Forgetting least squares estimation FIR filters without noise covariance information

This paper concerns with a new estimation filter with a finite impulse response (FIR) structure under a least squares (LS) criterion using a forgetting factor. This filter will be called the forgetting least squares estimation (FLSE) FIR filter. The proposed FLSE FIR filter does not require information of the noise covariances as well as the initial state. It will be shown that, in particular case, the proposed FLSE FIR filter can be reduced to the simple least squares estimation FIR filter called the LSE FIR filter. The proposed FLSE FIR filter has also some inherent properties such as time-invariance, unbiasedness and deadbeat. The proposed FLSE FIR filter will be represented in a batch form and then a recursive form, which will be remarkable in the view of computational advantage. From discussions about the choice of a forgetting factor and a horizon length, it will be shown that they can be considered as useful parameters to make the estimation performance of the proposed FLSE FIR filter as good as possible. Via simulations, it will be shown that the proposed FLSE FIR filter consistently outperforms the LSE FIR filter, and can outperform the existing best linear unbiased estimation (BLUE) FIR filter with incorrect noise covariances.