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中文摘要：
拟合推估常用于解决既含有倾向性参数又含有随机参数的参数估计问题。考虑更一般的拟合推估问题，即在拟合推估时不仅考虑随机误差二次型和随机信号二次型满足综合极小条件，而且同时考虑参数拟合推估解满足某些特定的几何条件或物理条件。在正常拟合推估模型的基础上，分别给出了含有随机信号约束条件、含有倾向参数约束条件及含有倾向参数与随机信号组合约束条件的拟合推估模型，并导出了相应的解式。利用导出的公式对一幅带有约束条件的数字化地图进行误差纠偏。结果表明，附有限制条件的拟合推估既能保证较高的拟合与推估精度，又能很好地满足给定的约束条件。
英文摘要：
Collocation is usually applied to deal with the parameter estimation, which contains the trend parameters and stochastic parameters. A more general collocation method is proposed, in which not only the two quadratic forms of residuals and signals are minimized, but also some geometrical or physical constraints must be satisfied. The collocation estimators, with stochastic signal constraints, trend parameter constraints, as well as the synthetic constraints of signals and trend parameters, are derived based on the standard collocation derivation process. An example of error correcting for a scanning map is given. It is shown that the collocation with constraints can not only improve the accuracy of scanning maps, but also satisfy the condition of map joint.
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