e[n] = b[n — 1] + K[n](o[n] — hTr[n]i3[n — 1]) [7*(0 — e[n])11 8 State Estimation : K[n] M[n — 1]h[n] M[n] = (I — K[n]h rrr[n])M[n — 1], where M[n] is the error covariance matrix: M[n] = E[(0 — Most of the materials presented so far in this chapter have concerned the problem of estimating parameters in statistical models. Some common statistical models used in signal processing, speech processing in particular, have been covered in Chapters 3 and 4. These models can be classified into two groups. The first group has the models with no "hidden" random variables or states. That is, all random variables defined in the

doi:10.1201/9781482276237-33

Chapter

e[n] = b[n — 1] + K[n](o[n] — hTr[n]i3[n — 1]) [7*(0 — e[n])11 8 State Estimation

Chapter

K[n] M[n — 1]h[n] M[n] = (I — K[n]h rrr[n])M[n — 1], where M[n] is the error covariance matrix: M[n] = E[(0 — Most of the materials presented so far in this chapter have concerned the problem of estimating parameters in statistical models. Some common statistical models used in signal processing, speech processing in particular, have been covered in Chapters 3 and 4. These models can be classified into two groups. The first group has the models with no "hidden" random variables or states. That is, all random variables defined in the

ABSTRACT

The second group of the models can be further classified into two types: 1) the hidden states are discrete random variables (e.g., HMM, and trended HMM); and 2) the hidden states are continuous random variables (e.g., dynamic system models). Section 5.3 already discussed the state estimation problem and solutions for discrete-state models based on the dynamic programming techniques or Viterbi algorithm. This section will thus focus on the state estimation problem for the models with continuous states. Solutions to the state estimation problem usually assume that the parameters in the model are known or have been estimated.