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Short Answer: Basic RLS (no forgetting, no weird weighting, etc.) is ALWAYS Lyapunov stable. If the regressor sequence for the LS problem is persistently exciting--which is data and problem dependent, not algorithm dependent--then RLS is exponentially stable. So I don't know what you mean by "LMS is more stable than RLS"--more stable in what sense? ...


3

Have you considered trying a constant jerk model as opposed to a constant acceleration model? Perhaps a higher order model would capture the acceleration better. See, for instance: K. Mehrotra and P. R. Mahapatra, "A jerk model for tracking highly maneuvering targets," in IEEE Transactions on Aerospace and Electronic Systems, vol. 33, no. 4, pp. 1094-1105, ...


3

I suggest this reference regarding the comparison between least-squares and Kalman filters : Fundamentals of Kalman Filtering: A Practical Approach by P. Zarchan & H. Mussof Especially Chapter 3 (Recursive Least-Squares Filtering) and Chapter 4 (Polynomial Kalman Filters). In Chapter 4, the authors show that the discrete (time) n-th order polynomial ...


3

With your edit it becomes clear that you've modeled your problem incorrectly: While the offending signal appears shortly with a frequency of 50 Hz, that is by no means the frequency content of the interference! (also, your filter isn't well-designed, probably too short, judging from the impulse response it displays, to filter out 50 Hz) You'll find that ...


2

The main reason why your Kalman filter is not working is because you are not converting lat and lon values to kms. In the code below, I defined a new function called lat_lon_posx_posy which converts lat and lon values to px and py values in mts. You will need to make the following changes to your code. Include the following function import utm def ...


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KF is actually a mixture of a deterministic state propagator and a statistical estimator. Despite it's name including the term filter, Kalman filter is not a simple frequency selective one. It's indeed a statistical recursive estimator of a state of a (linear) dynamic system. Yet on a broader sense it's called as a filter as it will separate a desired ...


2

Simple Description Imagine you're in a car that is traveling at 70MPH with cruise control. Because the cruise control isn't perfect, your actual speed might vary slightly. This imperfection is called "process noise". Now lets also imagine the car is being tracked using GPS. Because GPS isn't perfect, there will be some noise in the sensor reading. This ...


2

Starting at the top and working my way down. Good questions, by the way! So basically state and output is modelled as gaussian distributions that have slowly changing means (to be estimated), with additive zero-mean gaussian noise on top (to be cancelled)? Yes, that's correct. The KF formulation can work with other distributions, but the standard ...


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 ...


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I think the magic acronym is CHCV, "constant heading constant velocity". This returns at least a few results on Google.


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Actually the first section of the notes in the link your provided are about the most likely value in the Bayesian Framework. So we have a comparison between the Minimum Mean Square Error (MMSE) Estimator and the Maximum a Posterior Estimator. Both are Bayes Estimator, namely they are a loss function of Posterior Probability: $$ \hat{\theta} = \arg \min_{a} ...


1

Yes, the Doppler effect applies to any electromagnetic wave. No matter whether that is an actual Radar pulse, or a microwave oven falling from an office tower, or a passenger aircraft's transponder, or an LPWAN device. But, this possibility is especially limited for LPWAN devices, as I'll explain below. Low Doppler shift due to low carrier frequency The ...


1

A single frequency coming out of speaker is very much a stationary process, then why go for a Kalman filter? Use a Weiner filter instead, much more easier to setup and makes sense for your problem. Just go for a standard weiner filter, you could go for recursive least squares as well to model this.


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Let's start the right way (as Tim's comment says): let's start with the signal model of what you're doing. Let's assume that the measurements at time $k$ are just positions $x_k$ and $y_k$ and that these are also part of the state, which also includes $\dot{x}_k$, $\dot{y}_k$, $\ddot{x}_k$, and $\ddot{y}_k$: $$ \mathbf{x}_k = \left[ x_k \ \dot{x}_k \ \...


1

Yes, it's perfectly possible. All that you'll need is to model how you think the angular velocity components of the state will evolve. Usually simple brownian (random) motion is enough, at least to start with. If you know more about how the angular velocities are constrained, then you can include that in the model. All that it means is there are no ...


1

That depends on how many of the accelerometer parameters (mostly drift and misalignment) you're trying to estimate. If the IMU and the 'extra' accelerometer were in perfect alignment (and if their statistics are Gaussian), then the optimal combination of their outputs would be a simple weighted sum: $\vec {\hat a} = k_1 \vec a_1 + k_2 \vec a_2$ where (...


1

I only know the vastly simplified form: all satellite nav systems work by the satellites telling you where they are and what time it is. In GPS terms, that time is the "pseudorange", and it's all you need (in theory) to locate yourself. With no satellites in view, you have no clue where or when you are. With one satellite in view, you can place yourself ...


1

I can't provide a lot of theory but I can provide this qualitative description of the problem: Normally the output of your digital filter sampled every symbol period gives a point on your I/Q plane. Decision feedback usually selects the constellation point closest to this point and modifies your filter to make the output(given the same input) closer to the ...


1

Yes, sorta kinda. Basically, if you can model your system accurately and the resulting model fits the Kalman filter paradigm, then yes. However, I think it's a mistake to give the filter position and velocity -- were I doing this, I'd just give it the wheel position and let the Kalman filter determine the velocity -- which it will do well to the extent ...


1

but what are the steps when only one sensor is available and the physical model of the moving object is not available Then it's not a Kalman filter. A Kalman filter works because the system is observable. In hand-wavy terms, you need to have redundant information about your system states, either because you have actual redundant inputs, or because you ...


1

I am not use how you can success multiple sensors using batch filter, but, in sequential filtering you need to perform time update before each measurement. You can do it using the timetag information of each sensor measurement. You can modify the batch filter code however, I strongly recommend to write your own function depending on what you need.


1

See: What is the relationship between a Kalman filter and polynomial regression? In over-simplified form, eyeball a line though a cloud of data samples, look where that line might point one sample into the future; and, when you get a new sample check, how good that estimate might have been; then redo, but optimize for a lot less arithmetic per step. A ...


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You can model your system as a linear time varying, where only the measurement matrix $H_k$ varies in time \begin{align} x_{k+1} &= F\,x_k, \\ y_k &= H_k\,x_k. \end{align} Namely in your case you can consider $y_k^i=H^i\,x_k$ ($i$ is just an index, not a power) to be the output of the $i$th sensor. So at a time $k$ when only sensor 1 is active you ...


1

The authors cite this work in their response to the review: Zhao H, Lu L. Adaptive recursive algorithm with logarithmic transformation for nonlinear system identification in α-stable noise [J]. Digital Signal Processing, 2015:S1051200415002535. They take their inspiration from equation (14): $J_p(n)=\sum_{i=1}^n \lambda^{n-1} \cdot \log^p (1+|e(i)|...


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The process noise $w(t)$, which is typically assumed to be a zero mean, white Gaussian noise with (power) variance $\sigma^2$, is used to account for any mismatches between the assumed dynamic model of the states and the actual truth. If your assumed constant state (DC) model perfectly matches with the underlying nature of the observed signal, then you ...


1

I ended up with a quite satisfactory solution, not by using a Kalman filter, but by using the Savitzky-Golay differentiating filter. The algorithm is described more or less like this: In a for loop, apply a running window to get a segment of the unfiltered volume signal around a range of given time instants, as measured by the load cell; For each segment, ...


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I think the problem is in Q. Q are charging K with their values. I achieve good results when Q is preloaded with powers of delta_t. See any article about wiener model. It has a good Q matrix. A00 has to be multiple of delta_t power of 5 A11 delta_t power of 3 A22 delta_t power of 1 A01 multiple of delta_t power of 4 And so on Look at https://www.google....


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