Investigating a Noise Resistant Parameter Estimation Method

这是一项研究计划拨款，用于研究确定模型函数参数的方法。这种方法对噪声的敏感性较低，比常用的最小二乘及其变化等方法更普遍适用。该方法的算法是将原始模型函数与一组“测试函数”相乘，然后积分形成内积。数据点乘以相同的测试函数并进行数值积分。这两个结果被设为彼此相等，从而产生一个对未知参数的约束系统。对于足够多的测试函数，该约束系统可以求解未知参数。在规划期间，将确定该方法作为其他建模技术的替代方法是否可行。特别是，当测量误差未知或存在不希望删除的可能异常值时，它可能是有用的。该方法将应用于各种数据集，并将检查条件良好的测试函数以提高其性能。

This is a research planning grant to investigate a method for determining the parameters of model functions. This method may prove to be less sensitive to noise and more generally applicable than commonly used methods such as least-squares (LS) and its variations. The algorithm for this method consists of multiplying the original model function by a set of "test functions" and then integrating to form the inner products. The data points are multiplied by the same test functions and numerically integrated. The two results are set equal to one another, yielding a system of constraints on the unknown parameters. For sufficiently many test functions, this system of constraints can be solved for the unknown parameters. During the planning period it will be determined whether this method is feasible as an alternative to other modeling techniques. In particular, it may be useful when measurement errors are not known or there are possible outliers that one does not wish to delete. The method will be applied to a variety of data sets, and well-conditioned test functions will be examined to improve its performance.