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The trac parameter identification methods can be classified into two cat-
egories, according to their data requirements: the first is off-line identification
method [4], which mainly depends on the historical trac flow data, and param-
eters are obtained by nonlinear programming or other intelligent learning meth-
ods. The drawback of off-line schemes lies in that the parameters may change
due to variation of environmental factors. This method thus can not reflect the
variation of the trac dynamics promptly. In addition, the demanding compu-
tational loads usually renders such estimation methods useless in the context of
real-time trac control. Therefore, in view of the serious disadvantages of off-
line approach for trac estimation, the other method, i.e. the on-line parameter
identification method is more attractive and desirable. This is also the research
focus of the trac control and automation. The classical on-line identification
techniques include the well-known recursive least square algorithms (RLS) [5],
optimal filtering [6], (e.g. Kalman filter, EKF, UKF and PF), and asymptotic
observer [7]. In spite of many advantages of these methods, the existing identi-
fication techniques are usually complicated and have some common limitations
for practical use. For instance, these methods are usually sensitive to random
perturbations, precise priori information must be acquired beforehand, and the
computational load is usually heavy, which results in unsatisfactory identifica-
tion speed. These shortcomings pose the primary obstacles their employment for
the real-time trac control.
Algebraic identification is a novel kind of on-line and non-asymptotic identi-
fication method proposed by M.FLESS et al [8][9]. Compared with the common
probability meaning methods such as observers and filtering method, the merits
of algebraic parameter identification are its fast speed and robustness. Due to
these two important features, algebraic identification method has been applied in
various fields, for instance, continuous-time system identification, fault diagnosis,
and signal processing [10]. In intelligent trac system (ITS) field, the algebraic
identification has been applied in the trac state estimation [11], description
of the freeway network [12], vehicle stop-and-go control [13]. In particular, a
kind of algebraic parametric estimation scheme of LWR model is proposed by
[14]. Nonetheless, it is well-known that in LWR model the speed of vehicles
is assumed to be the equilibrium speed. This assumption cannot describe the
non-equilibrium characteristics which are pertinent to safety and environmental
concerns, for example, the stop-and-go wave and phantom congestion. To be
more realistic and address the non-equilibrium features, in most highway trac
control schemes, the second-order trac model is employed [15]. In summary, the
parameter identification for second-order macroscopic trac flow model plays a
very essential role in the context of highway real-time trac control and man-
agement.
Based on differential algebraic framework in [14], a parameter estimation
scheme for non-equilibrium macroscopic trac flow is proposed in this paper.
The rest of the paper is organized as follows: Section 2 presents the highway
second-order macroscopic trac flow model METANET which shall be used
as the prototype model in parameter estimation. Section 3 describes the basic
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