Abstract
Kwon et al. (1989) derived a recursive adjoint form of FIR filter and smoother for discrete-time state-space models. Even though it is algebraically identical to the FIR filter and the FIR smoother, unfortunately it is pointed out to be numerically unstable. This makes the recursive estimator (RFIR) seldomly used in real applications. So we have devised a stable recursive estimator (SRFIR) which can supplement the RFIR so that it could be stabilized, and show that the SRFIR has unbiased and minimum variance error.
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