A device implementing a system for estimating device location includes at least one processor configured to receive an estimated position based on a positioning system comprising a Global Navigation Satellite System (GNSS) satellite, and receive a set of parameters associated with the estimated position. The processor is further configured to apply the set of parameters and the estimated position to a machine learning model, the machine learning model having been trained based at least on a position of a receiving device relative to the GNSS satellite. The processor is further configured to provide the estimated position and an output of the machine learning model to a Kalman filter, and provide an estimated device location based on an output of the Kalman filter.

Method, apparatuses, and computer program products for automatically tracking a heading of an object. An example method comprising receiving, one or more internal measurement values which pertain to an object; determining an internal heading uncertainty value for each internal measurement value of the one or more internal measurement values; generating, using a probabilistic heading model, an estimated heading data object for the object based at least in part on the one or more internal measurement values; and providing the estimated heading data object to one or more associated user devices.

A method, apparatus and computer program product provide one or more of navigation-data parameters or correction-model parameters for one or more navigation satellites. In the context of a method, the method includes receiving (i) navigation data regarding one or more of a position of a respective navigation satellite or a clock offset of a clock of the respective navigation satellite and (ii) correction data regarding corrections to one or more of the position or the clock offset of the respective navigation satellite. The method also includes predicting an orbit and the clock of the respective navigation satellite based on the navigation data and the correction data. The method further includes fitting at least one of the navigation-data parameters or the correction-model parameters to the predicted data and, following the fitting, providing the at least one of the navigation-data parameters or the correction-model parameters to one or more navigation devices.

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.

A method for estimating a constrained zonotope enclosing a motion state of at least one mobile target, the method including: a) linearizing a nonlinear transition model at an element of a first zonotope (Z.sub.x(t.sub.k−1)), b) computing transition linearization errors at different elements of the first zonotope (Z.sub.x(t.sub.k−1)), c) computing a second zonotope that contains all linearization errors, d) propagating (102) the first zonotope so as to obtain an a priori zonotope ({circumflex over (Z)}.sub.x(t.sub.k)) enclosing the motion state at a second moment (t.sub.k) after the first moment (t.sub.k−1), wherein the a priori zonotope ({circumflex over (Z)}.sub.x(t.sub.k)) is a linear projection of a hypercube, the hypercube being subject to at least one linear constraint, e) updating (104) the a priori zonotope ({circumflex over (Z)}.sub.x(t.sub.k)) so as to obtain an a posteriori constrained zonotope (Z′.sub.x(t.sub.k)) enclosing the motion state at the second moment (t.sub.k).

Devices, systems, and methods of navigation in tracks and trails. A system includes a smartphone or other portable electronic device. The system generates and provides navigation data and mapping data to travelers, particularly in walking trails; and generates a video clip or other multimedia presentation that incorporates trip data, images, audio, and a reconstructed map of the route. An administrator or operator of a nature center or an attraction or other venue, operates the system to obtain real-time information about travelers within the venue, and to selectively provide data and messages to some or all of such travelers.

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.

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.

A PVT calculation device includes a memory; and one or more processors in communication with the memory configured to perform operations including: receiving observations and ephemerides from satellites to obtain PVT data of the satellites and predicted PVT results of the receiver; setting up observation functions respectively corresponding to the satellites; calculating by a least square solution first estimated PVT results of the receiver based on the observation functions; iteratively eliminating by a Random-Sampling Iterative Kalman Filter (RSIKF) algorithm fault observation functions from the observation functions in an inner cluster until no fault observation functions detected in the inner cluster; calculating by the RSIKF algorithm a second estimated PVT results of the receiver using the observation functions in the inner cluster; and outputting final estimated PVT results of the receiver. The PVT calculation device may calculate the PVT results of the receiver with improved accuracy and stability.

A method for detecting a probe signal at an estimated code delay and an estimated doppler frequency includes: (i) dividing a period of the probe signal into sections each of a predetermined duration; (ii) assigning to each section one of a multiple code categories, each code category being indicative of a signal pattern of the probe signal within the section; and (iii) selecting multiple phase categories for a sinusoidal signal, each phase category being indicative of a range of phases in the sinusoidal signal. Thereafter, the method includes (i) receiving a signal from which the probe signal is to be detected; (ii) dividing the received signal into sections each of the predetermined duration; (iii) assigning each section of the received signal both a corresponding code category and a corresponding phase category, based respectively on the estimated code delay and the doppler frequency; and (iv) separately accumulating sections of the received signal according to the assigned code and phase categories of each section.