Accurate real-time shape estimation is critical for continuum robots in applications such as minimally invasive surgery and confined-space exploration. Existing methods often rely on costly or impractical sensing technologies. This paper proposes a novel real-time, low-cost, high-accuracy shape estimation strategy that fuses data from embedded Hall-effect sensors and inertial measurement units (IMUs). The system employs an annular magnet at the base of the continuum robot and three sensor modules to measure magnetic fields and orientations. An optimization framework based on the fusion of magnetic field data and orientation data measured by the sensor module is developed for sensor positioning, while three curve-fitting methods, including piecewise quadratic Bezier, cubic Bezier, and Kasa least-squares circular arc, are developed for shape reconstruction. Experimental validation is conducted on a physical continuum robot platform, demonstrating that the proposed strategy combining the sensor positioning method and the Kasa least-squares circular-arc fitting method can achieve accurate shape estimation for the developed continuum robot, with an average error of less than 1 mm and a real-time frequency of 25 Hz.