Development of Analysis Methods Using Recent Data (2012) / Chapter Skim
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10 C H A P T E R 2 State-Space Model Chapter 1 illustrated the trajectory-based approach with simple braking-to-stop models estimated from data extracted from site-based video. An important objective of this project was to develop a common analytic framework that could be applied to data from either site- or vehicle-based sensor configurations and could accommodate events more complicated than constant speed followed by simple brakingto-stop.
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11 for the lead vehicle relative to the follower, obtained from the forward radar. This leads to an observation equation of the form y t y t y t 1 2 3 0 0 1 0 1 1 0 0 0 0 1 1 ( )
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12 suggests a three-phase model where a period of constant acceleration is followed by a period of roughly constant speed, which in turn is followed by a period of constant deceleration leading to a stop. Step 2: Nonlinear Least-Squares Estimation of Proposed Models It is necessary to estimate the following vehicle's initial speed, its acceleration during the first phase, the time at which deceleration began, and the deceleration characteristic of the second phase.
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13 search procedure to find the parameter values that minimized the sum-of-squares. The resulting estimates and initial approximate standard errors are shown in Table 2.1.
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14 Table 2.3. Posterior Summary for Trajectory Model Parameters Variable Mean Standard Deviation 2.5%ile 97.5%ile Following Vehicle Initial speed (ft/s)
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15 Extensibility. Statistics and Computing, Vol.
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