### Abstract

Fast Kalman algorithms are algorithms that solve, in a very efficient way, the recursive least-squares estimation problem. Unfortunately they are known to exhibit a very unstable behavior, due basically to the accumulation of roundoff errors. It is the structure of the algorithms that favors this accumulation, which is present even when the data are well behaved. In this paper, by introducing a redundant equation, that is, by computing a specific quantity of the algorithms in two different w ays, we use the difference of these two ways as a measure of the accumulation of the roundoff errors. This difference is consequently used to correct the variables of the algorithm at every time step in order to stabilize it. The correction is defined as the solution of a specific minimization problem. The resulting algorithm still has the nice complexity properties of the original algorithm (linear in the number of parameters to be estimated), but has a much more stable behavior.

Original language | English (US) |
---|---|

Pages (from-to) | 1342-1348 |

Number of pages | 7 |

Journal | IEEE Transactions on Acoustics, Speech, and Signal Processing |

Volume | 37 |

Issue number | 9 |

DOIs | |

State | Published - Jan 1 1989 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Signal Processing

### Cite this

*IEEE Transactions on Acoustics, Speech, and Signal Processing*,

*37*(9), 1342-1348. https://doi.org/10.1109/29.31289

}

*IEEE Transactions on Acoustics, Speech, and Signal Processing*, vol. 37, no. 9, pp. 1342-1348. https://doi.org/10.1109/29.31289

**Stabilizing the Fast Kalman Algorithms.** / Botto, Jean Luc; Moustakides, Georgios.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Stabilizing the Fast Kalman Algorithms

AU - Botto, Jean Luc

AU - Moustakides, Georgios

PY - 1989/1/1

Y1 - 1989/1/1

N2 - Fast Kalman algorithms are algorithms that solve, in a very efficient way, the recursive least-squares estimation problem. Unfortunately they are known to exhibit a very unstable behavior, due basically to the accumulation of roundoff errors. It is the structure of the algorithms that favors this accumulation, which is present even when the data are well behaved. In this paper, by introducing a redundant equation, that is, by computing a specific quantity of the algorithms in two different w ays, we use the difference of these two ways as a measure of the accumulation of the roundoff errors. This difference is consequently used to correct the variables of the algorithm at every time step in order to stabilize it. The correction is defined as the solution of a specific minimization problem. The resulting algorithm still has the nice complexity properties of the original algorithm (linear in the number of parameters to be estimated), but has a much more stable behavior.

AB - Fast Kalman algorithms are algorithms that solve, in a very efficient way, the recursive least-squares estimation problem. Unfortunately they are known to exhibit a very unstable behavior, due basically to the accumulation of roundoff errors. It is the structure of the algorithms that favors this accumulation, which is present even when the data are well behaved. In this paper, by introducing a redundant equation, that is, by computing a specific quantity of the algorithms in two different w ays, we use the difference of these two ways as a measure of the accumulation of the roundoff errors. This difference is consequently used to correct the variables of the algorithm at every time step in order to stabilize it. The correction is defined as the solution of a specific minimization problem. The resulting algorithm still has the nice complexity properties of the original algorithm (linear in the number of parameters to be estimated), but has a much more stable behavior.

UR - http://www.scopus.com/inward/record.url?scp=0024733203&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024733203&partnerID=8YFLogxK

U2 - 10.1109/29.31289

DO - 10.1109/29.31289

M3 - Article

VL - 37

SP - 1342

EP - 1348

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 9

ER -