35 results about "Sigma point" patented technology

The embodiment of the invention provides an aircraft motion state determination method based on Lie group unscented Kalman filtering, and the method comprises the steps: building a state model of a target aircraft, and a measurement model of the target aircraft; obtaining a final Lie group state estimation value of the target aircraft through iterative calculation according to the state model and the measurement model; and determining the motion state of the target aircraft according to the final Lie group state estimation value. According to the technical scheme, a Lie group unscented Kalman filtering navigation framework based on external measurement information is provided, specific forms of sigma point error propagation on Lie algebra and state updating on the Lie group are given, and a self-adaptive updating method of a state noise covariance matrix and a measurement noise covariance matrix is designed. Therefore, the self-adaptive Lie group unscented Kalman filtering method is provided, and the multi-sensor multi-beacon target state estimation precision is greatly improved by means of the self-adaptive Lie group unscented Kalman filtering method.

The invention provides an attitude monitoring method and system in navigation of an aircraft, and the method comprises the steps: determining a process noise covariance matrix through a high-frequency energy component of an angular velocity signal measured by a current gyroscope in each filtering period; predicting a prior state vector and a prior covariance matrix at the current moment according to the state vector at the previous moment, the angular velocity measured by the current gyroscope and the process noise covariance matrix; generating an asymmetric Sigma point set and determining a measurement noise covariance matrix; the asymmetric Sigma point set is substituted into a measurement model, and a predicted measurement value and a predicted measurement covariance are obtained through unscented transformation; calculating Kalman gain based on the predicted measurement covariance and the measurement noise covariance matrix, and performing weighted gating test on innovation formed by a real measurement value and a predicted measurement value; and updating a state vector and a covariance matrix on the basis of the adjusted Kalman gain and information so as to obtain attitude information of the aircraft at the current moment.

The invention provides a condenser state estimation method based on adaptive noise square root Kalman filtering. Firstly, mathematical models of a condenser evaporation area, a hot well water area and a cooling pipe area are established according to the operation mechanism of a thermal power generating unit condenser; an unscented Kalman filtering algorithm is selected as a basic algorithm for state estimation of a condenser system, and then an optimal adaptive noise square root unscented Kalman filtering algorithm is constructed. The method comprises the steps of filtering initialization, Sigma point set generation, time updating, Sigma point set reconstruction, measurement updating, filtering updating, adaptive factor construction, cross covariance matrix / square root correction, fading forgetting factor calculation and noise covariance matrix correction. And finally, estimating the pressure state and the liquid level state of the condenser by using an optimal adaptive noise square root unscented Kalman filtering algorithm.

The invention discloses an IGBT life prediction method based on adaptive unscented particle filtering of time sequence form perception optimization, and belongs to the technical field of health prediction and reliability engineering. The method aims at the problems that a traditional filtering algorithm is prone to falling into local optimum in a high-dimensional parameter space and prediction trajectory forms are discontinuous, and comprises the steps that firstly, an IGBT nonlinear degradation model is established through a state-space equation; performing Sigma point sampling and nonlinear propagation at a particle level by adopting an unscented transformation and particle filtering cooperation mechanism, and fusing process noise to realize dynamic state prediction; constructing a Gaussian likelihood function by using the deviation between a predicted value and an actual observed value to generate a system residual sequence; an FCD fusion index is innovatively introduced, the index fuses a Pearson correlation coefficient and a Frechet distance to synchronously quantify trend consistency and form similarity, and self-adaptive genetic optimization is driven accordingly; and repeating the behaviors before a preset termination condition is met, and continuously updating the parameters of the state-space equation.

The invention discloses a system inertia and primary frequency modulation coefficient estimation method and device, equipment and a medium. A Sigma point set is generated according to posterior state estimation including inertia, primary frequency modulation coefficient and frequency deviation at the last moment and covariance of the posterior state estimation; a prediction state and statistics thereof are obtained through nonlinear state transfer function transformation; obtaining a predicted measurement value and a statistic thereof through measurement function transformation, and calculating a cross covariance of a state and measurement; the prediction state is updated by using the actual frequency deviation and the Kalman gain calculated based on the measurement covariance and the cross covariance, and the current optimal state estimation is obtained; and finally, inertia and a primary frequency modulation coefficient are extracted from state estimation. According to the method, real-time, joint and online accurate identification of the inertia and the primary frequency modulation coefficient is realized, the problems of linearization error and parameter coupling neglect of a traditional method are effectively solved, the robustness and accuracy of estimation are remarkably improved, and reliable state sensing support is provided for stable analysis of the frequency of a power system.

The invention discloses a wide-working-condition steam turbine system operation data correction method based on digital twinning, and relates to the technical field of steam turbine equipment digitalization, and the method comprises the steps: collecting operation data of a wide-working-condition steam turbine system in real time; constructing a digital twinborn model of the steam turbine system; performing prior covariance estimation on the operation data according to the statistical distribution condition and the design parameters; generating a Sigma point by adopting an unscented Kalman filtering algorithm, iteratively updating a state vector and a covariance in combination with a state transition equation and an observation equation, and outputting an updated known variable; performing smoothing processing on the updated known variable in a plurality of time point regions by adopting an RLOESS algorithm to obtain corrected operation data; according to the method, the real dynamic characteristics of the wide-working-condition steam turbine are approached by building the digital twinborn model, the calculation complexity of dynamic data fusion of a steam turbine system can be remarkably reduced, and the problems that the convergence speed is low and calculation is complex due to strong nonlinearity of a traditional method are solved.

The application discloses a power distribution network prediction auxiliary state estimation method and system based on an improved iteration process, and the method comprises the following steps: establishing a nonlinear discrete time state space model; generating a group of Sigma points through an unscented transformation, and substituting the Sigma points into a state transition equation to calculate a state prediction value and a state prediction error covariance matrix at a current time; substituting the Sigma points into a measurement equation to obtain a measurement prediction value, and calculating a Kalman gain; calculating a process noise covariance matrix at a next time; and correcting the state prediction value and the state prediction error covariance matrix at the current time to obtain an optimal state estimation value and an error covariance matrix thereof. The application avoids the risk of losing semi-positive definiteness of the covariance matrix in the iteration process from the algorithm mechanism, significantly enhances the numerical stability and robustness of the UKF algorithm, and ensures reliable application in high-dimensional complex power distribution network state estimation.

The application belongs to the technical field of radio positioning and motion control, and specifically discloses a kind of exoskeleton control filtering methods based on UWB and IMU fusion, comprising: deploying UWB base station, UWB label and IMU module;First displacement of knee joint in horizontal direction is measured by UWB label, first forward speed is calculated, second displacement of knee joint in horizontal direction is measured by IMU module, and second forward speed is calculated;State equation and observation equation are constructed, Sigma point is generated and untraceable Kalman filtering iteration is executed, and prediction result is optimized until the confidence of prediction result reaches a preset value.The application applies PDOA algorithm to solve angle, the angle and angular velocity measured by IMU module are fused by untraceable Kalman filtering, the motion direction error caused by single sensor is avoided, and the attitude estimation precision of exoskeleton control is improved.The application is suitable for exoskeleton control.

The invention discloses a mine robot tracking method for trust adaptive event-driven unscented Kalman fusion filtering. Firstly, an RSS time-varying response radius-based trust adaptive event-driven anchor point scheduling and anchor point data transmission triggering mechanism is designed to adapt to distribution change scheduling of trust anchor points around a mine robot to be close to a preset number of trust anchor points and dynamically trigger data transmission as required. Then, randomly and uniformly distributed noise covariance is introduced to describe the uncertainty of mine robot motion modeling, and through iterative uniform sampling Sigma point weighted average, the consistency of square root unscented Kalman filter information estimation is ensured; and finally, a credible anchor point separation mechanism of K-means dimensionality reduction clustering is constructed, a credible measurement updating mine robot motion state estimation adaptive weight fusion strategy is constructed, and the accuracy, stability and robustness of mine robot tracking are improved.

The invention relates to the technical field of robot positioning, discloses a four-foot robot three-dimensional positioning method and system, a storage medium and a robot, and aims to solve the technical problems of height drift and foot end error accumulation of a four-foot robot in a visual degradation environment without a GPS (Global Positioning System) by a traditional positioning method. The method comprises the following steps: firstly, constructing an initial state vector containing motion states of a fuselage and four foot ends, and establishing a nonlinear continuous time state equation considering foot end dynamics; relying on an unscented Kalman filtering framework, a prior state is obtained through Sigma point sampling and time updating; a foot end observation value is corrected through foot bottom rolling compensation, a height absolute reference is provided by combining a local invariant elevation map, and multi-leg slippage detection and observation weight self-adaptive adjustment are synchronously completed; and finally, the optimal state is updated and output through observation. According to the invention, the visual sensor is used for topographic mapping instead of direct positioning, the height drift is effectively inhibited, the robustness and precision of positioning in a complex environment are improved, and the method is suitable for unstructured scenes such as rescue exploration and the like.

The invention belongs to the technical field of rigid body posture estimation, and discloses a rigid body posture estimation method, system and device based on generalized correlation entropy geometric filtering, and the method comprises the steps: obtaining target motion information, and building a discrete nonlinear kinematics model; the discrete nonlinear kinematics model is initialized; sigma points of a posterior state covariance matrix and a process noise covariance matrix are generated respectively, and the sigma points are propagated and updated through manifold fast unscented transformation; obtaining a prediction state mean value, a priori state covariance matrix and a square root of the priori state covariance matrix; updating the central parameters based on the information of the historical moments; calculating a pseudo measurement matrix and updating the gain; correcting the state estimation by using the gain; judging whether convergence occurs or not, and if not, continuing iteration; otherwise, outputting a posterior state estimation value as a final rigid body posture estimation result at the moment. According to the method, the problem that the robustness and precision of rigid body posture estimation in a non-zero mean value and non-Gaussian noise environment are reduced is effectively solved.

The present invention discloses a fast sensor data fusion method based on sigma point belief propagation, comprising the following steps: step (1), predicting the state and covariance of target k at time t; step (2), performing sigma point sampling on the predicted state; step (3), transferring sigma points on the sampled samples in step (2); step (4), calculating iterative data association within all sensors s in parallel; step (5), performing confidence calculation after completing the iterative data association within the sensor; step (6), estimating the state and covariance of each target k at time t+1 based on the distribution of the state of target k at time t+1. The method solves the problems of high computational complexity and poor scalability of traditional multi-sensor information fusion algorithms, and reduces computational complexity based on the implementation of the sigma point belief propagation algorithm.

The invention discloses a power distribution network prediction auxiliary state estimation method and system based on iteration process improvement. The method comprises the following steps: establishing a nonlinear discrete time state space model; generating a group of Sigma points through unscented transformation, substituting the Sigma points into a state transition equation, and calculating a state prediction value and a state prediction error covariance matrix at the current moment; substituting the Sigma point into a measurement equation to obtain a measurement predicted value, and calculating a Kalman gain; calculating a process noise covariance matrix at the next moment; and correcting the state prediction value and the state prediction error covariance matrix at the current moment to obtain an optimal state estimation value and an error covariance matrix thereof. According to the method, the risk that the covariance matrix loses the semi-positive qualitative property in the iteration process is avoided from the algorithm mechanism, the numerical stability and robustness of the UKF algorithm are remarkably enhanced, and reliable application in high-dimensional complex power distribution network state estimation is ensured.

Techniques for determining a collision probability between a candidate trajectory associated with a vehicle and an object (e.g., a vehicle or pedestrian) in the vehicle's environment. In some cases, the techniques include selecting a set of sampled states, where each sampled state represents a predicted state (e.g., a predicted position and / or orientation) of the object at a future time. The set of sampled states may then be used to determine the collision probability. In some cases, the set of sampled states associated with a future time t may be determined based on: (i) a probability distribution (e.g., a Gaussian distribution) associated with the predicted object state at the future time t, and / or (ii) a covariance of the probability distribution. In some cases, the set of sampled states selected based on a distribution includes a set of sigma points each associated with a probability.

Computer-implemented method for training a machine learning system. The machine learning system is configured to accept a sensor signal as input for anomaly detection and / or for sampling a trajectory of a traffic participant and / or for sampling of sensor signals and / or for determining a value characterizing a likelihood of a sensor signal with respect to a training dataset. The training includes: determining, by an encoder of the machine learning system and based on a training sensor signal, a first intermediate representation characterizing a mean of a latent distribution of a latent space and a second intermediate representation characterizing a variance and / or covariance of the latent distribution; determining, based on the first intermediate representation and the second intermediate representation, a plurality of sigma points with respect to the latent distribution; determining an output signal.

The invention relates to the technical field of hydrogen-electricity coupling, and provides a hydrogen-electricity coupling micro-grid energy management model adaptive updating method, which comprises the steps of generating a Sigma point based on unscented transformation, predicting a state and an observation value through a state and observation equation, and calculating statistical characteristics of the state and the observation value; according to the method, state-observation cross covariance and Kalman gain are further calculated, weighted fusion correction is carried out on state prior estimation by using actual observation residual, noise is effectively suppressed, nonlinear dynamics are accurately processed, and high-credibility state estimation is provided for energy management decision. A feature space is constructed based on real-time state estimation feedback information, fusion features are extracted through incremental principal component analysis and input into an energy management model to calculate a loss function, and a learning rate is adaptively adjusted by calculating first-order and second-order moments of gradient information in parameter vector loop iteration. The model parameters are updated according to the learning rate and the gradient of the loss function, and the problem that the model applicability in a traditional model updating mode is reduced is solved.

Approaches presented herein provide for the support of distorted cameras in 3D scene reconstruction. Objects in a scene can be represented by 3D Gaussian particles. To determine which 3D Gaussian particles contribute to individual pixels of an image to be rendered, an unscented transform-based approach can be used to project representative sigma points for the 3D Gaussian particles onto a 2D camera plane. The 3D Gaussian particles determined to potentially contribute to a given pixel can then have rays traced to determine a segment of intersection of the ray across a 3D Gaussian particle, and a value corresponding to the point of maximum response across that segment can be returned as a contribution value. The various contribution values for each pixel can then be blended to provide an output color value.

The invention discloses a self-adaptive UKF fusion positioning method for an outdoor cleaning robot. The method comprises the following steps: acquiring inertial measurement unit IMU data, point cloud data and RTK positioning data through a sensor; according to the system state of the robot, unscented Kalman filtering (UKF) is adopted for unscented transformation, IMU data serve as control input, a predicted sigma point set is obtained, and sigma points serving as the system state are updated; evaluating the quality of the point cloud data; according to the point cloud data quality evaluation and the RTK positioning data, a current positioning mode is adaptively selected through a state machine, and the positioning mode comprises a first mode with the point cloud data quality as the main mode, a second mode with the RTK positioning data as the main mode and a third mode fusing the point cloud data quality and the RTK positioning data; and according to a corresponding mode, observation updating and time-sharing dimension multiplexing are carried out based on unscented Kalman filter (UKF).

The application discloses a coordinate system transformation fusion filtering tracking method and system for a dual-base station radar, and relates to the technical field of radar target tracking. The method comprises the following steps: firstly, establishing state and observation equations, and determining an initial state of a target based on prior information in a Cartesian coordinate system. Then, a target motion state is obtained through one-step prediction, sigma points are generated by using U transformation, and a mean value and a covariance of state space prediction are calculated and constructed. Next, measurement data and prediction data are fused by using a Kalman filter to obtain optimal state estimation and a covariance matrix. Finally, the updated state estimation is converted back to the Cartesian coordinate system based on U transformation, and the process is repeated until the tracking is completed. The application can avoid the nonlinear filtering problem in the updating process, and improves the robustness and precision of tracking.

The invention relates to the technical field of attitude control, in particular to a propulsion control method, system and device applied to an underwater robot. According to the method, a sigma point of an unscented Kalman filtering process is obtained through an environment system state vector of a robot, and an adjustment limit vector of a sampling moment is obtained according to numerical fluctuation of different dimensions; a confusion degree evaluation index is obtained according to the unstable condition of continuous change of the adjustment limit vector; and performing self-adaptive regulation and control on the switching gain through the deviation condition of the current and initial limiting ranges and chaos degree evaluation, and outputting a control signal again in combination with the adjustment of the sampling frequency by the chaos degree evaluation. According to the method, in the process of adjusting the switching gain and the sampling frequency through the continuous environment interference chaos condition, the gain is improved, so that the system is rapidly converged, meanwhile, the limitation adjustment is considered, the jitter condition of control output is reduced, and the adjustment control of the attitude of the propulsion action of the AUV at each time is more accurate and efficient.

The application discloses a kind of based on SVD-ACUKF online model updating hybrid test method, belongs to the technical field of hybrid test.To solve the problem of insufficient parameter identification accuracy, inaccurate test substructure loading boundary, insufficient model updating accuracy and test error in online model updating hybrid test method, the initial value of the parameter to be identified is first determined, the displacement response of the overall structure is obtained based on ground motion, and then the displacement response of the physical substructure is obtained and tested to be loaded, to obtain the counterforce and displacement of the physical substructure, based on the state of the physical substructure at step k-1, 2n+1 Sigma points are generated, and they are sent to the numerical model of the equivalent physical substructure together with the displacement, 2n+1 times of nonlinear static analysis are completed to obtain the restoring force, and then the constitutive model parameters are obtained by using the counterforce and displacement of the physical substructure and the state estimation value of the equivalent physical substructure at step k-1, and then the finite element refined numerical model of the overall structure is updated, and the above process is repeated until the test is completed.

The invention discloses a building structure load identification method and equipment. The method comprises the steps of determining an initial state quantity and an initial state quantity covariance of a building structure; based on the UT transformation principle of an unscented Kalman filter, generating a group of Sigma points according to the state quantity and covariance at the previous moment, and writing the Sigma points into a matrix form; calculating information of each column of Sigma points in the matrix on the basis of the Alembert principle, the structural quality and the matrix information to obtain a plurality of accelerated speed predicted values with the number equal to that of the columns of the matrix; calculating a weighted average value of all acceleration predicted values based on a weight value of UT (Unscented Kalman Filter); constructing a target function about the unknown load of the structure based on the acceleration measurement value measured by the sensor and the weighted average value; based on a Levenberg-Marquardt optimization method, calculating a corresponding load estimation value when the target function obtains a minimum value; updating the state quantity and the state quantity covariance of the unscented Kalman filter based on the load estimation value; and circularly executing the steps until all time steps are calculated.

The invention discloses an SOC (State of Charge) estimation method of deep fusion neural network unscented Kalman filtering, relates to the technical field of all-vanadium redox flow batteries, and aims to realize high-precision estimation of the state of charge of the battery. The method comprises the following steps: establishing a second-order equivalent circuit model of a battery, and performing parameter identification on the second-order equivalent circuit model; obtaining a group of sigma points through unscented transformation, calculating propagation state estimation and propagation state prediction of each sigma point, obtaining a first-order statistical moment of prior state estimation, a first-order statistical moment of prior state prediction and a cross covariance through unscented transformation, and obtaining an observation difference and a state updating difference; and inputting the observation difference and the state updating difference into a neural network system to obtain a Kalman gain, and performing state updating on the priori state estimation through the Kalman gain to obtain prediction of the state of charge of the battery.

The invention discloses a correction method, device, equipment and medium for an inertial measurement unit of an unmanned aerial vehicle, and relates to the field of data processing, the correction method for the inertial measurement unit of the unmanned aerial vehicle comprises the following steps: constructing a sigma point at a k-1 moment through unscented transformation according to posterior state data at the k-1 moment of the inertial measurement unit of the unmanned aerial vehicle, the sigma point covers the sensor parameters of the inertial measurement unit and the probability distribution of the state of the unmanned aerial vehicle; performing prediction processing on the posterior state data at the k-1 moment by using unscented Kalman filtering based on the sigma point to obtain prior state data at the k moment of the inertial measurement unit of the unmanned aerial vehicle; according to the preset measurement data of the plurality of sensors at the moment k, constructing a sensor measurement model at the moment k; projecting the sigma point at the k-1 moment to a measurement space of a sensor measurement model, and determining a pre-measurement mean value and a measurement covariance of the sensor at the k moment; determining the state correction of the inertial measurement unit according to the pre-measured mean value, the measurement covariance and the sigma point; performing state parameter correction on the prior state data at the k moment according to the state correction quantity, and determining posterior state data of the inertial measurement unit of the unmanned aerial vehicle at the k moment; and determining the state information of the unmanned aerial vehicle at the moment k and the zero offset of the inertial measurement unit at the moment k according to the posterior state data, and performing sensor parameter correction on the inertial unit of the unmanned aerial vehicle according to the zero offset at the moment k.

The application discloses a UKF filtering algorithm based on secondary Sigma points and belongs to the field of filtering algorithms; specifically, firstly, the state estimation mean value of a trajectory reentry target plane model is selected as a center point, UT transformation is carried out according to the state estimation variance, and 2n+1 primary Sigma points are obtained; then, UT transformation is respectively carried out with each primary Sigma point as a center point, and 2n+1 secondary Sigma point sets corresponding to the dispersion range of the adaptive adjustment Sigma point set are calculated according to the state covariance matrix P zz,k+1 Finally, through a Sigma point set estimation effect evaluation algorithm, the degree that the secondary Sigma point set approximates to the real observation is represented by the scalarized innovation, and the secondary Sigma point set or the primary Sigma point set with the minimum scalarized innovation is selected as the Sigma point set with the optimal estimation precision, which is used for calculating the Kalman gain and updating the state estimation. The application has better convergence speed and stability, and based on the symmetry distribution characteristics of the Sigma point set, the calculation amount is reduced to a certain extent without affecting the estimation effect of the filtering algorithm.

This invention belongs to the field of rigid body pose estimation technology, and discloses a rigid body pose estimation method, system, and device based on generalized correlation entropy geometric filtering. The method includes: acquiring target motion information and establishing a discrete nonlinear kinematic model; initializing the discrete nonlinear kinematic model; generating sigma points for the posterior state covariance matrix and the process noise covariance matrix, respectively, and propagating and updating the sigma points through a manifold fast unscented transformation; obtaining the predicted state mean, the prior state covariance matrix, and the square root of the prior state covariance matrix; updating the center parameters based on the information from historical moments; calculating the pseudo-measurement matrix and updating the gain; correcting the state estimate using the gain; determining whether convergence has occurred, and if not, continuing the iteration; otherwise, outputting the posterior state estimate as the final rigid body pose estimation result for that moment. This invention effectively solves the problems of robustness and accuracy degradation in rigid body pose estimation under non-zero mean and non-Gaussian noise environments.

The application provides a kind of attitude monitoring method and system in aircraft navigation, in each filtering period, the high frequency energy component of current gyroscopic measurement angular velocity signal is used to determine process noise covariance matrix, according to the state vector of last time and the angular velocity obtained by current gyroscopic measurement and process noise covariance matrix, the prior state vector and prior covariance matrix of current time are predicted;Asymmetric Sigma point set is generated and measurement noise covariance matrix is determined;The asymmetric Sigma point set is substituted into measurement model, and the predicted measurement value and predicted measurement covariance are obtained by unscented transformation;Based on the predicted measurement covariance and the measurement noise covariance matrix, the Kalman gain is calculated, and the innovation composed of real measurement value and predicted measurement value is weighted gate inspection;Based on the adjusted Kalman gain and innovation, the state vector and covariance matrix are updated, and then the attitude information of current time aircraft is obtained.

The application discloses a robot dynamic target searching and tracking method based on adaptive particle filtering tree. The method can quickly and accurately calculate mutual information based on a mutual information estimation method of sigma points. In Monte Carlo tree search, a motion primitive meeting a kinematic model is used to form an action space, so that a smooth path meeting the kinematic constraint is generated. An adaptive stop strategy in the adaptive particle filtering tree can dynamically adjust a planning time domain according to reward information, so as to reduce the operation time. The application selectively searches the feasible paths in the future, and the adaptive property can dynamically adjust the planning time domain according to the current reward information, so as to save the computing resources. In combination with the action space formed by the motion primitive, the application can efficiently generate a long-time-domain smooth path meeting the kinematic model considering the influence of future observation, so as to efficiently complete the target searching and tracking problem.

The invention discloses a method for estimating the remaining capacity of a lithium iron phosphate power battery, and belongs to the technical field of power battery state monitoring. The method comprises the following steps: establishing a second-order RC equivalent circuit model of the lithium iron phosphate power battery, and constructing a continuous state space equation based on the Kirchhoff's law; discretizing the continuous state space equation through a circuit three-element method, and obtaining a discrete state space equation in combination with an ampere-hour integral method; identifying model parameters on line by using a forgetting factor recursive least square method; and inputting the identified model parameters into a state estimator constructed based on a multi-information square root unscented Kalman filtering algorithm in real time, and realizing SOC real-time estimation through Sigma point sampling, multi-information matrix updating and square root filtering. Through verification under DST and FUDS cycle working conditions, the maximum errors are respectively as low as 1.5% and 1.8%, the root mean square errors are 0.16% and 0.32%, and it is proved that high-precision and high-stability estimation of the SOC of the battery is achieved under the complex working conditions.

Techniques for determining a collision probability between a candidate trajectory associated with a vehicle and an object (e.g., a vehicle or pedestrian) in the vehicle's environment. In some cases, the techniques include selecting a set of sampled states, where each sampled state represents a predicted state (e.g., a predicted position and / or orientation) of the object at a future time. The set of sampled states may then be used to determine the collision probability. In some cases, the set of sampled states associated with a future time t may be determined based on: (i) a probability distribution (e.g., a Gaussian distribution) associated with the predicted object state at the future time t, and / or (ii) a covariance of the probability distribution. In some cases, the set of sampled states selected based on a distribution includes a set of sigma points each associated with a probability.