Kalman Filter Theory Research Articles

Characterizing the dynamics, reactivity and controllability of moods in depression with a Kalman filter.

Mood disorders involve a complex interplay between multifaceted internal emotional states, and complex external inputs. Dynamical systems theory suggests that this interplay between aspects of moods and environmental stimuli may hence determine key psychopathological features of mood disorders, including the stability of mood states, the response to external inputs, how controllable mood states are, and what interventions are most likely to be effective. However, a comprehensive computational approach to all these aspects has not yet been undertaken. Here, we argue that the combination of ecological momentary assessments (EMA) with a well-established dynamical systems framework-the humble Kalman filter-enables a comprehensive account of all these aspects. We first introduce the key features of the Kalman filter and optimal control theory and their relationship to aspects of psychopathology. We then examine the psychometric and inferential properties of combining EMA data with Kalman filtering across realistic scenarios. Finally, we apply the Kalman filter to a series of EMA datasets comprising over 700 participants with and without symptoms of depression. The results show a naive Kalman filter approach performs favourably compared to the standard vector autoregressive approach frequently employed, capturing key aspects of the data better. Furthermore, it suggests that the depressed state involves alterations to interactions between moods; alterations to how moods responds to external inputs; and as a result an alteration in how controllable mood states are. We replicate these findings qualitatively across datasets and explore an extension to optimal control theory to guide therapeutic interventions. Mood dynamics are richly and profoundly altered in depressed states. The humble Kalman filter is a well-established, rich framework to characterise mood dynamics. Its application to EMA data is valid; straightforward; and likely to result in substantial novel insights both into mechanisms and treatments.

Optimized Longitudinal and Lateral Control Strategy of Intelligent Vehicles Based on Adaptive Sliding Mode Control

To improve the tracking accuracy and robustness of the path-tracking control model for intelligent vehicles under longitudinal and lateral coupling constraints, this paper utilizes the Kalman filter algorithm to design a longitudinal and lateral coordinated control (LLCC) strategy optimized by adaptive sliding mode control (ASMC). First, a three-degree-of-freedom (3-DOF) vehicle dynamics model was established. Next, under the fuzzy adaptive Unscented Kalman filter (UKF) theory, the vehicle state parameter estimation and road adhesion coefficient (RAC) observer were designed to estimate vehicle speed (VS), yaw rate (YR), sideslip angle (SA), and RAC. Then, a layered control concept was adopted to design the path-tracking controller, with a target VS, YR, and SA as control objectives. An upper-level adaptive sliding mode controller was designed using RBF neural networks, while a lower-level tire force distribution controller was designed using distributed sequential quadratic programming (DSQP) to obtain an optimal tire driving force. Finally, the control strategy was validated using Carsim and Matlab/Simulink software under different road adhesion coefficients and speeds. The findings indicate that the optimized control strategy is capable of adaptively adjusting control parameters to accommodate various complex conditions, enhancing the tracking precision and robustness of vehicles even further.

Lateral Convergence Deformation Prediction of Subway Shield Tunnel Based on Kalman Model

In order to optimize the structure of a subway shield tunnel, minimize injuries, and avoid potential safety hazards, the lateral convergence deformation of subway shield tunnels should be predicted. In terms of accuracy and stability, existing prediction models perform poorly in obtaining the lateral convergence deformation value of a non-stationary small-sized sample of a subway shield tunnel. In this paper, a lateral convergence model of a subway shield tunnel based on the Kalman algorithm is constructed based on Kalman filtering theory. The model is efficient, adaptive, and robust and can accurately predict the lateral convergence deformation of a subway shield tunnel. Taking the horizontal diameter of a 200-ring shield segment in the interval section of a subway tunnel as an example, we have proved that the residuals of the Kalman prediction model are small, the residual distribution conforms to the normal distribution, and the prediction effect is great. The model is suitable for the prediction of more than five periods of data, and the prediction accuracy of the model improves with an increase in the number of data periods. In addition, in this paper, we compare the Kalman model with the GM(1,1) model and the GM–Markov model, and the RMSE, NRMSE, MAPE, and R2 are used as evaluation indices. The results show that the Kalman model has a higher prediction accuracy and is more suitable for predicting the lateral convergence deformation of a subway shield tunnel.

Non-destructive estimation of temperature field during laser-induced tumor hyperthermia based on Kalman filtering

Laser-induced thermal therapy (LITT) is an emerging minimally invasive treatment technique for tumors. Non-destructive acquisition of the transient temperature field in the target tissue is a key in studying and developing LITT technology. In this paper, a non-destructive temperature field estimation scheme based on Kalman filtering theory is proposed to address the challenge of temperature field monitoring during the LITT process. This scheme establishes a state space model that corresponds to the fundamental equations of heat transfer in biological tissues. Subsequently, the real-time estimation of the transient temperature field within the target tissue is conducted by integrating the temperature observations on the surface of the tissue with the state space model of heat transfer in biological tissues and the Kalman filtering theory. Numerical experiments are conducted in this study to estimate the transient temperature field inside the target tissue during the therapy of LITT. The effect of the number of temperature observation points on the surface of the target tissue, laser irradiation conditions, and measurement noise on the estimation results of the transient temperature field within the target tissue is also discussed.

Soft Measurement of Road Adhesion Coefficient Volumetric Kalman Filtering

In order to solve the problem that the road adhesion coefficient is not extensive enough and difficult to obtain in practice, this paper designs a soft measurement method of road adhesion coefficient based on the volumetric Kalman filter theory. A three-degree-of-freedom vehicle estimation model using the Dugoff tyre model is established, and the validity and accuracy of the algorithm are verified with the help of the joint simulation platform of Carsim and Matlab/Simulink. The results show that the estimation error of the proposed estimation algorithm is within 5% under the three road adhesion coefficients, and the initial design can be completed well in terms of accuracy and real-time performance.

Robust Fusion Kalman Estimator of the Multi-Sensor Descriptor System with Multiple Types of Noises and Packet Loss.

Under the influence of multiple types of noises, missing measurement, one-step measurement delay and packet loss, the robust Kalman estimation problem is studied for the multi-sensor descriptor system (MSDS) in this paper. Moreover, the established MSDS model describes uncertain-variance noises, multiplicative noises, time delay and packet loss phenomena. Different types of noises and packet loss make it more difficult to build the estimators of MSDS. Firstly, MSDS is transformed to the new system model by applying the singular value decomposition (SVD) method, augmented state and fictitious noise approach. Furthermore, the robust Kalman estimator is constructed for the newly deduced augmented system based on the min-max robust estimation principle and Kalman filter theory. In addition, the given estimator consists of four parts, which are the usual Kalman filter, predictor, smoother and white noise deconvolution estimator. Then, the robust fusion Kalman estimator is obtained for MSDS according to the relation of augmented state and the original system state. Simultaneously, the robustness is demonstrated for the actual Kalman estimator of MSDS by using the mathematical induction method and Lyapunov's equation. Furthermore, the error variance of the obtained Kalman estimator is guaranteed to the upper bound for all admissible uncertain noise variance. Finally, the simulation example of a circuit system is examined to illustrate the performance and effectiveness of the robust estimators.

Parameter estimation of the shell transfer arm of a loading mechanism

The shell transfer arm is a key component of gun automatic loading mechanism, the coordination speed and positioning accuracy have an important impact on gun ammunition delivery effect. Establishing an accurate dynamic model is the foundation for better control and prediction, therefore, it is necessary to identify the dynamic parameters of the shell transfer arm. In this paper, the dynamic model is established based on the topology method. The parameter identification model of the shell transfer arm is constructed by applying the dynamic model and unscented Kalman filter theory. Dynamic parameters of the shell transfer arm such as the mass, inertia and centroid position are estimated under unscented Kalman filter scheme. By comparing the parameter estimation results with the nominal design values, the feasibility and effectiveness of applying the proposed method to identify the dynamic parameters of the shell transfer arm are verified.

A survey of GNSS interference monitoring technologies

With the increasing economic and strategic significance of the global navigation satellite systems (GNSS), interference events also occur frequently. Interference monitoring technologies aim to monitor the interference that may affect the regular operation of the GNSS. Interference monitoring technologies can be divided into three parts: interference detection and recognition, interference source direction finding, and interference source location and tracking. Interference detection aims to determine whether interference exists. This paper introduces the classification of interference and the corresponding detection methods. The purpose of interference recognition is to recognize and classify interference. It is often combined with pattern recognition and machine learning algorithms. Interference source direction finding aims to estimate the direction of the interference signal. There are three kinds of methods: amplitude, phase, and spatial spectrum estimation. Interference source location aims to estimate the position of the interference signal. It is usually based on the received signal strength (RSS), time difference of arrival (TDOA), frequency difference of arrival (FDOA), angle of arrival (AOA) or direction of arrival (DOA). Interference source tracking aims to track moving interference sources, and it is generally based on Kalman filter theory. This paper summarizes the interference monitoring technologies and their latest progress. Finally, prospects for interference monitoring technologies are offered.

Integrated Sliding Mode Velocity Control of Linear Permanent Magnet Synchronous Motor with Thrust Ripple Compensation

In this paper, a compound sliding mode velocity control scheme with a new exponential reaching law (NERL) with thrust ripple observation strategy is proposed to obtain a high performance velocity loop of the linear permanent magnet synchronous motor (LPMSM) control system. A sliding mode velocity controller based on NERL is firstly discussed to restrain chattering of the conventional exponential reaching law (CERL). Furthermore, the unavoidable thrust ripple caused by the special structure of linear motor will bring about velocity fluctuation and reduced control performance. Thus, a thrust ripple compensation strategy on the basis of extend Kalman filter (EKF) theory is proposed. The estimated thrust ripple will be introduced into the sliding mode velocity controller to optimize the control accuracy and robustness. The effectiveness of the proposal is validated with experimental results.

Research on GPS/INS/WIFI Personnel Tight Combination Positioning Method

With the development of current information technology, it has become a common demand to obtain accurate location information quickly. However, in the indoor environment where people generally live, GPS signals are partially occluded, and the INS of inertial navigation system will significantly increase the error due to the integral accumulation error. In view of the problems of poor robustness and low accuracy of the existing loose combination positioning methods, a GPS/INS/WIFI personnel tight combination positioning method was proposed by using the WIFI network signals with wide coverage at present. Firstly, the characteristics of WIFI positioning technology were analyzed, and the INS positioning error model was established. The measurement equation under tight coupling was established by using the pseudo range value of GPS and the RSSI parameters of WIFI system, and the state equation was established by using the INS error model, so as to realize the establishment of the combined GPS/INS/WIFI positioning state space equation. Then, based on unscented Kalman filter theory, a GPS/INS/WIFI based compact combined position solution model is established. Finally, the human wearable combined positioning experiment platform was used for experimental verification. The experimental results show that the GPS/INS/WIFI based tight combined positioning method can significantly adapt to the indoor environment with complex interference, has high positioning stability and positioning accuracy, and the maximum positioning error is 0.45m. Compared with the extended Kalman filter and Kalman filter, the positioning accuracy of unscented Kalman filter is improved by 56% and 89% respectively, which can meet the requirements of field use.

Research on the network handoff strategy based on the best access point name decision.

To improve the network switching performance and efficiency of mobile phone terminals and establish an efficient mobile communication network connection, this paper constructs the SDN+MPTCP+CP (Software Defined Network, Multi-Path TCP, and Mobile Terminal) mobile communication network model and designs a network switching algorithm with a preselected available access point name (APN) based on the potential game method. The constructed network model integrates a 5G mobile communication network, satellite communication, the SDN network, and the MPTCP multi-way communication technology. APN access point is preselected by using Kalman filtering theory, and dual problems are resolved with the Lagrange function. To determine the MPTCP sub-flow transmission path, the differential derivative calculation is introduced. The performance of the network switching strategy is evaluated based on the Jacobian matrix. Then, the game coefficient is designed, and the game function is calculated. A potential game balance point is found, and an updating strategy is formulated to determine the best APN access point. The simulation network model is constructed, and the parameters of the performance evaluation are defined to find the performance comprehensively. The experimental results demonstrated the extreme reliability, stability, and compatibility of the proposed algorithm.

Moving Vehicle Tracking under Measurement Uncertainties, Multi-step Random Delays, and Packet Dropouts

The unbiased finite impulse response (UFIR) filter, Kalman filter (KF), and game theory <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty} $ </tex-math></inline-formula> filter are developed for vehicle tracking in wireless sensor networks (WSNs) with multi-step random delays and multiple dropouts. The problem with data delays is solved for given delay probabilities by converting a model with delays to another without delays. The dropouts are detected at the receiver by a data sensor, and lost data are compensated for by prediction. The filters developed are experimentally tested for accuracy and robustness using the Global Positioning System-based vehicle tracking database, where the measured coordinates are transmitted over WSN with delays. It is shown that the UFIR filter is the most robust to uncertain delays and the KF is the most accurate when the delay probabilities are known exactly. The game theory <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> filter is the most accurate under ideal conditions and prone to divergency otherwise.

АДАПТИВНЕ ОЦІНЮВАННЯ ПАРАМЕТРІВ РУХУ ПОВІТРЯНОГО СУДНА У РЕЖИМІ ДОТРИМАННЯ ЗАДАНОЇ ПОСАДКОВОЇ ТРАЄКТОРІЇ

The creation of a large number of new aircraft types and their intensive operation have led to an increase in air traffic. Guaranteeing the required level of safety requires continuous improvement of air traffic organization and control systems. This stimulates the modernization of existing and the creation of new types of radio equipment. In this work, the object of study is the processes of converting information signals in the goniometric channel of the radio landing system, and its goal is to achieve increased accuracy of angular measurements and their reliability by methods of secondary signal processing based on the basic principles of the theory of optimal linear discrete Kalman filter. It is shown that one of the possible ways to achieve this goal can be the use of a polymodel model of aircraft motion, supplemented by interacting logic of a stochastic type, as an effective, relatively simple resource-saving tool for overcoming a priori uncertainty of conditions and flight regime. Considerations are given regarding the adequacy of the mathematical model types used to describe a fixed aircraft approach trajectory. The issues of approximation of nonlinear dependences in the goniometric channel of the landing radar in the process of changing the coordinate system are considered. A technique for performing a computational experiment using the Monte Carlo method using the computing environment of the LabView modeling system is presented. The obtained results prove the effectiveness of the polymodel method for constructing a filter adapted to the needs of the aircraft landing process. The absence of discrepancies regarding the regulated standards for the accuracy of measuring the angular coordinates of the aircraft confirm this fact.

Study on torsional vibration characteristics and suppression of electric vehicles with dual-motor drive system

The battery electric vehicles with dual-motor coupling drive system have serious torsional vibration problems when the driving torque changes rapidly. This paper targets at reducing the negative effect of the torsional vibration with an active control strategy. The torsional vibration model of the dual-motor coupling drive system is established through the lumped mass method. A four-inertia modeling method which can reflect the powertrain configuration characteristics is proposed, by simplifying the traditional lumped mass model, and the feasibility is verified based on the error comparing of the torsional vibration characteristics between the two models. Combined Kalman filter theory, PID control theory and fuzzy control theory, a real-time self-tuning active control strategy is proposed to compensate motor torque by considering vehicle acceleration as the control input. Finally, the four-inertia model with the control strategy is simulated under such conditions as the torque abrupt change and the C-WTVC driving cycle. The simulation results indicated that the proposed active control strategy performs well in the torsional vibration suppression and the control effect is robust to the different structural parameters.

Design of Full-Order State Observer for Two-Mass Joint Servo System Based on the Fixed Gain Filter

This article mainly designs a novel full-order state observer for the two-mass elastic servo system. In order to observe all the states of the two-mass system without the aid of any additional sensors, the model of the observer is constructed that includes two relative parts. Based on the theory of steady-state Kalman filter (KF), the fixed gain filter (FGF) scheme is studied. To overcome the heavy computational processing burden from the KF, the mechanism of the only one adjustable parameter is studied for the FGF-based observer. The adjustable parameter can be further refined by stability analysis and control characteristics within a small range, and the exact value can be calculated according to the desired observation performance, by compromising both the noise sensitivity and tracking capability. The proposed full-order observer method is experimentally verified in a two-mass system to provide easy parameter tuning, decreased computational complexity, and flexible observation performance in all cases.

Optimal linear attack for multi-sensor network against state estimation

This paper is concerned with a security problem about malicious integrity attacks in state estimation system, in which multiple smart sensors locally measure information and transmit it to a remote fusion estimator though wireless channels. A joint constraint is considered for the attacker behaviour in each channel to keep stealthiness under a residual-based detector on the remote side. In order to degrade the estimator performance, the attacker will maximize the trace of the remote state estimation error covariance which is derived based on Kalman filter theory. It is proved that the optimal linear attack strategy design problem is convex and finally turned into a semi-definite programming problem. In addition, the tendency of attack behaviour on recursive and fixed Kalman filter system is analyzed. Several examples are given to illustrate the theoretical results.

Application of Tissue Engineered Nanomaterials in Meniscus Sports Injury Repair.

In daily life and sports activities, the knee joint is the dominant joint. Movements such as walking upstairs, running, and walking require the knee joint to function. The principle of tissue engineering and the technical methods of molecular biology to construct functional meniscus replacement products in vitro have become an ideal method to fundamentally solve the meniscus injury. This paper aims to study the application of tissue engineered nanomaterials in meniscal sports injury repair. In this paper, KOA exercise therapy based on Kalman filter theory is proposed, which has a great effect on the rehabilitation of bone tissue injuries. The experimental results of this paper show that in the number of people with meniscus injuries in 2013, the percentage of people younger than 25 years old was 13%, and the percentage of people younger than 25 years old in 2020 was 12%, which did not change much. However, the percentage of people over 40 years old was 57% in 2013, and by 2020, the percentage is 66%. Although the increase is not large, the percentage of people over the age of 40 is the highest every year, which means that older people have a higher proportion of meniscal injuries.

Robust fusion filter for multisensor descriptor system with uncertain‐variance noises and packet dropout

AbstractFor the multisensor linear stochastic descriptor system with uncertain‐variance noises and packet dropout, the standard state space model of the new reduced‐order augmented state is obtained based on the singular value decomposition (SVD) approach and augmented state approach. By applying the min‐max robust estimation principle and Kalman filtering theory, the local robust time‐varying Kalman filters of the reduced‐order augmented state and fictitious process noise are proposed. Then, the local robust time‐varying filters of the original descriptor system are presented according to the relation of the reduced‐order augmented state and the original state. And the distributed and covariance intersection (CI) fusion robust time‐varying filters are presented, and the actual and conservative filtering error variances are obtained. Further, the robustness of the local and fused robust filters are proved by applying Lyapunov equation approach, and the accuracy relation between them is analyzed. A simulation example applied to a circuit system shows its effectiveness and applicability.

Rice yield response to climate and price policy in high-latitude regions of China

Climate change has renewed interest in the production capacity of agriculture. Few researchers paid attention to price policy and heteroscedasticity in yield model. We incorporate rice price policy into the yield model at the expected price using a Tobit procedure and take Kalman filter theory to explore useful information, and then estimate the rice yield response to climate and rice price using a spatial autoregressive combined model in high-latitude regions of China from 1992 to 2018. Meanwhile, we apply two different Breusch-Pagan tests to examine heteroscedasticity. Our results suggest that spatial correlation of the error term is a more critical source of heteroscedasticity and cannot be completely solved by only allowing spatially autocorrelated errors due to possible technology diffusion effects. The results also show that rice price support policy is useful for constructing rice expected prices, and the price elasticities of rice and corn on rice yield are 0.194 and -0.097, respectively. Among climate variables, the total growing degree days in the growing season has positive effects, and monthly accumulated growing degree days also matter, especially in June. Precipitation in July and August has a significant effect with an inverse U shape. Projections of future climate change suggest that rice yield will mainly increase, ranging from 0.095% to 1.769%, but the rate of increase in yield will slow down in the higher-rate global warming. This study shows how price policy could be incorporated into yield response model and highlights the importance of climate factors and crop price policy for rice yield.

Kernel representation of Kalman observer and associated H-matrix based discretization

In deterministic estimation, applying a Kalman filter to a dynamical model based on partial differential equations is theoretically seducing but solving the associated Riccati equation leads to a so-called curse of dimensionality for its numerical implementation. In this work, we propose to entirely revisit the theory of Kalman filters for parabolic problems where additional regularity results proves that the Riccati equation solution belongs to the class of Hilbert-Schmidt operators. The regularity of the associated kernel then allows to proceed to the numerical analysis of the Kalman full space-time discretization in adapted norms, hence justifying the implementation of the related Kalman filter numerical algorithm with H-matrices typically developed for integral equations discretization.