singermeas
Syntax
Description
returns the expected measurement for state based on the Singer acceleration motion model,
which assumes the target acceleration decays over time. You can also use it as a measurement
function in a Kalman filter. The measurement
= singermeas(state
)states
argument specifies the current
states.
also specifies the sensor position, measurement
= singermeas(state
,frame
,sensorpos
,sensorvel
)sensorpos
, and the sensor velocity,
sensorvel
.
specifies the measurement parameters, measurement
= singermeas(state
,measurementParameters
)measurementParameters
.
[
returns the measurement bounds, used by a tracking filter (measurement
,bounds
] = singermeas(___)trackingEKF
, trackingUKF
, trackingCKF
,trackingIMM
, trackingMSCEKF
, or trackingGSF
) in residual
calculations.
Examples
Measurements for Singer Model
Define a state for a 2D 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
Display Residual Wrapping Bounds for singermeas
Specify a 2D state and specify a measurement structure such that the function outputs azimuth, range, and rangerate measurements.
state = [10 1 0 10 1 0]'; % [x vx ax y vy ay]' mp = struct("Frame","Spherical", ... "HasAzimuth",true, ... "HasElevation",false, ... "HasRange",true, ... "HasVelocity",false);
Output the measurement and wrapping bounds using the singermeas
function.
[measure,bounds] = singermeas(state,mp)
measure = 2×1
45.0000
14.1421
bounds = 2×2
180 180
Inf Inf
Input Arguments
state
— Current state
realvalued 3Nby1 vector  realvalued 3NbyM matrix
Current state for Singer acceleration motion model, specified as a realvalued 3Nby1 vector or a realvalued 3NbyM 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 

1D  [x;vx;ax] 
2D  [x;vx;ax;y;vy;ay] 
3D  [x;vx;ax;y;vy;ay;z;vz;az] 
For example, x
represents the
xcoordinate, vx
represents the velocity in the
xdirection, and ax
represents the
acceleration in the xdirection. If the motion model is in
onedimensional space, the y and zaxes are
assumed to be zero. If the motion model is in twodimensional space, values along the
zaxis are assumed to be zero. Position coordinates are in
meters. Velocity coordinates are in meters/second. Acceleration coordinates are in
m/s^{2}.
Example: [5;0.1;0.01;0;0.2;0.01;3;0.05;0]
frame
— Frame to report measurements
'rectangular'
(default)  'spherical'
Frame to report measurements, specified as 'rectangular'
or
'spherical'
. When you specify frame as
'rectangular'
, a measurement consists of x,
y, and z Cartesian coordinates. When you
specify frame as 'spherical'
, a measurement consists of azimuth,
elevation, range, and range rate.
Data Types: char
 string
sensorpos
— Sensor position
[0;0;0]
(default)  realvalued 3by1 column vector
Sensor position with respect to the navigation frame, specified as a realvalued 3by1 column vector. Units are in meters.
Data Types: single
 double
sensorvel
— Sensor velocity
[0;0;0]
(default)  realvalued 3by1 column vector
Sensor velocity with respect to the navigation frame, specified as a realvalued 3by1 column vector. Units are in m/s.
Data Types: single
 double
laxes
— Local sensor axes coordinates
[1,0,0;0,1,0;0,0,1]
(default)  3by3 orthogonal matrix
Local sensor axes coordinates, specified as a 3by3 orthogonal matrix. Each column specifies the direction of the local x, y, and zaxes, respectively, with respect to the navigation frame. The matrix is the rotation matrix from the global frame to the sensor frame.
Data Types: single
 double
measurementParameters
— Measurement parameters
structure  array of structure
Measurement parameters, specified as a structure or an array of structures. For more details, see Measurement Parameters.
Data Types: struct
Output Arguments
measurement
— Measurement of state
realvalued Nelement row vector  realvalued MbyN matrix
Measurement vector, returned as an Nelement realvalued row vector or an MbyN realvalued matrix. M, the size of each measurement, can vary depending on the syntax. For more information, see the following table. N, the number of measurements, is the same as the number of states. The format of the measurement vector depends on the syntax.
When you do not specify the
measurementParameters
argument and set theframe
argument to'rectangular'
, the function outputs measurement vectors in the format of[x;y;z]
.When you do not specify the
measurementParameters
argument and set theframe
argument to'spherical'
, the function outputs measurement vectors in the format of[az;el;r;rr]
.When you specify the
measurementParameters
argument and set theframe
field to'rectangular'
, the size of the measurement vector depends on the value of theHasVelocity
field in themeasurementParameters
structure. The measurement vector includes the Cartesian position and velocity coordinates of the tracked object with respect to the ego vehicle coordinate system.Rectangular Measurements
HasVelocity
='false'
[x;y;z]
HasVelocity
='true'
[x;y;z;vx;vy;vz]
Position units are in meters and velocity units are in m/s.
When you specify the
measurementParameters
argument and set theframe
field to'spherical'
, the size of the measurement vector depends on the value of theHasVelocity
,HasRange
, andHasElevation
fields in themeasurementParameters
structure. The measurement vector includes the azimuth angle, az, elevation angle, el, range, r, and range rate, rr, of the object with respect to the local ego vehicle coordinate system. Positive values for range rate indicate that an object is moving away from the sensor.Spherical Measurements
HasRange
='true'
HasRange
='false'
HasElevation
='false'
HasElevation
='true'
HasElevation
='false'
HasElevation
='true'
HasVelocity
='false'
[az;r]
[az;el;r]
[az]
[az;el]
HasVelocity
='true'
[az;r;rr]
[az;el;r;rr]
[az]
[az;el]
Angle units are in degrees, range units are in meters, and range rate units are in m/s.
Data Types: double
bounds
— Measurement residual wrapping bounds
realvalued twoelement row vector  Mby2 realvalued matrix
Measurement residual wrapping bounds, returned as a twoelement realvalued row vector or an
Mby2 realvalued matrix, where M is the size of each
measurement. Each row of the matrix corresponds to the lower and upper bounds, respectively,
of each measurement in the measurement
output.
The function returns different bound values based on the frame
input.
If you specify
frame
as'Rectangular'
, each row of the matrix is[Inf Inf]
, indicating that the filter did not wrap the measurement residual.
If you specify
frame
as'Spherical'
, the function returns bounds for each measurement based on the following:When
HasAzimuth
=true
, the matrix includes a row of[180 180]
, indicating that the filter wrapped the azimuth residual in the range of[180 180]
in degrees.When
HasElevation
=true
, the matrix includes a row of[90 90]
, indicating that the filter wrapped the elevation residual in the range of[90 90]
in degrees.When
HasRange
=true
, the matrix includes a row of[Inf Inf]
, indicating that the filter did not wrap the range residual.When
HasVelocity
=true
, the matrix includes a row of[Inf Inf]
, indicating that the filter did not wrap the range rate residual.
If you set any of the fields to false
, the returned
bounds
do not contain the corresponding row. For example, if
HasAzimuth
= true
, HasElevation
=
false
, HasRange
= true
,
HasVelocity
= true
, then the function returns the
bounds as:
180 180 Inf Inf Inf Inf
The filter wraps the measuring residuals based on this equation:
$${x}_{wrap}=mod(x\frac{ab}{2},ba)+\frac{ab}{2}$$
where x is the residual to wrap, a is the lower bound, b is the upper bound, mod is the remainder after division, and x_{wrap} is the wrapped residual.
Data Types: single
 double
More About
Azimuth and Elevation Angle Definitions
The azimuth angle of a vector is the angle between the xaxis and its orthogonal projection onto the xyplane. The angle is positive when going from the xaxis toward the yaxis. Azimuth angles lie between –180 and 180 degrees. The elevation angle is the angle between the vector and its orthogonal projection onto the xyplane. The angle is positive when going toward the positive zaxis from the xyplane.
Measurement Parameters
The 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 MeasurementParameters
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.
Field  Description 
Frame  Enumerated type indicating the frame used to report measurements. When detections are
reported using a rectangular coordinate system, set 
OriginPosition  Position offset of the origin of the child frame relative to the parent frame, represented as a 3by1 vector. 
OriginVelocity  Velocity offset of the origin of the child frame relative to the parent frame, represented as a 3by1 vector. 
Orientation  Frame orientation, specified as a 3by3 realvalued orthonormal frame rotation matrix.
The direction of the rotation depends on the

IsParentToChild  A logical scalar indicating whether 
HasElevation  A logical scalar indicating if the measurement includes elevation. For measurements
reported in a rectangular frame, if 
HasAzimuth  A logical scalar indicating if the measurement includes azimuth. 
HasRange  A logical scalar indicating if the measurement includes range. 
HasVelocity  A logical scalar indicating if the reported detections include velocity measurements.
For measurements reported in a rectangular frame, if

References
[1] Singer, Robert A. "Estimating optimal tracking filter performance for manned maneuvering targets." IEEE Transactions on Aerospace and Electronic Systems 4 (1970): 473483.
[2] Blackman, Samuel S., and Robert Popoli. "Design and analysis of modern tracking systems." (1999).
[3] 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. 212235. International Society for Optics and Photonics, 2000.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Version History
Introduced in R2020b
See Also
Functions
singer
singerjac
singermeasjac
singerProcessNoise
cvmeas
cameas
ctmeas
ctrvmeas
initsingerekf
Objects
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