulate the measurement update of CKF in square-root filtering framework, the proposed filter can exhibit robustness and numerical stability against deviation from Gaussian distribution assumption. In simulation tests, four versions of CKF—the standard, the square-root, Huber-based, and the proposed are evaluated in terms of estimation accuracy, numerical stability, and robustness under Gaussian and non-Gaussian distribution. The results are concluded that the square-root version outperforms the others under Gaussian distribution, whereas the proposed filter has improved performance in maintaining the robustness and numerical stability under non-Gaussian distribution. The investigated robust framework can be extended to other Gaussian filtering algorithms and the study is expected to facilitate applications of CKF in practical engineering as well.

Linear recursive passive target tracking filter for cooperative sea‐skimming anti‐ship missiles

This study addresses the passive target tracking problem using the range difference (RD) information measured by sea-skimming anti-ship missiles. Apart from the conventional non-linear filtering approaches, the RD-based passive target tracking problem is newly formulated within the framework of the recently developed non-conservative robust Kalman filter (NCRKF). By applying NCRKF, the authors are able to cope with the performance degradation in the process of adopting linear measurement model as well as to determine the desirable missile formation in view of target tracking performance. Moreover, the proposed filter might be adequate for the real-time multiple-missile applications for its linear recursive structure. Through the simulations for a typical missile homing scenario, it is shown that the proposed scheme could provide faster convergence rate and better target tracking performance than the previous methods.

Robust Centralized Fusion Kalman Filters with Uncertain Noise Variances

This paper studies the problem of the designing the robust local and centralized fusion Kalman filters for multisensor system with uncertain noise variances. Using the minimax robust estimation principle, the centralized fusion robust time-varying Kalman filters are presented based on the worst-case conservative system with the conservative upper bound of noise variances. A Lyapunov approach is proposed for the robustness analysis and their robust accuracy relations are proved. It is proved that the robust accuracy of robust centralized fuser is higher than those of robust local Kalman filters. Specially, the corresponding steady-state robust local and centralized fusion Kalman filters are also proposed and the convergence in a realization between time-varying and steady-state Kalman filters is proved by the dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A Monte-Carlo simulation example shows the robustness and accuracy relations. DOI : http://dx.doi.org/10.11591/telkomnika.v12i6.5490 Full Text: PDF

Distributed State Estimation for Discrete-Time Nonlinear System with Unknown Inputs

This paper investigated the problem of distributed estimation for a class of discrete-time nonlinear systems with unknown inputs in a sensor network. A modification scheme to the derivative-free versions of nonlinear robust two-stage Kalman filter (DNRTSKF) is first introduced based on recently developed cubature Kalman filter (CKF) technique. Afterward, a novel information filter is proposed by expressing the recursion in terms of the information matrix based upon DNRTSKF. In the end, distributed DNRTSKF is developed by applying a new information consensus filter to diffuse local statistics over the entire sensor network. In the implementation procedure, each sensor node only fuses the local observation instead of the global information and updates its local information state and matrix from its neighbors' estimates using Average-Consensus Algorithm. Simulation results illustrate that the proposed distributed filter reveals the performance comparable to centralized DNRTSKF and better than distributed CKF.

Robust Estimation Fusion in Wireless Senor Networks with Outliers and Correlated Noises

This paper addresses the problem of estimation fusion in a distributed wireless sensor network (WSN) under the following conditions: (i) sensor noises are contaminated by outliers or gross errors; (ii) process noise and sensor noises are correlated; (iii) cross-correlation among local estimates is unknown. First, to attack the correlation and outliers, a correlated robust Kalman filtering (coR2KF) scheme with weighted matrices on innovation sequences is introduced as local estimator. It is shown that the proposed coR2KF takes both conventional Kalman filter and robust Kalman filter as a special case. Then, a novel version of our internal ellipsoid approximation fusion (IEAF) is used in the fusion center to handle the unknown cross-correlation of local estimates. The explicit solution to both fusion estimate and corresponding covariance is given. Finally, to demonstrate robustness of the proposed coR2KF and the effectiveness of IEAF strategy, a simulation example of tracking a target moving on noisy circular trajectories is included.

Consensus Target Tracking in Switching Wireless Sensor Networks with Outliers

The problem of consensus-based distributed tracking in wireless sensor networks (WSNs) with switching network topologies and outlier-corrupted sensor observations is considered. First, to attack the outlier-corrupted measurements, a robust Kalman filtering (RKF) scheme with weighted matrices on innovation sequences is introduced. The proposed RKF possesses high robustness against outliers while having similar computational burden as traditional Kalman filter. Then, each node estimates the network-wide agreement on target state using only communications between one-hop neighbors. In order to improve the convergent speed of the consensus filter in case of switching topologies, an adaptive weight update strategy is proposed. Note that the proposed algorithm relaxes the requirement of Gaussian noise statistics in contrast to the decentralized/distributed Kalman filters. Besides, unlike the existing consensus-based filters, we do not need to perform consensus filtering on the covariance matrices, which will reduce the computational and communicational burden abundantly. Finally, simulation examples are included to demonstrate the robustness of the proposed RKF and effectiveness of adaptive consensus approach.

A Robust Extended Complex Kalman Filter and Sliding-mode Control Based Shunt Active Power Filter

—This article presents the design of a new shunt active power filter that employs a modified robust extended complex Kalman filter approach with an exponential robust term embedded for reference current estimation together with a current controller based on the sliding-mode control concept. The robust extended complex Kalman filter exploits a new weighted exponential function to handle these grid perturbations to estimate the reference signal in shunt active power filter system. The current controller in the proposed shunt active power filter has been designed using a sliding-mode control strategy because of its ability to handle parameter uncertainties and ease in implementation. To test the effectiveness of the proposed shunt active power filter, extensive simulations were performed using MATLAB/Simulink (The MathWorks, Natick, Massachusetts, USA), and real-time studies were made using OPAL-RT (Montreal, Quebec, Canada). Results obtained from the above studies using the proposed shunt active power filter together with the different variants of Kalman filter (Kalman filter, extended Kalman filter, extended complex Kalman filter) are analyzed, and it is observed that the proposed robust extended complex Kalman filter-sliding-mode control based shunt active power filter provides accurate and improved harmonics mitigation and reactive power compensation.