Simple kalman filter for water well level ultrasonic sensor

2015-06-22

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kalman.rb

require "matrix"
require "time"

class Kalman
  attr_accessor :state
  attr_accessor :process_noise
  attr_reader :control
  attr_accessor :model
  attr_reader :readings
  attr_reader :sensor_noise
  attr_reader :identity

  attr_accessor :error
  attr_accessor :system_uncertainty
  attr_accessor :kalman_gain

  attr_accessor :current_measurement
  attr_accessor :current_timestep

  attr_accessor :update_time, :predict_time

  def initialize
    # x = Estimate value (intial state)
    @state = Matrix[
      [247.0], # Height,
      [0.0],   # Velocity
      [0.0]    # Acceleration
    ]

    # P = Initial uncertainty (process noise)
    @process_noise = Matrix[
      [100, 0.0, 0.0],  # We're not certian about height
      [0.0, 100, 0.0],  # We're not certain about velocity
      [0.0, 0.0, 100],  # We're not certain about acceleration
    ]

    # u = External motion (control signal)
    # There no control signal in our case, so it's just zeroes
    @control = Matrix[
      [0.0], # Height control signal, none
      [0.0], # Velocity control signal, none
      [0.0], # Acceleration control signal, none
    ]

    # H = Measurement function (measured params)
    @readings = Matrix[[
      1.0, # We can measure height
      0.0, # But we can't measure velocity
      0.0  # Not acceleration
    ]].freeze

    # R = Measurement uncertainty (measurement noise)
    @sensor_noise = Matrix[
      [0.6] # We're sensing only height, and there some error associated with height
    ]

    # z = Current measurement (observed value)
    @current_measurement = Matrix[
      [0.0]
    ]

    # y = Error
    @error = Matrix[
      [0.0]
    ]

    # K = Kalman gain (current measurement uncertainty)
    @kalman_gain = Matrix[
      [0.0],
      [0.0],
      [0.0]
    ]

    # S = System Uncertainty
    @system_uncertainty = Matrix[
      [0.0]
    ]

    # I = Identity matrix
    @identity = Matrix.identity(3).freeze

    @update_time = 0.0
    @predict_time = 0.0
  end

  # F = Next state function (process model)
  # This is where everything is goes nuts:
  # You need to come up with a matrix, that will represent a model
  # of changes between states. So if you apply this matrix to previous
  # state vector, you will get the next state prediction vector.
  def model
    Matrix[
      [1.0, self.current_timestep, 0.0], # height       = height.prev + timestep * velocity.prev
      [0.0, 1.0, self.current_timestep], # velocity     = velocity.prev + time * acceleration
      [0.0, 0.0, 1.0]                    # acceleration = prev.acceleration
    ].freeze
  end

  def measure(value, timestep)
    self.current_timestep = timestep
    self.current_measurement = Matrix[
      [value]
    ]

    update!
    predict!
  end

  def runtime_ms
    (self.update_time + self.predict_time) * 1000.0
  end

  def to_s
    {state: self.state, noise: self.process_noise}
  end
  alias_method :inspect, :to_s

  private
  def update!
    time = Time.now
    ## Update stage

    # y = z - (H * x)
    self.error = self.current_measurement - (self.readings * self.state)

    # S = H * P * Ht + R
    self.system_uncertainty = self.readings * self.process_noise * self.readings.transpose + self.sensor_noise

    # K = P * Ht + S^-1
    self.kalman_gain = self.process_noise * self.readings.transpose * system_uncertainty.inverse

    # x = x + (K * y)
    self.state = self.state + (self.kalman_gain * error)

    # P = (I - (K * H)) * P
    self.process_noise = (self.identity - (kalman_gain * self.readings)) * self.process_noise

    self.update_time = Time.now - time
  end

  def predict!
    time = Time.now
    ## Prediction stage

    # x = (F * x) + u
    self.state = (self.model * self.state) + self.control

    # P = F * P * Ft
    self.process_noise = self.model * self.process_noise * self.model.transpose
    self.predict_time = Time.now - time
  end

  def benchmark
    time = Time.now.to_f
    yield
    return Time.now.to_f - time
  end
end

def parse_time(string, date)
  # Some lines might have space between HH:MM:SS and .ms
  string.gsub! /\s+/, ''
  string, ms = string.split(".")

  # And there a problem with ms's: 42ms will be .42, without leading zero,
  # so we need to add extra leading zeroes
  ms ||= ''
  ms = ms.rjust 3, "0"

  string = "#{string}.#{ms}"

  # Reconstruct Time object
  return Time.parse("#{date}T#{string}Z")
end

start_time = Time.now
name = ARGV.first.chomp

sensor_length = 155.0
well_height = 550.0
radius = 121.0
square_radius = radius ** 2.0

file = File.open("#{name}")
date = name.match(/(\d{4}-\d{2}-\d{2})/)[0]

last_time = nil
last_value = nil

kalman = Kalman.new

file.each do |line|
  time, raw = line.chomp.split(',')
  time = parse_time(time, date)

  # Set time for the first time
  last_time ||= time

  value = raw.to_f
  timestep = time - last_time

  kalman.measure value, timestep
  new_value = kalman.state.first.round(2)

  if last_value != new_value
    puts "%s,%.2f" % [time.xmlschema(3), new_value]
  end

  last_value = kalman.state.first.round(2)
end

puts "; Runtime: %.2f" % (Time.now - start_time)
puts "; #{RUBY_DESCRIPTION}"