作者:半闲居士链接:https://www.zhihu.com/question/46916554/answer/103411007来源:知乎著作权归作者所有。商业转载请联系作者获得授权,非商业转载请注明出处。
我怎么会写得那么长……如果您有兴趣可以和我一块把公式过一遍。 要讲清这个问题,得从状态估计理论来说。先摆上一句名言:
状态估计乃传感器之本质。(To understand the need for state estimation is to understand the nature of sensors.)
任何传感器,激光也好,视觉也好,整个SLAM系统也好,要解决的问题只有一个:如何通过数据来估计自身状态。每种传感器的测量模型不一样,它们的精度也不一样。换句话说,状态估计问题,也就是“如何最好地使用传感器数据”。可以说,SLAM是状态估计的一个特例。
1. 离散时间系统的状态估计
记机器人在各时刻的状态为 ,其中 是离散时间下标。在SLAM中,我们通常要估计机器人的位置,那么系统的状态就指的是机器人的位姿。用两个方程来描述状态估计问题:
解释一下变量:
-运动方程 - 输入 - 输入噪声 - 观测方程 - 观测数据 - 观测噪声 运动方程描述了状态 是怎么变到 的,而观测方程描述的是从 是怎么得到观察数据 的。 请注意这是一种抽象的写法。当你有实际的机器人,实际的传感器时,方程的形式就会变得具体,也就是所谓的参数化。例如,当我们关心机器人空间位置时,可以取 。进而,机器人携带了里程计,能够得到两个时间间隔中的相对运动,像这样 ,那么运动方程就变为: 同理,观测方程也随传感器的具体信息而变。例如激光传感器可以得到空间点离机器人的距离和角度,记为 ,那么观测方程为: 其中 是一个2D路标点。 举这几个例子是为了说明,运动方程和观测方程具体形式是会变化的。但是,我们想讨论更一般的问题:当我不限制传感器的具体形式时,能否设计一种方式,从已知的 (输入和观测数据)从,估计出 呢? 这就是最一般的状态估计问题。我们会根据 是否线性,把它们分为线性/非线性系统。同时,对于噪声 ,根据它们是否为高斯分布,分为高斯/非高斯噪声系统。最一般的,也是最困难的问题,是非线性-非高斯(NLNG, Nonlinear-Non Gaussian)的状态估计。下面先说最简单的情况:线性高斯系统。
2. 线性高斯系统(LG,Linear Gaussian)
在线性高斯系统中,运动方程、观测方程是线性的,且两个噪声项服从零均值的高斯分布。这是最简单的情况。简单在哪里呢?主要是因为高斯分布经过线性变换之后仍为高斯分布。而对于一个高斯分布,只要计算出它的一阶和二阶矩,就可以描述它(高斯分布只有两个参数 )。 线性系统形式如下: 其中 是两个噪声项的协方差矩阵。 为转移矩阵和观测矩阵。 对LG系统,可以用贝叶斯法则,计算 的后验概率分布——这条路直接通向卡尔曼滤波器。卡尔曼是线性系统的递推形式(recursive,也就是从 估计 )的无偏最优估计。由于解释EKF和UKF都得用它,所以我们来推一推。如果读者不感兴趣,可以跳过公式推导环节。 符号:用 表示 的后验概率,用 表示它的先验概率。因为系统是线性的,噪声是高斯的,所以状态也服从高斯分布,需要计算它的均值和协方差矩阵。记第 时刻的状态服从:![x_k\sim N({{\bar x}_k},{P_k})](http://zhihu.com/equation?tex=x_k%5Csim+N%28%7B%7B%5Cbar+x%7D_k%7D%2C%7BP_k%7D%29) 我们希望得到状态变量 的最大后验估计(MAP,Maximize a Posterior),于是计算: 第二行是贝叶斯法则,第三行分母和 无关所以去掉。 第一项即观测方程,有:
很简单。 第二项即运动方程
也很简单。 现在的问题是如何求解这个最大化问题。对于高斯分布,最大化问题可以变成最小化它的负对数。当我对一个高斯分布取负对数时,它的指数项变成了一个二次项,而前面的因子则变为一个无关的常数项,可以略掉(这部分我不敲了,有疑问的同学可以问)。于是,定义以下形式的最小化函数: 那么最大后验估计就等价于: 这个问题现在是二次项和的形式,写成矩阵形式会更加清晰。定义:![](http://zhihu.com/equation?tex=%5C%5B%5Cbegin%7Barray%7D%7Bl%7D%0Az+%3D+%5Cleft%5B+%5Cbegin%7Barray%7D%7Bl%7D%0A%7Bx_0%7D%5C%5C%0A%7Bv_1%7D%5C%5C%0A+%5Cvdots+%5C%5C%0A%7Bv_K%7D%5C%5C%0A%7By_0%7D%5C%5C%0A+%5Cvdots+%5C%5C%0A%7By_K%7D%0A%5Cend%7Barray%7D+%5Cright%5D%2Cx+%3D+%5Cleft%5B+%5Cbegin%7Barray%7D%7Bl%7D%0A%7Bx_0%7D%5C%5C%0A+%5Cvdots+%5C%5C%0A%7Bx_K%7D%0A%5Cend%7Barray%7D+%5Cright%5D%5C%5C%0AH+%3D+%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D%0A1%26%7B%7D%26%7B%7D%26%7B%7D%5C%5C%0A%7B+-+%7BA_0%7D%7D%261%26%7B%7D%26%7B%7D%5C%5C%0A%7B%7D%26+%5Cddots+%26+%5Cddots+%26%7B%7D%5C%5C%0A%7B%7D%26%7B%7D%26%7B+-+%7BA_%7BK+-+1%7D%7D%7D%261%5C%5C%0A%7B%7BC_0%7D%7D%26%7B%7D%26%7B%7D%26%7B%7D%5C%5C%0A%7B%7D%26+%5Cddots+%26%7B%7D%26%7B%7D%5C%5C%0A%7B%7D%26%7B%7D%26+%5Cddots+%26%7B%7D%5C%5C%0A%7B%7D%26%7B%7D%26%7B%7D%26%7B%7BC_K%7D%7D%0A%5Cend%7Barray%7D%7D+%5Cright%5D%2CW+%3D+%5Cleft%5B+%7B%5Cbegin%7Barray%7D%7B%2A%7B20%7D%7Bc%7D%7D%0A%7B%7BP_0%7D%7D%26%7B%7D%26%7B%7D%26%7B%7D%26%7B%7D%26%7B%7D%26%7B%7D%5C%5C%0A%7B%7D%26%7B%7BQ_1%7D%7D%26%7B%7D%26%7B%7D%26%7B%7D%26%7B%7D%26%7B%7D%5C%5C%0A%7B%7D%26%7B%7D%26+%5Cddots+%26%7B%7D%26%7B%7D%26%7B%7D%26%7B%7D%5C%5C%0A%7B%7D%26%7B%7D%26%7B%7D%26%7B%7BQ_K%7D%7D%26%7B%7D%26%7B%7D%26%7B%7D%5C%5C%0A%7B%7D%26%7B%7D%26%7B%7D%26%7B%7D%26%7B%7BR_1%7D%7D%26%7B%7D%26%7B%7D%5C%5C%0A%7B%7D%26%7B%7D%26%7B%7D%26%7B%7D%26%7B%7D%26+%5Cddots+%26%7B%7D%5C%5C%0A%7B%7D%26%7B%7D%26%7B%7D%26%7B%7D%26%7B%7D%26%7B%7D%26%7B%7BR_K%7D%7D%0A%5Cend%7Barray%7D%7D+%5Cright%5D%0A%5Cend%7Barray%7D%5C%5D)
就得到矩阵形式的,类似最小二乘的问题: 于是令它的导数为零,得到: (*) 读者会问,这个问题和卡尔曼滤波有什么问题呢?事实上,卡尔曼滤波就是递推地求解(*)式的过程。所谓递推,就是只用 来计算 。对(*)进行Cholesky分解,就可以推出卡尔曼滤波器。详细过程限于篇幅就不推了,把卡尔曼的结论写一下: 前两个是预测,第三个是卡尔曼增益,四五是校正。 另一方面,能否直接求解(*)式,得到 呢?答案是可以的,而且这就是优化方法(batch optimization)的思路:将所有的状态放在一个向量里,进行求解。与卡尔曼滤波不同的是,在估计前面时刻的状态(如 )时,会用到后面时刻的信息( 等)。从这点来说,优化方法和卡尔曼处理信息的方式是相当不同的。
3. 扩展卡尔曼滤波器
线性高斯系统当然性质很好啦,但许多现实世界中的系统都不是线性的,状态和噪声也不是高斯分布的。例如上面举的激光观测方程就不是线性的。当系统为非线性的时候,会发生什么呢? 一件悲剧的事情是:高斯分布经过非线性变换后,不再是高斯分布。而且,是个什么分布,基本说不上来。(摊手) 如果没有高斯分布,上面说的那些都不再成立了。于是EKF说,嘛,我们睁一只眼闭一只眼,用高斯分布去近似它,并且,在工作点附近对系统进行线性化。当然这个近似是很成问题的,有什么问题我们之后再说。 EKF的做法主要有两点。其一,在工作点附近 ,对系统进行线性近似化: 这里的几个偏导数,都在工作点处取值。于是呢,它就被活生生地当成了一个线性系统。 第二,在线性系统近似下,把噪声项和状态都当成了高斯分布。这样,只要估计它们的均值和协方差矩阵,就可以描述状态了。经过这样的近似之后呢,后续工作都和卡尔曼滤波是一样的了。所以EKF是卡尔曼滤波在NLNG系统下的直接扩展(所以叫扩展卡尔曼嘛)。EKF给出的公式和卡尔曼是一致的,用线性化之后的矩阵去代替卡尔曼滤波器里的转移矩阵和观测矩阵即可。 其中
![\[F_{k-1} = {\left. {\frac{{\partial f}}{{\partial {x_{k - 1}}}}} \right|_{{{\hat x}_{k - 1}}}},{G_k} = {\left. {\frac{{\partial f}}{{\partial {x_k}}}} \right|_{{{\tilde x}_k}}}\]](http://zhihu.com/equation?tex=%5C%5BF_%7Bk-1%7D+%3D+%7B%5Cleft.+%7B%5Cfrac%7B%7B%5Cpartial+f%7D%7D%7B%7B%5Cpartial+%7Bx_%7Bk+-+1%7D%7D%7D%7D%7D+%5Cright%7C_%7B%7B%7B%5Chat+x%7D_%7Bk+-+1%7D%7D%7D%7D%2C%7BG_k%7D+%3D+%7B%5Cleft.+%7B%5Cfrac%7B%7B%5Cpartial+f%7D%7D%7B%7B%5Cpartial+%7Bx_k%7D%7D%7D%7D+%5Cright%7C_%7B%7B%7B%5Ctilde+x%7D_k%7D%7D%7D%5C%5D) 这样做听起来还是挺有道理的,实际上也是能用的,但是问题还是很多的。 考虑一个服从高斯分布的变量 ,现在 ,问 服从什么分布? 我概率比较差,不过这个似乎是叫做卡尔方布。 应该是下图中k=1那条线。![](data:image/png;base64,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)
但是按照EKF的观点,我们要用一个高斯分布去近似 。假设我们采样时得到了一个 ,那么就会近似成一个均值为0.25的高斯分布,然而卡方分布的期望应该是1。……但是各位真觉得k=1那条线像哪个高斯分布吗? 所以EKF面临的一个重要问题是,当一个高斯分布经过非线性变换后,如何用另一个高斯分布近似它?按照它现在的做法,存在以下的局限性:(注意是滤波器自己的局限性,还没谈在SLAM问题里的局限性)。
即使是高斯分布,经过一个非线性变换后也不是高斯分布。EKF只计算均值与协方差,是在用高斯近似这个非线性变换后的结果。(实际中这个近似可能很差)。
系统本身线性化过程中,丢掉了高阶项。
线性化的工作点往往不是输入状态真实的均值,而是一个估计的均值。于是,在这个工作点下计算的 ,也不是最好的。
在估计非线性输出的均值时,EKF算的是 的形式。这个结果几乎不会是输出分布的真正期望值。协方差也是同理。
那么,怎么克服以上的缺点呢?途径很多,主要看我们想不想维持EKF的假设。如果我们比较乖,希望维持高斯分布假设,可以这样子改:
为了克服第3条工作点的问题,我们以EKF估计的结果为工作点,重新计算一遍EKF,直到这个工作点变化够小。是为迭代EKF(Iterated EKF, IEKF)。
为了克服第4条,我们除了计算 ,再计算其他几个精心挑选的采样点,然后用这几个点估计输出的高斯分布。是为Sigma Point KF(SPKF,或UKF)。
如果不那么乖,可以说:我们不要高斯分布假设,凭什么要用高斯去近似一个长得根本不高斯的分布呢?于是问题变为,丢掉高斯假设后,怎么描述输出函数的分布就成了一个问题。一种比较暴力的方式是:用足够多的采样点,来表达输出的分布。这种蒙特卡洛的方式,也就是粒子滤波的思路。 如果再进一步,可以丢弃滤波器思路,说:为什么要用前一个时刻的值来估计下一个时刻呢?我们可以把所有状态看成变量,把运动方程和观测方程看成变量间的约束,构造误差函数,然后最小化这个误差的二次型。这样就会得到非线性优化的方法,在SLAM里就走向图优化那条路上去了。不过,非线性优化也需要对误差函数不断地求梯度,并根据梯度方向迭代,因而局部线性化是不可避免的。 可以看到,在这个过程中,我们逐渐放宽了假设。
4. UKF 无迹卡尔曼
由于题主问题里没谈IEKF,我们就简单说说UKF和PF。 UKF主要解决一个高斯分布经过非线性变换后,怎么用另一个高斯分布近似它。假设 ,我们希望用 近似 。按照EKF,需要对 做线性化。但在UKF里,不必做这个线性化。 UKF的做法是找一些叫做Sigma Point的点,把这些点用 投影过去。然后,用投影之后的点做出一个高斯分布,如下图: 这里选了三个点: 。对于维数为N的分布,需要选2N+1个点。篇幅所限,这里就不解释这些点怎么选,以及为何要这样选了。总之UKF的好处就是:
不必线性化,也不必求导,对 没有光滑性要求。
计算量随维数增长是线性的。
5. PF 粒子滤波
UKF的一个问题是输出仍假设成高斯分布。然而,即使在很简单的情况下,高斯的非线性变换仍然不是高斯。并且,仅在很少的情况下,输出的分布有个名字(比如卡方),多数时候你都不知道他们是啥……更别提描述它们了。 因为描述很困难,所以粒子滤波器采用了一种暴力的,用大量采样点去描述这个分布的方法(老子就是无参的你来打我呀)。框架大概像下面这个样子,就是一个不断采样——算权重——重采样的过程: 越符合观测的粒子拥有越大的权重,而权重越大就越容易在重采样时被采到。当然,每次采样数量、权重的计算策略,则是粒子滤波器里几个比较麻烦的问题,这里就不细讲了。 这种采样思路的最大问题是:采样所需的粒子数量,随分布是指数增长的。所以仅限于低维的问题,高维的基本就没办法了。
6. 非线性优化
非线性优化,计算的也是最大后验概率估计(MAP),但它的处理方式与滤波器不同。对于上面写的状态估计问题,可以简单地构造误差项: 然后最小化这些误差项的二次型: 这里仅用到了噪声项满足高斯分布的假设,再没有更多的了。当构建一个非线性优化问题之后,就可以从一个初始值出发,计算梯度(或二阶梯度),优化这个目标函数。常见的梯度下降策略有牛顿法、高斯-牛顿法、Levenberg-Marquardt方法,可以在许多讲数值优化的书里找到。 非线性优化方法现在已经成为视觉SLAM里的主流,尤其是在它的稀疏性质被人发现且利用起来之后。它与滤波器最大不同点在于, 一次可以考虑整条轨迹中的约束。它的线性化,即雅可比矩阵的计算,也是相对于整条轨迹的。相比之下,滤波器还是停留在马尔可夫的假设之下,只用上一次估计的状态计算当前的状态。可以用一个图来表达它们之间的关系: 当然优化方式也存在它的问题。例如优化时间会随着节点数量增长——所以有人会提double window optimization这样的方式,以及可能落入局部极小。但是就目前而言,它比EKF还是优不少的。
7. 小结
卡尔曼滤波是递归的线性高斯系统最优估计。
EKF将NLNG系统在工作点附近近似为LG进行处理。
IEKF对工作点进行迭代。
UKF没有线性化近似,而是把sigma point进行非线性变换后再用高斯近似。
PF去掉高斯假设,以粒子作为采样点来描述分布。
优化方式同时考虑所有帧间约束,迭代线性化求解。
呃好像题主还问了FastSLAM,有空再写吧……注:* 本文大量观点来自Timothy. Barfoot, "State estimation for Robotics: A Matrix Lei Group Approach", 2016. 图片若有侵权望告知。
PS:
SLAM中,状态变量经常是六自由度的位姿,由旋转矩阵和平移向量构成。然而问题是,旋转矩阵并不存在加法,只有对应到李代数上才可以清楚地定义它的运算。因此,当我们讨论这个位姿的噪声,说它服从高斯分布时,我们究竟在说什么,是一个很严重的问题。今后的博客将更深入地介绍李群李代数的知识。
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