Sparse Grid Trajectory Tracking for High-Dimensional State Estimation
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Solution Overview
Problem
Existing methods for tracking the trajectory of moving objects, such as missiles, face challenges in accurately determining state variables like position and velocity in real-time, especially when dealing with non-linear movements and higher-dimensional systems, leading to inaccuracies and high computational complexity.
Innovation Solution
The method employs sparse grids to discretize and solve stochastic partial differential equations, allowing for efficient prediction and recalculation of probability densities, which reduces computational time by adapting grid resolution and processing only relevant areas, enabling real-time tracking even in high-dimensional systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional grid methods are used to solve stochastic partial differential equations for tracking, then measurement precision is improved, but computational complexity increases exponentially with dimensionality
Solution Approach 1:
The state space is divided into discrete grid points that can be independently processed. The patent applies sparse grid techniques where only relevant grid points are computed based on the probability density distribution, segmenting the computational domain to reduce overall complexity while maintaining tracking accuracy.
Solution Approach 2:
The patent implements adaptive local refinement where grid resolution is increased in regions of high probability density and decreased in low-probability regions. This local quality adjustment ensures accurate tracking where needed while reducing computational effort in less critical areas, resolving the contradiction between precision and complexity.
2Measurement precision
If higher-dimensional state vectors are used to capture complex missile maneuvers, then tracking accuracy is improved, but calculation time increases significantly
Solution Approach 1:
The patent employs dynamic grid adaptation where the grid structure and resolution are adjusted in real-time based on the evolving probability density function. This allows the system to maintain high-dimensional state tracking capability while optimizing calculation time by concentrating computational resources on dynamically relevant state spaces.
Solution Approach 2:
The patent changes the parameter of grid density and resolution adaptively based on the problem dimensions and probability distribution. By varying grid parameters dynamically rather than using fixed high-resolution grids, the system achieves accurate high-dimensional tracking with reduced computational burden.
3Speed
If real-time tracking is implemented with frequent updates, then responsiveness is improved, but computational load increases
Solution Approach 1:
The patent implements periodic tracking updates at optimized intervals rather than continuous processing. By determining optimal update frequencies based on missile dynamics and measurement availability, the system achieves real-time responsiveness while reducing computational energy consumption through periodic rather than continuous operation.
Solution Approach 2:
The tracking system uses the probability density function itself to guide computational effort, with the density distribution automatically identifying regions requiring updated calculations. This self-service mechanism prioritizes computational resources to the most critical state variables, enabling responsive tracking with minimized energy consumption.
Data Source
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Figure 4A~4B
AI summary
The method involves determining an initialization and a prediction of probability density at a point of time. The determination is made whether measured data is present. The probability density is recalculated with the measured data, if the measured data is present. The predicted values to be determined are recalculated based on state variable of the probability density. The calculated predicted values are output to a subsequent data processing device. The steps are repeated by discretization of the probability density on sparse grids. Independent claims are also included for the following: (1) a computer program having a set of instructions for tracking trajectory of a moving object (2) a computer program product comprising a set of instructions for tracking trajectory of a moving object (3) a data carrier including a set of instructions for tracking trajectory of a moving object (4) a device for detecting and tracking a moving object.