On Kalman-Like Finite Impulse Response Filters
For researchers working on FIR filtering, this paper clarifies the connection between two popular filters, but the contribution is primarily analytical and incremental.
The paper reveals an explicit relationship between the Kalman-like unbiased FIR filter (UFIR) and the receding horizon Kalman FIR filter (RHKF), showing that the only difference is UFIR's ignorance of noise statistics and its initial condition construction strategy. This insight can help improve one filter by learning from the other.
This note reveals an explicit relationship between two representative finite impulse response (FIR) filters, i.e. the newly derived and popularized Kalman-Like unbiased FIR filter (UFIR) and the receding horizon Kalman FIR filter (RHKF). It is pointed out that the only difference of the two algorithms lies in the noise statistics ignorance and appropriate initial condition construction strategy in UFIR. The revelation can benefit the performance improvement of one by drawing lessons from the other. Some interesting conclusions have also been drawn and discussed from this revelation.