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TOA Estimator

Estimate time of arrival, time-difference of arrival, and position

Since R2024a

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  • Time-of-arrival estimator block icon

Libraries:
Phased Array System Toolbox / Direction of Arrival

Description

The TOA Estimator block Simulink® estimates time-of-arrival (TOA) or time-difference of arrival (TDOA) at multiple devices. The block estimates TOA or TDOA from an active device to multiple passive anchors or from multiple active anchors to a passive device. TOA and TDOA are estimated based on a frequency-domain channel estimation. Using TOA, the block then estimates target position.

Ports

Input

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Channel estimation matrix, specified as a N-by-M complex-valued matrix, an N-by-M-by-L complex-valued array, or a 1-by-L cell array. Each row of the N-by-M channel estimation matrix represents M samples (e.g., M spatial streams of MIMO communication, M pulses of radar) of a channel estimate on one subband, and each column of the matrix represents a sample of a channel estimate on N uniformly-spaced subbands.

  • When the channel estimation matrix is N-by-M-by-L array, each page of the array is an N-by-M channel estimation matrix. All channel estimation matrices must have the same size.

  • When the channel estimation matrices is a1-by-L cell array, each cell contains a frequency-domain channel estimation matrix from one of the L anchors. The size of a channel estimation matrix can vary for different anchors.

Data Types: single | double
Complex Number Support: Yes

Frequency spacings of channel estimates, specified as a positive scalar or as a 1-by-L vector of positive values. If FreqSpacing is a scalar, the frequency spacing is the same for all L anchors. If FreqSpacing is a 1-by-L vector, the frequency spacing can be different for different anchors. Units are in Hz.

Example: [10e6 15e6 20e6]

Data Types: single | double

Known delay offset between the target and each anchor, specified as a scalar or a real-valued 1-by-L vector. If DelayOffset is a scalar, the delay offset is the same for all signals from or to all L anchors. If DelayOffset is a 1-by-L vector, the delay offset can be different for different anchors. DelayOffset compensates all TOA/TDOA estimation results, Y. Units are in seconds.

Dependencies

To enable this port, select the Enable known delay offset input check box.

Data Types: single | double

Gaussian white noise power, specified as scalar or positive real-valued 1-by-L vector. If npow is a scalar, the noise power is the same for all L anchors. If NPow is a 1-by-L vector, a different noise power value can be applied to each of the L anchors. Units are in watts.

Example: 0.4

Dependencies

To enable this port, select the Output variance of TOA/TDOA estimates check box, and then set the Source of noise power port to 'Input port'.

Data Types: single | double

Anchor positions, specified as a Q-by-L real-valued matrix representing the position of the L anchors in the Q-dimensional Cartesian space (Q can be 2 or 3). Each column denotes the position of each anchor in the Q-dimensional Cartesian space.

Dependencies

To enable this port, select the Output estimated target position check box.

Data Types: single | double

Output

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Times-of-arrival (TOA) or time-differences of arrival (TDOA) estimation from a target at L anchors, output as a 1-by-L real-valued vector or a 1-by-(L-1) real-valued vector.

  • If the TOA/TDOA Measurement parameter is 'TOA', Y is a 1-by-L real-valued vector. The signal model of the TOA output at the lth-anchor can be written as Y(l) = min(taul), for l = 1,2,...,L, where taul is the vector of received multipath delays at the lth anchor.

  • If the TOA/TDOA Measurement parameter is set to 'TDOA', Y is a 1-by-(L-1) real-valued vector. The signal model of the TDOA output at the (l-1)th anchor can be written as Y(l-1) = min(taul)-min(reftau), l = 2,3,...,L, where taul is the vector of received multipath delays at the lth anchor and reftau is the vector of received multipath delays at the first anchor.

Units are in seconds.

Data Types: single | double

  • If the Measurement is 'TOA', Var is a 1-by-L vector representing the estimated TOA variance.

  • If the Measurement property is 'TDOA', Var is a 1-by-(L-1) vector representing the estimated TDOA variance.

Units are in seconds-squared. Var is obtained through the Cramer-Rao lower bound (CRLB) of the TOA/TDOA estimator.

Dependencies

To enable this port, select the Output variance of TOA/TDOA estimates check box, and then set the Source of noise power port to 'Input port'.

Data Types: single | double

Estimated target positions, output as a Q-by-1 vector representing the estimated target position obtained from TOA and TDOA measurements. Target positions are obtained using a two-step weighted linear least squares (WLLS) algorithm that approximates a maximum-likelihood estimation algorithm The algorithm can achieve the position estimation CRLB when the TOA and TDOA estimation errors are small. Units are in meters.

Dependencies

To enable this port, select the Output estimated target position check box.

Data Types: single | double

Target position covariance estimates, output as a Q-by-Q real positive semi-definite symmetric matrix. The matrix represents the estimated target position covariance using TOA/TDOA measurements. The covariance is obtained from the CRLB of the TOA/TDOA position estimate. Units are m2.

Dependencies

To enable this port, select the Output estimated target position check box.

Data Types: single | double

FFT-based TOA response, output as:

If the channel estimate X is an N-by-M-by-L array, toaresp is a P-by-M-by-L array.

If the channel estimate X is a 1-by-L cell array, toaresp is a 1-by-L cell array, containing the TOA response for each of the s anchors.

Dependencies

To enable this port, select the Output FFT-based TOA response check box.

Data Types: single | double
Complex Number Support: Yes

Times of arrival grid, output as P-by-L matrix or a 1-by-L cell array. Times of arrival are restricted to this grid.

  • If the channel estimate X is a N-by-M-by-L array, toagrid is returned as a P-by-L matrix, where P is the number of TOA grid samples.

  • If the channel estimate X is a 1-by-L cell array, toagrid is a 1-by-L cell array, containing the TOA grid for each of the L anchors. Units are in seconds.

Dependencies

To enable this port, select the Output FFT-based TOA response check box.

Data Types: single

Parameters

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To edit block parameters interactively, use the Property Inspector. From the Simulink Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Signal propagation speed, specified as a real-valued positive scalar. The default value of the speed of light is the value returned by physconst('LightSpeed'). Units are in meters per second.

Example: 3e8

Data Types: double | single

Measurement type, specified as TOA or TDOA. When TOA is chosen, TOA measurements are estimated using TOA spectrum analysis and a TOA positioning algorithm. When TDOA is chosen, TDOA measurements are calculated based on TOA measurements and a TDOA positioning algorithm is used.

Data Types: char | string

TOA spectrum analysis method, specified as FFT or MUSIC. When FFT is chosen, an FFT is used to obtain the TOA spectrum. When MUSIC is chosen, a MUSIC super-resolution algorithm is used to obtain the TOA spectrum.

Data Types: char | string

Select this check box to enable input of known delay offsets or estimated delay offsets between anchors and a target using the DelayOffset input port. When not selected, the DelayOffset input port is disabled and delay offsets are assumed to be zero.

Data Types: Boolean

Select this check box to enable the output of variances of the TOA or TDOA estimates using the Var output port. Unselect this check box to not output the estimated variances. Selecting this check box also enables the Source of noise power and Noise power (W) parameters and the Npow input port.

Data Types: Boolean

Select this check box output and FFT-based TOA response. Unselect this check box to not output the TOA response.

Dependencies

To enable this parameter, set the TOA/TDOA Measurement parameter to TOA and set the TOA spectrum analysis method to FFT.

Data Types: Boolean

Select this check box to enable forward-backward averaging. Forward-backward averaging is used to mitigate rank deficiency in the source covariance matrix used in the MUSIC spectrum analysis estimation method. This is useful when the number of independent samples of the channel estimate is small.

Dependencies

To enable this parameter, set the TOA spectrum analysis method to MUSIC.

Data Types: Boolean

Effective reduction in the number of subbands for TOA estimation due to spatial smoothing, specified as a nonnegative integer. Spatial smoothing can be used to mitigate the rank deficiency issue in the source covariance matrix estimation of the MUSIC spectrum analysis method. This technique is useful when the number of independent samples of channel estimate is small.

If there are N subbands and the value of the Spatial smoothing parameter is K, then (K+1) maximally overlapped bands of N-K subbands are formed. Then, (K+1) covariance matrices are estimated for signals on the (K+1) overlapped bands and these (K+1) covariance matrices are averaged together to produce a spatially smoothed covariance matrix of size (N-K)-by-(N-K). Incrementing K by 1 increases the rank of the spatially smoothed covariance matrix by 1 until the range reaches its maximum. However, the effective number of subbands for TOA estimation is reduced by 1. The minimum value of K is 0 which result in no spatial smoothing. The maximum value of K is N-2, resulting in (N-1) overlapped bands of two subbands.

If Spatial smoothing is a scalar, the spatial smoothing value is the same for all L anchors. If Spatial smoothing is a length-L vector, each spatial smoothing value is applied to one of the L anchors.

Dependencies

To enable this parameter, set the TOA spectrum analysis method to MUSIC.

Data Types: single | double

Select this check box to enable output of estimated target positions using the TgtPosEst port and the estimated target position covariances using the TgtPosCov port. Selecting this check box also allows input of anchor positions using the AnchorPos port.

Data Types: Boolean

Specify how the object determines the noise power values used for TOA and TDOA variance estimation as 'Property' or 'Input port'. When you set Source of noise power parameter to 'Property', the Noise power (W) parameter then represents the noise power of the received data. When you set Source of noise power to 'Input port', then set the noise power through the input NPow port.

Example: Input port

Dependencies

To enable this parameter, select the Output estimated target position check box.

Data Types: char | string

Gaussian white noise power, specified as a positive scalar or 1-by-L real-valued vector of positive values.

Dependencies

To enable this parameter, select the Output estimated target position check box and then select Source of noise power as Property.

Data Types: single | double

Block simulation, specified as Interpreted Execution or Code Generation. If you want your block to use the MATLAB® interpreter, choose Interpreted Execution. If you want your block to run as compiled code, choose Code Generation. Compiled code requires time to compile but usually runs faster.

Interpreted execution is useful when you are developing and tuning a model. The block runs the underlying System object™ in MATLAB. You can change and execute your model quickly. When you are satisfied with your results, you can then run the block using Code Generation. Long simulations run faster with generated code than in interpreted execution. You can run repeated executions without recompiling, but if you change any block parameters, then the block automatically recompiles before execution.

This table shows how the Simulate using parameter affects the overall simulation behavior.

When the Simulink model is in Accelerator mode, the block mode specified using Simulate using overrides the simulation mode.

Acceleration Modes

Block SimulationSimulation Behavior
NormalAcceleratorRapid Accelerator
Interpreted ExecutionThe block executes using the MATLAB interpreter.The block executes using the MATLAB interpreter.Creates a standalone executable from the model.
Code GenerationThe block is compiled.All blocks in the model are compiled.

For more information, see Choosing a Simulation Mode (Simulink).

Programmatic Use

Block Parameter:SimulateUsing
Type:enum
Values:Interpreted Execution, Code Generation
Default:Interpreted Execution

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2024a

See Also