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5

The brutally honest answer here is: The noise is considered zero-mean because that's what the author decided to do. Without looking deeper into the signal model employed, it's impossible to answer. However, for many systems this makes a lot of sense physically, since the processes leading to a noise realization are very often zero-mean in nature. For ...


4

Regarding your next question, I will try to give you some long description explainig a general way of transforming filters defined by their transfer function into discrete domain. If you are not interested in the details, you can skip to the bottom, where I wrote a C code (tested). The transfer function of a first-order low pass filter (with unit gain) is ...


4

As with any question like this, the answer is: It depends. What does it depend on? Your signal model. If your signal model generates $X$ and $Y$ axis velocities independently from each other so that there is no transfer function between the two channels, then two 1D Kalman filters will work the same as one 2D Kalman filter. If your signal model allows ...


3

There are several ways you can do this, however this is highly specific to the data you are analyzing. I will describe some of very general (not domain/data specific) approaches below: One possible approach I can think of that'd deal with this sudden, HF noise is to run a window with desired length through the signal. In every iteration, you'd take several ...


3

The answer to the first question is yes, it is possible to fuse data coming from the same type of sensor. For example, the fusion of two different accelerometers, each with a measurement quality, gives a weighted average where the weights are the inverse of individual variances (see Kays's[1] book for details). The answer for the second is yes as well, it ...


3

Let me put a practical answer with the following Matlab / Octave Code : L = 2*1000; % signal sample count n = 0:L-1; % discrete-time index Fs = 44100; % sampling frequency am = [1, 0.5, 2, 0.5, 0.3, 0.6, 0.1, 0.2]; % magnitudes of 8 components fm = [882, 2646, 4410, 6615, 8820, 10000, 13230, 15876]; % frequencies % Time domain ...


3

There's a lot of things that influence your choice of sampling rate. First of all, of course, the Nyquist theorem, which says you need to sample at more than twice of the signal's single-sided bandwidth $B$ (for real signals)┬╣. Then, you often choose a sampling rate that is useful for your system. For example, a lot of 3G/4G/5G systems use sampling rates ...


2

That really will depend on the variance (standard deviation) of the measurements you get from the five vs the one. Suppose your expensive IMU gives a measurement distributed as: $$ x_\mbox{expensive} \sim N\left(x_\mbox{truth}, \sigma^2_\mbox{expensive}\right) $$ and suppose your cheaper ones give measurements distributed as: $$ x_\mbox{cheap}^i \sim N\...


2

No physical system suffers from, or produces, complex Gaussian noise. Quadrature systems can be modelled as being complex, with the in-phase branch corresponding to a real value, and the quadrature branch corresponding to an imaginary value. If each branch presents Gaussian (thermal) noise, then the noise can be modelled as complex Gaussian, too. However, ...


2

What could cause such a shape? Could it be due to the laser source which could not be perfectly single-mode? Or could it be due to the sensor? There is nothing particularly wrong with the "shape", but there are a few things you can do on the sensor and data processing side, to improve the extraction of an accurate profile. Your "biggest" problem is ...


2

I believe the best strategy is to filter prior to calculating the magnitude. To see this easily, consider the low pass filtering as an averaging process and consider the noise as a zero mean Gaussian white noise. The distribution of the noise prior to the magnitude computation as zero-mean Gaussian will average to zero if the noise is white. The distribution ...


2

Your expression $A=\sqrt{a_x^2+a_y^2+a_z^2}$ calculates the length of the 3-dimensional vector with coordinates $(a_x, a_y, a_z)$. So, it is the magnitude of the acceleration. Your expression $a=\Delta_v/\Delta_t$ also gives magnitude of acceleration, but in a slightly different context. This comes from measuring speed at different times, and then you ...


2

May be you can find variance of acceleration along x,y, and z direction in SET A and in set B separately and choose the the device which has least variance. As this Wikipedia page suggests, you can combine the two by weighting by their respective variances. So, to get $x_C$ simply: $$ x_C = \frac{1}{\sigma_1^{-2} + \sigma_2^{-2}} \left( \frac{x_A}{\...


2

If you have the flexibility to alter the circuit, then you can make the problem easier by adding an R-C filter to the LM35 analog output. Temperature changes slowly, so you can take advantage of that. The sensor drive capability is probably not very strong (thousands to hundreds of thousands of Ohm). if you connect a 100k resistor to the LM35 output, and ...


2

The significance is a statistical measure of frequency error you would get if you averaged the frequency error over that duration of time, $\tau$, as compared to the average over a same duration of time, that much time prior. So it is a measure of the difference in error, and specifically the rms value of many of these measurements. This is useful for non-...


2

According to this app note by Freescale: http://cache.freescale.com/files/sensors/doc/app_note/AN5087.pdf which came from this recent related question: How to interpret Allan Deviation plot for gyroscope? with a copied graphic below where they give the bias instability for each axis. What a specific manufacturer does on their datasheet, you would be best ...


2

The lower the cut-off frequency of the anti-aliasing filter, the higher the delay thus degrading your phase margin. You need to be really careful when implementing an anti-aliasing filter in control loops applications. First question, what is the amount of noise above 500 Hz? Based on the picture, you have noise at about 3 kHz, the main purpose of your anti-...


2

Assuming that the sensors share the same characteristics, have the same timing (acceleration signals are aligned), the model with $y_1= x + n_1$ and $y_2= x + n_2$, $n_1$ and $n_2$ being uncorrelated noises of the same power, averaging them is a way to reduce the noise. The theory that asymptotically, averaging $N$ sensors reduce the variance by a factor of $...


2

If you add an accelerometer to the project, a Kalman filter can give a good estimation of vertical speed. With only a barometric sensor, I don't think it's possible to reduce the lag below 1 second. import numpy as np import matplotlib.pyplot as plt import random from filterpy.kalman import KalmanFilter from filterpy.common import Q_discrete_white_noise ...


2

Only requirement for sampling frequency is that it should be more than twice the maximum frequency component in desired signal. Any other constraint can only be because of the oscillator design of the ADC circuit. So, the sensor you are working with might be able to generate a fundamental frequency of 32Hz and, using squaring non-linearity to produce 2x, 4x, ...


1

First, you should note that the FFT refers to an algorithm for the fast computation of the DFT taking advantage of its symmetry. The signals you have are: where $\mathbf{a}_y$ and $\mathbf{a}_x$ can both have negative a positive values depending on the direction along the $x$ and $y$-axis. These signals are the output of your accelerometers. What you ...


1

LM35 is a stable chip whose output is not noisy, however, noise may build up while LM35 output is transmitted to ADC input. You must first do your best in minimizing the electrical interference, by adjusting the impedences and adding analog filters if necessary. Then you may look for mathematical methods to reduce it further after its being ADC converted. ...


1

If the data is cyclic by its nature the best thing would work using its spectrum. You can easily build a system which checks sub set of data to verify periodic and the once you establish your groups checking the affinity of new data is easy - add it to each series. It should belong to the one creates less spread in the frequency (Namely, it follows the ...


1

I assume you set the first momentum of your true measure to $\mu=0$, so your question actually reads gyroscope with sensor drift does that mean that $E[f(x)] \ne \mu$? No. It might still be the case that the sensor value, in the long term, drifts centred around the true value. The thing is that $f(x)$ is a random variable with non-zero variance and a ...


1

Yes an FFT approach will work to identify frequency content, but you may need longer data sets to see something useful. For the FFT you will see the frequencies from 0 to your sampling rate (25000), and there will be the same number of samples in frequency as you have in time. Therefore your frequency resolution is 25000/N where N is the number of samples. ...


1

One suggestion (non-simple): Obtain thousands of recordings from a broad spectrum of thousands of people engaged in your chosen activities to measure (with the activity externally logged, witnessed log book, video, etc.). Feed all that data to several contemporary machine learning algorithms (DNN, etc.), and hope for a resulting inference method that meets ...


1

To add on @MarcusM├╝ller: in image processing, a constant pixel value shift is often not perceived (as a global scaling), leaving aside saturation issues. In video sequences, illumination may change from one frame to the other. This may induce the noise to have a mean (as a scaling). Also, quantization on integers can change the mean. So often the presence ...


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