Navigation

./_Navigation

AUV position estimation with seabed acoustic sensing and DOA measurements (extended Kalman filter and conditionnaly minimax nonlinear filter)

Setting for simulation experiments for the AUV position estimation [1] are defined in ./_Navigation/TestNavigation.py

The AUV dynamic model is provided in ./ControlledModel/AUV.py

The estimation is made by

conditionnaly minimax nonlinear filter
extended Kalman filter
Kalman fiter for linear system with pseudo measurements

The measurements are the DOA of the acoustic signals from a set of beacons with known positions.

The prediction of all three filters may be defined

by virtue of the system (== the actual AUV speed is known)
by means of acoustic seabed sensing algorithm from [2,3] (== external speed predictor)

Tracking

./_Tracking

AUV position estimation with DOA and Doppler measurements (conditionnaly minimax nonlinear filter)

The dynamic model of an AUV performing a coordinate turn in a random plane and the observers, which provide the direction cosines and Doppler shift measurements is available in ./_Tracking/TrackingModel.py. The simulation settings are defined in the same file. The detailed description of the model can be found in [4].

The estimation in a static (AUV detection) is available in ./_Tracking/TestStatic.py. Available estimates:

best linear estimate (conditionally minimax estimate on DOA measurements)
least squares estimate given the observations of a single point
Lasso regression estimate
conditionally minimax estimate on combined DOA measurements and least squares estimate
conditionally minimax estimate on combined DOA measurements and Lasso regression estimate

The estimation in a dynamic (AUV tracking) is avaliable ./_Tracking/TestTrackingFast.py. The version in ./_Tracking/TestTrackingSlow.py does not use precompiled prediction and correction functions and hence is much slower. Available filters/estimates:

least squares estimate given the observations of a single point
Lasso regression estimate
Conditionally minimax nonlinear filter given the DOA measurements only
Conditionally minimax nonlinear filter given the DOA and Doppler shift measurements
Conditionally minimax nonlinear filter given the DOA measurements plus the least square estimate
Conditionally minimax nonlinear filter given the DOA measurements plus the Lasso regression estimate
Conditionally minimax nonlinear filter given the DOA/Doppler measurements plus the least square estimate
Conditionally minimax nonlinear filter given the DOA/Doppler measurements plus the Lasso regression estimate

Conditionnaly minimax nonlinear filter Python implementation

The CMNF filter is implemented in ./Filters/CMNFFilter.py

Conditionnaly minimax nonlinear filter for a nonlinear stchastic dicret-time model:

x(t) = Phi(t-1, x(t-1), xHat(t-1)) + W(t) - state dynamics

y(t) = Psi(t, x(t)) + Nu(t) - observations

with

t in [0, N]
W, N - Gaussian white noise with zero mean and covariances DW, DNu
Xi, Zeta - basic prediction and correction functions, in general case can be chosen as follows:

Xi = Phi - by virtue of the system

Zeta = y - Psi - residual

if the structure functions Phi, Psi can not be defined in the inline manner or require some history, an external object may be used: Phi = Phi(model, ...), Psi = Psi(model, ...)

./Filters/SimpleCMNFFilter.py version is less general and may be used for faster calcultaions

Extended Kalman filter Python implementation

The Kalman filter is implemented in ./Filters/KalmanFilter.py

Extended Kalman filter for a nonlinear stchastic dicrete-time model:

x(t) = Phi1(t-1, x(t-1), xHat(t-1)) + Phi2(t-1, x(t-1), xHat(t-1)) W(t) - state dynamics

y(t) = Psi1(t, x(t)) + Psi1(t, x(t)) Nu(t) - observations

with

t in [0, N]
W, N - Gaussian white noise with means MW, MNu and covariances DW, DNu

Extended Kalman filter requires the matrices of partial derivatives dPhi1/dx and dPsi1/dx

Can be used for linear systems:

x(t) = Phi(t-1, xHat(t-1)) x(t-1) + Phi2(t-1, x(t-1), xHat(t-1)) W(t)

y(t) = Psi(t) x(t) + Psi1(t, x(t)) Nu(t),

then Phi1 = Phi * x, dPhi1/dx = Phi and Psi1 = Psi * x, dPsi1/dx = Psi

Can be used for systems with linear pseudo measurements Y, which depend on real measurements y:

x(t) = Phi(t-1, xHat(t-1)) x(t-1) + Phi2(t-1, x(t-1), xHat(t-1)) W(t)

Y(t) = Psi(t, x(t), y(t)) x(t) + Psi1(t, x(t), y(t)) Nu(t)

if the structure functions Phi, Psi can not be defined in the inline manner or require some history, an external object may be used: Phi1,2 = Phi1,2(model, ...), Psi1,2 = Psi1,2(model, ...)

References

[1] A. Miller, B. Miller, G. Miller, On AUV Control with the Aid of Position Estimation Algorithms Based on Acoustic Seabed Sensing and DOA Measurements // Sensors 2019, 19(24), 5520. DOI: 10.3390/s19245520

[2] A. Miller, B. Miller, G. Miller, AUV navigation with seabed acoustic sensing // 2018 Australian & New Zealand Control Conference (ANZCC), Melbourne, Australia, 7-8 Dec. 2018 DOI: 10.1109/ANZCC.2018.8606561

[3] A. Miller, B. Miller, G. Miller, AUV position estimation via acoustic seabed profile measurements // 2018 IEEE/OES Autonomous Underwater Vehicle Symposium - AUV 2018, University of Porto, Porto, Portugal, 6-9 Nov. 2018 DOI: 10.1109/AUV.2018.8729708

[4] 49. A. Borisov, A. Bosov, B. Miller, G. Miller, Passive Underwater Target Tracking: Conditionally Minimax Nonlinear Filtering with Bearing-Doppler Observations // Sensors 2020, 20(8), 2257. DOI: 10.3390/s20082257