Abstract: A system and a method for tracking an expanded state of an object including a kinematic state indicative of a position of the object and an extended state indicative of one or combination of a dimension and an orientation of the object is provided herein. The system comprises at least one sensor configured to probe a scene including a moving object with one or multiple signal transmissions to produce one or multiple measurements of the object per the transmission, and a processor configured to execute a probabilistic filter tracking a joint probability of the expanded state of the object estimated by a motion model of the object and a measurement model of the object, wherein the measurement model includes a center-truncated distribution having truncation intervals. The system further comprises an output interface configured to output the expanded state of the object.

Abstract: A system calibrates a function of a tire friction of a vehicle traveling on a road from motion data including a sequence of control inputs to the vehicle that moves the vehicle on the road and a corresponding sequence of measurements of the motion of the vehicle moved by the sequence of control inputs. The system updates iteratively the probability distribution of the tire friction function until a termination condition is met, wherein, for an iteration, the system samples the probability distribution of the tire friction function, determines a state trajectory of the vehicle to fit the sequence measurements according to the measurement model and the sequence of control inputs according to the motion model including the sample of the tire friction function, and updates the probability distribution of the tire friction function based on the state trajectory of the vehicle.

Abstract: A system for controlling an operation of a machine for performing a task is disclosed. The system submits a sequence of control inputs to the machine and receives a feedback signal. The system further determines, at each control step, a current control input for controlling the machine based on the feedback signal including a current measurement of a current state of the system by applying a control policy transforming the current measurement into the current control input based on current values of control parameters in a set of control parameters of a feedback controller. Furthermore, the system may iteratively update a state of the feedback controller defined by the control parameters using a prediction model predicting values of the control parameters and a measurement model updating the predicted values to produce the current values of the control parameters that explain the sequence of measurements according to a performance objective.

Abstract: Stochastic nonlinear model predictive control (SNMPC) allows to directly take uncertainty of the dynamics and/or of the system's environment into account, e.g., by including probabilistic chance constraints. However, SNMPC requires the approximate computation of the probability distributions for the state variables that are propagated through the nonlinear system dynamics. This invention proposes the use of Gaussian-assumed density filters (ADF) to perform high-accuracy propagation of mean and covariance information of the state variables through the nonlinear system dynamics, resulting in a tractable SNMPC approach with improved control performance. In addition, the use of a matrix factorization for the covariance matrix variables in the constrained optimal control problem (OCP) formulation guarantees positive definiteness of the full trajectory of covariance matrices in each iteration of any optimization algorithm.

Abstract: A tracking system for tracking an expanded state of an object is provided. The tracking system comprises at least one processor and a memory having instructions stored thereon that, when executed by the at least one processor, cause the tracking system to execute a probabilistic filter that iteratively tracks a belief on the expanded state of the object, wherein the belief is predicted using a motion model of the object and is further updated using a compound measurement model of the object. The compound measurement model includes multiple probabilistic distributions constrained to lie on a contour of the object with a predetermined relative geometrical mapping to the center of the object. Further, the tracking system tracks the expanded state of the object based on the updated belief on the expanded state.

Abstract: An apparatus for controlling a system includes a memory to store a model of the system including a motion model of the system subject to process noise and a measurement model of the system subject to measurement noise, such that one or combination of the process noise and the measurement noise forms an uncertainty of the model of the system with unknown probabilistic parameters, wherein the uncertainty of the model of the system causes a state uncertainty of the system with unknown probabilistic parameters. The apparatus also includes a sensor to measure a signal to produce a sequence of measurements indicative of a state of the system, a processor to estimate a Gaussian distribution representing the state uncertainty, and a controller to determine a control input to the system using the model of the system with state uncertainty represented by the Gaussian distribution and control the system according to the control input.

Abstract: A system is controlled using particle filter executed to estimate weights of a set of particles based on fitting of the particles into a measurement model, wherein a particle includes a motion model of the system having an uncertainty modeled as a Gaussian process over possible motion models of the system and a state of the system determined with the uncertainty of the motion model of the particle, wherein a distribution of the Gaussian process of the motion model of one particle is different from a distribution of the Gaussian process of the motion model of another particle. Each execution of the particle filter updates the state of the particle according to a control input to the system and the motion model of the particle with the uncertainty and determines particle weights by fitting the state of the particle in the measurement model subject to measurement noise.

Abstract: A system for tracking a state of a GNSS receiver uses a subset of the measurements of satellite signals selected to minimize a loss of information with respect to the set of measurements available to the GNSS receiver. The system uses a probabilistic state estimator that tracks the state of the GNSS receiver using a probabilistic motion model subject to noise and a probabilistic measurement model relating the selected subset of the measurements of satellite signals to the current state of the receiver.

Abstract: A server jointly tracks states of multiple vehicles using measurements of satellite signals received at each vehicle and parameters of the probabilistic distribution of the state of each vehicle. The server fuse states and measurements into an augmented state of the multiple vehicles and an augmented measurement of the augmented state subject to augmented measurement noise defined by a non-diagonal covariance matrix with non-zero off-diagonal elements, each non-zero off-diagonal elements relating errors in the measurements of a pair of corresponding vehicles. The server executes a probabilistic filter updating the augmented state and fuses the state of at least some of the multiple vehicles with a corresponding portion of the updated augmented state.

Abstract: A probabilistic system for tracking a state of a vehicle using unsynchronized cooperation of information includes a probabilistic multi-head measurement model relating incoming measurements with the state of the vehicle. The first head of the model relates measurements of the satellite signals subject to measurement noise with a belief on the state of the vehicle, and a second head relates an estimation of the state of the vehicle subject to estimation noise with the belief on the state of the vehicle. A probabilistic filter of the system updates recursively the belief on the state of the vehicle based on the multi-head measurement model accepting one or a combination of the measurements of the satellite signals subject to the measurement noise and the estimation of the state of the vehicle subject to the estimation noise.

Abstract: A vehicle dynamics control system receives a feedback state signal including values of a roll rate and a roll angle of the motion of the vehicle and updates parameters of a model of roll dynamics of the vehicle by fitting the received values into the roll dynamics model. The roll dynamics model explains the evolution of the roll rate and the roll angle based on the parameters including a center of gravity (CoG) parameter modeling a location of a CoG of the vehicle, and a spring constant and a damping coefficient modeling suspension dynamics of the vehicle. The system determines a control command for controlling at least one actuator of the vehicle using a motion model including the updated CoG parameter and submits the control command to the vehicle controller to control the motion of the vehicle.

Abstract: A stochastic model predictive controller (SMPC) estimates a current state of the system and a probability distribution of uncertainty of a parameter of dynamics of the system based on measurements of outputs of the system, and updates a control model of the system including a function of dynamics of the system modeling the uncertainty of the parameter with first and second order moments of the estimated probability distribution of uncertainty of the parameter. The SMPC determines a control input to control the system by optimizing the updated control model of the system at the current state over a prediction horizon and controls the system based on the control input to change the state of the system.

Abstract: A system for tracking a state of a GNSS receiver uses a subset of the measurements of satellite signals selected to avoid the need for intermediate integers ambiguity estimate. The system selects the subset of measurements for the state tracking such that each measurement in the selected subset of measurements is formed by a weighted combination of multiple different measurements from the set of measurements. The system uses a probabilistic state estimator that tracks the state of the GNSS receiver using a probabilistic motion model subject to noise and a probabilistic measurement model relating the selected subset of the measurements of satellite signals to the current state of the receiver.

Abstract: Controller of a vehicle uses control functions to transition the current state of the vehicle into a target state. A control function is probabilistic to output a parametric probability distribution over the target state defined by a first moment and at least one higher order moment. The controller submits the current state into at least a subset of control functions consistent with the next driving decision to produce a subset of parametric probability distributions over the target state, combines the subset of parametric probability distributions to produce a joint parametric probability distribution of the target state, and determines the control command based on the first moment and at least one higher order moment of the joint parametric probability distribution of the target state.

Abstract: A system control a vehicle using a friction function describing a friction between a type of surface of the road and a tire of the vehicle as a function of a slip of a wheel of the vehicle. The parameters of each friction function include an initial slope of the friction function defining a stiffness of the tire and one or combination of a peak friction, a shape factor and a curvature factor of the friction function. Upon estimating a slip and a stiffness of the tire, the system selects from the memory parameters of the friction function corresponding to the current stiffness of the tire, determines a control command using a value of the friction corresponding to the slip of the tire according to the friction function defined by the selected parameters, and submits the control command to an actuator of the vehicle.

Abstract: A controller is provided for operating a system under admissible states. The controller includes an interface configured to connect the system storing a set of measured system states, a set of reference inputs and a set of system parameters in a storage arranged inside or outside the system, a memory storing measured system states, admissible reference inputs and admissible parameter sets and computer-executable programs including a parameter estimator and an adaptive reference governor (ARG), a processor, in connection with the memory. The processor is configured to perform the ARG and the parameter estimator. The parameter estimator extracts a pair of a reference input and the system state and compute a system parameter estimate based on the reference input and system state.

Abstract: A system for controlling a vehicle by jointly estimating a state of a vehicle and a function of a tire friction of a vehicle traveling on a road uses a particle filter maintaining a set of particles. Each particle includes an estimation of a state of the vehicle, an estimation of probability density function (pdf) of the tire friction function, and a weight indicative of a probability of the particle. The system executes the particle filter to update the particles based on a motion model and a measurement model of the vehicle, control commands moving the vehicle and measurements of the state where the vehicle moved according to the control commands. A control command is generated based on the motion of the vehicle, the weighted combinations of the state of the vehicle and the pdf of the tire friction function weighted according corresponding weights of the particles.

Abstract: A system for tracking a state of a GNSS receiver uses a subset of the measurements of satellite signals selected to avoid the need for intermediate integers ambiguity estimate. The system selects the subset of measurements for the state tracking such that each measurement in the selected subset of measurements is formed by a weighted combination of multiple different measurements from the set of measurements. The system uses a probabilistic state estimator that tracks the state of the GNSS receiver using a probabilistic motion model subject to noise and a probabilistic measurement model relating the selected subset of the measurements of satellite signals to the current state of the receiver.

Abstract: A system for controlling a vehicle by jointly estimating a state of a vehicle and a function of a tire friction of a vehicle traveling on a road uses a particle filter maintaining a set of particles. Each particle includes an estimation of a state of the vehicle, an estimation of probability density function (pdf) of the tire friction function, and a weight indicative of a probability of the particle. The system executes the particle filter to update the particles based on a motion model and a measurement model of the vehicle, control commands moving the vehicle and measurements of the state where the vehicle moved according to the control commands. A control command is generated based on the motion of the vehicle, the weighted combinations of the state of the vehicle and the pdf of the tire friction function weighted according corresponding weights of the particles.

Abstract: A system and a method for tracking an expanded state of an object including a kinematic state indicative of a position of the object and an extended state indicative of one or combination of a dimension and an orientation of the object is provided herein. The system comprises at least one sensor configured to probe a scene including a moving object with one or multiple signal transmissions to produce one or multiple measurements of the object per the transmission, and a processor configured to execute a probabilistic filter tracking a joint probability of the expanded state of the object estimated by a motion model of the object and a measurement model of the object, wherein the measurement model includes a center-truncated distribution having predetermined truncation intervals. The system further comprises an output interface configured to output the expanded state of the object.