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Meta-optimization of the Extended Kalman filter’s parameters for improved feature extraction on hyper-temporal images. B.P. Salmon1,2* , W. Kleynhans1,2, F. van den Bergh2, J.C. Olivier1, W.J. Marais3 and K.J. Wessels2 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 Year Estimated Population Change 2000 8,038,200 - 2001 8,243,719 2.56% 2002 8,499,900 3.11% 2003 8,775,200 3.23% 2004 8,851,455 0.87% 2005 9,002,534 1.71% 2006 9,193,800 2.12% 2007 9,665,841 5.13% 2008 10,450,000 8.11% 2009 10,531,300 0.77% Time Series Analysis Band 2 Separation Band 2 Separation Band 2 Vegetation Band 2 Settlement MODIS Band 2 Band 1 Separation Band11 MODIS Band Separation Band 1 Vegetation 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. Triply modulated time series • Time series modelled as a triply modulated cosine function • Where = Mean = Seasonal cycle (8/365) = Amplitude = Phase = Angular frequency = Noise = Spectral band = Pixel index = Time index Extended Kalman Filter Framework Mean • State vector • Process model • Observation model Amplitude Phase Modelling the time series Unstable parameter Mean Unstable parameter Unstable parameter Amplitude Phase Tuneable parameters • Process model • Observation model Initial estimates of state vector Process covariance matrix Observation noise covariance matrix Tuneable parameters Initial estimates of state vector Process covariance matrix Observation noise covariance matrix Tunable parameters Where j denotes the epoch number What do we want? Tunable parameters Absolute Error Mean Amplitude Phase Creating extreme conditions Tunable parameters Absolute Error 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 Amplitude 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 Phase Set Capture a probability density function (PDF) for each time Increment k using all the pixels and if ideal will be denoted by 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 1 Mean Amplitude Absolute Error 1142 MODIS pixels = 285.5km2 Results: Standard deviation for MODIS spectral band 2 Mean Amplitude Absolute Error 1142 MODIS pixels = 285.5km2 Results: Standard deviation for MODIS bands 1142 MODIS pixels = 285.5km2 Results: Classification on labelled data K-means (Band 1, Band 2) Vegetation Accuracy Settlement accuracy 1142 MODIS pixels = 285.5km2 Results: Accuracy for MODIS bands 1142 MODIS pixels = 285.5km2 Results: Gauteng province settlements 23.16% Settlement 78704 MODIS pixels = 19676km2 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? Mining Informal settlements Expansion of irrigation Commercial forestry Alien tree removal