噪声数据分析

这是我的解决方案,使用 Kalman filter . 如果希望或多或少地平滑,则需要调整参数(甚至+数量级)。

#!/usr/bin/env octave

% Kalman filter to smooth measures of altitude and estimate
% speed and acceleration. The continuous time model is more or less as follows:
% derivative of altitude := speed
% derivative of speed := acceleration
% acceleration is a Wiener process

%------------------------------------------------------------
% Discretization of the continuous-time linear system
% 
%   d  |x|   | 0 1 0 | |x|
%  --- |v| = | 0 0 1 | |v|   + "noise"
%   dt |a|   | 0 0 0 | |a|
%
%   y = [1 0 0] |x|     + "measurement noise"
%               |v|
%               |a|
%
st = 0.05;    % Sampling time
A = [1  st st^2/2;
     0  1  st    ;
     0  0  1];
C = [1 0 0];

%------------------------------------------------------------
% Fine-tune these parameters! (in particular qa and R)
% The acceleration follows a "random walk". The greater is the variance qa,
% the more "reactive" the system is expected to be, i.e.
% the more the acceleration is expected to vary
% The greater is R, the more noisy is your measurement instrument
% (less "accuracy" of the barometric altimeter);
% if you increase R, you will smooth the estimate more
qx = 1.0;                      % Variance of model noise for position
qv = 1.0;                      % Variance of model noise for speed
qa = 50.0;                     % Variance of model noise for acceleration
Q  = diag([qx, qv, qa]);
R  = 100.0;                    % Variance of measurement noise
                               % (10^2, if 10ft is the standard deviation)

load data.txt  % Put your measures in this file

est_position     = zeros(length(data), 1);
est_speed        = zeros(length(data), 1);
est_acceleration = zeros(length(data), 1);

%------------------------------------------------------------
% Kalman filter
xhat = [0;0;0];     % Initial estimate
P    = zeros(3,3);  % Initial error variance
for i=1:length(data),
   y = data(i);
   xpred = A*xhat;                                    % Prediction
   Ppred = A*P*A' + Q;                                % Prediction error variance
   Lambdainv = 1/(C*Ppred*C' + R);
   xhat  = xpred + Ppred*C'*Lambdainv*(y - C*xpred);  % Update estimation
   P = Ppred - Ppred*C'*Lambdainv*C*Ppred;            % Update estimation error variance
   est_position(i)     = xhat(1);
   est_speed(i)        = xhat(2);
   est_acceleration(i) = xhat(3);
end

%------------------------------------------------------------
% Plot
figure(1);
hold on;
plot(data, 'k');               % Black: real data
plot(est_position, 'b');       % Blue:  estimated position
plot(est_speed, 'g');          % Green: estimated speed
plot(est_acceleration, 'r');   % Red:   estimated acceleration
pause

您可以尝试通过低通过滤器运行数据。这将消除高频噪声。也许是一棵简单的冷杉。

您是否尝试过对您的值执行滚动窗口平均值?基本上,您执行一个窗口,比如10个值(从0到9),然后计算其平均值。然后将窗口滚动一个点(从1到10)并重新计算。这将平滑值,同时保持点数相对不变。窗口越大,数据越平滑,代价是丢失更多的高频信息。

如果数据出现异常值峰值,则可以使用中位数而不是平均值。

您也可以尝试使用 Autocorrelation

分析数据的一种方法是尝试将数据与某个模型匹配,生成一个函数,然后 test its fitness to your data set

至于在飞行中产生一些速度和加速度的感觉,这应该是从几个不同的结果中简单地平均速度。大致如下:

我对火箭一无所知。我画出了你的观点,它们看起来很可爱。

根据我在那张图上看到的,让我假设,通常只有一个远地点,产生点的函数在那个远地点没有导数wrt时间。

建议:

2. 通过(简单地说)将最近的几个点与当前的最大点进行比较,持续观察远地点。
3. 在达到最大值之前,使用(0,0)固定结和一些任意结集计算当前海拔高度的自然样条线集合。使用样条曲线的残差来决定要丢弃的数据。重新计算样条曲线。
4. 最多保留最近计算的样条曲线。开始为远地点以外的曲线计算一组新的样条曲线。