Change Detection in State Space Models, with Unknown
(supported by NSF, Power Control and Adaptive Networks Program of ECCS (Engineering), $265,529, August 2007 - 2010) NSF link
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Change detection is required in many practical problems arising in quality control, flight control, fault detection, in target tracking problems were the motion model may change over time, as well as in surveillance problems like abnormal activity detection ,  or activity recognition. We study the online change detection problem in partially observed linear or nonlinear systems (also called a general HMM), when (i) the changed system parameters are unknown and (ii) the change can be “slow” or sudden. A linear, Gaussian state space model can be tracked using a Kalman filter (KF), while in other situations, a particle filter (PF) can be used. Sudden changes, which result in significant loss of track, are easily detected using existing statistics such as tracking error (TE) or observation likelihood (OL). We propose a statistic called ELL (and its generalization, gELL) which uses the tracked component of the change to detect it. Hence it detects ``slow” changes (changes which result in small loss of track) faster than TE or OL. We show, both analytically and experimentally, that ELL complements OL, i.e. it detects changes which OL misses and vice-versa.
The fact that ELL can detect a change before significant loss of track is useful in target(s) tracking problem where the target(s)’ dynamics might change over time. If the change in target motion dynamics is slow, it may not immediately result in loss of track. If one can detect the change before loss of track, one can try to learn its parameters on the fly (or at least increase the system noise variance), before completely losing track of the target. For example, a target may be moving with a constant velocity model in a given direction and this may slowly (or suddenly) change to a changing velocity model in a different direction. We have demonstrated application of ELL in detecting "slow" changes in a bearings-only tracking problem and for change detection in landmark shape dynamical models. This has application in abnormal human activity detection, in abnormal human action detection and in activity segmentation (segmenting a long activity into piecewise stationary elementary pieces). Other applications of ELL are in neural signal processing (detecting changes in response of animals’ auditory neurons to changes in stimuli provided to them) and in acoustic tracking of targets with changing dynamics.
a) Bound on Errors in Particle Filtering with Incorrect Model Assumptions and its Implication for Change Detection
convergence (under certain assumptions) of the modeling and particle
errors in ELL approximation using a particle filter optimal for the
system. We generalize the ELL approximation problem to study the errors
using a particle filter with incorrect system model parameters to
posterior expectation of any statistic.
We quantify the "incorrectness" in the model by a distance
metric between the correct and incorrect state transition kernels
as system model error per time step). The total error in approximating
posterior distribution of the state given noisy observations can be
modeling error and particle filtering error in tracking with the
model. We show that the bound on both errors is a monotonically
function of the error in the system model per time step. The bound on
particle filtering error blows up very quickly since it has increasing
derivatives of all orders. We apply this result to bounding the errors
ELL, where it implies that the approximation of ELL is more accurate
ICASSP 2005, Philadelphia, March 2005: Slow and Sudden Change Detection
UC-Berkeley, Computer Vision Seminar Series, Nov 22, 2005 (invited): Abnormal "Shape Activity" Detection & Tracking
Plots and MATLAB Code: coming soon...