Wi-Fi位置三角剖分 [英] Wi-Fi position triangulation

问题描述

考虑此地图:

我需要了解Wi-Fi三角测量的基本原理.上图中描绘了该场景.为了实施Wi-Fi三角测量，我至少需要三个Wi-Fi热点及其位置.设置:

1. 为简单起见，假设我有一个 1平方公里乘1平方公里的区域，并且该区域有三个Wi-Fi热点.坐标系如下:正方形区域的一个角为(0,0,0)，对角最远的角将具有坐标(1,1,1).所有位置确定都将仅相对于此坐标系完成(为简单起见，我不希望使用全局xyz坐标).在其中，我有三个Wi-Fi热点，分别位于(x1，y1，z1)，(x2，y2，z2)，(x3，y3，z3).

2. 我们有一个设备能够接收Wi-Fi信号并计算位置(x，y，z)的信号强度的人.该设备可以是手机，平板电脑等.

问题:当您现在有了以下输入时，动态地计算人员的位置(x，y，z):

1. 从每个Wi-Fi热点接收的信号的信号强度

2. 以前存储在变量或数据库中的Wi-Fi热点的坐标.

第一个问题:如何根据上述输入来计算排名?我假设信号强度与到路由器的距离成正比，但是确切的关系是什么? Skyhook 如何做到如此精确?

第二个问题:我相信以上输入已经足够.还有其他需要吗?

解决方案

这很容易.这只是一些基本的数学.将其分为两部分:

1. 查找水平位置(无高度).

要找到您的位置，您需要三点，但第二秒只需要关注两点即可.通过使用两个点，您可以自己创建一个三角形，并根据两个点之间的信号强度找到位置.这将找出您在两个路由器之间的位置.例如，如果您位于路由器3和4之间，并且与3相比，信号强度为-89，而与4相比，信号强度为-54，那么您知道自己比3更接近3.如果您将距离与信号强度进行比较，则可以非常准确地了解路由器3和4之间的位置.剩下的问题就是确定您在3和4之间处于哪一侧.，因为您可能在路由器的上方或下方具有相同的信号强度值(-89，-54)(请参见图表)

  6你可能会在这里3 -------------------------- 4你也可以在这里5 

然后只是找到另一个路由器，并注意您的信号强度.您只需看一下5个和6个路由器之间的信号强度关系即可(图中)轻松地确定要站在哪一侧.

2. 您可以用高度做同样的事情.

要完成上述所有操作，您实际上仅需要距离与信号强度之间的近似值，以及路由器之间的距离即可.根据我的测试(我编写了自己的Wi-Fi三角测量代码)，跨移动设备的信号强度非常均匀，因此一台设备应具有与其附近设备相同的结果.

Skyhook 我认为这是通过GPS定位(可能是硬编码的)，或与此基本相同的原理.Skyhook是Apple唯一为此批准的服务，因此Apple基本上做了同样的事情，然后确保其他应用程序无法使用它(任何使用受限制的Skyhook do this so accurately?

Second Question: I believe the above inputs are sufficient. Is there anything else required?

解决方案

This is pretty easy. It's just some basic maths. Break it down into two parts:

1. Finding your horizontal location (no height).

To find your location, you need three points, but just focus on two points for a second. By using two points, you can create a triangle with yourself, and find your location based on your signal strength between two points. This will find out where you are in between two routers. For instance, if you're in between routers 3 and 4, and your signal strength in comparison to 3 is -89 and your signal strength to 4 is -54, you know that you're closer to 3 than you are to 4. If you do an approximation of distance vs signal strength, you can come up with a pretty accurate read of where you are in between routers 3 and 4. The problem left over then, is determining which side you're on in between 3 and 4, since you could have the same signal strength values (-89, -54) either above or below the routers (look at diagram)

           6

   You could be here

3--------------------------4

  You could also be here

            5

Then just find another router, and notice your signal strength. You should be able to determine which side you're on pretty easily just by taking a look at signal strength relationships between 5 and 6 routers (in the diagram).

2. You can do the same thing with height.

To do all of the above, you really only need an approximation of distance vs signal strength, and the distances between the routers. From my testing (I wrote my own Wi-Fi triangulation code), the signal strength is pretty uniform across mobile devices, so one device should have the same results as the device next to it.

Skyhook does this I think either through GPS positioning (it might be hard coded in), or basically the same principle as this. Skyhook is the only service that is Apple approved for this, so Apple basically did this same thing and then made sure other apps couldn't use it (any iPhone app that uses the restricted 802.11 library that contains the functions in order to do this will be denied from the App Store).

How to find distance:

You need to do some simple approximations. These approximations will not be all the same depending on your environment, so -89 feet (27 m) might mean you're 15 feet (4.5 m) away from Router 3, but -89 feet (27 m) from router 4 might mean you're 13 feet (4 m) away. No matter what you do, this isn't going to be 100 percent accurate, but that's okay, because you can get within 5 feet (1.5 m) for sure.

So what you do is you find a bunch of points where you get a reading from -89 from router 3, and you jot down what your distance was. Then, you take an average, and you use this average to put down in your database (which says when you're -89 from router 3, you're 15 feet (4.5 m)). You then do this for other values, like -50 or whatever, and you jot down your values and find an average. Now, if -89 means you're 15 feet (4.5 m) away, and -50 means you're 25 feet (4.5 m) away (just an example), you have to approximate your distance when you're -75 from router 3 unless you want to go get an approximation by hand for -75. This would be cumbersome for tons of values, but you'll have to experiment to see how accurate you can be with as few data points as you can get.

You can approximate between two signal strength averages by realizing that signal strength is logarithmic, so you can estimate that since -89 is 15 feet (4.5 m), then -75 would be logarithmically (base 10 or base 2, I can't remember, but I'm leaning towards base 10) further away than -89 by a factor of 14/100.

Asking for code

I have the code somewhere, but it was a couple years ago so I'd have to dig through a lot of stuff to find it. I think conceptually, it should be easy to replicate without code. It took me about 50 lines of Java code for the android devices I was testing.

Essentially I took an android phone and created an application that allows me to at any moment display the current ID of the connected Wi-Fi device, its signal strength, other nearby Wi-Fi ID's and their signal strength, and then GPS location. This is all accessible through Android's API. I think you need an Android device on API 4 or higher or something. This was like three or four years ago, so I'm just throwing this out from what I remember.

The GPS location part was to make the mapping between physical and Wi-Fi strength easier, rather than having to create a blueprint map of my facility in some other way, I could just have google maps do it for me at the same time since I can overlay their map and the GPS coordinates essentially, while creating the distance map. You'd still need a depth map to map floor levels though, which we can do by hand pretty easily by finding if you're in the middle of two routers.

We know that signal strength is strongest to Wi-Fi hubs on the same floor, and then can double check by making sure you have weaker signals to Wi-Fi hubs on different floors. This depth map is essentially a list of Wi-Fi hubs, and their respective floors.

We do not need their positions, since we can best fit the signal strength to the GPS locations we grabbed when walking around the facility and grabbing the signal strength to certain hubs. This is some simple math. So for 2D plane position, looking down from the top, we have a bunch objects like such:

BestFitObject{
   Tuple<long, long> GPSLocation;
   List<Tuple<WifiDevice, signedInt>> WifiReadings; //WifiDeviceName(through UUID or some other way), tupled with the signalStrength when that bestFit reading was taken
}

WifiDevice{
   UUID ID; // Think a string should work fine, might be an internal type that encompasses UUID which would be better.
   int floorNumber;
   Tuple<long, long> GPSLocation; // Not entirely necessary, could provide better accuracy though
}

And then when we ping the client device and want to best fit it, it returns an object like this:

ClientPosition{
   List<Tuple<UUID, signedIt> NearbySignals; // Tuple of the UUID of the Wi-Fi device and the signal strength taken during the time of the ping.
}

Then we can easily best fit our ClientPosition to the 2D map that we created with the above two objects.

The above is pretty simple, and the depth map is even simpler in my opinion.

Ideally, you'd want to try and hit a couple different devices that encompass a couple different wireless techs (some a devices, some b devices, n, g etc) just to get more accurate results. What I found though, was that accuracy isn't that big of a deal, and you'll be within 5 feet (1.5 m) or so. That was accurate enough for my needs. Ideally, all the Wi-Fi hubs are the same model, and they usually are in large facilities/companies, but even then, it's not that big of a deal. The variability is so small, and if you don't need crazy accuracy, it won't matter.

这篇关于Wi-Fi位置三角剖分的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！