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Inertial navigation technology composed of inertial sensors is widely used in foot-mounted pedestrian positioning. However, inertial sensors are susceptible to noise, which affects the performance of the system. The zero-velocity update (ZUPT) as a traditional method is utilized to suppress the cumulative error. Unfortunately, the walking distance calculated by a Kalman filter still has position error. To improve the positioning accuracy, a nonlinear Kalman filter with spatial distance inequality constraint for single foot is proposed in this work. Since the stride distance between adjacent stance phases has an upper bound in plane and height, an inertial navigation system (INS) established by one inertial measurement unit (IMU) is adopted to constrain the stride process. Eventually, the performance of the proposed method is verified by experiments. Compared to the single foot-mounted ZUPT method, the proposed method suppresses the plane error and the height error by 46.04% and 65.48%, respectively. For the dual foot constraint method, the proposed constraint method can reduce the number of sensors while ensuring the positioning accuracy. Moreover, the height error is reduced by 59.98% on average by optimizing the constraint algorithm. The experimental results show that the trajectory estimated by the proposed method is closer to the actual path.

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