A constrained extended Kalman filter (CEKF) based on least-squares variance component estimation (LS-VCE) is generally developed by condition equations since the proper prediction of dispersion matrices is one of the main bottlenecks in the KF algorithms. Here we investigate four problems which have not been simultaneously considered yet. These problems are examination of non-linearty of dynamic model, VCE, general non-linear state constraints and fairly general stochastic model. Although a few contributions proposed some adaptive KF in particular based on Helmert’s VCE method, they developed their filters for special problems with some restrictive conditions such as independence of all variables and/or linearity of the dynamic model. Also some of these filters did not apply VCE methods to all parts of the dynamic model. In this contribution, we try to overcome all of these restrictions. Moreover, LS-VCE method gives some added advantages over other VCE methods. First the new formulation of CEKF is developed by condition equations with prediction of all possible cross-covariances as algorithm 1. Then the LS-VCE method is applied to it after some modifications which results in an adaptive constrained extended Kalman filter (ACEKF) as the second algorithm.

基于最小二乘方差分量估计 (LS-VCE) 的约束扩展卡尔曼滤波器 (CEKF) 通常由条件方程开发，因为对色散矩阵的正确预测是 KF 算法的主要瓶颈之一。在这里，我们调查尚未同时考虑的四个问题。这些问题是检查动态模型的非线性、VCE、一般非线性状态约束和相当一般的随机模型。尽管一些贡献提出了一些特别基于 Helmert 的 VCE 方法的自适应 KF，但他们针对具有一些限制条件的特殊问题开发了过滤器，例如所有变量的独立性和/或动态模型的线性。此外，其中一些过滤器并未将 VCE 方法应用于动态模型的所有部分。在这个贡献中，我们试图克服所有这些限制。此外，LS-VCE 方法比其他 VCE 方法具有一些额外的优势。首先，CEKF 的新公式是由条件方程开发的，预测所有可能的交叉协方差作为算法 1。然后在一些修改后将 LS-VCE 方法应用于它，导致自适应约束扩展卡尔曼滤波器 (ACEKF) 作为第二种算法。