There are some flawed sensor data because of the sensor’s precision and environmental disturbances. That is, errors about ambient information that affect the accuracy of path planning caused by the mismatch of data acquired by sensor and the actual environment. In order to improve accuracy of environment recognition, for most sensor data, data preprocessing is required before data analysis. The preprocessing by using the least square method and the median filtering algorithm is applied in this paper.

Median Filtering Algorithm: The main idea of Median filtering is to is to run through the data in a digital image entry by entry, finding the median of neighboring entries and replacing each entry with it. The data points of a digital image or a set of data were sorted and replaced according to this principle.

Least Square Method: The Least Square Method is a standard approach in regression analysis. Setting (x_i, y_i) (i = 0, 1, ⋯, m) for points of a dataset and w_i > 0 (i = 0, 1, ⋯, m) for the weight coefficient of each point. In function space S = span{φ₀(x), φ₁(x), ⋯, φ_n(x)}, and ask for S^*(x) in the Formula (1)satisfy the Formula (2).

The method of acquiring function S^*(x) is called least square method of data fitting.

As we can see from Figure 1, median filtering can filter a small amount of noise data (as shown in Figure 1(b)), and the data smoothing could be much better by using the least square method together.

The basic principle of K-Means clustering is elaborated as [4]: Firstly, k initial “means” are randomly generated within the data domain, Then, k clusters are created by associating every observation with the nearest mean. Finally, the centroid of each of the k clusters becomes the new mean. For example, the dataset is set as

.

Step 1: K1 [Initialization]: k data points {c₁, c₂, …, c_k}of dataset are selected as the initial cluster centers.

Step 2: K2 [Assign x_i]: Calculating the distance d_ij, j = 1, 2, …, k from {[x_i], i = 1, 2, ⋯, n} to each initial cluster center {c₁, c₂, …, c_k}, the data x_i are classified into the nearest class.

Step 3: K3 [Revise c_i]: The new class cluster center of each class is acquired through calculating the average of all the data in each class.

Step 4: K4 [Deviation calculation]:

Step 5: K5 [Whether the D is convergent]: If D is convergent, the whole algorithm will end. Otherwise, it returns to K2 until convergence has been reached.

The parking space detection result is shown in Figure 2.

The environment perception coordinate system of automatic parking system includes the global coordinate and the vehicle coordinate system. The origin of vehicle coordinate system is set to the midpoint of the rear axle. X-axis is projected to the vehicle rear axle and directs right, and Y-axis lies in the vehicle longitudinal axis and directs forward. The midpoint of the rear axle serves as the coordinates of the vehicle position in the global coordinate system. The course angle of the vehicle is shown as the direction of the vehicle and donated by (). Course angle is defined as the intersection angle between the vehicle longitudinal axis and the global X-axis, and the positive direction is counterclockwise, which is shown in Figure 3.

Regarding the vehicle as a rigid body with low speed and assuming vehicle movement direction is consistent with the movement direction of rear wheels, and the motion trajectory of rear wheels could be considered as the motion trajectory of the vehicle body. Under this condition, the center coordinate of the rear wheel axis

can be considered as vehicle body’s coordinate and the trajectory of the vehicle can be expressed by.

The membership function of each input and output and the parameter settings of fuzzy controller is elaborated in literature [5]. The driver needs to stop the vehicle initially before starting the automatic parking system. But it is very difficult for most people to make the vehicle body parallel to the lane direction perfectly at initial point. Even if the body course angle is zero, the initial course angle of body should be controlled between −10˚ - 10˚. Three different kinds of simulation results are shown below when the initial course angle is −10˚, 0˚ and 10˚ respectively.

Red rectangle represents the car model in Figure 4 and the black thick solid line represents the border of the parking space. It is said in Figure 4 that the vehicle won’t encounter the border in the process of reversing. The course angle of the vehicle body is 90˚ at the end of automatic parking. The change curve of the vehicle course angle is shown in Figure 5.

If q = 10˚, movement track of vehicle and the change curve of the vehicle course angle are shown in Figure 6 and Figure 7.

When the initial course angle is 10˚, it is necessary for successfully parking to keep unchanged course angle for a period of time, then gradually increase its value when the vehicle close enough to the parking space, as it is shown in Figure 6. The vehicle has been parked successfully as shown in two figures below and the eventually course angle is 90˚.

If q = −10˚, movement track of vehicle and the change curve of the vehicle course angle are shown in Figure 8 and Figure 9.

When the initial course angle q = −10˚, the course angle should be increased obviously to make the automobile aligned quickly. The simulation results are shown in Figure 8 and Figure 9.

Compared three different kinds of parking simulation results. We can draw the conclusion that the parking simulation is best when q = 0˚. When q is −10˚ or 10˚, the parking simulation result is not as better as q = 0˚.