67 lines
3.7 KiB
Plaintext
67 lines
3.7 KiB
Plaintext
{
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"# ISAM2 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 `ISAM2` class in GTSAM is an incremental smoothing and mapping algorithm that efficiently updates the solution to a nonlinear optimization problem as new measurements are added. This class is particularly useful in applications such as SLAM (Simultaneous Localization and Mapping) where real-time performance is crucial.\n",
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"\n",
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"## Key Features\n",
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"\n",
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"- **Incremental Updates**: `ISAM2` allows for incremental updates to the factor graph, avoiding the need to solve the entire problem from scratch with each new measurement.\n",
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"- **Bayesian Inference**: Utilizes Bayes' rule to update beliefs about the state of the system as new information becomes available.\n",
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"- **Nonlinear Optimization**: Capable of handling nonlinear systems, leveraging iterative optimization techniques to refine estimates.\n",
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"- **Efficient Variable Reordering**: Dynamically reorders variables to maintain sparsity and improve 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 Configuration\n",
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"\n",
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"- **ISAM2 Constructor**: Initializes the `ISAM2` object with optional parameters for configuring the behavior of the algorithm, such as relinearization thresholds and ordering strategies.\n",
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"\n",
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"### Updating the Graph\n",
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"\n",
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"- **update**: Incorporates new factors and variables into the existing factor graph. This method performs the core incremental update, refining the solution based on new measurements.\n",
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"\n",
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"### Accessing Results\n",
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"\n",
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"- **calculateEstimate**: Retrieves the current estimate of the variables in the factor graph. This method can be called with specific variable keys to obtain their estimates.\n",
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"- **marginalCovariance**: Computes the marginal covariance of a specified variable, providing insight into the uncertainty of the estimate.\n",
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"\n",
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"### Advanced Features\n",
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"\n",
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"- **relinearize**: Forces relinearization of the entire factor graph, which can be useful in scenarios where significant nonlinearities are introduced.\n",
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"- **getFactorsUnsafe**: Provides access to the internal factor graph, allowing for advanced manipulations and custom analyses.\n",
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"\n",
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"## Mathematical Formulation\n",
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"\n",
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"The `ISAM2` algorithm is based on the factor graph representation of the problem, where the joint probability distribution is expressed as a product of factors:\n",
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"\n",
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"$$ P(X|Z) \\propto \\prod_{i} \\phi_i(X_i, Z_i) $$\n",
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"\n",
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"Here, $X$ represents the set of variables, $Z$ the measurements, and $\\phi_i$ the individual factors.\n",
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"\n",
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"The update process involves solving a nonlinear optimization problem, typically using the Gauss-Newton or Levenberg-Marquardt algorithms, to minimize the error:\n",
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"\n",
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"$$ \\min_{X} \\sum_{i} \\| h_i(X_i) - Z_i \\|^2 $$\n",
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"\n",
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"where $h_i(X_i)$ are the measurement functions.\n",
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"\n",
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"## Conclusion\n",
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"\n",
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"The `ISAM2` class is a powerful tool for real-time estimation in dynamic environments. Its ability to efficiently update solutions with new data makes it ideal for applications requiring continuous adaptation and refinement of estimates. Users can leverage its advanced features to customize the behavior and performance of the algorithm to suit specific needs."
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