Strong Tracking Unscented Kalman Filter Research Articles

Research on collision warning strategy considering characteristics of drivers and road conditions

Collision warning strategy considering different characteristics of drivers and complex road conditions is of great importance for active safety control of autonomous vehicles. However,existing estimation methods for Tire-road friction coefficient (TRFC) cannot deal with the problem of estimation accuracy degradation caused by state mutation. Therefore, an adaptive cascaded strong tracking unscented Kalman filter (ACSTUKF) is proposed to estimate TRFC. The proposed algorithm consists of two strong tracking filters, which are connected in series with each other. Fuzzy control is introduced to estimate the reaction time of different drivers. Simulation experiments and real vehicle tests are carried out to demonstrate the effectiveness of the proposed strategy. Results show that the proposed ACSTUKF has a more excellent performance for TRFC than EKF and UKF, which greatly reduces the impact of state mutation. Moreover, ACSTUKF shows a strong robustness to driving conditions and road conditions. The established collision warning strategy is consistent with the actual situation, which realizes the adaptation of human and road.

Estimation of road adhesion coefficient and sideslip angle for electric vehicles with slip-aware constraints using strong tracking unscented Kalman filter

Accurate estimation of road adhesion coefficient and sideslip angle are crucial for safer driving and ride quality of electric vehicles (EVs). To that end, an estimation algorithm of road adhesion coefficient and sideslip angle for EVs with slip-aware constraints and strong tracking unscented Kalman filter (SSTUKF) algorithm is designed in this paper. First, a vehicle system model is established as the basis for deriving the desirable estimation algorithm. Then, a strong tracking unscented Kalman filter (STUKF) algorithm with fading factor is presented to strengthen the correction effect of error covariance matrix used in unscented Kalman filter (UKF) algorithm. Meanwhile, slip-aware constraints are considered to calculate the adaptive compensated steering angle, which is obtained by repeated iteration of the fitness function. Additionally, a data fusion estimator is established based on the extremum theory to solve the problem of inaccurate estimation of sideslip angle under complex driving conditions. Finally, the CarSim-MATLAB/Simulink simulation platform is used to simulate under different driving conditions, and the simulation results reveal that the presented SSTUKF algorithm can enhance the estimation performance.

Strong Tracking UKF-Based Hybrid Algorithm and Its Application to Initial Alignment of Rotating SINS With Large Misalignment Angles

In this paper, the fast and precise initial alignment of the low-cost rotary strapdown inertial navigation system under mooring conditions is investigated. The unscented Kalman filter (UKF) is used to address model nonlinearity and to achieve fast alignment for large misalignment angles. A generalized multi-fading strong tracking UKF (GSTUKF) is proposed to effectively compensate for the kinematic model errors caused by mooring and rotary motions. The performance of the standard strong tracking UKF cannot be optimal because only a portion of the fading factors associated with the directly observable state variables can be obtained approximately using the analytical method. By contrast, using the iteration method to calculate the full-dimension fading factors precisely, the GSTUKF has greater robustness and adaptability. To find out the optimal fading factors in real time, the multivariate nonlinear optimization model is first designed, and then the iteration approach based on a hybrid algorithm consisting of particle swarm optimization and beetle antennae search is developed, which has no risk of falling into a local minimum. Simulations and experiments are conducted to validate the GSTUKF's effectiveness. The experiments demonstrate that the proposed method reduces the yaw error by 47.2% compared with the standard strong tracking UKF.

An Integrated Scheme for Coefficient Estimation of Tire–Road Friction With Mass Parameter Mismatch Under Complex Driving Scenarios

The accurate knowledge of tire–road friction coefficient (TRFC) contributes to the optimization of driver maneuvers for further improving the safety of intelligent vehicles. The performance of the existing estimation methods would decline when a vehicle performs complex driving maneuvers. In addition, the mass parameter mismatch also deteriorates the estimation accuracy of TRFC. To address these problems, in this article, an integrated scheme for TRFC estimation is proposed by combining a strong tracking unscented Kalman filter and an interactive multiple model unscented Kalman filter. Real-time experiments are implemented on a mass-produced vehicle to demonstrate the feasibility and effectiveness of the proposed method. The results show that the proposed approach has better estimation accuracy than the existing ones under various driving scenarios.

A Comprehensive Vehicle Stability Assessment System Based on Enabling Tire Force Estimation

This paper presents an enabling comprehensive vehicle stability assessment system covering vehicle longitudinal, yaw and roll stability. First, the longitudinal, lateral and vertical tire forces are separately estimated using the strong tracking unscented Kalman filter and the conventional Kalman filter based on low-cost on-board sensors. Then, a comprehensive vehicle longitudinal, yaw and roll stability space is established by utilizing the normalized tire friction ellipse and the Load Transfer Ratio value. Finally, the vehicle stability is determined and predicted based on current driver's inputs. The hardware-in-loop experimental results show that the proposed vehicle stability assessment system can accurately estimate the longitudinal, lateral and vertical tire forces with the normalized root mean square errors of 1.87 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> , 1.07 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> and 1.43 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> , and exhibits satisfying performance for vehicle longitudinal, yaw and roll stability evaluation and prediction. This bears significance for the efficient functioning of active control systems to improve vehicle safety under critical driving conditions.

Application of Adaptive Weighted Strong Tracking Unscented Kalman Filter in Non-Cooperative Maneuvering Target Tracking

An adaptive weighted strong tracking unscented Kalman filter is proposed in this paper for long-range relative navigation alongside non-cooperative maneuvering targets. First, an equation for obtaining the relative motion of two bodies is derived, it can be well adapted for a problem that has medium or long-distance. Secondly, a variance statistics function is introduced in the method to calculate residual weight in real time. The residual weight can be used to adjust the contribution of different measurement information to the fading factor. In this way, the sensitivity of the system to small pulse maneuvers is improved. Finally, the mean and covariance of the posterior state are calculated by the unscented transformation. A replacement equation for the fading factor is derived to improve the first-order approximation accuracy for a strong tracking system. Impulsive maneuvers with three different magnitudes are employed in a series of tests. Results from different methods showed that the proposed method could effectively detect pulse maneuvers with low latency. The proposed method is also numerically stable.

Automatic emergency braking/anti‐lock braking system coordinated control with road adhesion coefficient estimation for heavy vehicle

The road adhesion coefficient is a key factor influencing automatic emergency braking (AEB) and anti-lock braking system (ABS) safety control of trucks. With the fading factor introduced, and the covariance gain adjusted in real time, the strong tracking unscented Kalman filter (STUKF) algorithm is modified to estimate the road adhesion coefficient more accurately. Composed of an ABS fuzzy sliding mode controller (SMC) and an AEB controller, an AEB/ABS coordinated control strategy with an adhesion coefficient estimation is designed for a three-axle heavy vehicle. The control effects are verified through experiments on various road conditions based on a hardware-in-loop test platform. The test results show that the proposed control strategy has a better braking efficiency than the traditional AEB/ABS and AEB control strategy without adhesion coefficient estimation and can decrease braking distance by 8.4% and braking time by 5.9%, which is beneficial to the vehicle longitudinal safety.

Robust strong tracking unscented Kalman filter for non‐linear systems with unknown inputs

This paper proposes a state estimation approach ‘robust strong tracking unscented Kalman filter with unknown inputs’ that can be applied to non-linear systems with unknown inputs. Specifically, the non-linear state and measurement equations are linearised by statistical linearisation. Then, the estimation equation of the unknown input is derived based on the weighted least squares method. The multiple suboptimal fading factor is introduced into a priori error covariance matrix to improve the tracking ability for the inaccuracy of the system model and the abrupt change of state variables caused by unknown inputs. Finally, based on the unbiased minimum variance estimation, the unbiased state estimation and the error covariance matrix are derived. Singular value decomposition is performed on the error covariance matrix to improve the stability of the algorithm. Simulated results validate the effectiveness of the proposed method.

Multiplicative modified Rodrigues-parameters-based strong tracking unscented Kalman filter for satellite attitude estimation

In this paper, an improved strong tracking unscented Kalman filter based on multiplicative modified Rodrigues parameters (MRPs) is proposed for satellite attitude estimation. The multiplicative MRPs are superior to additive MRPs in terms of attitude representation, especially when attitude angles are large. By minimizing the loss function in Wahba’s problem, a novel method of weighted average for MRPs is derived to replace the simple procedure. The generation of Sigma points, update of state variables, and calculation of covariance matrices are all different from the existing literature to maintain the multiplicative property of MRPs. Simulation results by raw telemetry data from the on-orbit CubeSat Enlai-1 demonstrate the excellent performance of the proposed filter under large attitude angles.

An escape strategy in orbital pursuit-evasion games with incomplete information

The orbital pursuit-evasion game is typically formulated as a complete-information game, which assumes the payoff functions of the two players are common knowledge. However, realistic pursuit-evasion games typically have incomplete information, in which the lack of payoff information limits the player’s ability to play optimally. To address this problem, this paper proposes a currently optimal escape strategy based on estimation for the evader. In this strategy, the currently optimal evasive controls are first derived based on the evader’s guess of the pursuer’s payoff weightings. Then an online parameter estimation method based on a modified strong tracking unscented Kalman filter is employed to modify the guess and update the strategy during the game. As the estimation becomes accurate, the currently optimal strategy gets closer to the actually optimal strategy. Simulation results show the proposed strategy can achieve optimal evasive controls progressively and the evader’s payoff of the strategy is lower than that of the zero-sum escape strategy. Meanwhile, the proposed strategy is also effective in the case where the pursuer changes its payoff function halfway during the game.

Adaptive estimations of tyre–road friction coefficient and body’s sideslip angle based on strong tracking and interactive multiple model theories

Vehicle dynamic states and parameters, such as the tyre–road friction coefficient and body’s sideslip angle especially, are crucial for vehicle dynamics control with close-loop feedback laws. Autonomous vehicles also have strict demands on real-time knowledge of those information to make reliable decisions. With consideration of the cost saving, some estimation methods employing high-resolution vision and position devices are not for the production vehicles. Meanwhile, the bad adaptability of traditional Kalman filters to variable system structure restricts their practical applications. This paper introduces a cost-efficient estimation scheme using on-board sensors. Improved Strong Tracking Unscented Kalman filter is constructed to estimate the friction coefficient with fast convergence rate on time-variant road surfaces. On the basis of previous step, an estimator based on interactive multiple model is built to tolerant biased noise covariance matrices and observe body’s sideslip angle. After the vehicle modelling errors are considered, a Self-Correction Data Fusion algorithm is developed to integrate results of the estimator and direct integral method with error correction theory. Some simulations and experiments are also implemented, and their results verify the high accuracy and good robustness of the cooperative estimation scheme.

Development of an algorithm for tuning a suboptimal scaling factor in the SINS filtering problem

A modified strong tracking unscented Kalman filter for nonlinear dynamical systems is proposed. A matrix of the suboptimal scaling factor is introduced into the prediction covariance to ensure evaluation stability and smoothness at appearance of the process model uncertainty. It is shown that the use of a fuzzy algorithm to adjust the softening coefficient in real time allows to avoid the loss of accuracy in the segments in which the process model is defined. As a result of modeling the SINS correction task, it was found that the proposed fuzzy filter has good evaluation smoothness and high accuracy. Keywords SINS; suboptimal scaling factor; softening coefficient; fuzzy Takagi — Sugeno model

A Novel Online Estimation and Compensation Method for Strapdown Phased Array Seeker Disturbance Rejection Effect Using Extended State Kalman Filter

The radome error and beam pointing error found commonly in the strapdown phased array radar seeker can cause coupling between the missile body motion and the seeker model, impacting the output precision of the seeker and causing the disturbance rejection effect (DRE). Aiming to address the serious impact of DRE on the missile guidance and control system, a strapdown phased array radar seeker DRE parasitic loop (considering radome error and beam pointing error) is established. The DRE parasitic loop is analyzed. The main aim of this paper was to develop a novel online estimation and compensation method for a DRE parasitic loop using an extended state Kalman filter, which was compared with an extended Kalman filter and a strong tracking unscented Kalman filter. The simulation results show that the proposed online estimation and compensation method for the DRE parasitic loop can estimate the radome error slope and beam pointing error slope stably and accurately from the initial velocity pointing error input and the large initial estimation error. Effective suppression of the DRE problem and compensation for the line-of-sight angular rate output in real time is achieved. Furthermore, the guidance system performance and precision are both improved.

Infrared measurement and composite tracking algorithm for air-breathing hypersonic vehicles

Air-breathing hypersonic vehicles have capabilities of hypersonic speed and strong maneuvering, and thus pose a significant challenge to conventional tracking methodologies. To achieve desirable tracking performance for hypersonic targets, this paper investigates the problems related to measurement model design and tracking model mismatching. First, owing to the severe aerothermal effect of hypersonic motion, an infrared measurement model in near space is designed and analyzed based on target infrared radiation and an atmospheric model. Second, using information from infrared sensors, a composite tracking algorithm is proposed via a combination of the interactive multiple models (IMM) algorithm, fitting dynamics model, and strong tracking filter. During the procedure, the IMMs algorithm generates tracking data to establish a fitting dynamics model of the target. Then, the strong tracking unscented Kalman filter is employed to estimate the target states for suppressing the impact of target maneuvers. Simulations are performed to verify the feasibility of the presented composite tracking algorithm. The results demonstrate that the designed infrared measurement model effectively and continuously observes hypersonic vehicles, and the proposed composite tracking algorithm accurately and stably tracks these targets.

A new direct filtering approach to INS/GNSS integration

This paper presents a novel direct filtering approach to INS/GNSS (Inertial Navigation System / Global Navigation Satellite System) integration. This approach establishes a kinematic model for INS/GNSS integration by combining inertial navigation equations and IMU (Inertial Measurement Unit) error equations. Subsequently, a refined strong tracking unscented Kalman filter (RSTUKF) is developed to enhance the UKF robustness against kinematic model error. This RSTUKF adopts the strategy of assumption test to identify kinematic model error. Based on this, a suboptimal fading factor (SFF) is derived and embedded in the predicted covariance to weaken the influence of prior information on the filtering solution only in the presence of kinematic model error. In addition to correction of the UKF estimation in the presence of kinematic model error, the RSTUKF also maintains the optimal UKF estimation in the absence of kinematic model error. Simulation and experimental analysis demonstrate the performance of the proposed approach to INS/GNSS integration.

State Estimation for Sampled-Data Descriptor Nonlinear System: A Strong Tracking Unscented Kalman Filter Approach

This paper proposes a state estimation method for a sampled-data descriptor system by the Kalman filtering method. The sampled-data descriptor system is firstly discretized to obtain a discrete-time nonsingular model. Based on the discretized nonsingular system, a strong tracking unscented Kalman filter (STUKF) algorithm is designed for the state estimation. Then, a defined suboptimal fading factor is proposed and added to the prediction covariance for decreasing the weight of the prior knowledge on the conventional UKF filtering solution. Finally, a simulation example is given to show the effectiveness of the proposed method.

A combination Kalman filter approach for State of Charge estimation of lithium-ion battery considering model uncertainty

An accurate battery State of Charge estimation plays an important role in battery electric vehicles. This paper makes two contributions to the existing literature. (1) A recursive least squares method with fuzzy adaptive forgetting factor has been presented to update the model parameters close to the real value more quickly. (2) The statistical information of the innovation sequence obeying chi-square distribution has been introduced to identify model uncertainty, and a novel combination algorithm of strong tracking unscented Kalman filter and adaptive unscented Kalman filter has been developed to estimate SOC (State of Charge). Experimental results indicate that the novel algorithm has a good performance in estimating the battery SOC against initial SOC errors and voltage sensor drift. A comparison with the unscented Kalman filter-based algorithms and adaptive unscented Kalman filter-based algorithms shows that the proposed SOC estimation method has better accuracy, robustness and convergence behavior.

Application of the Strong Tracking UKF in the Maneuvering Target Tracking

Maneuvering target tracking is one of the key technologies in the space tracking system. The strong tracking unscented Kalman filter is presented for the data processing which uses a fading factor in the state estimation. Using the current statistical model, the strong tracking UKF is tested with the real data obtained in a mission measured by the space tracking ship. Simulation results show the good performance of the proposed method.

Modified strong tracking unscented Kalman filter for nonlinear state estimation with process model uncertainty

SummaryThis paper presents a modified strong tracking unscented Kalman filter (MSTUKF) to address the performance degradation and divergence of the unscented Kalman filter because of process model uncertainty. The MSTUKF adopts the hypothesis testing method to identify process model uncertainty and further introduces a defined suboptimal fading factor into the prediction covariance to decrease the weight of the prior knowledge on filtering solution. The MSTUKF not only corrects the state estimation in the occurrence of process model uncertainty but also avoids the loss of precision for the state estimation in the absence of process model uncertainty. Further, it does not require the cumbersome evaluation of Jacobian matrix involved in the calculation of the suboptimal fading factor. Experimental results and comparison analysis demonstrate the effectiveness of the proposed MSTUKF. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Strong Tracking Unscented Kalman Filtering Algorithm Based-on Satellite Attitude Determination System

Combined with strong tracking filter (STF) theory, the Strong Tracking Square-Root Unscented Kalman Filter (UKF)-based satellite attitude determination algorithm is proposed in this paper. QR decomposition and Cholesyk decomposition are introduced in this paper, which improves the stability of filter. In addition, by introduced adaptive fading factor, the prediction error covariance matrix can be adjusted, thus it can guarantee the strong tracking performance of the proposed algorithm. At last, simulation results show that strong tracking square-root UKF has better stability, robustness and mutation status tracking capability than Square-Root UKF and Strong Tracking UKF.