Robust Adaptive Cubature Kalman Filter and Its Application to Ultra-Tightly Coupled SINS/GPS Navigation System

Robust Cubature Kalman Filter for Moving-Target Tracking with Missing Measurements

Handling the challenge of missing measurements in nonlinear systems is a difficult problem in various scientific and engineering fields. Missing measurements, which can arise from technical faults during observation, diffusion channel shrinking, or the loss of specific metrics, can bring many challenges when estimating the state of nonlinear systems. To tackle this issue, this paper proposes a technique that utilizes a robust cubature Kalman filter (RCKF) by integrating Huber's M-estimation theory with the standard conventional cubature Kalman filter (CKF). Although a CKF is often used for solving nonlinear filtering problems, its effectiveness might be limited due to a lack of knowledge regarding the nonlinear model of the state and noise-related statistical information. In contrast, the RCKF demonstrates an ability to mitigate performance degradation and discretization issues related to track curves by leveraging covariance matrix predictions for state estimation and output control amidst dynamic disruption errors-even when noise statistics deviate from prior assumptions. The performance of extended Kalman filters (EKFs), unscented Kalman filters (UKFs), CKFs, and RCKFs was compared and evaluated using two numerical examples involving the Univariate Non-stationary Growth Model (UNGM) and bearing-only tracking (BOT). The numerical experiments demonstrated that the RCKF outperformed the EKF, EnKF, and CKF in effectively handling anomaly errors. Specifically, in the UNGM example, the RCKF achieved a significantly lower ARMSE (4.83) and ANCI (3.27)-similar outcomes were observed in the BOT example.

Maximum correentropy-based robust Square-root Cubature Kalman Filter for vehicular cooperative navigation

As the core method of cooperative navigation, relative positioning plays a key role in realizing intelligent vehicle driving and vehicle self-assembling network collaboration algorithms. However, when the contamination rate of measurement noise is high, the performance of filtering will be seriously affected. To better address the filtering performance degradation problem due to noise contamination, this paper proposes a vehicular cooperative localization method based on the Maximum Correentropy Robust Square-root Cubature Kalman Filter (MCSCKF). The algorithm not only retains the advantages of Square-root Cubature Kalman Filter (SCKF) but also has strong robustness to non-Gaussian noise. The experimental results of tightly integrated vehicular cooperative navigation show that compared with the Extended Kalman Filter (EKF) and Cubature Kalman Filter (CKF), the localization accuracy of MCSCKF is improved by 35.08% and 31.83%, respectively, which verified the effectiveness in improving the accuracy and robustness of the relative position estimation.

Improved Strong Tracking Cubature Kalman Filter for UWB Positioning

For the problems of Non-Line-of-Sight (NLOS) observation errors and inaccurate predictive dynamics model in wireless ultra-wideband (UWB) positioning systems, an improved strong tracking cubature Kalman filter (ISTCKF) positioning algorithm is proposed in this paper. The main idea of the algorithm is as follows. First, the observations are reconstructed based on the weighted positioning results obtained from the predictive dynamics model and the least squares algorithm. Second, the difference in statistical properties between the observation noise and the NLOS errors is utilized to identify the NLOS observations by the corresponding judgment statistics obtained from the operation between the original observations and the reconstructed observations. The main positioning error of the UWB positioning system at the current moment is then judged by the NLOS identification results, and the corresponding fading factors are calculated according to the judgment results. Finally, the corresponding ISTCKF is constructed based on the fading factors to mitigate the main positioning error and obtain accurate positioning result in the UWB positioning system. In this paper, the reconstructed observations mitigate the observation noise in the original observation, and then the ISTCKF mitigates the main errors in the UWB positioning system. The experimental results show that the ISTCKF algorithm reduces the positioning error by 55.2%, 32.3% and 28.9% compared with STCKF, ACKF and RSTCKF, respectively. The proposed ISTCKF algorithm significantly improves the positioning accuracy and stability of the UWB system.

A Novel Adaptive Robust Cubature Kalman Filter for Maneuvering Target Tracking with Model Uncertainty and Abnormal Measurement Noises

The features of measurement and process noise are directly related to the optimal performance of the cubature Kalman filter. The maneuvering target model's high level of uncertainty and non-Gaussian mean noise are typical issues that the radar tracking system must deal with, making it impossible to obtain the appropriate estimation. How to strike a compromise between high robustness and estimation accuracy while designing filters has always been challenging. The H-infinity filter is a widely used robust algorithm. Based on the H-infinity cubature Kalman filter (HCKF), a novel adaptive robust cubature Kalman filter (ARCKF) is suggested in this paper. There are two adaptable components in the algorithm. First, an adaptive fading factor addresses the model uncertainty issue brought on by the target's maneuvering turn. Second, an improved Sage-Husa estimation based on the Mahalanobis distance (MD) is suggested to estimate the measurement noise covariance matrix adaptively. The new approach significantly increases the robustness and estimation precision of the HCKF. According to the simulation results, the suggested algorithm is more effective than the conventional HCKF at handling system model errors and abnormal observations.

UWB Localization Based on Improved Robust Adaptive Cubature Kalman Filter

Aiming at the problems of Non-Line-of-Sight (NLOS) observation errors and inaccurate kinematic model in ultra-wideband (UWB) systems, this paper proposed an improved robust adaptive cubature Kalman filter (IRACKF). Robust and adaptive filtering can weaken the influence of observed outliers and kinematic model errors on filtering, respectively. However, their application conditions are different, and improper use may reduce positioning accuracy. Therefore, this paper designed a sliding window recognition scheme based on polynomial fitting, which can process the observation data in real-time to identify error types. Simulation and experimental results indicate that compared to the robust CKF, adaptive CKF, and robust adaptive CKF, the IRACKF algorithm reduces the position error by 38.0%, 45.1%, and 25.3%, respectively. The proposed IRACKF algorithm significantly improves the positioning accuracy and stability of the UWB system.

General Periodic Cruise Guidance Optimization for Hypersonic Vehicles

Periodic cruise has the potential to improve the fuel efficiency of a hypersonic vehicle. However, the optimization of periodic cruise is very difficult and can only be performed inefficiently through trial-and-error due to the parameterized form. In this paper, we systematically optimized the hypersonic periodic cruise using the pseudo-spectral method (PSM) scheme. We specify the main variables as the given forms of periodic functions and parameterize the periodic guidance. The characteristic parameters can then be considered as augmented states to generate augmented dynamics. Therefore, periodic cruise optimization can be directly obtained by using GPOPS (Gauss Pseudo-spectral OPtimization Software). The numerical results demonstrate the effectiveness of the proposed method. The approach in this case study can be generalized to solve similar trajectory optimization problems that can be parameterized in a unified manner.

Reliable Indoor Pseudolite Positioning Based on a Robust Estimation and Partial Ambiguity Resolution Method

The unscented Kalman filter (UKF) can effectively reduce the linearized model error and the dependence on initial coordinate values for indoor pseudolite (PL) positioning unlike the extended Kalman filter (EKF). However, PL observations are prone to various abnormalities because the indoor environment is usually complex. Standard UKF (SUKF) lacks resistance to frequent abnormal observations. This inadequacy brings difficulty in guaranteeing the accuracy and reliability of indoor PL positioning, especially for phase-based high-precision positioning. In this type of positioning, the ambiguity resolution (AR) will be difficult to achieve in the presence of abnormal observations. In this study, a robust UKF (RUKF) and partial AR (PAR) algorithm are introduced and applied in indoor PL positioning. First, the UKF is used for parameter estimation. Then, the anomaly recognition statistics and optimal ambiguity subset of PAR are constructed on the basis of the posterior residuals. The IGGIII scheme is adopted to weaken the influence of abnormal observation, and the PAR strategy is conducted in case of failure of the conventional PL-AR. The superiority of our proposed algorithm is validated using the measured indoor PL data for code-based differential PL (DPL) and phase-based real-time kinematic (RTK) positioning modes. Numerical results indicate that the positioning accuracy of RUKF-based indoor DPL is higher with a decimeter-level improvement compared that of the SUKF, especially in the presence of large gross errors. In terms of high-precision RTK positioning, RUKF can correctly identify centimeter-level anomalous observations and obtain a corresponding positioning accuracy improvement compared with the SUKF. When relatively large gross errors exist, the conventional method cannot easily realize PL-AR. By contrast, the combination of RUKF and the PAR algorithm can achieve PL-AR for the selected ambiguity subset successfully and can improve the positioning accuracy and reliability significantly. In summary, our proposed algorithm has certain resistance ability for abnormal observations. The indoor PL positioning of this algorithm outperforms that of the conventional method. Thus, the algorithm has some practical application value, especially for kinematic positioning.

Adaptive Estimation and Cooperative Guidance for Active Aircraft Defense in Stochastic Scenario

The active aircraft defense problem is investigated for the stochastic scenario wherein a defending missile (or a defender) is employed to protect a target aircraft from an attacking missile whose pursuit guidance strategy is unknown. For the purpose of identifying the guidance strategy, the static multiple model estimator (sMME) based on the square-root cubature Kalman filter is proposed, and each model represents a potential attacking missile guidance strategy. Furthermore, an estimation enhancement approach is provided by using pseudo-measurement. For each model in the sMME, the model-matched cooperative guidance laws for the target and defender are derived by formulating the active defense problem as a constrained linear quadratic problem, where an accurate defensive interception and the minimum evasion miss distance are both considered. The proposed adaptive cooperative guidance laws are the result of mixing the model-matched optimal cooperative guidance laws in the criterion of maximum a posteriori probability in the framework of the sMME. By adopting the adaptive cooperative guidance laws, the target can facilitate the defender's interception with the attacking missile with less control effort. Also, simulation results show that the proposed guidance laws increase the probability of successful target protection in the stochastic scenario compared with other defensive guidance laws.