嵌入式算法空间矢量角公式及其应用响应及时。软件需求是在安装角度异常时提醒用户改变位置。设备如何感知当前方向？它需要加速度传感器硬件支持，辅以算法。1、重力加速度根据物理学常识，地面上的任何物体静止时都会受到1g的重力加速度，方向是垂直向下。由于倾角不同，1g的加速度根据向量分解到xyz三个轴上：acc_x=1g.sinθ.cos?acc_y=-1g.sinθ.sin?acc_z=1g.cos?符号。表示乘法，读取加速度传感器的xyz三个轴，轴数据的细节不在本文讨论范围之内。由于传感器的数字精度和量程不同，同样的1g，读寄存器的值是不同的。为了下面的描述统一，假设值255对应1g的加速度。当物体水平静止时，理想的加速度值为(0,0,255)，当物体水平放置时，理想的加速度值为(0,0,-255)。该值的缩小或放大不会影响角度的判断。2、空间矢量的夹角在预期的正确安装方式下假设三轴为（x0，y0，z0），实际三轴数据为（x1，y1，z1）。那么如何获取当前偏差的角度呢？已知两个空间向量的坐标为a=(x1,y1,z1),b=(x2,y2,z2)，则两个向量夹角的余弦cosθ公式为：在实际应用中，当翻转角为181度，按179度处理。本文只考虑0-180度的应用，超过180度的应用需要另外计算翻转。根据空间矢量与反余弦夹角的余弦值，可得出0-180度之间的夹角，以判断设备的安装角度是否正确。3.代码实现#include"math.h"#include"stdio.h"#definePI3.1415926typedefstruct{unsignedshortx;unsignedshorty;unsignedshortz;}sensor_data_struct;staticsensor_data_structref={0,0,255};staticsensor_data_structtest={0,180/18当前计算的角度在矢量和参考矢量之间(data.x*data.x+data.y*data.y+data.z*data.z))*\(sqrt(ref.x*ref.x+ref.y*ref.y+ref.z*ref.z)));temp=acos(cosine);angle=(temp*180)/PI;returnangle;}intmain(intargc,char*argv[]){floatangle;printf("referencevector(%d,%d,%d)\r\n",ref.x,ref.y,ref.z);printf("测试向量(%d,%d,%d)\r\n",test.x,测试。y,test.z);angle=get_angle(test);printf("angle=%f'\r\n",angle);return0;}参考向量(0,0,255)测试向量(0,180,180)angle=45.000004'4.优化完善用于求解角度的三角函数，部分单片机可能不支持；为了角度的准确性，使用整形。以此条件为基础，可以建立cosθ的数组表，步进1度-2度-3度---180度，按照以下代码生成数组表：voidcreat_table(void){floati;for(i=0;i<180;i++)//i的步长值决定精度{if((unsignedchar)i%9==0){printf("\r\n");}printf("%f,",cos(i*PI/180));//角度转为弧度再传入}}根据代码生成数组表后，查找余弦表，数组下标是角度。staticconstfloatcos_table[180]={1.000000,0.999848,0.999391,0.998630,0.997564,0.996195,0.994522,0.992546,0.990268,0.987688,0.984808,0.981627,0.978148,0.974370,0.970296,0.965926,0.961262,0.956305,0.951057,0.945519,0.939693,0.933580,0.927184,0.920505,0.913545,0.906308,0.898794,0.891007,0.882948,0.874620,0.866025,0.857167,0.848048,0.838671,0.829038,0.819152,0.809017,0.798636,0.788011,0.777146,0.766044,0.754710,0.743145,0.731354,0.719340,0.707107,0.694658,0.681998,0.669131,0.656059,0.642788,0.629320,0.615661,0.601815,0.587785,0.573576,0.559193,0.544639,0.529919,0.515038,0.500000,0.484810,0.469472,0.453991,0.438371,0.422618,0.406737,0.390731,0.374607,0.358368,0.342020,0.325568,0.309017,0.292372,0.275637,0.258819,0.241922,0.224951,0.207912,0.190809,0.173648,0.156434,0.139173,0.121869,0.104528,0.087156,0.069756,0.052336,0.034900,0.017452,0.000000,-0.017452,-0.034899,-0.052336,-0.069756,-0.087156,-0.104528,-0.121869,-0.139173,-0.156434,-0.173648,-0.190809,-0.207912,-0.224951,-0.241922,-0.258819,-0.275637,-0.292372,-0.309017,-0.325568,-0.342020,-0.358368,-0.374607,-0.390731,-0.406737,-0.422618,-0.438371,-0.453990,-0.469472,-0.484810,-0.500000,-0.515038,-0.529919,-0.544639,-0.559193,-0.573576,-0.587785,-0.601815,-0.615661,-0.629320,-0.642788,-0.656059,-0.669131,-0.681998,-0.694658,-0.707107,-0.719340,-0.731354,-0.743145,-0.754710,-0.766044,-0.777146,-0.788011,-0.798635,-0.809017,-0.819152,-0.829038,-0.838671,-0.848048,-0.857167,-0.866025,-0.874620,-0.882948,-0.891007,-0.898794,-0.906308,-0.913545,-0.920505,-0.927184,-0.933580,-0.939693,-0.945519,-0.951057,-0.956305,-0.961262,-0.965926,-0.970296,-0.974370,-0.978148,-0.981627,-0.984808,-0.987688,-0.990268,-0.992546,-0.994522,-0.996195,-0.997564,-0.998630,-0.999391,-0.999848,};unsignedshortget_angle(sensor_data_structdata){floatcosine;unsignedshorti;cosine=(data.x*ref.x+data.y*ref.y+data.z*ref.z)/\((sqrt(data.x*data.x+data.y*data.y+data.z*data.z))*\(sqrt(ref.x*ref.x+ref.y*ref.y+ref.z*ref.z)));for(i=0;i<180;i++){if(cos_table[i]
