Abstract: Provided is an array antenna divided into a plurality of sub-arrays disposed along a first dimension, wherein each sub-array comprises: a plurality of frequency scannable elements disposed along the first dimension and a plurality of phase shifters or transmit/receive (T/R) modules disposed along a second spatial dimension, each phase shifter or T/R module connected to a plurality of frequency scannable elements disposed along the first spatial dimension; and one or more processors being configured to generate a recurring radar waveform having a transmit portion, the transmit portion having multiple successive pulses at different frequencies to generate transmit beams by the array antenna at different angles in the first dimension; control at least one of the plurality of phase shifters or T/R modules along the second dimension to cause the transmit beams to be generated by the array antenna at different angles in the second dimension; and process return signals received by the plurality of sub-arrays to esti

Abstract: In some embodiments, space objects may be detected within shortwave infrared (SWIR) images captured during the daytime. Some embodiments include obtaining a stacked image by stacking shortwave infrared (SWIR) images. A spatial background-difference image may be generated based on the stacked image, and a matched-filter image may be obtained based on the spatial background-difference image. A binary mask may be generated based on the matched-filter image. The binary mask may include a plurality of bits each of which including a first value or a second value based on whether a signal-to-noise ratio (SNR) associated with that bit satisfies a threshold condition. Output data may be generated based on the spatial background-difference image and the binary mask, where the output data provides observations on detected space objects in orbit.

Abstract: In some embodiments, space objects may be detected within shortwave infrared (SWIR) images captured during the daytime. Some embodiments include obtaining a stacked image by stacking shortwave infrared (SWIR) images. A spatial background-difference image may be generated based on the stacked image, and a matched-filter image may be obtained based on the spatial background-difference image. A binary mask may be generated based on the matched-filter image. The binary mask may include a plurality of bits each of which including a first value or a second value based on whether a signal-to-noise ratio (SNR) associated with that bit satisfies a threshold condition. Output data may be generated based on the spatial background-difference image and the binary mask, where the output data provides observations on detected space objects in orbit.

Abstract: Systems and methods are described herein for dynamically generating and updating a patrol schedule for a shift based on historic demand event data, and a predicted-demand model based on the historic demand event data. The systems and methods also receive information associated with patrol officers assigned to a shift and constraints on the officers' availability, and generate a patrol schedule comprising patrol assignments for the assigned patrol officers optimized based on at least one policing objective. The patrol schedule may be dynamically updated based on changing information and provided to the patrol officer via mobile device or display in the patrol officer's vehicle.

Abstract: A method for compressing a cloud of points with imposed error constraints at each point is disclosed. Surfaces are constructed that approach each point to within the constraint specified at that point, and from the plurality of surfaces that satisfy the constraints at all points, a surface is chosen which minimizes the amount of memory required to store the surface on a digital computer.

Abstract: Embodiments of the present invention are directed to reducing the computational cost of propagating the uncertainty in the state of an object, which requires the numerical solution of an initial value problem (IVP) ensemble, by means of a computer. The present invention uses an implicit-Runge-Kutta-based (IRK) method that exploits the proximity of the initial conditions within the IVP ensemble. More specifically, one of the IVPs can be solved over a given time span consisting of one or more time steps with an IRK method, and the resulting trajectory can be recorded. The system of equations that arises on each time step of the IRK method can be solved using various iterative methods. The remaining IVPs can be solved over the same timespan using the same IRK method and time steps, together with the recorded trajectory from the first propagation.

Abstract: Embodiments of the present invention characterizing the uncertainty of the orbital state of an Earth-orbiting space object hereof using a Gauss von Mises probability density function defined on the n+1 dimensional cylindrical manifold n×. Additionally, embodiments of the present invention can include transforming a Gauss von Mises distribution under a diffeomorphism and approximating the output as a Gauss von Mises distribution. Embodiments of the present invention can also include fusing a prior state represented by a Gauss von Mises distribution with an update report, wherein the update can be either another Gauss von Mises distribution of the same dimension as the prior or an observation related to the prior by a stochastic measurement model. A Gauss von Mises distribution can be calculated from a plurality of reports, wherein the reports are either Gauss von Mises distributions or observations related to the state space by a stochastic measurement model.

Abstract: Embodiments of the present invention characterizing the uncertainty of the orbital state of an Earth-orbiting space object hereof using a Gauss von Mises probability density function defined on the n+1 dimensional cylindrical manifold n×. Additionally, embodiments of the present invention can include transforming a Gauss von Mises distribution under a diffeomorphism and approximating the output as a Gauss von Mises distribution. Embodiments of the present invention can also include fusing a prior state represented by a Gauss von Mises distribution with an update report, wherein the update can be either another Gauss von Mises distribution of the same dimension as the prior or an observation related to the prior by a stochastic measurement model. A Gauss von Mises distribution can be calculated from a plurality of reports, wherein the reports are either Gauss von Mises distributions or observations related to the state space by a stochastic measurement model.

Abstract: Embodiments of the present invention characterizing the uncertainty of the orbital state of an Earth-orbiting space object hereof using a Gauss von Mises probability density function defined on the n+1 dimensional cylindrical manifold n×. Additionally, embodiments of the present invention can include transforming a Gauss von Mises distribution under a diffeomorphism and approximating the output as a Gauss von Mises distribution. Embodiments of the present invention can also include fusing a prior state represented by a Gauss von Mises distribution with an update report, wherein the update can be either another Gauss von Mises distribution of the same dimension as the prior or an observation related to the prior by a stochastic measurement model. A Gauss von Mises distribution can be calculated from a plurality of reports, wherein the reports are either Gauss von Mises distributions or observations related to the state space by a stochastic measurement model.

Abstract: A method of tracking and inferring the underlying dynamics of a tagged molecule in a living cell may include receiving an ordered data set of time-valued location observations of the molecule, dividing the data set into time windows, and assigning a stochastic differential equation (SDE) model to each of the time windows with a set of parameters. The method may also include fitting the SDE models assigned to each of the plurality of time windows using likelihood-based techniques, and determining an initial value for each parameter. The method may further include fitting the set of parameters for each of the SDE models using a nonlinear maximum likelihood estimation search, applying an optimization routine to generate a set of computed parameters, determining whether the computed parameters are valid using goodness-of-fit tests, and determining whether each of the SDE models is valid based on the goodness-of-fit-tests.

Abstract: A method for compressing a cloud of points with imposed error constraints at each point is disclosed. Surfaces are constructed that approach each point to within the constraint specified at that point, and from the plurality of surfaces that satisfy the constraints at all points, a surface is chosen which minimizes the amount of memory required to store the surface on a digital computer.