Meta-optimization of the Extended Kalman filter’s parameters for improved feature extraction on hyper-temporal images. B.P. Salmon 1,2*, W. Kleynhans 1,2, F. van den Bergh 2, J.C. Olivier 1, W.J. Marais 3 and K.J. Wessels 2 1. Department of Electrical Engineering, University of Pretoria, South Africa 2. Remote Sensing Research Unit, Meraka, CSIR, South Africa 3. Space Science and Engineering Center, University of Wisconsin-Madison, Wisconsin, USA * Presenting author

Overview Problem statement – Reliable surveying of land cover and transformation Discuss the importance of time series analysis Study area: Gauteng province, South Africa Using the EKF as feature extractor from time series data Meta-optimization of EKF’s parameters Results: Land cover classification Conclusions

Problem Statement Reliable surveying of land cover and transformation YearEstimated PopulationChange 20008,038, ,243, % 20028,499, % 20038,775, % 20048,851, % 20059,002, % 20069,193, % 20079,665, % ,450, % ,531, %

Time Series Analysis MODIS Band 1 MODIS Band 2 Band 2 Separation Band 1 Separation Band 2 Separation Band 1 Separation Band 2 Vegetation Band 1 Vegetation Band 2 Settlement Band 1 Settlement

Objective Time series can be modulated with a triply modulated cosine function [1]. [1] W. Kleynhans et. al, 'Improving land cover class separation using an extended Kalman filter on MODIS NDVI time-series data', IEEE Geoscience and Remote Sensing Letters, vol. 6, no. 4. April 2010

Objective Parameters of a triply modulated cosine can be used to distinguish between several different land cover classes. Parameters derived using a EKF framework has been proven as a feasible solution. Introduce a meta-optimization approach for setting the parameters of a Extended Kalman filter to rapidly estimate better features for a triply modulated cosine function.

Time series modelled as a triply modulated cosine function Where = Mean = Amplitude = Angular frequency = Spectral band = Time index Triply modulated time series = Seasonal cycle (8/365) = Phase = Noise = Pixel index

State vector Process model Observation model Extended Kalman Filter Framework Mean Amplitude Phase

Modelling the time series Unstable parameter Mean Amplitude Phase

Process model Observation model Tuneable parameters Observation noise covariance matrix Process covariance matrix Initial estimates of state vector

Tuneable parameters Observation noise covariance matrix Process covariance matrix Initial estimates of state vector Tunable parameters Where j denotes the epoch number

What do we want? Mean Amplitude Phase Absolute Error Tunable parameters

Creating extreme conditions Absolute Error Tunable parameters Set Capture a probability density function (PDF) for each time increment k using all the pixels and if ideal will be denoted by

Creating extreme conditions Tunable parameters Mean Set Capture a probability density function (PDF) for each time Increment k using all the pixels and if ideal will be denoted by

Creating extreme conditions Tunable parameters Set Capture a probability density function (PDF) for each time Increment k using all the pixels and if ideal will be denoted by Amplitude

Creating extreme conditions Tunable parameters Set Capture a probability density function (PDF) for each time Increment k using all the pixels and if ideal will be denoted by Phase

Creating a metric Set an initial (candidate) state as Calculated the f-divergent distance as Absolute error Mean Amplitude Phase

Define a comparison metric Create a vector containing all the f-divergent distances as Define a metric for an unbiased Extended Kalman filter Optimize the vector using comparison metric

Iterative updates

Results: Standard deviation for MODIS spectral band MODIS pixels = 285.5km 2 Mean Amplitude Absolute Error

Results: Standard deviation for MODIS spectral band MODIS pixels = 285.5km 2 Mean Amplitude Absolute Error

Results: Standard deviation for MODIS bands 1142 MODIS pixels = 285.5km 2

Results: Classification on labelled data K-means (Band 1, Band 2) 1142 MODIS pixels = 285.5km 2 Vegetation Accuracy Settlement accuracy

Results: Accuracy for MODIS bands 1142 MODIS pixels = 285.5km 2

Results: Gauteng province settlements MODIS pixels = 19676km % Settlement

Conclusions Temporal property is of high importance in remote sensing A meta-optimization for the EKF using a spatio-temporal window was proposed. Proper feature analysis can greatly enhance analysis of data. Presentation of features to any machine learning algorithm

Questions? Expansion of irrigation Commercial forestry MiningInformal settlements Alien tree removal