Maneuvering Target Tracking Based on Adaptive Square Root Cubature Kalman Filter Algorithm

Kalman filters are very popular in turbofan engine community for health monitoring purposes. In this study, in order to get better performance in terms of filtering accuracy and noise adaptability, an Adaptive Square Root Cubature Kalman Filter (ASRCKF) was proposed to estimate health parameters of the turbofan engine gas path components. In the ASRCKF algorithm, the mean value and covariance of the engine nonlinear function were calculated by cubature rule-based numerical integration method and used as a substitute for nonlinear model in nonlinear Kalman filter. The latest information of measurement parameters in the recursion and filtering process was used to estimate and self-adjust the noises cross-covariance by removable window method to get higher filtering accuracy. Compared with the Extended Kalman Filter (EKF) and Square Root Cubature Kalman Filter (SRCKF), the simulation results in the gradual and rapid deterioration process of turbofan engine gas path components indicate that the higher accuracy and faster convergence can be obtained through ASRUKF, which can be used in health parameters estimation and condition monitoring of turbofan engine gas path.1

In order to solve the problems of model performance error and abnormal measurement value, the square-root Cubature Kalman filter (SRCKF) algorithm has problems such as filter performance degradation or filter effect divergence, this paper proposes a self-estimation based on M. Adaptive Square-root Cubature Kalman Filter based on M estimation (M-ASRCKF) algorithm, this filter algorithm uses an improved Huber weight function to improve the robustness of the SRCKF algorithm; and then adds the Sage-Husa order Excellent unbiased maximum a posteriori (MAP) estimator, real-time monitoring and estimation of unknown or inaccurate noise statistics, improving the tracking accuracy of the traditional SRCKF algorithm. MATLAB simulation results show that the proposed M-estimation-based adaptive SRCKF (M-ASRCKF) algorithm has better anti-non-linearity and anti-outlier interference capabilities, and this algorithm has strong robustness and high accuracy of results.

This article introduces an efficient and high-precision estimation framework for four-wheel independently actuated (FWIA) autonomous vehicles based on a novel tire model and adaptive square-root cubature Kalman filter (SCKF) estimation strategy. Firstly, a reliable and concise tire model that considers the tire’s nonlinear mechanics characteristics under combined conditions through the piecewise affine (PWA) identification method is established to improve the accuracy of the lateral dynamics model of FWIA autonomous vehicles. On this basis, the longitudinal relaxation length of each tire is integrated into the lateral dynamics modeling of FWIA autonomous vehicle. A novel nonlinear state function, including the PWA tire model, is proposed in this paper. To reduce the impact of the uncertainty of noise statistics on the estimation accuracy, an adaptive SCKF estimation algorithm based on the maximum a posteriori (MAP) criterion is proposed in the estimation framework. Finally, the estimation accuracy and stability of the adaptive SCKF algorithm are verified by the co-simulation of CarSim and Simulink. The simulation results show that when the statistical characteristics of noise are unknown and the target state changes suddenly under critical maneuvers, the estimation framework proposed in this paper still maintains high accuracy and stability.

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

Aiming at the tracking filters are liable to diverge and the tracking precision is low when tracking nonlinear maneuvering target, an Interacting Multiple Model Square-root Cubature Kalman Filter (IMMSCKF) is developed by introducing Square-root Cubature Kalman Filter (SCKF) into Interacting Multiple Model (IMM). This method uses SCKF for filtering each model, the weighted sum of the outputs of all parallel SCKF is taken as the output of IMMSCKF. Simulation shows that IMMSCKF has higher precision, quicker model switching speed, and smaller calculation cost compared with IMMUKF.

Aiming at the problems of the poor trajectory-tracking performance and low control accuracy of unmanned vehicles under complex working conditions, we first estimate the lateral force of tires using the square root cubature Kalman filter (SRCKF) in order to correct the lateral stiffness of the tires online, which reduces the model bias caused by constant lateral stiffness, and then adopt a Gaussian function-based adaptive time-domain model predictive control method to improve the trajectory-tracking control accuracy of unmanned vehicles under complex working conditions. Finally, the proposed control algorithm is validated via Carsim and MATLAB/Simulink joint simulation. The results show that compared with the classical model predictive control (MPC) algorithm, the proposed control algorithm reduces the average lateral tracking error by 73.07% and the peak beta and the peak yaw rate by 50.89% and 47.51%, respectively, so that the unmanned vehicle is able to maintain good tracking performance and control accuracy.

To improve the accuracy and efficiency of multi-maneuvering target tracking in dense clutter environments, an improved interactive multi-model generalized probabilistic data association (IMM-GPDA) algorithm is proposed in this paper. The algorithm introduces Doppler information into the measurement data. Firstly, the measurement data is pre-processed by double-threshold regional density clutter elimination, and then the pre-processed data is put into the improved IMM-GPDA algorithm with square-root cubature Kalman filter (SRCKF) and model transition probability adaptation for interaction, association, and filtering. Simulation results show that the algorithm has advanced accuracy, instantaneity, and robustness in tracking environments with multi-maneuvering targets and dense clutters.

Development of a GNSS/INS-based automatic navigation land levelling system

In maneuvering target tracking, since target's maneuvering capability has greatly increased, it is more difficult to describe and found the target's movement model. Now, variable structure multiple model (VSMM) algorithm is an effective method for strong maneuvering target tracking. Based on fuzzy control theory, it is proposed that a likely model set with system noise fuzzy adaptation (FNA-LMS) algorithm using two-dimensional fuzzy controller. The system noise of each model in VSMM algorithm is adjusted by self adaptation. Monte Carlo simulation comparison shows that FNA-LMS algorithm has better performance in tracking accuracy and computing efficiency than basic likely model set algorithm. Also it is convenient for application.

To solve the problem of missing measurements in highly manoeuvring target tracking, an expected‐mode‐augmentation‐based unscented Kalman filter with missing measurements compensation (EMA‐MMCUKF) is designed based on the variable‐structure multiple model method. In the proposed EMA‐MMCUKF, the random missing measurements are described by the Bernoulli distribution, and the one‐step prediction is used as the compensation. Based on the proposed EMA‐MMCUKF, a Bayesian estimation‐based expected‐mode‐augmentation unscented Kalman filter with missing measurements compensation (BE‐EMA‐MMCUKF) is proposed for adaptive estimation of the sensor measurement reception rate, where the unknown measurement reception rate can be estimated by fully utilising prior information. Simulation results demonstrate that the proposed EMA‐MMCUKF can effectively track the manoeuvring target at different measurement reception rates. Moreover, when the sensor prior information differs significantly from the true measurement reception rate, the proposed BE‐EMA‐MMCUKF can effectively estimate the unknown sensor measurement reception rate and improve the accuracy of manoeuvring target tracking compared with non‐estimation of the sensor measurement reception rate.

This paper presents a tracking algorithm based on the interacting multiple model (IMM) algorithm and pseudo linear Kalman filter (PKF) in order to improve the performance of traditional methods in maneuvering target tracking. The IMM-PKF algorithm uses the constant velocity (CV) model and coordinated turn (CT) model to form a model set, and the filtering algorithm uses PKF. In target tracking, IMM is used to improve the matching between state prediction and actual motion, therefore improving the accuracy of maneuvering tracking. The performance of extended Kalman filter (EKF), PKF, and IMM-PKF is compared through simulation and experiment. The results show that the IMM-PKF method has the best tracking accuracy among the three methods in helicopter tracking.

Modern radars employ linear frequency modulated (LFM) waveforms for target tracking as the range-Doppler coupling enables better track accuracy in range. When tracking maneuvering targets with a nearly constant velocity (NCV) Kalman filter, the selection of the process noise variance is complicated by the fact that the process errors are modeled as white Gaussian, while target maneuvers are deterministic or highly correlated in time. In recent years, the deterministic tracking index was introduced and used to develop a relationship between the maximum acceleration of the target and the process noise variance that minimizes the maximum mean squared error (MMSE) in position. A lower bound on the process noise variance was also expressed in terms of the maximum acceleration and deterministic tracking index. In this paper, the design methods for NCV Kalman filters are extended to radar tracking with linear frequency modulation (LFM) waveforms. The effectiveness of the design methods are confirmed via Monte Carlo simulations.

Multi-radar cooperative detection has significant advantages in maneuvering target tracking because of its wide coverage, good detection performance and strong survivability. As a key technology in cooperative detection of networking, multisource data fusion requires high precision and stability of fusion tracking. In this paper, Centralized Kalman Filter method is used to build a mathematical model by expanding dimension and direction finding quantity, and a new method is proposed to solve the fusion tracking problem of multi-radar in cooperative detection of maneuvering target by extending the estimation of nonlinear system for single sensor to the data fusion estimation of multi-sensor nonlinear system.

Tracking of manoeuvring targets is a problem of a great practical and theoretical interest. The real-world tracking applications meet a number of difficulties caused by the presence of different kinds of uncertainty due to the unknown or not precisely known system model and random processes’ statistics or because of their abrupt changes. 2-5, 9 These problems are especially complicated in the marine navigation practice, 7, 14, 15, 19 where the commonly used simple models of rectilinear or curvilinear target motions do not match the highly non-linear dynamics of the manoeuvring ship. A solution of these problems is to derive more adequate descriptions of the real ship dynamics and to design adaptive estimation algorithms.

Maneuvering target tracking, as a core task in multi-sensor information fusion, is widely used in unmanned vehicles, missile navigation, and underwater ship localization, where real-time and robust state estimation is critical. Due to the uncertainty of the moving characteristics of maneuvering targets and the low sensor measurement accuracy, trajectory tracking has always been an open research problem and challenging work. This paper proposes a Bayesian-inspired stacked LSTM fusion network (SLSTM) for uncertain motion characteristics. The network consists of two LSTM fusion networks with stacked serial relationships, one of which is used to predict the movement dynamics, and the other is used to update the track's state. Compared with the classical Kalman filter based on the maneuver model, the method proposed here does not need to model the motion characteristics and sensor characteristics. It can achieve high-performance tracking by learning historical data dynamics and sensor characteristics. Experimental results show that this method can effectively improve the trajectory estimation performance when the target motion is unknown and uncertain.