FADING-MEMORY (DISCOUNTED LEAST-SQUARES) FILTER
7.1 DISCOUNTED LEAST-SQUARES ESTIMATE The fading-memory ﬁlter introduced in Chapter 1, is similar to the ﬁxedmemory ﬁlter in that it has essentially a ﬁnite memory and is used for tracking a target in steady state. As indicated in Section 1.2.6, for the fading-memory ﬁlter the data vector is semi-inﬁnite and given by Y ðnÞ ¼ ½ y n ; y nÀ1 ; . . . T ð7:1-1Þ
The ﬁlter realizes essentially ﬁnite memory for this semi-inﬁnite data set by having, as indicated in section 1.2.6, a fading-memory. As for the case of the ﬁxed-memory ﬁlter in Chapter 5,...