Kalman Filter in Real Time URBIS

Richard Kranenburg

06-01-2010

Introduction

TNO – Technisch Natuurwetenschappelijk Onderzoek

Kerngebied – Bouw en Ondergrond Business Unit – Milieu en Leefomgeving

Introduction - Uncertainty analysis - Kalman filter - Application on population

Introduction

AccompanistsMichiel Roemer (TNO)Jan Duyzer (TNO)Arjo Segers (TNO)Kees Vuik (TUDelft)

Introduction - Uncertainty analysis - Kalman filter - Application on population

Problem

Current situation Real Time URBIS model gives one value for

the concentration NOx in the DCMR area Wanted situation

Uncertainty interval for the concentration NOx

Uncertainty interval dependent of the place in the domain

Introduction - Uncertainty analysis - Kalman filter - Application on population

DCMR-area

Introduction - Uncertainty analysis - Kalman filter - Application on population

URBIS model

11 emission sources Traffic

CAR Zone Cards Road near Road far

Background Abroad Rest of the Netherlands DCMR-area

Shipping Ship sea Ship inland

Industry Industry

Rest

Winddirections North East South West

Wind speeds 1.5 m/s 5.5 m/s

Total 88 standard concentration fields for the concentration NOx

Introduction - Uncertainty analysis - Kalman filter - Application on population

Real Time URBIS

Gives for every hour an expected concentration NOx for the whole DCMR-area, based on input parameters Wind direction (φ) Wind speed (v) Temperature (T) Month (m) Weekday (d) Hour (h)

State equation:

88

1iii

RTUk mC

Introduction - Uncertainty analysis - Kalman filter - Application on population

Measurement locations

DCMR-Stations Schiedam Hoogvliet Maassluis Overschie Ridderkerk Rotterdam Noord

RIVM-Stations Schiedamsevest Vlaardingen Bentinckplein

Introduction - Uncertainty analysis - Kalman filter - Application on population

Uncertainty Real Time URBIS

Compare Real Time URBIS simulations with the observations on the nine measurement locations

Both observations and model simulations have a log-normal distribution

Introduction - Uncertainty analysis - Kalman filter - Application on population

Log-normal distributions

Introduction - Uncertainty analysis - Kalman filter - Application on population

Correction of the model

Differences between model and measurements plotted with respect to 6 input parameters

h: hour of the day φ: wind direction

eCC RTUcorr

)()( hc

Introduction - Uncertainty analysis - Kalman filter - Application on population

Uncertainty of the model

Standard deviation of the differences between the corrected model and the observations

v: wind speed

)(v

Introduction - Uncertainty analysis - Kalman filter - Application on population

Result of uncertainty analysis

Introduction - Uncertainty analysis - Kalman filter - Application on population

Kalman filter

Smooth random errors in the model of a dynamical system

In a real time application, measurements on time k are directly available to filter the state on time k.

Two results after application New expected concentration NOx Uncertainty interval for the concentration NOx

New state equation:

88

1iii

KF iemC

Introduction - Uncertainty analysis - Kalman filter - Application on population

Kalman filter equations

Forecast

Analysis

k

f

kA

1

kT

kfk QAAPP 1

f

kk

m

kkf

k

a

kcHyK

111111lnln

111T

1111 kkkkfkk

ak KRKHKIPHKIP

Introduction - Uncertainty analysis - Kalman filter - Application on population

Kalman filter on emission source ‘Background’ In the vector all values are equal to zero,

except the entries corresponding with the source ‘background’

Linearization of the Kalman filter equations Matrix A estimated with measurements in

Schipluiden and Westmaas Matrix R estimated with measurements at

Bentinckplein

Introduction - Uncertainty analysis - Kalman filter - Application on population

Kalman filter on emission source ‘Background’ Screening criterion:

Pfabs,k : Model uncertainty after forecast step

Rabs,k : Uncertainty of the measurements

kabsfkabs

i

sd

iikRPemy

fki

fki

,,2

288

1

2

,21

,

Introduction - Uncertainty analysis - Kalman filter - Application on population

Kalman filter on emission source ‘Background’

Introduction - Uncertainty analysis - Kalman filter - Application on population

Kalman filter on all emission sources State equation:

Screening Criterion

88

1iii

KF iemC

Introduction - Uncertainty analysis - Kalman filter - Application on population

Kalman filter on all emission sources Matrix A estimated with measurements in

Schipluiden, Westmaas, Overschie, Ridderkerk, Maassluis, Vlaardingen

Matrix R estimated with measurements at Bentinckplein

Introduction - Uncertainty analysis - Kalman filter - Application on population

Kalman filter on all emission sources

Introduction - Uncertainty analysis - Kalman filter - Application on population

Connection with population

Each grid cell, every hour a certainty interval Annual mean of the width of these intervals per grid

cell Amount of large widths of these intervals per grid cell

Number of postal zipcodes per grid cell Population density 1.99 people per grid cell Number of people per grid cell

Introduction - Uncertainty analysis - Kalman filter - Application on population

Connection with population

Introduction - Uncertainty analysis - Kalman filter - Application on population

Connection with population

Introduction - Uncertainty analysis - Kalman filter - Application on population

Connection with population

Introduction - Uncertainty analysis - Kalman filter - Application on population

Connection with population

Introduction - Uncertainty analysis - Kalman filter - Application on population

Conclusions

The differences between the observations and the model simulation are not only caused by inaccuracies in the background

Uncertainty interval has large width in the industrial region around Pernis and on the main roads

The application of the Kalman filter makes it possible to correct the model values every hour, with help of the observations

Further investigation

Add measurement stations to reduce uncertainty of the Kalman filter results

State optimal setting of measurement stations

Increase time scale (Day, Week or Month)