Measurement function for Singer acceleration motion model
Measurements for Singer Model
Define a state for a 2-D Singer acceleration motion.
state = [1;10;3;2;20;5];
Obtain the measurement in a rectangular frame.
measurement = singermeas(state)
measurement = 3×1 1 2 0
Obtain the measurement in a spherical frame.
measurement = singermeas(state, 'spherical')
measurement = 4×1 63.4349 0 2.2361 22.3607
Obtain the measurement in a spherical frame relative to a stationary sensor located at [1;-2;0].
measurement = singermeas(state, 'spherical', [1;-2;0], [0;0;0])
measurement = 4×1 90 0 4 20
Obtain the measurement in a spherical frame relative to a stationary sensor located at [1;-2;0] that is rotated by 90 degrees around the z axis relative to the global frame.
laxes = [0 -1 0; 1 0 0; 0 0 1]; measurement = singermeas(state, 'spherical', [1;-2;0], [0;0;0], laxes)
measurement = 4×1 0 0 4 20
Obtain measurements from multiple 2D states in a rectangular frame.
states = [1 2 3; 10 20 30; 2 4 5; 20 30 40; 5 6 11; 1 3 1.5]; measurements = singermeas(states)
measurements = 3×3 1 2 3 20 30 40 0 0 0
states — Current states
real-valued 3N-by-1 vector | real-valued 3N-by-M matrix
Current states, specified as a real-valued 3N-by-1 vector or a real-valued 3N-by-M matrix. N is the spatial degree of the state, and M is the number of states.
The state vector in each column takes different forms based on its spatial dimensions.
|Spatial Degrees||State Vector Structure|
x represents the
vx represents the velocity in the
ax represents the
acceleration in the x-direction. If the motion model is in
one-dimensional space, the y- and z-axes are
assumed to be zero. If the motion model is in two-dimensional space, values along the
z-axis are assumed to be zero. Position coordinates are in
meters. Velocity coordinates are in meters/second. Acceleration coordinates are in
measurementParameters — Measurement parameters
structure | array of structure
Measurement parameters, specified as a structure or an array of structures. For more details, see Measurement Parameters.
measurements — Measurements
N-by-1 column vector of scalar | N-by-M matrix of scalar
Measurement vector, returned as an N-by-1 column vector of scalars or an N-by-M matrix of scalars. The form of the measurement depends upon which syntax you use.
When the syntax does not use the
measurementParametersargument, the measurement vector is
frameinput argument is set to
frameis set to
When the syntax uses the
measurementParametersargument, the size of the measurement vector depends on the values of the
HasElevationfields in the
Specifies the azimuth angle,
az, elevation angle,
r, and range rate,
rrof the measurements.
HasElevation false true HasVelocity false
Angle units are in degrees, range units are in meters, and range rate units are in m/s.
Specifies the Cartesian position and velocity coordinates of the measurements.
Position units are in meters and velocity units are in m/s.
Azimuth and Elevation Angle Definitions
Define the azimuth and elevation angles used in the toolbox.
The azimuth angle of a vector is the angle between the x-axis and its orthogonal projection onto the xy plane. The angle is positive in going from the x axis toward the y axis. Azimuth angles lie between –180 and 180 degrees. The elevation angle is the angle between the vector and its orthogonal projection onto the xy-plane. The angle is positive when going toward the positive z-axis from the xy plane.
MeasurementParameters property consists of an array of
structures that describe a sequence of coordinate transformations from a child frame to a
parent frame or the inverse transformations (see Frame Rotation). If
MeasurementParameters only contains one structure, then it represents
the rotation from one frame to the other. If
contains an array of structures, then it represents rotations between multiple frames.
The fields of
MeasurementParameters are shown here. Not all fields
have to be present in the structure.
Enumerated type indicating the frame used to report measurements. When detections are
reported using a rectangular coordinate system,
Position offset of the origin of the child frame relative to the parent frame, represented as a 3-by-1 vector.
Velocity offset of the origin of the child frame relative to the parent frame, represented as a 3-by-1 vector.
3-by-3 real-valued orthonormal frame rotation matrix. The direction of the rotation depends on the
A logical scalar indicating whether
A logical scalar indicating if the measurement includes elevation. For measurements
reported in a rectangular frame, if
|A logical scalar indicating if the measurement includes azimuth.|
|A logical scalar indicating if the measurement includes range.|
A logical scalar indicating if the reported detections include velocity measurements. For measurements reported in the rectangular frame, if
 Singer, Robert A. "Estimating optimal tracking filter performance for manned maneuvering targets." IEEE Transactions on Aerospace and Electronic Systems 4 (1970): 473-483.
 Blackman, Samuel S., and Robert Popoli. "Design and analysis of modern tracking systems." (1999).
 Li, X. Rong, and Vesselin P. Jilkov. "Survey of maneuvering target tracking: dynamic models." Signal and Data Processing of Small Targets 2000, vol. 4048, pp. 212-235. International Society for Optics and Photonics, 2000.