Connected Vehicles: Intelligent Transportation Systems

250 A. H. Sakr et al. Although, in general, there is no closed-form solution for the integrals in Eq. (7), many approximations have been proposed in the literature [7, 8]. Here, we use a ln second-order Taylor series expansion around s = 2 . Hence, the n-th segment in the Cartesian coordinate system can be approximated as xn(s) = x0n + A1ns + A2ns2 + A3ns3 (9) . yn(s) = y0n + B1ns + B2ns2 + B3ns3 Let C = cos ϕn ln , S = sin ϕn ln , and K = c ln , the coefficients Ain 2 2 2 and Bin can be given by A1n = C + 1 KSln − 1 (ln)2(c1S + K2C) 2 8 An2 = −1KS + 1 ln(c1S + K2C) 2 4 A3n = − 1 l n(c1 S + K2C) 6 B1n = S − 1 KCln + 1 (ln)2(c1C − K2S) 2 8 B2n = 1 − 1 ln (c1C − K2S) KC 4 2 B3n = 1 ln(c1C − K2S) 6 Measurement Vector Representation The ego vehicle is equipped with GPS receiver, speed and yaw rate sensor, radar, lane markings camera, and DSRC transceiver. GPS Receiver and Speed and Yaw Rate Sensor GPS receiver, and speed and yaw rate sensor provide measurements related to the current state of the ego vehicle. We define the ego vehicle measurement vector as ⎡⎤ x¯k zke = ⎢⎢⎢⎢⎣⎢ ⎥⎥⎥⎦⎥⎥ (10) y¯k v¯k φ¯k ψ¯ k where the bar above each symbol is used to denote measurements.