We propose a new approach for solving the filtering problem in linear systems based on incomplete measurements, where the characteristics of the dynamic noise are not known exactly, and measurements may contain anomalous non-Gaussian errors. The proposed algorithm is based on the idea of using the adaptive Kalman filter and the generalized least absolute deviations method jointly. With numerical modeling, we show that, compared to the classical optimal linear filtering method, our solution has lower sensitivity to short-term outliers in measurements and provides a quick adjustment of the parameters of the system dynamics. The proposed algorithm can be used to solve onboard navigation and tracking problems on aircrafts. To implement the method of least absolute deviations, we use an efficient L₁-optimization algorithm.

我们提出了一种基于不完整测量来解决线性系统中的滤波问题的新方法，其中动态噪声的特征尚不清楚，并且测量中可能包含异常的非高斯误差。该算法基于自适应卡尔曼滤波和广义最小绝对偏差法联合使用的思想。通过数值建模，我们表明，与经典的最佳线性滤波方法相比，我们的解决方案对测量中的短期异常值具有较低的灵敏度，并且可以快速调整系统动力学参数。所提出的算法可用于解决飞机的机载导航和跟踪问题。为了实现最小绝对偏差的方法，我们使用有效的L ₁优化算法。