74 lines
4.0 KiB
Plaintext
74 lines
4.0 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "2b6fc012",
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"metadata": {},
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"source": [
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"# NonlinearISAM 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 `NonlinearISAM` class in GTSAM is a powerful tool for incrementally solving nonlinear factor graphs. It is particularly useful in applications where the problem is continuously evolving, such as in SLAM (Simultaneous Localization and Mapping) or incremental structure-from-motion. The class leverages the iSAM (incremental Smoothing and Mapping) algorithm to efficiently update solutions as new measurements are added.\n",
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"\n",
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"## Key Features\n",
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"\n",
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"- **Incremental Updates**: `NonlinearISAM` allows for the efficient update of the solution when new factors are added to the graph. This is crucial for real-time applications where the problem is continuously changing.\n",
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" \n",
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"- **Batch Initialization**: The class can perform a full batch optimization to initialize the solution, which can then be refined incrementally.\n",
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"\n",
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"- **Marginalization**: It supports marginalizing out variables that are no longer needed, which helps in maintaining computational efficiency.\n",
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"\n",
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"## Main Methods\n",
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"\n",
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"### Initialization and Update\n",
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"\n",
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"- **`update`**: This method is central to the `NonlinearISAM` class. It allows for the addition of new factors and variables to the existing factor graph. The update is performed incrementally, leveraging previous computations to enhance efficiency.\n",
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"\n",
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"- **`estimate`**: After performing updates, this method retrieves the current best estimate of the variable values.\n",
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"\n",
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"### Batch Operations\n",
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"\n",
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"- **`batchStep`**: This method performs a full batch optimization, which can be useful for reinitializing the solution or when a significant change in the problem structure occurs.\n",
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"\n",
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"### Marginalization\n",
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"\n",
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"- **`marginalize`**: This method allows for the removal of variables from the factor graph. Marginalization is useful for reducing the problem size and maintaining efficiency.\n",
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"\n",
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"## Mathematical Background\n",
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"\n",
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"The `NonlinearISAM` class operates on factor graphs, which are bipartite graphs consisting of variable nodes and factor nodes. The goal is to find the configuration of variables that maximizes the product of all factors, often expressed as:\n",
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"\n",
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"$$\n",
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"\\max_{\\mathbf{x}} \\prod_{i} \\phi_i(\\mathbf{x}_i)\n",
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"$$\n",
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"\n",
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"where $\\phi_i(\\mathbf{x}_i)$ are the factors depending on subsets of variables $\\mathbf{x}_i$.\n",
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"\n",
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"The iSAM algorithm updates the solution by incrementally solving the linearized system of equations derived from the factor graph:\n",
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"\n",
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"$$\n",
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"\\mathbf{A} \\Delta \\mathbf{x} = \\mathbf{b}\n",
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"$$\n",
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"\n",
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"where $\\mathbf{A}$ is the Jacobian matrix of the factors, $\\Delta \\mathbf{x}$ is the update to the variable estimates, and $\\mathbf{b}$ is the residual vector.\n",
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"\n",
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"## Usage Notes\n",
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"\n",
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"- **Efficiency**: The incremental nature of `NonlinearISAM` makes it highly efficient for large-scale problems where new data is continuously being integrated.\n",
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"\n",
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"- **Robustness**: The ability to perform batch optimizations and marginalize variables provides robustness against changes in the problem structure.\n",
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"\n",
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"- **Applications**: This class is particularly suited for robotics and computer vision applications where real-time performance is critical.\n",
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"\n",
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"In summary, the `NonlinearISAM` class is a sophisticated tool for handling dynamic nonlinear optimization problems, offering both incremental and batch processing capabilities to efficiently manage evolving factor graphs."
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]
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