定位技术由来已久。通过GPS，百度，谷歌的定位技术，为目前社交网络发展提供了更进一步的精确和方向，同时也会各种智能家具自动化情景模式提供了解决方案。

室内定位在智能化家具的场景协议处理中具有十分有用，如果能精确的了解室主人的精确位置，就能制定更智能化更节约能源的自动化。比如智能电灯或者插座在主人进屋后自动亮灭，智能风扇在主人离开时自动停止，室内的电动门自动开关等等。

利用室内不同地点的无线发射源，比如WIFI，蓝牙，新BLE技术，可以实现室内定位。假设室内有ABC三个无线设备，根据信号误减算出距离，建立坐标，已知某人位于P（x，y）点，这与A（x1，y1），B（x2，y2），C（x3，y3）的距离分别为a，b，c。求P点座标

可以得到三个方程：

( x₁ - x )² + ( y₁- y)² = a²

( x₂ - x)² + ( y₂ -y)² = b²

( x₃ - x)² + ( y₃ -y)² = c²

使用多项式定理，可以化解方程并求解这个二元二次方程。

或者使用解析几何处理，对原坐标系进行旋转和平移，使A点为原点（0，0），B点位于x轴（d，0），C点在新坐标系为（i，j），根据勾定理和圆的解析方程，得到简化方程

方程1：

a² = x² + y²

方程2:

b² = (x - d)² + y²

方程3:

c² = (x - i)² + (y - j)²

1和2相减得到新坐标系中x的值为
x = (r₁² - r₂²+ d²) / 2d

然后得到y值

y = (r₁² - r₃²- x² + (x - i)² + j²) / 2j

而d的值为：

d²  = （x2-x1）² + (y2-y1) ²

I,j的值是（x3，y3）经过平移和旋转后得到

B原本不在x轴，B顺时针旋转B角度后使其位于X轴，

标准的数学模型中，三个圆会完美的相交于一点，但由于使用无线信号，信号强度衰减既与本身物理属相相关，也与室内装修布局有关，所以实际衰减会比理论衰减更多，所以根据理论衰减度与距离的关系方程算出的距离会比实际偏大。这样得到的圆的半径比实际长，三圆没办法相交于或者相切于一点，而可能是相交于一个区域。理论上来讲，用户处于的某一点就在该区域内。

以view左上角为原点，右为x轴，下为y轴，建立坐标系。计算人在室内的相对位置。

屏幕坐标系中点顺时针和逆时针加平移公式,x1，y1原坐标系坐标，x2，y2为新坐标系坐标，逆时针变换后可以顺时针还原

点顺时针或者坐标轴逆时针

X1=x2cosb-y2sinb+x0

Y1=y2cosb+x2sinb-y0

点逆时针或者坐标轴顺时针

X2=(x1-x0)*cosb+(y1-y0)*sinb

Y2=(y1-y0)*cosb-(x1-x0)*sinb

//BLE1 position
	private int m_x1 = 300;
	private int m_y1 = 180;
	//BLE2 position
	private int m_x2 = 600; //180;
	private int m_y2 = 420; //580;
	//BLE3 position
	private int m_x3 = 180; //600;
	private int m_y3 = 580; //420;
    //user position
	private int m_x = 600;
	private int m_y = 600;
    //
//	private int m_r1 = 130, m_r2 = 300, m_r3 = 300;
	
//	private int m_xx = 0;
//	private int m_yy = 0;

	/*
	private int m_x1 = 100;
	private int m_y1 = 100;
	//BLE2 position
	private int m_x2 = 400; //180;
	private int m_y2 = 100; //580;
	//BLE3 position
	private int m_x3 = 100; //600;
	private int m_y3 = 400; //420;
    //user position
	private int m_x = 400;
	private int m_y = 400;
	*/
//	private int times = 10000;
	//以A为原点 ，B为x轴上的点，转换坐标系
	public double getSinx(int x, int y, int x1, int y1)
	{
		return (((y-y1)*1.0f)/Math.sqrt((x-x1)*(x-x1)+(y-y1)*(y-y1)));
	}
	public double getCosx(int x, int y, int x1, int y1)
	{
		return (((x-x1)*1.0f)/Math.sqrt((x-x1)*(x-x1)+(y-y1)*(y-y1)));
	}
	//获得B点x坐标
	public int getDD(int x1, int y1, int x2, int y2)
	{
		return ((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));
	}
	//get new x
	public int getX(int x1, int y1, int x2, int y2, int x3, int y3, int r1,
			int r2, int r3) {
		int x = 0;
		int dd = getDD(x1, y1, x2, y2);
		Log.i(tag, "getX d1=" + dd);
		double d = (Math.sqrt(dd));
		Log.i(tag, "getX d=" + d);
		x = (int) ((r1 * r1 - r2 * r2 + dd) / (2 * d));
		Log.i(tag, "getX x=" + x);
		return x;
	}
	//get old x
	public int getXX(int x, int y, int x2, int y2, int x1, int y1) {
		int nx = 0;
		//x=x‘cost-y‘sint+x0,
		double cosbx = getCosx(x2, y2, x1, y1);
		double sinbx = getSinx(x2, y2, x1, y1);
		
		nx = ((int)(x*cosbx-y*sinbx))+x1;	
		Log.i(tag, "getXX nx=" + nx);
		return nx;
	}
	//get new y
	public int getY(int x1, int y1, int x2, int y2, int x3, int y3, int r1,
			int r2, int r3) {
		int y = 0;
		// y = (r12 - r32 - x2 + (x - i)2 + j2) / 2j
		double cosx = getCosx(x2, y2, x1, y1);
		double sinx = getSinx(x2, y2, x1, y1);
		Log.i(tag, "getY sinx=" + sinx + "cosx="+cosx);
		//int i = (int)(((x3*x2+y3*y2)*1.0f)/Math.sqrt(x2*x2+y2*y2))-x1;//x3 - x1;
		int i = (int)(((x3-x1)*cosx+(y3-y1)*sinx));
	
		Log.i(tag, "getY i=" + i);
		//int j = (int)(((x2*y3-y2*x3)*1.0f)/Math.sqrt(x2*x2+y2*y2))-y1;//y3 - y1;
		int j = (int)((y3-y1)*cosx-(x3-x1)*sinx);

		Log.i(tag, "getY j=" + j);
		int x = getX(x1, y1, x2, y2, x3, y3, r1, r2, r3);
		y = (int)((r1 * r1 - r3 * r3 - x * x + (x - i) * (x - i) + j * j) / (2 * j));
		Log.i(tag, "getY y=" + y);
		return y;
	}
	//get old y
	public int getYY(int x, int y, int x2, int y2, int x1, int y1) {
		int ny = 0;
		//y=x‘sint+y‘cost+y0.
		//double cosx = getCosx(x2, y2, x1, y1);
		//double sinx = getSinx(x2, y2, x1, y1);
		double cosbx = getCosx(x2, y2, x1, y1);
		double sinbx = getSinx(x2, y2, x1, y1);
		
		ny = (int)((x*sinbx+y*cosbx))+y1;	
		Log.i(tag, "getYY ny=" + ny);
		return ny;
	}
	public int getR1(int x1, int y1, int x, int y) {
		int r1 = 0;

		int d1 = (x1 - x) * (x1 - x) + (y1 - y) * (y1 - y);
		Log.i(tag, "getR1 d1=" + d1);
		double d = Math.sqrt(d1);
		Log.i(tag, "getR1 d=" + d);
		r1 = (int) d;
		return r1;
	}

	public int getR2(int x2, int y2, int x, int y) {
		int r2 = 0;

		int d1 = (x2 - x) * (x2 - x) + (y2 - y) * (y2 - y);
		Log.i(tag, "getR2 d1=" + d1);
		double d = Math.sqrt(d1);
		Log.i(tag, "getR2 d=" + d);
		r2 = (int) d;
		return r2;
	}

	public int getR3(int x3, int y3, int x, int y) {
		int r3 = 0;

		int d1 = (x3 - x) * (x3 - x) + (y3 - y) * (y3 - y);
		Log.i(tag, "getR3 d1=" + d1);
		double d = Math.sqrt(d1);
		Log.i(tag, "getR3 d=" + d);
		r3 = (int) d;
		return r3;
	}
	public Point getManPoint(int x1, int y1, int x2, int y2, int x3, int y3,
			int r1, int r2, int r3) {
		Point p = new Point(0,0);
		for (int j = 0; j < scr_h; j++) {
			for (int i = 0; i < scr_w; i++) {

				if (((i - x1) * (i - x1) + (j - y1) * (j - y1) <= r1 * r1)
						&& ((i - x2) * (i - x2) + (j - y2) * (j - y2) <= r2
								* r2)
						&& ((i - x3) * (i - x3) + (j - y3) * (j - y3) <= r3
								* r3)) {
                        p.set(i, j);
                        return p;
				}
			}
		}
		return p;
	}
	public void setValue(int x1, int y1, int x2, int y2, int x3, int y3, int x, int y)
	{
		this.m_x1 = x1;
		this.m_y1 = y1;
		this.m_x2 = x2;
		this.m_y2 = y2;
		this.m_x3 = x3;
		this.m_y3 = y3;
		this.m_x = x;
		this.m_x = y;
	    this.invalidate();
	}
	void onDrawView(Canvas canvas) {
		// add and modify
		
		Paint p = new Paint();
		canvas.drawBitmap(img, 0, 0, p);
		p.setColor(Color.BLUE);
		
		canvas.drawCircle(m_x1, m_y1, 10, p);
		p.setTextSize(50);
		canvas.drawText("A", m_x1+10, m_y1+10, p);
		canvas.drawCircle(m_x2, m_y2, 10, p);
		canvas.drawText("B", m_x2+10, m_y2+10, p);
		canvas.drawCircle(m_x3, m_y3, 10, p);
		canvas.drawText("C", m_x3+10, m_y3+10, p);
		p.setColor(Color.RED);
		canvas.drawCircle(m_x, m_y, 20, p);
		canvas.drawText("P", m_x+20, m_y+20, p);
		p.setColor(Color.BLUE);
		p.setStyle(Paint.Style.STROKE);// 设置空心
		p.setStrokeWidth(10);
		/*
		canvas.drawCircle(m_x1, m_y1, m_r1, p);
		canvas.drawCircle(m_x2, m_y2, m_r2, p);
		canvas.drawCircle(m_x3, m_y3, m_r3, p);

		int x = getX(m_x1, m_y1, m_x2, m_y2, m_x3, m_y3, m_r1, m_r2, m_r3);

		int y = getY(m_x1, m_y1, m_x2, m_y2, m_x3, m_y3, m_r1, m_r2, m_r3);
		x = getXX(x, y, m_x2, m_y2, m_x1);
		y = getYY(x, y, m_x2, m_y2, m_y1);
		canvas.drawCircle(x, y, 100, p);
		*/
		int r1= getR1(m_x1, m_y1, m_x, m_y);
		int r2= getR1(m_x2, m_y2, m_x, m_y);
		int r3= getR1(m_x3, m_y3, m_x, m_y);
		canvas.drawCircle(m_x1, m_y1, r1, p);
		canvas.drawCircle(m_x2, m_y2, r2, p);
		canvas.drawCircle(m_x3, m_y3, r3, p);
		
		int x = getX(m_x1, m_y1, m_x2, m_y2, m_x3, m_y3, r1+10, r2+10, r3+10);
		int y = getY(m_x1, m_y1, m_x2, m_y2, m_x3, m_y3, r1+10, r2+10, r3+10);
		Log.i(tag, "onDrawView x="+x+"y="+y);
		int xx = getXX(x, y, m_x2, m_y2, m_x1, m_y1);
		int yy = getYY(x, y, m_x2, m_y2, m_x1, m_y1);
		Log.i(tag, "onDrawView xx="+xx+"yy="+yy);
		Log.i(tag, "onDrawView this.m_x="+this.m_x+"this.m_y="+this.m_y);
		p.setColor(Color.YELLOW);
		canvas.drawCircle(xx, yy, 30, p);
	}

智能家具中室外定位和室内无线信号定位研究