Kalman filtering methods have long been regarded as efficient adaptive Bayesian
techniques for estimating hidden states in models of linear dynamical systems
under Gaussian uncertainty. Recent advents of the Cubature Kalman filter (CKF)
have extended this efficient estimation property to nonlinear systems, and also to
hybrid nonlinear problems where by the processes are continuous and the
observations are discrete (continuous-discrete CDCKF). Employing CKF techniques,
therefore, carries high promise for modeling many biological phenomena where the
underlying processes exhibit inherently nonlinear, continuous, and noisy dynamics
and the associated measurements are uncertain and time-sampled. This paper
investigates the performance of cubature filtering (CKF and CD-CKF) in two
flagship problems arising in the field of neuroscience upon relating brain
functionality to aggregate neurophysiological recordings: (i) estimation of the firing
dynamics and the neural circuit model parameters from electric potentials (EP)
observations, and (ii) estimation of the hemodynamic model parameters and the
underlying neural drive from BOLD (fMRI) signals. First, in simulated neural
circuit models, estimation accuracy was investigated under varying levels of
observation noise (SNR), process noise structures, and observation sampling
intervals (dt). When compared to the CKF, the CD-CKF consistently exhibited
better accuracy for a given SNR, sharp accuracy increase with higher SNR, and
persistent error reduction with smaller dt. Remarkably, CD-CKF accuracy shows
only a mild deterioration for non-Gaussian process noise, specifically with Poisson
noise, a commonly assumed form of background fluctuations in neuronal systems.
Second, in simulated hemodynamic models, parametric estimates were consistently
improved under CD-CKF. Critically, time-localization of the underlying neural
drive, a determinant factor in fMRI-based functional connectivity studies, was
significantly more accurate under CD-CKF. In conclusion, and with the CKF
recently benchmarked against other advanced Bayesian techniques, the CD-CKF
framework could provide significant gains in robustness and accuracy when
estimating a variety of biological phenomena models where the underlying process
dynamics unfold at time scales faster than those seen in collected measurements.

제 1편 : MATLAB 기본편
1. MATLAB 기본사용편 ···················· 003
1.1 MATLAB 시작하기 ·························· 003
명령창(command Window)에서의 입력 005
도움말(Help)의 이용 ······························· 007
1.2 입력 오류의 수정 ····························· 008
계산의 중지 ·············································· 009
MATLAB 종료하기 ································· 009
1.3 연산과 변수의 할당 ·························· 009
연산자 우선순위 ······································· 011
내장함수 ···················································· 012
1.4 데이터의 표현 ··································· 013
1.5 변수의 처리 ······································· 015
변수 이름 ·················································· 015
clear 명령어 ············································· 016
특수변수와 정수 ······································· 017
whos 명령어 ············································ 017
1.6 벡터와 행렬 ······································· 018
벡터 ··························································· 018
행렬 ·························································· 023
스크린 출력과 억제 ································· 024
1.7 랜덤(Random)수와 복소수 ·············· 025
랜덤 수 ····················································· 025
복소수 ······················································· 027
1.8 기호를 이용한 연산 ·························· 028
기호식에서의 치환 ··································· 029
1.9 코드 파일 ·········································· 030
스크립트 코드 파일 ································· 030
코멘트의 추가 ·········································· 032
함수 코드 파일 ···································· 033
사용자 정의함수 ······································ 036
1.10 간단한 그래프의 생성 ····················· 037
ezplot을 이용한 그래프 ·························· 037
plot을 이용한 그래프 ·························· 039
3차원 그래프 ··········································· 042
1.11 MATLAB과 엑셀(Excel)의 접속 043 엑셀 데이터 불러오기 ····························· 043
데이터 가져오기 옵션 ························· 046
스크립트 생성 옵션 ································· 049
함수 생성 옵션 ········································ 049
생성된 데이터를 엑셀파일로 저장하기 ·· 050

제 2편 : 연구논문
Hybrid Cubature Kalman filtering for identifying nonlinear models
from sampled recording: Estimation of neuronal dynamics

1. Introduction 52
2. Neuronal model description 55
3. Other types of noise processes 61
4. Results 65
5. Hemodynamic model 78
6. Conclusion and discussion 84
7. Hemodynamic model estimation 88
8. Appendix 90
9. References 96