Opened 2 months ago

Closed 2 months ago

## #182 closed task (fixed)

# Kalman filter implementation clarification

Reported by: | Owned by: | stuerze | |
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Priority: | normal | Component: | BNC |

Version: | Keywords: | kalman filter | |

Cc: |

## Description (last modified by )

What is the exact kalman filter implementation used in BNC? I was not able to find this exact square root filter implementation anywhere in the literature or understand it properly. The Cholesky decomposition used in combination with a QRZ Decomposition used on an Augmentation Matrix including weights, the square root of the filter covariances and a combination of the the square root of the filter covariances and Design Matrix seems unusual. A clarification would be appreciated a lot.

### Attachments (2)

### Change History (9)

### comment:1 by , 2 months ago

Description: | modified (diff) |
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Priority: | minor → normal |

### follow-up: 3 comment:2 by , 2 months ago

In 10501/ntrip:

(The changeset message doesn't reference this ticket)

### comment:3 by , 2 months ago

Replying to stoecker:

In 10501/ntrip:

(The changeset message doesn't reference this ticket)

Hello stoecker, could you clearify what you mean? The .PPP or Log Files?

I am aware of the Filter states and values in there, but I would be interested in some implementation Details regarding the Kalman filter.

e.g. the usage of computed - observed (ll) for the updated States instead of the observations here:

xx += KT.t() * (ll - AA * xx);

the computation of the transposed Kalman Gain KT. (what is YY?) SHi is the inverted Decomposed Measurement sensitivity Matrix H? y = Hx, y: observations

Matrix KT = SHi * YY;

And Especially the usage of the QR Decomposition of an Augmented Matrix SRF for the measurement update. Here the closest I have gotten is in:

Tiberius 1998 Recursive Data Processing for Kinematic GPS Surveying p.47-48 (see attachment)

where it is used for the time update.

Any explanation on these topics would be appreciated.

Regards

Max

### by , 2 months ago

Attachment: |
QRZ-SRF.PNG
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Tiberius 1998 Recursive Data Processing for Kinematic GPS Surveying p.47-48

### comment:5 by , 2 months ago

Status: | new → assigned |
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The square root filter was implemented by Leos Mervart and is described e.g. on page 10 of the attachment.

Best regrads, Andrea

### by , 2 months ago

Attachment: |
Mervart_GW_Koll_20140127-08-10.pdf
added |
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### comment:6 by , 2 months ago

Thank you very much for the clarification.

This helps a lot.

Regards, Max

### comment:7 by , 2 months ago

Resolution: | → fixed |
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Status: | assigned → closed |

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A source in form of a paper name or Link would be sufficient as well.