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中文摘要：
卡尔曼滤波是研究如何从被噪声污染的观测信号中过滤噪声，尽可能消除噪声影响，求未知真实信号或系统状态的一种估计方法。首先简要回顾了无约束离散时间不变系统卡尔曼滤波的模型及解算方法、统计性质。然后将其扩展到等式约束情形，推导了等式约束卡尔曼滤波的解及其统计性质。根据有效约束集的思想阐明了附不等式约束和等式约束卡尔曼滤波问题的内在联系，指出其解具有相同的性质，并提出用积极集法解决具有二次规划形式的不等式约束卡尔曼滤波问题。
英文摘要：
Kalman filtering is a method to estimate the unknown true signal or state of a system that researches on how to filter the noise in the polluted measure signal and exclude it as soon as possible. The model and solution and the statistical properties of uncon- strained Kalman filtering summarized first. Then we extend it to equality - constrained filtering and induce the solution and statistical properties. According to active constraint set,the intrinsic relations between equality -constrained and inequality -constrained Kalman filtering are demonstrated and the solutions have the same properties. An active set method is proposed to solve the inequality - constrained Kalman filtering with the form of quadratic programming.
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