卡尔曼滤波算法

建议编辑一下这个帖子作为滤波专用的，这样大家查起来也方便。下面是卡尔曼滤波，不是扩展的，但是输出平稳的俯仰和滚转应该够了(凑乎用吧我也不是专业写代码的，欢迎大家拍)

1. #include <Wire.h> // I2C library, gyroscope
   
2. 
   
3. // Accelerometer ADXL345
   
4. #define ACC (0x53)    //ADXL345 ACC address
   
5. #define A_TO_READ (6)        //num of bytes we are going to read each time (two bytes for each axis)
   
6. 
   
7. 
   
8. // Gyroscope ITG3200
   
9. #define GYRO 0x68 // gyro address, binary = 11101000 when AD0 is connected to Vcc (see schematics of your breakout board)
   
10. #define G_SMPLRT_DIV 0x15   
    
11. #define G_DLPF_FS 0x16   
    
12. #define G_INT_CFG 0x17
    
13. #define G_PWR_MGM 0x3E
    
14. 
    
15. #define G_TO_READ 8 // 2 bytes for each axis x, y, z
    
16. 
    
17. 
    
18. // offsets are chip specific.
    
19. int a_offx = 0;
    
20. int a_offy = 0;
    
21. int a_offz = 0;
    
22. 
    
23. int g_offx = 0;
    
24. int g_offy = 0;
    
25. int g_offz = 0;
    
26. ////////////////////////
    
27. 
    
28. ////////////////////////
    
29. char str[512];
    
30. 
    
31. void initAcc() {
    
32.   //Turning on the ADXL345
    
33.   writeTo(ACC, 0x2D, 0);      
    
34.   writeTo(ACC, 0x2D, 16);
    
35.   writeTo(ACC, 0x2D, 8);
    
36.   //by default the device is in +-2g range reading
    
37. }
    
38. 
    
39. void getAccelerometerData(int* result) {
    
40.   int regAddress = 0x32;    //first axis-acceleration-data register on the ADXL345
    
41.   byte buff[A_TO_READ];
    
42.   
    
43.   readFrom(ACC, regAddress, A_TO_READ, buff); //read the acceleration data from the ADXL345
    
44.   
    
45.   //each axis reading comes in 10 bit resolution, ie 2 bytes.  Least Significat Byte first!!
    
46.   //thus we are converting both bytes in to one int
    
47.   result[0] = (((int)buff[1]) << 8) | buff[0] + a_offx;   
    
48.   result[1] = (((int)buff[3]) << 8) | buff[2] + a_offy;
    
49.   result[2] = (((int)buff[5]) << 8) | buff[4] + a_offz;
    
50. }
    
51. 
    
52. //initializes the gyroscope
    
53. void initGyro()
    
54. {
    
55.   /*****************************************
    
56.   * ITG 3200
    
57.   * power management set to:
    
58.   * clock select = internal oscillator
    
59.   *     no reset, no sleep mode
    
60.   *   no standby mode
    
61.   * sample rate to = 125Hz
    
62.   * parameter to +/- 2000 degrees/sec
    
63.   * low pass filter = 5Hz
    
64.   * no interrupt
    
65.   ******************************************/
    
66.   writeTo(GYRO, G_PWR_MGM, 0x00);
    
67.   writeTo(GYRO, G_SMPLRT_DIV, 0x07); // EB, 50, 80, 7F, DE, 23, 20, FF
    
68.   writeTo(GYRO, G_DLPF_FS, 0x1E); // +/- 2000 dgrs/sec, 1KHz, 1E, 19
    
69.   writeTo(GYRO, G_INT_CFG, 0x00);
    
70. }
    
71. 
    
72. 
    
73. void getGyroscopeData(int * result)
    
74. {
    
75.   /**************************************
    
76.   Gyro ITG-3200 I2C
    
77.   registers:
    
78.   temp MSB = 1B, temp LSB = 1C
    
79.   x axis MSB = 1D, x axis LSB = 1E
    
80.   y axis MSB = 1F, y axis LSB = 20
    
81.   z axis MSB = 21, z axis LSB = 22
    
82.   *************************************/
    
83. 
    
84.   int regAddress = 0x1B;
    
85.   int temp, x, y, z;
    
86.   byte buff[G_TO_READ];
    
87.   
    
88.   readFrom(GYRO, regAddress, G_TO_READ, buff); //read the gyro data from the ITG3200
    
89.   
    
90.   result[0] = ((buff[2] << 8) | buff[3]) + g_offx;
    
91.   result[1] = ((buff[4] << 8) | buff[5]) + g_offy;
    
92.   result[2] = ((buff[6] << 8) | buff[7]) + g_offz;
    
93.   result[3] = (buff[0] << 8) | buff[1]; // temperature
    
94.   
    
95. }
    
96. 
    
97. 
    
98. float xz=0,yx=0,yz=0;
    
99. float p_xz=1,p_yx=1,p_yz=1;
    
100. float q_xz=0.0025,q_yx=0.0025,q_yz=0.0025;
     
101. float k_xz=0,k_yx=0,k_yz=0;
     
102. float r_xz=0.25,r_yx=0.25,r_yz=0.25;
     
103.   //int acc_temp[3];
     
104.   //float acc[3];
     
105.   int acc[3];
     
106.   int gyro[4];
     
107.   float Axz;
     
108.   float Ayx;
     
109.   float Ayz;
     
110.   float t=0.025;
     
111. void setup()
     
112. {
     
113.   Serial.begin(9600);
     
114.   Wire.begin();
     
115.   initAcc();
     
116.   initGyro();
     
117.   
     
118. }
     
119. 
     
120. //unsigned long timer = 0;
     
121. //float o;
     
122. void loop()
     
123. {
     
124.   
     
125.   getAccelerometerData(acc);
     
126.   getGyroscopeData(gyro);
     
127.   //timer = millis();
     
128.   sprintf(str, "%d,%d,%d,%d,%d,%d", acc[0],acc[1],acc[2],gyro[0],gyro[1],gyro[2]);
     
129.   
     
130.   //acc[0]=acc[0];
     
131.   //acc[2]=acc[2];
     
132.   //acc[1]=acc[1];
     
133.   //r=sqrt(acc[0]*acc[0]+acc[1]*acc[1]+acc[2]*acc[2]);
     
134.   gyro[0]=gyro[0]/ 14.375;
     
135.   gyro[1]=gyro[1]/ (-14.375);
     
136.   gyro[2]=gyro[2]/ 14.375;
     
137.   
     
138.    
     
139.   Axz=(atan2(acc[0],acc[2]))*180/PI;
     
140.   Ayx=(atan2(acc[0],acc[1]))*180/PI;
     
141.   /*if((acc[0]!=0)&&(acc[1]!=0))
     
142.     {
     
143.       Ayx=(atan2(acc[0],acc[1]))*180/PI;
     
144.     }
     
145.     else
     
146.     {
     
147.       Ayx=t*gyro[2];
     
148.     }*/
     
149.   Ayz=(atan2(acc[1],acc[2]))*180/PI;
     
150.   
     
151.   
     
152. //kalman filter
     
153.   calculate_xz();
     
154.   calculate_yx();
     
155.   calculate_yz();
     
156.   
     
157.   //sprintf(str, "%d,%d,%d", xz_1, xy_1, x_1);
     
158.   //Serial.print(xz);Serial.print(",");
     
159.   //Serial.print(yx);Serial.print(",");
     
160.   //Serial.print(yz);Serial.print(",");
     
161.   //sprintf(str, "%d,%d,%d,%d,%d,%d", acc[0],acc[1],acc[2],gyro[0],gyro[1],gyro[2]);
     
162.   //sprintf(str, "%d,%d,%d",gyro[0],gyro[1],gyro[2]);
     
163.     Serial.print(Axz);Serial.print(",");
     
164.     //Serial.print(Ayx);Serial.print(",");
     
165.     //Serial.print(Ayz);Serial.print(",");
     
166.   //Serial.print(str);
     
167.   //o=gyro[2];//w=acc[2];
     
168.   //Serial.print(o);Serial.print(",");
     
169.   //Serial.print(w);Serial.print(",");
     
170.   Serial.print("\n");
     
171. 
     
172.   
     
173.   //delay(50);
     
174. }
     
175. void calculate_xz()
     
176. {
     
177. 
     
178. xz=xz+t*gyro[1];
     
179. p_xz=p_xz+q_xz;
     
180. k_xz=p_xz/(p_xz+r_xz);
     
181. xz=xz+k_xz*(Axz-xz);
     
182. p_xz=(1-k_xz)*p_xz;
     
183. }
     
184. void calculate_yx()
     
185. {
     
186.   
     
187.   yx=yx+t*gyro[2];
     
188.   p_yx=p_yx+q_yx;
     
189.   k_yx=p_yx/(p_yx+r_yx);
     
190.   yx=yx+k_yx*(Ayx-yx);
     
191.   p_yx=(1-k_yx)*p_yx;
     
192. 
     
193. }
     
194. void calculate_yz()
     
195. {
     
196.   yz=yz+t*gyro[0];
     
197.   p_yz=p_yz+q_yz;
     
198.   k_yz=p_yz/(p_yz+r_yz);
     
199.   yz=yz+k_yz*(Ayz-yz);
     
200.   p_yz=(1-k_yz)*p_yz;
     
201. 
     
202. }
     
203. 
     
204. 
     
205. //---------------- Functions
     
206. //Writes val to address register on ACC
     
207. void writeTo(int DEVICE, byte address, byte val) {
     
208.    Wire.beginTransmission(DEVICE); //start transmission to ACC
     
209.    Wire.write(address);        // send register address
     
210.    Wire.write(val);        // send value to write
     
211.    Wire.endTransmission(); //end transmission
     
212. }
     
213. 
     
214. 
     
215. //reads num bytes starting from address register on ACC in to buff array
     
216. void readFrom(int DEVICE, byte address, int num, byte buff[]) {
     
217.   Wire.beginTransmission(DEVICE); //start transmission to ACC
     
218.   Wire.write(address);        //sends address to read from
     
219.   Wire.endTransmission(); //end transmission
     
220.   
     
221.   Wire.beginTransmission(DEVICE); //start transmission to ACC
     
222.   Wire.requestFrom(DEVICE, num);    // request 6 bytes from ACC
     
223.   
     
224.   int i = 0;
     
225.   while(Wire.available())    //ACC may send less than requested (abnormal)
     
226.   {
     
227.     buff[i] = Wire.read(); // receive a byte
     
228.     i++;
     
229.   }
     
230.   Wire.endTransmission(); //end transmission
     
231. }

复制代码