64 lines
3.6 KiB
Plaintext
64 lines
3.6 KiB
Plaintext
{
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"# FixedLagSmoother Class Documentation\n",
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"\n",
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"*Disclaimer: This documentation was generated by AI and may require human revision for accuracy and completeness.*\n",
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"\n",
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"## Overview\n",
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"\n",
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"The `FixedLagSmoother` class in GTSAM is designed for incremental smoothing and mapping in robotics and computer vision applications. It maintains a fixed-size window of the most recent states, allowing for efficient updates and marginalization of older states. This is particularly useful in scenarios where real-time performance is crucial, and memory usage needs to be controlled.\n",
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"\n",
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"## Key Features\n",
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"\n",
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"- **Incremental Updates**: The `FixedLagSmoother` allows for efficient updates as new measurements are received, making it suitable for real-time applications.\n",
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"- **Fixed-Lag Smoothing**: It maintains a fixed window of recent states, which helps in managing computational resources by marginalizing out older states.\n",
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"- **Nonlinear Optimization**: Utilizes nonlinear optimization techniques to refine the estimates of the states within the fixed lag window.\n",
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"\n",
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"## Main Methods\n",
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"\n",
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"### Update\n",
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"\n",
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"The `update` method is central to the `FixedLagSmoother` class. It incorporates new measurements and updates the state estimates within the fixed lag window. The method ensures that the estimates are consistent with the new information while maintaining computational efficiency.\n",
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"\n",
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"### Marginalization\n",
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"\n",
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"Marginalization is a key process in fixed-lag smoothing, where older states are removed from the optimization problem to keep the problem size manageable. This is done while preserving the essential information about the past states in the form of a prior.\n",
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"\n",
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"### Optimization\n",
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"\n",
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"The class employs nonlinear optimization techniques to solve the smoothing problem. The optimization process aims to minimize the error between the predicted and observed measurements, leading to refined state estimates.\n",
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"\n",
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"## Mathematical Formulation\n",
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"\n",
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"The `FixedLagSmoother` operates on the principle of minimizing a cost function that represents the sum of squared errors between the predicted and observed measurements. Mathematically, this can be expressed as:\n",
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"\n",
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"$$\n",
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"\\min_x \\sum_i \\| h(x_i) - z_i \\|^2\n",
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"$$\n",
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"\n",
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"where $h(x_i)$ is the predicted measurement, $z_i$ is the observed measurement, and $x_i$ represents the state variables within the fixed lag window.\n",
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"\n",
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"## Applications\n",
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"\n",
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"The `FixedLagSmoother` is widely used in applications such as:\n",
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"\n",
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"- **Simultaneous Localization and Mapping (SLAM)**: Helps in maintaining a consistent map and robot trajectory in real-time.\n",
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"- **Visual-Inertial Odometry (VIO)**: Used for estimating the motion of a camera-equipped device by fusing visual and inertial data.\n",
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"- **Sensor Fusion**: Combines data from multiple sensors to improve the accuracy of state estimates.\n",
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"\n",
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"## Conclusion\n",
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"\n",
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"The `FixedLagSmoother` class is a powerful tool for real-time state estimation in dynamic environments. Its ability to handle incremental updates and maintain a fixed-size problem makes it ideal for applications where computational resources are limited. By leveraging nonlinear optimization, it provides accurate and consistent state estimates within the fixed lag window."
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