The classic approach for estimating parameters of a model using historical data is to solve a nonlinear least squares optimization problem using numerical methods. We develop an I-frame methodology to solve the nonlinear least squares problem quickly which can be applied to both offline and online (where data is streamed in real time) parameter estimation. Using the concept of I-frames from imaging and animation, we approximate a solution to the nonlinear least squares problem via a two-step process, an I-frame optimization, and an incremental optimization. The I-frame optimization solves for the parameters using a subset of data points and the incremental optimization adjusts the parameters in between the I-frames. We show that the criterion of generating I-frames can affect the average squared error of the final solution. Our methodology benefits from being scalable as the number of parameters and amount of data increases with an appropriate I-frame generation criterion.

中文翻译：

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逼近非线性最小二乘法的 I 帧方法

使用历史数据估计模型参数的经典方法是使用数值方法解决非线性最小二乘优化问题。我们开发了一种 I 帧方法来快速解决非线性最小二乘问题，该方法可以应用于离线和在线（数据实时流式传输）参数估计。使用来自成像和动画的 I 帧概念，我们通过两步过程、I 帧优化和增量优化来近似非线性最小二乘问题的解决方案。I 帧优化使用数据点的子集求解参数，增量优化调整 I 帧之间的参数。我们表明生成 I 帧的标准会影响最终解决方案的平均平方误差。