feat: add UnscentedKalmanFilter, the Kalman filter that samples the model instead of differentiating it

[alxkm]

Adds the unscented Kalman filter: a Kalman filter for a nonlinear model that samples the model instead of differentiating it. It completes the pair with the ExtendedKalmanFilter merged in #7615.

The extended filter pushes the covariance through a Jacobian, which is a straight line drawn at one point. That needs the model to be differentiable, needs somebody to write the derivative, and throws away everything the model does beyond first order. The unscented filter takes the opposite route: it picks a small deterministic set of sigma points whose mean and covariance are exactly those of the current estimate, sends every one of them through the real model, and reads the new mean and covariance off where they land.

lambda = alpha^2 (n + kappa) - n
X_0 = x,   X_i = x + [sqrt((n + lambda) P)]_i,   X_{i+n} = x - [sqrt((n + lambda) P)]_i
Wm_0 = lambda / (n + lambda),   Wc_0 = Wm_0 + 1 - alpha^2 + beta,   W_i = 1 / (2 (n + lambda))

The square root is a Cholesky factor, so a step costs 2n + 1 evaluations of the model and one factorisation, roughly what the extended filter costs, with no Jacobian anywhere. The payoff is accuracy: the transformed mean and covariance are right to second order for any model, where the extended filter is right to first.

That claim is tested rather than asserted. For x^2 with x ~ N(3, 0.5^2) the true mean is mu^2 + sigma^2 = 9.25 and the true variance 4 mu^2 sigma^2 + 2 sigma^4 = 9.125. The unscented filter returns both exactly; the extended filter returns 9.0 for each, missing the sigma^2 the spread contributes to the mean and the 2 sigma^4 of the variance. The test runs both and checks both.

A few decisions that are worth a reviewer's attention:

• The defaults are alpha = 1, beta = 2, kappa = 0, not the alpha = 1e-3 often quoted. That value puts the sigma points almost on top of the mean and compensates with a central weight of about minus a million, which is exact on paper and a loss of six digits in floating point. beta = 2 is optimal for a Gaussian prior and is what makes the variance of the quadratic above come out exact. All three stay configurable, and parameters that would collapse the sigma points onto the mean are refused at construction.
• The covariance is symmetrised explicitly after an update. P - K S K' is symmetric in exact arithmetic but not after rounding, and a covariance that has drifted out of symmetry eventually fails the Cholesky factorisation of the next step.
• A covariance that is no longer positive definite is refused with an ArithmeticException that says so, instead of carrying on with a square root that does not exist.
• The innovation covariance is inverted with matrix.InverseOfMatrix, as in the extended filter, on a defensive copy because it overwrites its input, with the result checked for finiteness.

UnscentedKalmanFilterTest covers 24 cases. Besides the quadratic: the sigma points are checked to reproduce the mean and the covariance of the estimate exactly; on a linear model the filter agrees with the extended filter, state and covariance, to 1e-9 at every one of 500 steps, which is the statement that it reduces to the ordinary Kalman filter; a target seen only as a range is tracked and its never-measured velocity recovered to within 0.2 without a single derivative written; the covariance stays symmetric and its variances positive over 500 steps of a model with a sin in it; the mean weights sum to one for four different spreads; and prediction through the identity adds exactly the process noise.

Checklist

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized it.
• All filenames are in PascalCase.
• All functions and variable names follow Java naming conventions.
• All new algorithms have a URL in their comments that points to Wikipedia or other similar explanations.
• All new algorithms include a corresponding test class that validates their functionality.
• All new code is formatted with clang-format -i --style=file path/to/your/file.java

[codecov-commenter]

Codecov Report

❌ Patch coverage is 98.94737% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 81.62%. Comparing base (550a7ed) to head (36d5b6a).

Files with missing lines	Patch %	Lines
...thealgorithms/streaming/UnscentedKalmanFilter.java	98.94%	0 Missing and 2 partials ⚠️

Additional details and impacted files

@@             Coverage Diff              @@
##             master    #7622      +/-   ##
============================================
+ Coverage     81.49%   81.62%   +0.12%     
- Complexity     8078     8161      +83     
============================================
  Files           836      837       +1     
  Lines         25466    25656     +190     
  Branches       4966     5011      +45     
============================================
+ Hits          20754    20941     +187     
  Misses         3924     3924              
- Partials        788      791       +3     

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.