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New Classes of Finite Dimensional Filters With Non-Maximal Rank

机译：具有非最大秩的新型有限维滤波器

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摘要

Ever since the technique of Kalman filter was popularized, there has been an intense interest in finding new classes of finite dimensional recursive filters. In the late seventies, the idea of using estimation algebra to construct finite-dimensional nonlinear filters was first proposed by Brockett and Mitter independently. It has been proven to be an invaluable tool in the study of nonlinear filtering problem. For all known finite dimensional estimation algebras, the Wong's Ω-matrix has been proven to be a constant matrix. However, the Wong's Ω-matrix is shown not necessary to be a constant matrix in this letter when we consider finite dimensional estimation algebras with state dimension 3 and rank equal to 1. Several easily satisfied conditions are established for an estimation algebra of a special class of filtering systems to be finite-dimensional. Finally, we give the construction of finite dimensional filters of non-maximal rank.
机译：自从卡尔曼滤波器技术普及以来，人们对寻找新的有限维递归滤波器类产生了浓厚的兴趣。七十年代后期，Brockett和Mitter首次提出使用估计代数构造有限维非线性滤波器的想法。它已被证明是研究非线性滤波问题的宝贵工具。对于所有已知的有限维估计代数，Wong的Ω矩阵已被证明是常数矩阵。但是，当我们考虑状态维数为3且秩为1的有限维估计代数时，Wong的Ω矩阵在本信中不必表示为常数矩阵。为特殊类的估计代数建立了几个容易满足的条件过滤系统是有限维的。最后，我们给出了非最大秩的有限维滤波器的构造。

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