estimate

Builtin index · Statistics & ML

result = state.estimate()

Input: no input · Output: result

What it is

Estimation-family only: reads a point estimate off a filter state Record state with no arguments.

Overloads

One call shape — this function is not overloaded.

Code	Input	Output	Description
`result = state.estimate()`	no input	`result` vector	Returns the particle filter's weighted-mean particle vector, or a Kalman/EKF/UKF filter's `state.x` vector directly.

Examples

From the documentation, and run by the build -- the output and the figure below are what the engine actually produced. Simplest first.

process(p) := p + 0.05*randn()                       # process_fn injects its

                                                        # own noise, like monte_carlo

likelihood(p, z) := exp(-(p[0]-z[0])^2 / (2*0.25))    # Gaussian likelihood, sigma=0.5


pf = particle_filter_init([0], 200, spread=2.0, seed=1)   # 200 particles around x0=0

for i = 1 to 10
    pf = pf.predict("process")
    pf = pf.update("likelihood", [2])    # repeatedly measuring z=2

end for
est = pf.estimate()   # weighted-mean point estimate, converges toward 2

from numerics-dsp

truth = zeros(60)
meas = zeros(60)
for t = 0 to 59
    truth[t] = 0.5 * t
    meas[t] = truth[t] + randn() * 2
end for

F = [1, 0, 1, 1] as matrix(2, 2)     # column-major: rows are [1, 1] and [0, 1]

Q = [0.01, 0, 0, 0.01] as matrix(2, 2)
H = [1, 0] as matrix(1, 2)
R = [4] as matrix(1, 1)

s = kalman_init([0, 0], [10, 0, 0, 10] as matrix(2, 2))
est = zeros(60)
for t = 0 to 59
    s = s.predict(F, Q)
    s = s.update(H, [meas[t]], R)
    est[t] = s.estimate()[0]
end for

print("measurement error: {round(rmse(truth, meas), 3)}")
print("filtered error:    {round(rmse(truth, est), 3)}")
scatter(0 to 59, meas, color = "#94a3b8", label = "measured")
plot(0 to 59, truth, color = "#0f172a", label = "truth")
plot(0 to 59, est, color = "#e11d48", width = 2, label = "Kalman")
legend()
title("constant-velocity Kalman filter")

output

measurement error: 2.197
filtered error:    1.193
· scatter: figure 11 (60 points)
· plot: figure 12 (60 points)
· plot: figure 13 (60 points)

from statistics-ml

How it works

estimate(state) — callable as state.estimate(). The particle filter's weighted-mean point estimate (plain mean(state.particles) would silently ignore the weights); for the linear/EKF/UKF filters this is just state.x, kept here too so every estimation-theory state answers the same question the same way.

From the note above this builtin in the interpreter, where the reasoning was written down as it was built.