55 lines
3.2 KiB
Plaintext
55 lines
3.2 KiB
Plaintext
{
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"# BatchFixedLagSmoother Class Documentation\n",
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"\n",
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"*Disclaimer: This documentation was generated by AI and requires 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 `BatchFixedLagSmoother` class in GTSAM is a specialized smoother designed for fixed-lag smoothing in nonlinear factor graphs. It extends the capabilities of fixed-lag smoothing by maintaining a sliding window of the most recent variables and marginalizing out older variables. This is particularly useful in real-time applications where memory and computational efficiency are critical.\n",
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"\n",
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"## Key Functionalities\n",
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"\n",
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"### Smoothing and Optimization\n",
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"\n",
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"- **update**: This method is the core of the `BatchFixedLagSmoother`. It processes new factors and variables, updating the current estimate of the state. The update method also manages the marginalization of variables that fall outside the fixed lag window.\n",
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"\n",
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"### Factor Graph Management\n",
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"\n",
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"- **marginalize**: This function handles the marginalization of variables that are no longer within the fixed lag window. Marginalization is a crucial step in maintaining the size of the factor graph, ensuring that only relevant variables are kept for optimization.\n",
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"\n",
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"### Parameter Management\n",
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"\n",
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"- **Params**: The `Params` structure within the class allows users to configure various settings for the smoother, such as the lag duration and optimization parameters. This provides flexibility in tuning the smoother for specific applications.\n",
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"\n",
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"## Mathematical Formulation\n",
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"\n",
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"The `BatchFixedLagSmoother` operates on the principle of fixed-lag smoothing, where the objective is to estimate the state $\\mathbf{x}_t$ given all measurements up to time $t$, but only retaining a fixed window of recent states. The optimization problem can be expressed as:\n",
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"\n",
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"$$\n",
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"\\min_{\\mathbf{x}_{t-L:t}} \\sum_{i=1}^{N} \\| \\mathbf{h}_i(\\mathbf{x}_{t-L:t}) - \\mathbf{z}_i \\|^2\n",
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"$$\n",
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"\n",
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"where $L$ is the fixed lag, $\\mathbf{h}_i$ are the measurement functions, and $\\mathbf{z}_i$ are the measurements.\n",
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"\n",
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"## Usage Considerations\n",
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"\n",
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"- **Real-time Applications**: The `BatchFixedLagSmoother` is ideal for applications requiring real-time processing, such as robotics and autonomous vehicles, where the computational burden must be managed efficiently.\n",
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"- **Configuration**: Proper configuration of the lag duration and optimization parameters is essential for optimal performance. Users should experiment with different settings to achieve the desired balance between accuracy and computational load.\n",
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"\n",
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"## Conclusion\n",
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"\n",
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"The `BatchFixedLagSmoother` class provides a robust framework for fixed-lag smoothing in nonlinear systems. Its ability to efficiently manage the factor graph and perform real-time updates makes it a valuable tool in various applications requiring dynamic state estimation."
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